Handbook of Atmospheric Electrodynamics, Volume I [1 ed.] 9780849386473, 9780138719503, 9780429607295, 9780429601774, 9780429612817, 9780203719503, 9781351443265, 9781351443258, 9781351443272

Table of contents :

Ion Chemistry and Composition of the Atmosphere, A.A. Viggiano and F. Arnold

Meteorologic Aspects of Thunderstorms, E.R. Williams

Thunderstorm Electrification, C.P.R. Saunders

Lightning Currents, T. Ogawa

Lightning Detection from Ground and Space, R.E. Orville

Artificially Triggered Lightning, K. Horii and M. Nakano

Ball Lightning, H. Kikuchi

Lightning and Atmospheric Chemistry: The Rate of Atmospheric NO Production, M.G. Lawrence, W.L. Chameides, P.S. Kasibhatla, H.Levy II, and W. Moxim

Lightning Within Planetary Atmospheres, K. Rinnert

Quasistatic Electromagnetic Phenomena in the Atmosphere and Ionosphere, R.H. Holzworth

Schumann Resonances, D.D. Sentman

Low-Frequency Radio Noise, A.C. Frazer-Smith

Radio Noise Above 300 kHz due to Natural Causes, D.E. Proctor

Atmospheric Noise and Its Effects of Telecommunication System Performance, A.D. Spaulding

Citation preview

Handbook of

ATMOSPHERIC ELECTRODYNAMICS Volume I

Edited by Hans Volland Radioastronomical Institute University of Bonn Bonn, Germany

CRC Press T a y lo r &. F ra n c is G ro u p Boca Raton London New York C R C Press is an im p rin t of the Taylo r & Francis G ro u p , an inform a business

CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 1995 by Taylor & Francis Group, LLC CRC Press is an im print of Taylor & Francis Group, an Inform a business No claim to original U.S. G overnm ent works This book contains inform ation obtained from authentic and highly regarded sources. Reasonable efforts have been m ade to publish reliable data and inform ation, but the author and publisher cannot assum e responsibility for the validity of all m aterials or the consequences of th eir use. T he authors and publishers have attem pted to trace the copyright holders of all m aterial repro­ duced in th is publication and apologize to copyright holders if perm ission to publish in th is form has not been obtained. If any copyright m aterial has not been acknowledged please w rite and let us know so we may rectify in any future reprint. Except as perm itted under U.S. C opyright Law, no p a rt of this book may be reprinted, reproduced, transm itted, or utilized in any form by any electronic, m echanical, or other means, now know n or hereafter invented, including photocopying, m icrofilm ing, and recording, or in any inform ation storage or retrieval system, w ithout w ritten perm ission from the publishers. For perm ission to photocopy or use m aterial electronically from th is work, please access ww w .copyright.com (http://www.copyright.com /) or contact th e C opyright C learance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization th at provides licenses and registration for a variety of users. For organizations th at have been granted a photocopy license by the CCC, a separate system of paym ent has been arranged. Trademark Notice: Product or corporate nam es may be tradem arks or registered tradem arks, and are used only for identifica­ tion and explanation w ithout intent to infringe. Visit the Taylor & Francis Web site at http://ww w.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

PREFACE

Atmospheric Electrodynamics is a term coined to emphasize the importance of unifying two often separately treated subjects of research: geoelectricity, which deals with low frequency electric fields and currents within the lower atmosphere (in particular thunderstorms and related phe­ nomena), and low frequency electric and magnetic fields of upper atmospheric origin. For phys­ icists of the 19th and early 20th centuries, geoelectricity and geomagnetic variations of external origin were generally considered to be related subjects, which we presently refer to as low fre­ quency electromagnetic fields, excited by various sources throughout the atmosphere. This tra­ ditional connection is still evident from the choice of names of scientific journals. For instance, there still exists the Japanese Journal of Geomagnetism and Geoelectricity and the former name of the present American Journal of Geophysical Research was Terrestrial Magnetism and At­ mospheric Electricity. Whereas geomagnetism became the root of modem magnetospheric physics, culminating in the space age exploration of the earth’s environment, geoelectricity evolved as a stepchild of meteorology. The reason for this is clear. The quasistatic atmospheric electric field, generated by thunderstorm activity and observed on the ground, is intimately associated with the local weather and all of its frustrating unpredictability. However, the variable external geomagnetic field, which can also be measured on the ground, is a useful indicator of ionospheric and magnetospheric electric current systems. Only in the past three decades have ionospheric and magnetospheric physicists rediscovered the importance of electric fields of upper atmospheric origin. Following the development of new instruments and their carriers (balloons, rockets, satellites), electric fields and currents of lower and upper atmospheric origin are now measured throughout the atmosphere from the ground to the magnetosphere and beyond. These recent technological advances basically closed the gap between geoelectricity and geomagnetism that existed for more than half a century. This handbook is the extension of the two-volume CRC Handbook of Atmospherics, published in 1982, which covered only the first subject: geoelectricity, with particular emphasis on lightning and sferics phenomena. The present handbook updates the 1982 edition and also includes the second subject: low-frequency electric and magnetic fields and currents in the ionosphere and magnetosphere. Twenty-eight experts in their fields review a broad range of research in this area. Hopefully it will help to enhance the mutual understanding between lower and upper atmospheric physicists. Hans Volland

Bonn, Germany August 1994

THE EDITOR

Hans Volland studied Geophysics and Meteorology at the Humboldt University in Berlin from 1948 until 1952. He was scientist at the Heinrich-Hertz-Institut in Berlin (East) from 1952 to 1958 and in the Heinrich-Hertz-Institut Berlin (West) from 1958 to 1964 working in the fields of geomagnetism, ionospheric physics, and electromagnetic wave propagation. In 1964 he became a lecturer at the Radioastronomical Institute, University of Bonn, where his main research subjects were solar radioastronomy, solar-terrestrial physics, and atmospheric physics. He has been retired since 1990. He is author of numerous scientific articles, three books, and editor of the CRC Handbook of Atmospherics.

CONTRIBUTORS

Frank Arnold Max Planck Institut fur Kemphysik 69029 Heidelberg, Germany WJL. Chameides School of Earth and Atmospheric Sciences Georgia Institute of Technology Atlanta, Georgia 30332 Antony C. Fraser-Smith STAR Laboratory Stanford University Stanford, California 94305 Robert H. Holzworth Space Sciences Division Geophysics Program University of Washington Seatde, Washington 98195 Kepji Horii Toyota College of Technology Toyota, Japan 471 P.S. Kasibhatla School of Earth and Atmospheric Sciences Georgia Institute of Technology Atlanta, Georgia 30332 Hiroshi Kikuchi College of Science and Technology Nihon University Tokyo, Japan 101 M.G. Lawrence School of Earth and Atmospheric Sciences Georgia Institute of Technology Atlanta, Georgia 30332 H. Levy, II Geophysical Fluid Dynamics Laboratory Princeton, New Jersey 08540 W. Moxim Geophysical Fluid Dynamics Laboratory Princeton, New Jersey 08540

Minoru Nakono Toyota College of Technology Toyota, Japan 471 Toshio Ogawa Science Laboratory International Kochi, Japan 780 Richard E. Orville Department of Meteorology College of Geosciences and Maritime Studies Texas A&M University College Station, Texas 77843 David E. Proctor CSIR, Division of Earth, Marine and Atmospheric Science 2040 Pretoria, South Africa K. Rinnert Max Planck Institut fur Aeronomie 37189 Katlenburg-Lindau, Germany CJ*.R. Saunders Department of Pure and Applied Physics University of Manchester Manchester, England M60 1QD Davis D. Sentman Geophysical Institute University of Alaska Fairbanks, Alaska 99775 AJ). Spaulding Institute for Telecommunications Sciences Boulder, Colorado 80303 A A . Viggiano Phillips Laboratory Geophysics Directorate Ionospheric Effects Division (GPED) Hanscom Air Force Base Massachusetts 01731 Earle R. Williams Department of Earth, Atmospheric and Planetary Sciences Massachusetts Institute of Technology Cambridge, Massachusetts 02139

CONTENTS

1 Ion Chemistry and Composition of the Atmosphere.............................................................. 1 A A . Viggiano and Frank Arnold 2 Meteorological Aspects of Thunderstorms..........................................................................27 Earle R. Williams 3 Thunderstorm Electrification............................................................................................... 61 C.P.R. Saunders 4 Lightning Currents................................................................................................................93 Toshio Ogawa 5 Lightning Detection from Ground andSpace..................................................................... 137 Richard E. Orville 6 Artificially Triggered Lightning.......................................................................................... 151 Kenji Horii and Minoru Nakano 7 Ball Lightning...................................................................................................................... 167 Hiroshi Kikuchi 8 Lightning and Atmospheric Chemistry: The Rate of Atmospheric NO Production M.G. Lawrence, W L Chameides, P-S. Kasibhatla, H. Levy, n , and W. Moxim

189

9 Lightning within Planetary Atmospheres........................................................................... 203 K. Rinnert 10 Quasistatic Electromagnetic Phenomena in the Atmosphere and Ionosphere................. 235 Robert H. Holzworth 11 Schumann Resonances........................................................................................................ 267 Davis D. Sentman 12 Low-Frequency Radio Noise...............................................................................................297 Antony C. Fraser-Smith 13 Radio Noise Above 300 kHz Due to Natural Causes........................................................311 David E. Proctor 14 Atmospheric Noise and Its Effects on Telecommunication System Performance A.D. Spaulding Index

359

397

Chapter 1

Ion Chemistry and Composition of the Atmosphere A A . Viggiano and Frank Arnold

CONTENTS

Introduction............................................................................................................................. I Ionization Sources and Sinks................................................................................................ 2 2.1. Sources......................................................................................................................... 2 2.2. Sinks............................................................................................................................. 5 3. Instrumentation.......................................................................................................................6 4. Ion Composition of theAtmosphere...................................................................................... 8 4.1. Positive Ions..................................................................................................................8 4.2. Negative Ions.............................................................................................................. 10 5. Ionic Processes and Evolution............................................................................................. 13 5.1. Ionic Processes............................................................................................................ 13 5.2. Positive Ions................................................................................................................ 15 5.3. Negative Ions.............................................................................................................. 18 6. Trace Neutral Derivations from Ion Composition Measurements...................................... 19 References......................................................................................................................................22 1. 2.

1.

INTRODUCTION

Atmospheric ions not only are important in controlling atmospheric electrical properties, but also play a role in aerosol processes and can be used to measure trace neutral concentrations very sensitively. Figure 1.1.1 shows the ion concentradon of the atmosphere as a function of altitude (Arnold, 1980). The ion density varies between about 103 and 106 ions cm-3. The high densities are at high altitudes where the gas density is low. At altitudes below 100 km, the ionization density is relatively constant, varying by less than a factor of 10 around 103 ions cm-3. The neutral gas density changes by a factor of approximately 4 x 106 in this altitude range. The mixing ratio of ions to neutrals therefore decreases substantially from high altitude to low altitude. At ground level, there is only one ion for approximately 1016 neutral molecules. Mass spectrometrie measurements of the ion composition are more difficult at lower altitudes due to the small relative concentration of ions and large neutral density. As a result, the ion composition of the upper atmosphere was measured before that of the lower atmosphere, even though the difficulty in using the various in situ measuring platforms increases with height. The various platforms are trailer, aircraft, balloon, sounding rocket, and satellite in order of increasing height range. The last portion of the atmosphere where in situ measurements have been made is the troposphere. The purpose of this chapter is to give a survey of the various ionic processes that occur in the atmosphere. Emphasis will focus on the main processes, and the interested reader is referred to numerous sources for the details. The field of atmospheric chemistry has previously been the subject of numerous reviews (Reid, 1976; Arnold and Krankowsky, 1977; Ferguson et al., 1979; Arnold, 1980; Smith and Adams, 1980; Ferguson and Arnold, 1981; Arnold, 1982; Thomas, 1983; Arnold and Viggiano, 1986; Brasseur and De Baets, 1986; Brasseur and Solomon, 1986; Reid, 1989). 0-8493-8647-0/95/S0.00+ $.50 © 1995 by C R C Press. Inc.

1

Handbook o f Atm ospheric Electrodynam ics, Volume /

2

1 "i U IKJ ‘

103

| 8

3

10 2

t i ttth —

1 1 1 1 rrrq— 1 1 1 rrrrq— i— i 11 m i H*H0+,*r

=~f

H*(HiO)n.e-,C03.N03. MSP', CT

-

H * (H jp )n

££ _1_

HMCHaCNUHjO^ N03 B- + HA

(14)

As with ligand exchange, proton transfer often occurs at or near the collision rate when exothermic. Along with the recombination reactions discussed earlier, these are essentially all the types of reactions involving ions that take place in the atmosphere. However, ligand transfer often accom­ panies processes such as proton transfer and atom rearrangement. 5.2.

POSITIVE IONS

The primary positive ions formed in the atmosphere are NJ, OJ, N+, 0 +, and NO+. Figure 13.1 shows a schematic of the positive ion evolution in the atmosphere. Only the most important processes are shown for clarity. More detailed discussion can be found elsewhere (Reid, 1976; Arnold and Krankowsky, 1977; Ferguson et al., 1979; Arnold, 1980; Smith and Adams, 1980; Ferguson and Arnold, 1981; Arnold, 1982; Thomas, 1983; Arnold and Viggiano, 1986; Brasseur and De Baets, 1986; Brasseur and Solomon, 1986; Reid, 1989). At the altitudes of interest here, the primary ions are converted rapidly to mainly 0 2 and NO+. These two ions then undergo a series of clustering and ligand switching reactions forming 0 2(H20 ) and N0 +(H20 )3, respec­ tively. The clustering of H20 occurs not only by direct association but also by association of more abundant but more weakly bonded species such as N2 and CQ2 followed by switching with H20 . The processes that form Q2+(H20 ) and N0 +(H20)3 ions are reactions with relatively abun­ dant species. The intermediates are rarely observed, although it is possible that the weakly bonded intermediates such as NO+(N2) are dissociated in sampling. This chemistry is described in detail by Ferguson and co-workers (Ferguson, 1979; Ferguson et al., 1979). The ions ( V ^ O ) and N 0 +(H20 )3 do not cluster further but instead react with H20 to form proton hydrates, H30 +(H20 )n, by the following reactions: 0 2+(H20 ) + H20

H30 +(H 0) + 0 2 -» H30 + + HO + 0 2

(15)

and N0*(H20 )3 + H20 -* HjO^HjO^ + HN02

(16)

H30 +(H0) further reacts with H20 to form H30 +(H20). Once formed the proton hydrates estab­ lish an equilibrium distribution. The proton hydrates H30 +(H20)„ are quite stable. In the strato­ sphere and troposphere the conversion to them can be considered complete in about 10-3 s, and n peaks around 3 to 5 in the stratosphere. In the troposphere, where the H-.O concentration is large, n increases. The conversion time to proton hydrates in the lower atmosphere is much shorter than the ion-ion recombination lifetime (which normally controls the ion residence time) of ap­ proximately 100 to 10,000 s. In the lower atmosphere, the chemistry leading to theH30 +(H20)n series of ions issorapid that for many purposes they can be considered thestarting ions for subsequent positive ion chemistry.

16

Handbook o f Atm ospheric Electrodynam ics, Volume /

Figure 1.5.1 A schematic of the positive ion evolution in the atmosphere. Only the most important processes are shown for clarity.

After the H30+(H20 )„ ions are formed, the chemistry becomes that of Brrinsted acids and bases, i.e., all subsequent reactions involve proton transfer except for ligand switching and as­ sociation reactions. The latter reactions leave the core ion unchanged. H30+(H20 )„ will react only with compounds that have a proton affinity greater than that of H20 . Proton transfer will produce species of the form, H+Xn(H20)m. The number of ligands transferred will depend on the proton affinity difference; the less exothermic, the more ligands are transferred. Regardless of the number of ligands transferred, the distribution of H20 ligands quickly reaches an equilibrium due to the relatively high water concentrations found in the lower atmosphere. The concentration of H20 is about 1000 times the concentrations of the other trace gases that play a role in the chemistry. If the concentration of X is relatively large, species such as H+fXJnfFkOXn may be formed by ligand exchange of X for H20 . These ions can then react further with species of even higher proton affinity forming similar series with the identity of X changed. For compounds that have a proton affinity only slightly larger than that of H20 , essentially all the ligands must be transferred to keep the reactions exothermic. In fact, when the proton affinity difference is small, the different bond strengths of the ligands to the core ions can change the direction of the exothermicity. This prevents species such as CH20 from being involved in the ion chemistry. CH20 reacts with the proton hydrates for small n but does not react when n is larger than 2 (Fehsenfeld et al., 1978), i.e., with the most abundant ions in the lower atmosphere.

Ion Chem istry and Com position o f the Atmosphere

17

In the stratosphere, the most important molecule with a proton affinity larger than that of H20 is CH3CN (acetonitrile). Thus, the following reactions take place (Bohringer and Arnold, 1981; Smith et al., 1981; Viggiano et al., 1988): H30 +(H20 ) n + CH3CN -► H+(CH3CN)(H20)„ + H20

(17)

H+(CH3CN)m(H20)„ + CH3CN -* H+(CH3CN)„,+, (H2OX,_, + H20

(18)

and

Note that the proton affinity of CH3CN is only slighter higher than H20 , and therefore all the ligands must be transferred for these reactions to be allowed energetically (Lias et al., 1988). This series of reactions stops when n = 1. This is due to the fact that for H+(CH3CN)m(H20 )n ions, the core ion can be thought of as H30 + when n + m is greater than 2. The energetics therefore do not allow the last H20 to be switched out of the cluster. Reactions similar to these take place with other bases, both with proton hydrates and with other protonated bases. A good example is at ground level where NH|(NH3)m(H2OXi ions are formed in high abundance. The number of H20 ligands can be quite large due to the large amounts of water at ground level. The NHi+(NH3)in(H20 )I, ions subsequently react with other amines such as pyridine and picoline among others (Perkins and Eisele, 1984, 1986, 1988, 1989; Schulte and Arnold, 1990). Protonated acetone and methanol enter into the chemistry near the tropopause (Arijs et al., 1982; Hauck and Arnold, 1984; Knop and Arnold, 1987). This chemistry is fast even for large values of n (Viggiano et al., 1988; Viggiano et al., 1988). 5.3.

NEGATIVE IONS

For most of the atmosphere negative ions are formed by electron attachment to 0 2. In the upper atmosphere energetic electrons can produce O'. For most of the atmosphere the primary negative ion is O2 made by three-body electron attachment. The rate coefficient for this process is small but 0 2 is much more abundant than any other gas that readily attaches electrons. Figure 1.5.2 shows a schematic of the negative ion chemistry of the atmosphere. The early stages of evolution consist of a series of reactions producing ever more stable core ions. These reactions involve several chains, which ultimately form C0J(H20)„ ions. These reactions are with the relatively abundant species O, O* CO2 , 0 3, and H20 . In the lower atmosphere the time scale for this conversion is on the order of 10~3 s. Several side chains produce ions such as Cl (not shown) and HC03. These reactions are discussed in detail elsewhere (Ferguson, 1979; Ferguson et al., 1979). The next stage of evolution involves converting C 03(H20 )n ions into the more stable N 0j(H N 03)n ions. The reactions leading to these ions are with essentially all nitrogen oxides, and the time scale for this conversion is on the order of 1 s in the stratosphere and considerably faster in the troposphere. The slow time scale is a result of two factors: (1) the reaction of C0J(H20)„ ions with NO is slow (1 x 10“" cm3 s-1 molecule ’) (Dotan et al., 1978), although NO is relatively abundant in many parts of the atmosphere. This reaction produces N 0 3 cores in the upper atmosphere. (2) Although C0J(H20)„ ions react rapidly with most other nitrogen oxides such as HN03 (Fehsenfeld et al., 1975), C10N02 (Viggiano et al., 1994), and N2Os (Davidson et al., 1978), these neutrals are found only in trace quantities. Once formed the N 03“ ions are very stable and are the dominant ions in much of the lower atmosphere. Initially the NOj ions are hydrated, N 0 3(H20)„. These undergo ligand switching reactions with HN03 to produce N 0 3(HNOj)n ions. These very stable ions are the starting point for the rest of the ion chemistry of the lower atmosphere.

18

Handbook o f Atm ospheric Electrodynam ics, Volume /

Figure 1S .2 A schematic of the negative km evolution in the atmosphere. Only the most important processes are shown for clarity.

After NOJ cores are formed, it is the proton affinity difference or, more commonly, the gas phase acidity difference that drives the chemistry. Only Brdnsted acids that are more acidic than HNO3 will react with N 0 3(HN03)n. An important example is H2S 04 (Arnold and Henschen, 1978; Arnold and Fabian, 1980; Viggiano and Arnold, 1981): N 0 3(HN03)„ + H2SO4 -» H S0;(H N 03)n + H N03

(19)

Reaction 19 is known to be fast (Viggiano et al., 1980, 1982) for n = 0 to 2 and is probably rapid for all values of n since the proton transfer is quite exothermic (Viggiano et al., 1992). The HS04(H N03)„ ions can further react with H2S 0 4 to produce the very stable ions HSO4(H2S0 4)m(HN0 3)n. These ions are found throughout the lower atmosphere and are dominant in the region between 30 and 40 km (Arnold and Henschen, 1978; Arijs et al., 1981; McCrumb and Arnold, 1981; Viggiano and Arnold, 1981; Arijs et al., 1982; Arijs, 1983; Arijs et al., 1983; Heitmann and Arnold, 1983; Viggiano and Arnold, 1983; Arnold and Qiu, 1984; Qiu and Arnold, 1985; Schlager and Arnold, 1987; Pfeilsticker and Arnold, 1989). Both HS04(H2S0 4)m(HN0 3)n and N 0j(H N 03)n ions also cluster to other trace gases, mainly acids. Examples of ligands are HC1, H20 , HNO* and HOC1. At ground level, two other acids have been found to react with N0 j(HN03)„, namely, methanesulfonic acid and malonic acid, which produce CH3S 0 3 and core ions (Perkins and Eisele, 1984, 1986, 1988, 1989a, 1989b; Tanner and Eisele, 1991). H2S04 is a vety strong acid, and there is no known acid in the atmosphere that will react with HS04 core ions.

Ion Chem istry and Com position o f the Atmosphere 6.

19

TRACE NEUTRAL DERIVATIONS FROM ION COMPOSITION MEASUREMENTS

One of the most interesting aspects of ion composition measurements has been the ability to derive the trace neutral concentrations involved in the chemistry. For some of the trace neutrals, ion composition measurements provided the first hint that these molecules existed in the atmos­ phere. For others the ion composition provided the first confirmation of their existence, and for many it is still the only way to measure the atmospheric concentration. The extreme sensitivity derives from several factors: (1) there is the long atmospheric lifetime of the ions; (2) minor ions can be detected that are present in approximately 1 part in 10,000; (3) the rate constants for ion-molecule reactions are frequently very large, on the order of 10~9 cm3 s_l molecule'1; and (4) both the positive and the negative ion chemistry of the atmo­ sphere proceeds in very discrete steps with time scales separated by orders of magnitude (for instance, both NOj(HNOj)n and H30 +(H20)„ can be thought of as being produced instantaneously compared to the atmospheric lifetime of the ions.) A detailed discussion of how the concentrations of trace neutrals are derived from ion com­ position measurements is beyond the scope of this chapter. However, one straightforward example to show the general technique is useful, namely, that of H2SO4. The only known source of ions with HSO4 cores is Reaction 19, with a rate constant k. There is also only one known sink for HSO4 core ions, namely, recombination with positive ions, which proceeds with a recombination coefficient a Ions in the atmosphere are in a steady state and the production rate of HSO4 core ions can be set equal to the loss rate. Doing so yields the following expression for the concentration of H2SO4: (20) where [HSO4 ] and [NO3 ] = the number densities of all ions with HSO4 and NOj cores, respectively a = the ion-ion recombination rate constant A* = the total positive ion density k = the rate constant for conversion of NOJ cores to HSO4 cores (Reaction 19) Note that the numerator is the loss rate, and the denominator times [H2SO4] is the production rate. It is assumed that all ions with NOj cores convert into HSO4 cores with the same rate. Laboratory measurements show that this is approximately true (Viggiano et al., 1980; Viggiano et al., 1982). More accurate measurements can be obtained by multiplying specific rate constants times specific concentrations. The ratio of ions with HSO4 cores to those with NO, cores is measured in situ by mass spectrometers. Notice that only relative concentrations need to be measured. Laboratory measurements are available for a and k (Viggiano et al., 1980; Viggiano et al., 1982; Smith and Adams, 1983). The total positive ion density can be measured in situ by various techniques. The accuracy of the derivations is about a factor of 2, while the precision is much better, on the order of tens of percent Employing this technique, H2SO4 concentrations have been measured as a function of altitude over most of the lower atmosphere (Arnold et al., 1981; Viggiano and Arnold, 1981; Arijs et al., 1983; Arnold and Buhrke, 1983; Viggiano and Arnold, 1983; Qiu and Arnold, 1984; Schlager and Arnold, 1987; Mohler and Arnold, 1992; Eisele and Tanner, 1993). An example of H2S 0 4 concentrations derived from in situ negative ion composition measurements is shown in Figure 1.6.1. The large bulge in the concentration in the midstratosphere is responsible for the dominance of ions with HSO4 cores in this region (see

Handbook o f Atm ospheric Electrodynam ics, Volume /

20

I H2S04 Number Density (on*) Figure 1.6.1 An example of H 2SO, concentrations derived from in situ negative ion composition measurements as a function of altitude. Data from the following references: Arnold, 1992 and Krieger and Arnold, 1993.

Figure 1.4.5). Concentrations as low as 104 cm-3 are found, and the sensitivity would allow concentrations considerably smaller than this to be derived. At present this is the only way to measure gas-phase H2S 0 4 concentrations, even though H2S04 is quite important in controlling the stratospheric aerosol layer and acid rain. By titrating OH with into H214S 04, OH concentrations on the ground have been measured by a similar method using artificially produced NOj ions (Eisele and Tanner, 1991; Mount and Eisele, 1992). Using natural NOJ and S 0 2, OH was inferred at heights around the tropopause (Mohler and Arnold, 1992). This and similar techniques have now been applied to a variety of gases. The most significant extension is to produce ions in an ion source external to the mass spectrometer. By adding trace gases in small concentrations, the primary ions can be controlled allowing gases that do not enter into the ambient ion chemistry to be measured. This technique has now produced data on a large number of compounds, which are listed in Table 1.6.1 and reviewed elsewhere (Viggiano, 1993). Table 1.6.1

Neutrals whose concentrations have been derived from ion composition measurements in the

stratosphere and troposphere Altitude (km)

Detect by + /- ion

0-4

+

6-14

CH jCN (acetonitrile)

NH,

Chemical

CjHsN

Artificial/ ambient ions

Concentration range

Ref.

Both

1—10 pptv

+

Both

1-100 pptv

10-45

+

Ambient

0 . 1-10 pptv

0 -1 0

+

Both

0 . 1- 101 pptv

Eisele, 1988; Shulte and Arnold, 1990; Tanner and Eisele, 1991 Hauck and Arnold, 1984: Arnold et al., 1986; Knop and Arnold, 1987 Arijs et al., 1982, 1983; Brasseur et al., 1983; Arnold and Hauck, 1985; Ingels et al, 1986; Arnold and Knop, 1987; Knop and Arnold, 1987a, 1987b; Schlager and Arnold, 1987 Ziereis and Arnold, 1986; Tanner and Eisele, 1991

(pyridine) CH3COCH3

(acetone)

(ammonia)

Ion Chem istry and Com position o f the Atmosphere Table 1.6.1

21

(continued)

Chemical

HOC1 (hypochtorous acid) OH (hydroxyl)

Altitude (km)

Detect by +/— ion

Artificial/ ambient ions

Concentration range

35-39

-

Ambient

0 . 1-1 ppbv

0-11.4

Artificial

McCrumb and Arnold, 1981; Viggiano and Amokl, 1981; Schlager and Arnold, 1987 Eisele and Tanner, 1991; Mohler and 1-10 ppqv Arnold, 1992; Mount and Eisele, 1992 10~2-1 ppbv Eisele and Berresheim, 1992; Mohler and Arnold, 1992 Arnold et al., 1980; McCrumb and 1—10* pptv Arnold, 1981; Arijs et al., 1982; Heitmann and Arnold, 1983; Viggiano and Arnold, 1983; Arnold and Qiu, 1984; Knop and Arnold, 1985; Arnold and Knop. 1987; Knop and Arnold, 1987; Arnold and Knop, 1989; Arnold et al., 1989; Pfeilsticker and Arnold, 1989; Arnold et aL, 1990. Schlager et al., 1990, Amok) et al., 1992 0 .01-1 0 pptv Arnold and Fabian, 1980, Arnold et al., 1981; Viggiano and Arnold, 1981; Arijs et aL, 1982, 1983a, 1983b; Heitmann and Arnold, 1983; Viggiano and Arnold, 1983; Arnold and Qiu, 1984; Schlager and Arnold, 1987; Arnold et al., 1990, Eisele and Tanner, 1991; Tanner and Eisele, 1991; Mohler and Arnold, 1992; Mount and Eisele, 1992

SCb (sulfur dioxide) HNOj (nitric acid)

0-11

4-50

Both

H2SO4 (sulfuric acid)

0-45

Ambient

HzO (water) CH3SO3H (methanesulfonic acid) c *h 7n (picoline) C 7H9N (lutidine) C3H4O. (malonic acid) CH3SCH3 (dimethyl sulfide) C 15Hm (P-Caryophyllene) CHjSOCHj (dimethyl sulfoxide) NO (nitric oxide) NOz (nitrogen dioxide) HNO2 (nitrous acid)

38-40

+

Ambient

1-10 ppmv

0

-

Both

r, NOj~ and halide ions with N2O5 at 300 K, J. Chem. Phys., 68 , 2085. Dotan, 1., Albritton, D. L., Fehsenfeld, F. C , Streit, G. E , and Ferguson, E. E. (1978). Rate constants for the reactions of O-, O2-, NO2-, CO3-, and CO4- with HD and CIO with NO, NO2, SQt, and CO2 at 300 K, J. Chem. Phys.. 68 , 5414. Eisele, F. L. (1986). Identification of tropospheric ions, J. Geophys. Res., 91, 7897. Eisele, F. L. (1988). First tandem spectrometric measurement of tropospheric ions, J. Geophys. Res., 93,716. Eisele, F. L. (1989a). Natural and anthropogenic negative ions in the troposphere, J. Geophys. Res., 94, 2183. Eisele, F. L. (1989b). Natural and transmission line produced positive kms, J. Geophys. Res., 94, 6309. Eisele, F. E and Berresheim, H. (1992). High pressure chemical ionization flow reactor for real gases and unsaturated hydrocarbons in air. Anal. Chem.. 64, 283. Eisele, F. L. and Tanner, D. J. (1991). Ion assisted tropospheric OH measurement, J. Geophys. Res., 96,9295. Eisele, F. L. and Tanner, D. J. (1993). Measurement of gas phase concentration of H2SO4 and MSA and estimates of H2SO4 production and loss in the atmosphere, J. Geophys. Res., 98, 9001. Fehsenfeld, F. C„ Dotan, I., Albritton. D. L , Howard, C. J., and Ferguson, E. E. (1978). Stratospheric positive ion chemistry of formaldehyde and methanol, J. Geophys. Res, 83, 1333. Fehsenfeld, F. C., Howard, C. J., and Schmeltekopf, A. L. (1975). Gas phase ion chemistry of HNOj, J. Chem. Phys.. 63, 2835. Ferguson, E E. (1972). Atmospheric metal ion chemistry. Radio Sci., 7, 397. Ferguson, E E (1979). lon-molecule reactions in the atmosphere, in Kinetics o f lon-Mdecule Reactions, P. Ausloos, Ed., Plenum Publishing, New York, 377. Ferguson, E E. and Arnold. F. (1981). Ion chemistry of the stratosphere. Acc. Chem. Res., 14, 327. Ferguson, E E and Fehsenfeld, F. C. (1968). Some aspects of the metal ion chemistry of the earth’s atmosphere, J. Geophys. Res., 73,6215. Ferguson, E. E , Fehsenfeld, F. G . and Albritton, D. L. (1979). Ion chemsitry of the earth’s atmosphere, in Gas Phase Ion Chemistry. M. T. Bowers, Ed., Academic, San Diego, 45. Goldberg, R. A. and Aikin, A. C. (1973). Comet Encke meteor metallic ion identification by mass spectrometer. Science, 180, 294. Graul, S. and Squires, R. R. (1988). Advances in flow reactor techniques for the study of gas-phase ion chemistry. Mass Spectrom. Rev., 7, 263. Hauck, G. and Arnold, F. (1984). Improved positive ion composition measurements in the upper troposphere and lower stratosphere and the detection of acetone. Nature (London), 311, 547. Heitmann, H. and Arnold, F. (1983). Composition measurements of tropospheric kms. Nature (London), 306, 747. Herbst, E. (1980). Refined calculations of km-molecule association rates, J. Chem. Phys., 72, 5284. Ikezoe, Y., Matsuoka, S., Takebe. M.. and Viggiano, A. A. (1987). Gas Phase lon-Molecule Reaction Rate Constants Through 1986, Manizen Company, Tokyo. lngels, J., Nevejans, D., Frederick, P., and Arijs, E. (1986). Stratospheric positive ion composition measurements between 22 and 45 km: an updated analysis, J. Geophys. Res., 91,4017. Knop, G. and Arnold, F. (1985). Nitric acid vapqur measurements in the troposphere and lower stratosphere by chemical ionisation mass spectrometry. Planet. Space Sci., 33, 983. Knop, G. and Arnold, F. (1987a). Atmospheric acetonitrile measurements in h e tropopause region using aircrafi-bome active chemical ionization mass spectrometry, Planet. Space ScL, 35, 259.

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Knop, G. and Arnold, F. (1987b). Stratospheric trace gas detection using a new balloon-borne arims method: acetonitrile, acetone, and nitric acid, Geophys. Res. Lett.. 14, 1262. Kopp. E. (1984). Mesospheric H^O and HjOj densities inferred from in situ positive ion composition measurement. Adv. Space Res., 4, 13. Kopp, E. (1990). Hydrogen constituents of the mesosphere inferred from positive ions: H£), CH*. HjCX), H2O2, and HCN, J. Geophys. Res., 93, 5613. Kopp, E., Eberhardt, P., and Herrmann. U. (1983). Positive ion composition of the high latitude summer D region with noctilucent clouds, J. Geophys. Res., 90, 13041. Kopp, E. and Herrmann, U. (1984). Ion composition in the lower ionosphere, Ann. Geophys., 2, 83. Krankowsky, D„ Arnold, F„ Wieder, H., and Kissel, I. (1972). The elemental and isotopic abundance of metallic ions in the lower E-region as measured by a cryogenically pumped quadrupole mass spectrometer. Int. J. Mass. Spectrom. Ion. Phys., 8 , 379. Krieger, A. and Arnold, F. (1994). First composition measurements of stratospheric negative ions and inferred gaseous sulfuric acid in the winter arctic vortex — implications for aerosols and hydroxyl radical formation, Geophys. Res. Lett., 21, 1259. Lias, S. G„ Bartmess, J. E , Liebman, J. F., Holmes, J. L , Levin, R. D„ and Mallard, W. G. (1988). Gas-phase ion and neutral thermochemistry, J. Phys. Chem. Ref. Data, 17 (Suppl. 1), 1. McCrumb, J. L. and Arnold, F. (1981). High-scnsitivity detection of negative ions in the stratosphere. Nature (London), 294, 136. Mtihler, O. and Arnold, F. (1992). Gaseous sulfuric acid and sulfur dioxide measurements in the arctic troposphere and lower stratosphere: implications for hydroxl radical abundances, Geophys. Res. Lett., 17, 1763. MOhler, O., Reiner, T., and Arnold, F. (1993). A novel aircraft based tandem mass spectrometer for atmospheric ion and trace gas measurements. Rev. Sci. Instrum., 64, 1199. Mount, G. H. and Eisele, F. L. (1992). An intercomparison of tropospheric OH measurements at Fritz Peak Observatory, Colorado, Science, 256, 1187. Narcisi, R. S., A.D. Bailey, Della Lucca, G, Sherman, C , and Thomas, D. M. (1971). Mass spectrometric measurements of negative kms in the D- and lower F-regions, J. Atmos. Terr. Phys.. 33, 1147. Narcisi, R. S. and Bailey, A. D. (1963). Mass spectrometric measurements of positive ions at altitudes from 64 to 112 kilometers, J. Geophys. Res. 70, 3687. Perkins, M. D. and Eisele, F. L. (1984). Fust mass spectrometric measurements of atmospheric kms at ground level, J. Geophys Res, 89,9649. Pfeilsticker, K. and Arnold, F. (1989). Fust km composition measurement in the stratopause region using a rocket borne parachute drop sonde. Planet. Space Sci. 37,328. Qiu, S. and Arnold, F. (1984). Stratospheric in situ measurements of H2SO4 and HSOj vapors during a volcanically active period. Planet. Space Sci., 32,87. Qiu, S. and Arnold, F. (198S). In situ measurements of the upper stratospheric negative km composition and inferred sulphuric acid km thermochemistry. Chin. J. Space Set, 5, 286. Reid, G. C. (1976). Ion chemistry of the D-region, in Advances in Atomic and Molecular Physics D. R. Bates and B. Bederson, Eds., Academic. Orlando, 375. Reid, G. C. (1989). Ion chemistry of the cold summer mesopause region, J. Geophys Res, 94, 14653. Schlager, H. and Arnold, F. (1987). Balkxm-bome composition measurements of stratospheric negative kms and inferred sulfuric acid vapor abundances during the map/giobus 1983 campaign. Planet. Space Sci, 35,693. Schlager, H. and Amokl, F. (1987). On stratospheric acetonitrile detection by passive chemical ionization mass spectrom­ etry, Planet. Space Sci, 35,715. Schlager, H.. Arnold, F„ Hofmann, D. J., and Deshler, T. (1990). Balloon observations of nitric acid aerosol formation in the arctic stratosphere. I. Gaseous nitric acid, Geophys Res Lett., 17, 1275. Schulte, P. and Arnold, F. (1992). Detection of upper atmospheric negatively charged microclusters by a rocket-borne mass spectrometer, Geophys. Res. Lett., 19, 2297. Schulte, P. and Arnold, F. (1990). Pyridinium kms and pyridine in the free troposphere, Geophys Res Lett., 17, 1077. Smith, D. and Adams, N. G. (1980). Elementary plasma reactions of environmental interest, in Topics in Current Chemistry, F. L. Bosdike, Ed., Springer-Verlag, Berlin, 1. Smith, D. and Adams, N. G. (1988). The selected km flow tube (SIFT): studies of non-neutral reactions. Adv. At. Molec. Phys, 24, I. Smith, D., Adams, N. G., and Alge, E (1981). Ion-km mutual neutralization and ion-neutral switching reactions of some stratospheric ions. Planet. Space Set, 29, 449. Smith, D. and Adams, R. G. (1983). Studies of km-ion recombination using flowing afterglow plasmas, in Physics o f Ion­ ian and Electron-lon Collisions, F. Brouillard and J. W. McGowan, Eds., Plenum, New York, 501. Tanner, D. J. and Eisele, F. L. (1991). Ions in oceanic and continental air masses, J. Geophys Res. 96, 1023. Thomas, L. (1974). Recent developments and outstanding problems in the theory of the D region. Radio Set, 9,121. Thomas, L. (1983). Modelling of the km composition of the middle atmosphere, Ann. Geophys, 1, 61.

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Viggiano, A. A. (1986). The temperature dependence of ion-moiecule association rate coefficients in the low pressure limit, J. Chem. Phys.. 84. 244. Viggiano, A. A. (1993). In-situ mass spectrometry and ion chemistry in the stratosphere and troposphere. Mass Spectrom. Rev.. 12. 115. Viggiano, A. A. and Arnold, F. (1981). Extented sulfuric acid concentration measurements in the stratosphere, Geophys. Res Lett., 8 , 583. Viggiano, A. A. and Arnold, F. (1981). The first height measurements of the negative ion composition of the stratosphere. Planet. Space Sci., 29, 895. Viggiano, A. A. and Arnold, F. (1983). Stratospheric negative ions — detailed height profiles, Planet. Space. Sci.. 31,813. Viggiano. A. A. and Arnold, F. (1983). Stratospheric sulfuric add vapor — new and updated results, J. Geophys. Res., 88 , 1457. Viggiano, A. A., Arnold, F„ Fahey, D. W., Fehsenfeld, F. C., and Ferguson. E. E. (1982). Silicon negative ion chemistry in the atmosphere — in situ and laboratory measurements. Planet. Space Sci., 30, 499. Viggiano, A. A., Dale, F., and Paulson, J. F. (1988). Proton transfer reactions of H*(HjO)„_2-ii with methanol, ammonia, pyridine, acetonitrile, and acetone, J. Chem. Phys., 88 , 2469. Viggiano, A. A., Henchman, M. J., Dale, F., Deakyne, C. A., and Paulson, J. F. (1992). Gas-phase reactions of weak Bi^nsted bases; I", PO3', HS04', FSOj', and CFjSQj' with strong Brtynsted acids; H2SO4, FSO3H, and CF3SO3H. A quantitative intrinsic superacidity scale for the sulfonic adds XSOjH (X = HO, F, and CFj). J. Am. Chem. Soc.. 114,4299. Viggiano, A. A., Morris, R. A., Dale, F„ and Paulson, J. F. (1988). Tropospheric reactions H*(NM3)„,(H:>0)„ with pyridine and picoline, J. Geophys. Res., 93. 9534. Viggiano. A. A., Morris, R. A., and Doren, J. M. V. (1994). Ion chemistry of OONOj involving N fV core ions; a detection scheme for CIONO2 in the atmosphere, J. Geophys. Res., 99, 8221. Viggiano, A. A., Perry, R. A., Albritton, D. L., Ferguson, E. E., and Fehsenfeld, F. C. (1980). The role of H2S0 4 in stratospheric negative-ion chemistry, J. Geophys. Res., 85,4551. Viggiano, A. A.. Peny, R. A., Albritton, D. L.. Ferguson, E. E„ and Fehsenfeld, F. C. (1982). Stratospheric negabve-ion reacbon rates with HjSO* J. Geophys. Res., 87, 7340. Zbinden, P. A., Hidalgo, M. A., Eberhardt, P., and Geiss, J. (1975). Mass spectrometric measurements of the posibve ion composibon of the D and E regions of the ionosphere. Planet. Space Sci., 23, 1621. Ziereis, H. and Arnold, F. (1986). Gaseous ammonia and ammonium ions in the free troposphere, Nature (London), 321, 503.

Chapter 2

Meteorological Aspects of Thunderstorms Earle EL Williams

CONTENTS 1. Introduction,.......................................................................................................................... 27 2. Physical Basis of Moist Convection ..................................................................... 28 2.1. Physical Basis for Convection.............................................................................. ...28 2.2. Clausius-Clapeyron Relation....................................................................................28 2.3. Parcel Theory ........................................................... 29 2.4. Conditional Instability .............................................................................................33 2.5. Precipitation Treatment in Parcel Theory.................................................................34 2.6. Precipitation Processes..............................................................................................35 2.6.1. Collisional Coalescence............................................................................... 35 2.6.2. Bergeron Process and Mixed-Phase Microphysics..................................... 36 2.7. Shape of the CAPE and Its Influence on Thunderstorm Behavior.........................38 3. Meteorological Conditions Supporting Thunderstorms ......................................... 41 3.1. Air Mass Thunderstorms ....... 44 3.2. Cold Front Convection............................................................................................. 49 3.3. Warm Front Convection and Snowstorms.............................................................. 49 3.4. Monsoon Convection................................................................................................50 3.5. Stratiform Precipitation ....................................................................................... 50 3.6. Severe Storm s........................................................................................................... 51 3.7. Tropical Cyclones: Hurricanes and Typhoons .......................................................52 4. Global Distribution of Thunderstorms........................................................................ 54 5. Response of Global Thunderstorm Activity to Global Temperature Change.................... 54 Acknowledgments .......................................................................................................................56 References......................................................................................................................................56

1.

INTRODUCTION

Convective clouds that succeed in producing lightning are thunderstorms by definition. A rather wide range of convective conditions satisfy this definition. The most violent convective clouds in the atmosphere, with vertical air motions of many tens of meters per second, are invariably thunderstorms and usually exhibit frequent lightning. In other situations gentle convection with vertical motions of tens of centimeters per second can occasionally attain thunderstorm status. Thunderstorms are a major source of global precipitation and by virtue of their vertical mass transport are major players in determining the distribution of water substance throughout the atmosphere. The origin of thunderstorm electrification has been a long-standing controversy over the rel­ ative roles of precipitation and convection. The weight of the evidence supports the idea that the primary role of the convection is in lifting water substance from its source at the earth’s surface to the subfreezing part of the atmosphere where ice particles can form, collide, and separate electric charge. The thermodynamics of moist convection (Section 2) and the microphysics re­ sponsible for the formation of precipitation (Section 2.6) are reasonably well understood. The 0-8493-8647-0/95/SO.0O+ $.50 « 1995 by CRC Press, Inc.

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28

vertical distribution of precipitation (Section 2.7) and the vertical air motions in thunderstorms are reasonably well documented with meteorological radar. In contrast, the microphysics of charge separation, the subject of Chapter 3 in this volume, is comparatively poorly understood. This lack of understanding at the particle scale has not discouraged progress at the global scale. Thunderstorm convection is characterized by an interplay between temperature, water vapor, instability to convection, formation of ice-phase precipitation, and production of lightning. A consideration of this interplay is valuable toward understanding the distribution of thunderstorms and lightning over the planet (Section 4). The strongly nonlinear relationship between temperature and lightning suggests that the monitoring of lightning (Section 5) on a global basis may provide a sensitive diagnostic for global temperature change. 2. 2.1.

PHYSICAL BASIS OF MOIST CONVECTION

PHYSICAL BASIS FOR CONVECTION

The sun is the ultimate source of energy for thunderstorm convection and, at a larger scale, for the general circulation of the atmosphere. Because of the clear atmosphere transparency to solar radiation, more than half of the incoming sunlight is absorbed by the earth's surface. This dif­ ferential heating of the atmosphere near the earth’s surface relative to the atmospheric column aloft is ultimately responsible for an instability that is the basis for thunderstorm convection: latent instability or conditional instability. The instability is driven by simple Archimedian buoyancy: parcels of low-density fluid immersed in environmental air of higher density experience upward forces. For ordinary gases such as atmospheric air that obey the ideal gas law, parcel density at any altitude (or pressure) is determined by temperature; and the buoyancy force is proportional to the temperature difference between the air parcel and its surroundings. In considering the behavior of moist convection in the earth’s atmosphere, one need also be concerned with the contributions of water vapor content and condensate (liquid water and ice) to parcel buoyancy. 2.2.

CLAUSIUS-CLAPEYRON RELATION

The participation of water substance in all three phases, vapor, liquid, and solid, gives thunder­ storm convection a special status relative to ordinary dry convection of fluid. The temperature dependence of the vapor density in equilibrium with the liquid and solid phase is the ClausiusClapeyron law, perhaps the most important thermodynamic relationship in physical meteorology. Water vapor concentration is quantified by a variety of parameters in meteorology (dew point temperature, vapor pressure, vapor density, and specific humidity). The equilibrium vapor density in grams per cubic meter cubed is used in this discussion because of its connection with cloud mictophysics. The temperature dependence of vapor density is shown in Figure 2.2.1 for a range of temperatures from +30°C (typical of surface air temperature in the tropical atmosphere) to —90°C (typical of the lowest temperatures encountered near the top of the tropical troposphere). Over this range of temperatures, the equilibrium vapor density varies by more than five orders of magnitude. Near 0°C, a rough rule of thumb is a doubling of vapor density for every 10°C of temperature change. For temperatures lower than (TC, two vapor density curves must be consid­ ered, one for supercooled water and one for ice. Supercooled water is a prevalent constituent in thunderstorms, primarily because of the scarcity of ice nucleating agents, which act to transform the supercooled water to ice. Near a temperature of —40°C, liquid water is transformed sponta­ neously to ice by a process called homogeneous nucleation (Pruppacher and Klett, 1980). The corresponding temperature range in thunderstorms (0“C to -40°C) defines the mixed-phase region of moist convection. As shown clearly in Figure 2.2.1, the equilibrium vapor density of supercooled water is sys­ tematically greater than that of ice. This apparently subtle difference is responsible for the Ber­ geron process of precipitation formation, a fundamental player in the cloud mictophysics of the mixed-phase region, discussed in Section 2.6.

M eteorologicalAspects o f Thunderstorms

29

Figure 2.2.1 Equilibrium water vapor density vs. temperature, over a range of temperature encountered in the troposphere. Curves for both liquid water and for ice are shown in the mixed-phase range of temperature (0 to —40°C). Adiabatic water contents are shown for comparison.

2.3.

PARCEL THEORY

Despite the fact that thunderstorm convection is highly turbulent, it is both convenient and in­ structive to assume that the convection consists of individual air parcels that remain intact along their trajectories. The molecular and eddy diffusion processes, which are completely ignored in parcel theory, are most effective on small scales, and it is therefore expected that this approximate theory will be most accurate few the largest parcels. Observations to be discussed support this expectation. In effect, the parcels to be considered are blobs of air and water substance contained by imaginary massless membranes that are perfectly extensible but impermeable to energy exchange. The latter assumption is identified by the term adiabatic. For parcels undergoing vertical displacements in the earth’s gravitational field (but not under­ going phase changes) two energy contributions must be considered: the gravitational potential energy and the internal energy. For a parcel exhibiting ideal gas behavior, the internal energy is given by the product of heat capacity at constant pressure Cp and the absolute temperature T. Energy conservation for the parcel (per unit mass) for a vertical displacement dz is represented by: CpdT + g dz = 0

(1)

or

— = dz

g

= T„ - 9.8°K/km

(2)

Handbook o f Atm ospheric Electrodynam ics, Volume /

30

where g is the acceleration due to gravity. Increases in parcel altitude are accompanied by a decrease of parcel temperature: the adiabatic cooling process, which ultimately leads to the for­ mation of clouds when water substance is included. The so-called dry adiabatic gradient Yj given by Equation 2 is largely independent of altitude (or pressure). Dry adiabatic displacements are characterized by a conservative quantity: potential temperature, 0, which is referenced to the 1000 mbar pressure level (P„) by: (3) where R is the gas constant for dry air. Parcels at pressures less than 1000 mbar are adiabatically warmed in their hypothetical displacement to the 1000-mbar level, and acquire a temperature T substantially larger than the parcel’s original temperature at altitude. Every air parcel in the atmosphere has a potential temperature and an associated dry adiabat on a thermodynamic dia­ gram, which is labeled with that potential temperature. When the effects of water substance are considered in the process of parcel displacement, the latent heat energy must be included in the energetics. Equation 1 then takes on a source term: -LdW s = CpdT + g dz

(4)

where L is the latent heat of condensation (or evaporation) (2.5 x 106 J kg-1) and VV, is the equilibrium vapor content of the air given earlier by the Clausius-Clapeyron relation. The source term on the left of Equation 4 is negative, because a decrease in parcel water vapor dW, is associated with an increase in parcel condensate and a positive contribution to the heat and temperature of the parcel. Rearranging Equation 4 we have: dT

- L dW5 d J

dz

Cp dT dz

g Cp

-r„

(5)

This modified temperature gradient is called the moist adiabatic (or pseudoadiabatic) lapse dWs rate, T,. The derivative —— in the denominator is essentially the slope of the Clausius-Clapeyron curve in Frgure 2.2.1, which is positive over the entire range of temperature. Hence, the conclusion that: (6 )

This result is an important aspect of conditional instability, discussed in Section 2.4. Parcels undergoing moist adiabatic displacements are also characterized by conservative quan­ tities; however, because water vapor-saturated parcels can be either cooled by evaporation of condensate or warmed by condensation of vapor, two alternative conservative variables are in common use. These variables are wet bulb potential temperature, 0„., and equivalent potential temperature, 0„ respectively. Like potential temperature 0, the reference level for 0„. and 0, is 1000 mbar, and the determination of these values is best illustrated in graphic form below. Frgure 2.2.2 shows a standard thermodynamic diagram (or tephigram), which is constructed based on the thermodynamics of the Clausius-Clapeyron relationship and the adiabatic displace­ ments previously discussed. The diagram enables a quantitative representation of parcel theory based on atmospheric observations of pressure, temperature, and water vapor. Horizontal lines represent constant pressure (or altitude). Straight lines sloping upward to the right at 45° are lines

M eteorological Aspects o f Thunderstorms

Figure 2.2.2

31

An atmospheric thermodynamic diagram.

of constant temperature (isotherms). Straight lines sloping more steeply upward to the right are lines of constant water vapor mixing ratio in grams per kilogram, another conservative quantity for dry adiabatic displacements. Straight lines sloping downward to the right are dry adiabats and are labeled with potential temperature, 0. Curved lines sloping more steeply downward to the right are moist adiabats, labeled with either wet bulb potential temperature, 0M ., or equivalent potential temperature, 0,.

Air parcels are characterized in radiosonde observations by their pressure, temperature, and some measure of water vapor content. Dew point temperature (rather than vapor density, which

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figure 2.2.3 Illustration of temperature, T; dew point temperature, TD; equivalent potential temperature, 6,; and wet bulb potential temperature, 0„ on a thermodynamic diagram.

is difficult to measure aloft) is frequently used to characterize the water vapor, this is the tem­ perature to which a subsaturated air parcel must be cooled (at constant pressure) to reach satu­ ration. At every pressure level, two points on the tephigram characterize the parcel: the temperature and the dew point temperature. These points are identified by (1) and (2) in Figure 2.2.3. If this subsaturated parcel undergoes a dry adiabatic displacement, two quantities are conserved: 0 and the water vapor mixing ratio. The parcel displacement is therefore represented by both a translation along a dry adiabat (from the initial dry bulb temperature) and along an isopleth of mixing ratio from the initial dew point temperature). The intersection of these two lines at some lower pressure (point (3) in Figure 2.2.3) represents a condition of water saturation. This pressure level is referred to as the cloud condensation level ((XL) and is the altitude at which the first cloud forms. Further (upward) adiabatic parcel displacement now follows a moist process and a moist adiabat, and both 0, and 0». are conserved. To determine 0,, the parcel is lifted to very low pressure (point 4) where the moist adiabat is tangential to a dry adiabat, with all condensate removed in the process but with a retention of the latent heat of condensation. Then the moisture-free parcel is adiabatically wanned by bringing it back down to the 1000-mbar pressure level along a dry adiabat. The parcel temperature at the 1000-mbar pressure level is the equivalent potential temperature 0,.

M eteorological Aspects o f Thunderstorms

Figure 2.2.4

33

Illustration of ingredients of conditional instability on a thermodynamic diagram.

To determine 0„. for the parcel, displace it from point (3) in the opposite (downward) direction. To follow a moist adiabat from point (3), liquid water must be evaporated into the parcel as it descends. The parcel temperature at the 1000-mbar level is the wet bulb potential temperature, 0HIn effect, 0„ is the lowest temperature and 0, the highest temperature a parcel can attain by virtue of the latent heat of vaporization of water. 2.4.

CONDITIONAL INSTABILITY

Conditional instability is the mechanism by which thunderstorms are formed. The energy that drives conditional instability is convective available potential energy (CAPE). Conditional insta­ bility can take place in a wide variety of meteorological environments, discussed in greater detail in Section 3, but in all cases two conditions of conditional instability are the same: (1) air parcels must be lifted from lower levels of the troposphere to a level sufficient for condensation to occur and latent heat to be released, and (2) the parcel must eventually find itself positively buoyant with respect to its surroundings. An illustration of conditional instability according to parcel theory is shown in the thermodynamic diagram of Figure 2.2.4.

The vertical temperature gradient in the troposphere frequently lies between the dry adiabatic value (Equation 2) and the moist adiabatic value (Equation 5). A typical sounding of temperature

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Handbook o f Atm ospheric Electrodynam ics, Volume /

is shown by the dashed line in Figure 2.2.4. The temperature of the surface parcel is T and its dew point temperature is To. According to the thermodynamic constructions discussed earlier, if this surface parcel is lifted, by whatever physical process, first along the dry adiabat horn the surface ( 1) to the cloud condensation level (2), and then moist adiabatically through the remainder of the troposphere to point (3), we have a graphical basis for the essential features of conditional instability. If for the moment we assume that parcel density is determined by temperature alone, then according to the simple principal of Archimedes the parcel buoyancy force is proportional to the temperature difference between parcel and environment. The wet bulb adiabat, labeled by the value of 8„. (or 0f) for the parcel, provides an estimate of the parcel temperature in the updraft The wet bulb adiabat intersects the environmental sounding at points (3) and (4). Point (3) is the level of free convection (LFC), the altitude at which the parcel first becomes upwardly buoyant; and point (4) is the level of neutral buoyancy (LNB), where the upward buoyancy vanishes. The integral with altitude of the upward buoyancy force is the positive area on the thermodynamic diagram and is identified as CAPE: CAPE - r

, 7|- “ ~ T‘" „ d z

J U *~

Jk g '

(7)

' env

with units of energy per unit parcel mass. In order for CAPE to be released, the small negative area identified as convective inhibition energy (CINE) must be supplied. In practice, the energy is supplied by boundary layer thermals, by frontal forcing, or by orographic effects. Much of the small-scale cumulus convection early in the day over land is confined to altitudes between the CCL and the LFC (Figure 2.2.4). Observations disclose that maximum thunderstorm tops (later in the afternoon) are generally found in the vicinity of the LNB (Cruz, 1973; Ludlam, 1980). However, if all of the stored energy represented by CAPE at midlatitude locations were trans­ formed without loss to parcel kinetic energy, updraft parcels could in principle rise against down­ ward buoyancy forces to level (5) in Figure 2.2.4, typically several kilometers above the tropopause in the stratosphere. Such overshooting is most common in large severe storms (Vonnegut and Moore, 1958; Roach, 1967) for which parcel theory is probably most accurate (Bluestein et al., 1989). The pronounced diurnal variation of thunderstorm activity over land (Williams and Heckman, 1993) is partly explained by the construction in Figure 2.2.4. Daytime insulation heats the earth’s surface, thereby enhancing the wet bulb potential temperature of surface air, which in turn enhances CAPE. 2.5.

PRECIPITATION TREATMENT IN PARCEL THEORY

Precipitation is characteristic of the convection that produces lightning and is generally (although not exclusively) believed to be an essential ingredient of the electrification process. Rain, snow, sleet, graupel, and hail are all precipitation forms that evolve from condensate (cloud water and ice) and share the common feature that their terminal fall speeds are of the order of meters per second or greater speeds sufficient to carry the particles out of the air parcels in which they form in a short time compared to a thunderstorm lifetime. As a consequence, parcel theory, which assumes no exchange between parcel and environment, has inherent limitations in its treatment of precipitation. Historically, two extreme assumptions have been made, which bound the behavior of precipitating parcels but which, like parcel theory itself, are only approximations to reality. The simplest assumption was encountered earlier in the derivation of the moist adiabatic temperature gradient In this case, the rising parcel condensate is removed continuously as it forms, and thus precipitation has no opportunity to form. This assumption obviates the need to consider the complications of the gravitational loading effect of precipitation on parcel buoyancy and the heat capacity contribution of the condensate to parcel temperature. Because latent heat released in the condensation process is retained, this process is dubbed pseudoadiabatic. Because no condensate is retained to evaporate, the downward displacement of a previously lifted parcel

M eteorological Aspects o f Thunderstorms

35

follows a dry adiabat rather than a moist adiabat; thus the term irreversible is associated with this process. The other extreme scenario is the reversible process, in which all condensate is retained by the parcel, but no precipitation is allowed to form. The condensate heat capacity contribution and the negative buoyancy effect of the condensate are now retained. The latter effect is appreciable, as the loading effect of a modest condensate mixing ratio of 3 X 10-3 (3 g kg-1) is equivalent to 1°C of parcel buoyancy. A further complication inherent to thunderstorm convection is the existence of ice and the associated phase change from both vapor to ice and liquid to ice as parcels rise to colder levels of the troposphere. In the pseudoadiabatic process, we can replace L in Equation 3 with the latent heat of deposition (~2800 J g_l) instead of the latent heat of condensation (~2500 J g-1) to determine ice adiabats. In the reversible process, the transformation of supercooled cloud water to ice (riming) at subfreezing temperatures must be considered, as well as the variable contribution of the condensate heat capacity to parcel buoyancy. All of the complications of parcel theory noted above can be considered in the determination of CAPE based on atmospheric soundings (Williams and Renno, 1993). These results show that the negative buoyancy effect of gravitational loading in the reversible process is roughly com­ pensated for by the additional latent heat contribution from the ice phase. As a rule of thumb, numerical values of CAPE calculated from the standard pseudoadiabatic assumption (without ice), and shown in Figure 2.2.4, are comparable to values calculated by the more complicated reversible process with the ice phase included. The latter result casts considerable doubt on the suggestion that the tropical atmosphere is in a moist neutral state with no conditional instability (Emanuel, 1988; Xu and Emanuel, 1989; Emanuel, 1989). The influence of the ice phase in the evaluation of atmospheric stability has also been considered by Saunders (1957), Chappell and Smith (1975), Johnson and Kriete (1982), and Raymond and Blyth (1992). 2.6.

PRECIPITATION PROCESSES

The processes of precipitation formation, which are evidently glossed over in the thermodynamics of parcel theory, must be considered in more detail to understand thunderstorm electrification. The main processes are conveniently divided into two specific categories: (1) droplet collision and coalescence and (2) the Bergeron process followed by riming. The regions of the atmosphere in which these two processes are prevalent are generally separated by the 0°C isotherm. For this reason the two processes are often accompanied by the names ‘warm cloud’ and ‘cold cloud’, respectively. 2.6.1.

Collisional Coalescence

A raindrop 1 mm in diameter is equivalent in volume to one million cloud droplets, each with 10-pm radius. Such large liquid drops cannot be explained by condensation of water vapor, the diffusion times are far too long. Instead, the smaller cloud droplets with relative terminal velocities collide with each other and coalesce to form still larger drops. As shown by the interaction diagram in Figure 2.2.5, this behavior is most prevalent in the earth’s atmosphere for an intermediate range of droplet sizes. If the droplets are too small, there is insufficient inertia to guarantee a collision and coalescence. If the interacting drops are too large, the kinetic energy of the collision over­ whelms the surface energy (surface tension) and many smaller droplets are created. Nevertheless, Figure 2.2.5 shows that coalescence is the preferred outcome for a substantial range of droplet sizes. A sufficiently deep cloud of droplets is necessary for the formation of precipitation-sized particles. At low latitudes (i.e., the tropics) where the water vapor mixing ratios are quite large (15 to 20 g kg-1), the cloud condensation level (CCL; Figure 2.2.4) is quite low, and the 0°C isotherm is higher than usual (4000 to 5000 m); convective clouds often form, which produce intense rainfall exclusively by collision-coalescence. Despite a few published ground-based observations

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DROP DIAMETER Figure 2.2.5 Drop/droplet interaction diagram, illustrating outcomes of drop/droplet collisions with particles falling at their respective terminal velocities.

to the contrary (Foster, 1950; Pietrowski, 1960; Moore and Vonnegut, 1960; Michnowski, 1963), the author’s experience in the tropics and subtropics with calibrated radar and sensitive groundbased lightning detection equipment indicates that such warm clouds do not produce lightning and hence do not achieve thunderstorm status. All instrumental aircraft observations now available support the notion that the ice phase is essential for thunderstorm status (Williams, 1989; Christian, personal communication; Mikhailovsky et al., 1992). 2.6.2.

Bergeron Process and Mixed-Phase Microphysics

Parcels undergoing upward displacements above the CCL at atmospheric temperatures less than (fC (but greater than - 4 0 “C) will likely exhibit mixed-phase conditions, i.e., the presence of water substance in all three phases. As noted in Section 2.2 liquid water with a temperature less than 0°C, referred to as supercooled water, is a prevalent feature of cold convective clouds because of the relative scarcity of ice-forming nuclei in the atmosphere that would ordinarily hasten the transition to the solid phase at subzero temperatures. Following the Clausius-Clapeyron relation (Figure 2.2.1) there exist two distinct equilibrium vapor pressures for liquid water and for ice. The disequilibrium of the mixed phase set up by this situation is essential to the initiation of precipitation in cold clouds and is referred to as the Bergeron process, after one of its investigators. In a cloudy parcel that is saturated with respect to liquid water and therefore supersaturated with respect to ice, the ice will grow spontaneously at the expense of the liquid. In a stationary parcel, this process would ordinarily continue until the supercooled water disappears. In a parcel under­ going convective displacements, the supply of supercooled water is sustained by the lifting pro­ cess. In such an environment, ice crystals can grow by vapor deposition to sizes for which their terminal fall speeds are appreciable. The falling ice crystals then begin to collect supercooled droplets by accretion; droplets that quickly freeze on contact with the ice surface in a process called riming (Langmuir, 1960). The ice particles enlarge further to become small graupel particles resembling miniature (1 to 10 mm in diameter) snowballs. The average density of graupel is

M eteorological Aspects o f Thunderstorms

37

substantially less than that of pristine ice (0.92 g cm-3) because of its porous nature. A wide range of graupel density is observed in convective clouds. Measured values of rimed ice particle density are shown in Figure 2.2.6 over the complete range of convective situations. The latent heating of freezing is communicated to the graupel particle during the riming process and serves to raise its temperature relative to its environment. In convective situations characterized by large updrafts and large liquid water contents in the mixed-phase region, the surface temperature of the rimed particle can approach 0°C. This limit is termed wet growth and normally defines the transition from graupel to hail (Schuman, 1938; Ludlam, 1938). These largest ice particles (up to 10 cm in diameter) that exhibit layers of nearly transparent ice (density 0.92 g cm-3) in concentric zones around its center are found in the most violent thunderstorms, as shown in the upper histogram of Figure 2.2.6. As noted in Chapter 3 by C.P.R. Saunders in this volume, thunderstorm electrification is believed to result from ice particle collisions primarily in a region of the atmosphere bounded by the 0°C and -40°C isotherms. It is therefore important to characterize the microphysical state of the particles one expects to encounter in the mixed-phase region of thunderstorm convection. Williams et al. (1991) have used the heat balance equation of Macklin and Payne (1967) for riming ice spheres (simulated graupel): EW VALf + Cw (Ta ~ Tm) + C,{Tm - Ts)} 4 X Re05{Prl/3 kjTs - Ta) + Sc^LJX p, - pf)} 2R to characterize the microphysical growth state of ice particles in the parameter space of cloud parcel temperature and liquid water content. Here E is the collection efficiency; W is the concen­ tration of supercooled water, T„ is the ambient temperature; T„ is the melting temperature; Ts is the graupel surface temperature; CH.and C, are heat capacities of liquid water and ice, respectively. VT is the graupel fall speed; x is the heat transfer coefficient; Re is the Reynolds number, Pr is the Prandtl number, Sc is the Schmidt number, k is the thermal conductivity of air, and L* is the latent heat of vaporization; and p„ p3 are the density of water vapor in the environment and at the graupel surface, respectively. The results for one particle diameter (2R) are shown in Figure 2.2.7. At low liquid water content, the effects of riming are negligible and the preferred state is depositional growth from the vapor. At high liquid water content, wet growth is achieved, with an evaporating liquid surface. At intermediate values of liquid water content which are most common in ordinary thunderstorms (Musil and Smith, 1989; Williams et al., 1993), the graupel particles are growing in dry growth by riming but simultaneously are losing mass by sublimation. According to laboratory simulations by Takahashi (1978), such particles should acquire negative charges in collisions with ice crystals and thereby account for the main negative charge region in thunderclouds (Williams et al., 1991; Williams, 1995). Mixed-phase growth of ice particles ceases when the particles fall to the 0°C isotherm, and melting commences. Studies of the melting evolution of large ice particles below the CPC isotherm (Rasmussen and Heymsfield, 1987; Srivastava, 1987) provide important information about the particle characteristics higher in the cloud prior to the onset of melting. Figure 2.2.8 summarizes the evolution of ice particle size (unmelted ice particle diameters) with height below the 0°C isotherm, for a large range of initial ice particle sizes and all with a density of 0.9 g cm-3. Generally speaking, ice particles must be close to 10 mm in diameter to survive a fall of 5000 m without melting. The millimeter-sized graupel that predominates in the mixed-phase region of ordinary thunderstorms (with generally subadiabatic liquid water contents) does not survive unmelted to ground level unless ground level is substantially elevated with respect to sea level. Graupel observations on mountain peaks (Kuettner, 1950; List, 1958; Raymond and Blyth, 1992) with

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38

Macklin, et al (1960) Violent Hailstorm, England (6mm - 50mm)

a

08

1.0

List (1958) Davos, Switzerland (lmm - 8mm)

Knight St Heymsfield (1983) Early Spring Storm, Colorado (6mm • 16mm) 0.4

o

0.6

Heymsfield (1978) Cumulus Congestus Clouds Colorado (lmm - 8mm)

O w.

3t 6

Heymsfield A Dye (unpublished) Cumulus Congestus Clouds New Mexico (2mm - 6mm)

4s

LocateUi & Hobbs (1974) Winter Storms Cascade Mountains (0.5mm - 3mm)

o"6

oi

n

Bulk Density (gm/cm5) Figure 2.2.6 Measurements of bulk density for graupal and hail particles in convective situations ranging from weakly convective winter storms (lower figure) to intense hailstorms (upper figure).

elevations of a few thousand meters beneath ordinary thunderstorms are quite common, as Figure 2.2.8 would suggest. 2.7.

SHAPE OF THE CAPE AND ITS INFLUENCE ON THUNDERSTORM BEHAVIOR

Convective available potential energy is an important link between thermodynamics, thunderstorm dynamics, and ice mictophysics which is likely responsible for lightning. While the limitations of parcel theory are well recognized (Stommel, 1947; Warner, 1955), particularly for the small clouds with narrower updrafts that dominate the global thunderstorm population, CAPE continues to provide an upper bound for the kinetic energy of the updraft In fact maximum updraft velocity at any height z is given by: w(z) = V2 • CAPE(z)

(9)

M eteorological Aspects o f Thunderstorms

39

I EZ

W EZ O U K w E-

Q D O J u

TEMPERATURE (°C) Figure 2.2.7 Microphysical growth states of spherical rimed ice particles in the mixedphase region, according to Equation 8, for particle of one diameter. (After Williams, E. R. et al. (1991). J. Atmos. Sci., 48,2195. With permission.) Initial Diameter (mm)

Figure 2.2.8 Evolution of melting with distance below the 0°C isotherm, for ice particles with a range of initial diameter. The initial bulk density for all ice particles is 0.9 g cm*1.

where

(l0 ) The maximum updraft speed at any given level sets an upper limit to the size of ice particles (graupel and hail) that grow by riming in the mixed-phase region. A particle whose fall speed is

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Handbook o f Atm ospheric Electrodynam ics, Volume i

Figure 2.2.9 Fall speeds of ice spheres (vs. diameter) at 400 mbar and T « -20"C. The ice bulk density is 0.9 g cm-J. The diameter dependence follows Equation 11.

exactly matched by the local updraft speed will remain suspended in the airstream and continue to grow by accretion of supercooled water. The fall speed VT of a spherical particle of diameter D is given by:

where p* = the particle density pa = air density g = acceleration due to gravity Cd = the drag coefficient Figure 2.2.9 shows the fall speed dependence on particle diameter for representative conditions (Ludlam, 1980) at 400 mbar (7 km) and T = -20°C. The so-called particle balance level (Atlas, 1966; Lhermitte and Williams, 1985) is a characteristic feature of Doppler radar observations at vertical incidence in thunderstorms. Given that the ice particles aloft adapt to the updraft speed, one can estimate the maximum particle size in the mixed-phase region on the basis of updraft velocity, which in turn can be estimated on the basis of Equation 9. Note here that the updraft speed of interest is typically at an altitude significantly less than the LNB, as shown by Figure 2.2.4 and the CAPE examples in Figure 2.2.10a-l. Based on the fall speed behavior of ice spheres shown in Figure 2.2.9, it is apparent that updrafts in the range of 10 to 20 m s-1, which are typical of ordinary thunderstorms (Byers and Braham, 1949; Williams, 1995) in the mixed-phase region, could support the growth of graupel particles in the 1- to 10-mm diameter range. For typical observed subadiabatic liquid water contents (Musil and Smith, 1989) the results of the calculations based on Equation 2.2.8 suggest that most of these particles will exhibit dry growth and subli­ mation, and furthermore that most will not survive the fall from the 0°C level to ground. By contrast, for severe thunderstorms with updraft speeds in the 20-50 m s_l range (Ludlam, 1963; Williams, 1985, 1995; Price and Rind, 1993), the prediction based on Figure 2.2.9 is for ice particles with diameters of centimeters. Such particles are expected to exhibit wet growth

M eteorological Aspects o f Thunderstorms

41

(following the heat balance in Equation 2.2.8), to take on a density close to that of pristine ice (0.92 g cm-3), and to survive the fall from 5000-m altitude to ground without melting (Figure 2.2.8). Such storms are classified as hailstorms. The dependence of fall speed on diameter in Equation 11 is Dm. When the stronger power law dependences of particle mass (D3), gravitational power (Din) (Williams and Lhermitte, 1983), and radar reflectivity (D5) are considered, it is apparent that rather modest increases in CAPE and updraft velocity are associated with substantial increases in the mass, gravitational power, and radar reflectivity of ice-phase precipitation. The role of this dependence in determining the struc­ ture and lightning flash rate of tropical convection has been investigated by Rutledge et al. (1992) and by Williams et al. (1992). Based on the foregoing discussion, it is apparent that the shape of the CAPE is as important as CAPE itself in determining the vertical structure of precipitation, which in turn appears to control the vigor of electrification and lightning. Figures 2.2.10a-l illustrate the shapes of CAPE on thermodynamic diagrams used in the prior discussion of parcel theory associated with a wide variety of thunderstorm convection. These blackened positive areas represent CAPE by the stan­ dard pseudoadiabatic (irreversible) process, which has been shown to closely approximate the value of CAPE calculated for a reversible process in which the ice phase is incorporated (Williams and Renno, 1993). The values range from a few hundred joules per kilogram in the case of arctic hurricanes (Figure 2.2.10a) and small air mass thunderstorms (Figure 2.2.10b) to more than 5000 J kg-1 for the giant tropical thunderstorm and the Plainfield, Dlinois tomadic hailstorm (Figure 2.2. lOi) (Seimon, 1993; MacGorman and Burgess, 1994). In view of the evidence for an important role for the mixed-phase region in thunderstorm electrification, both the 0 and —40°C isotherms are highlighted on these thermodynamic diagrams. The growth of large ice particles is most strongly stimulated by the presence of substantial CAPE below and within the lower portion of the mixed-phase region. The existence of CAPE above the mixed-phase region can provide little stimulus to precipitation growth, because without supercooled water there is no recognized growth mechanism. The shape of CAPE for the elec­ trically inactive monsoon (long and thin) and the shape of CAPE for the electrically active storm (short and fat) producing 4-in. hailstones illustrate the dramatic impact on cloud microphysics and electrification. The long and thin condition is favored by a large areal fraction of persistent deep convection, a condition most prevalent in the tropical monsoon and along the intertropical convergence zone (ITCZ) where the atmosphere is most effectively stirred in the vertical by moist convection. The short and fat condition is favored by the presence of cold air aloft and warm, moist air of high 0„- near the surface, a condition most prevalent at midlatitude in North America in the springtime. The total CAPE in the monsoon case (Figure 2.2.100 is comparable to CAPE for ordinary summer thunderstorms at midlatitude (Figure 2.2.10), but the latter storms are often more electrically active than the monsoon, presumably because more of the CAPE is available below the mixed-phase growth region. This suggestion is supported by the radar cross sections shown in Figure 2.3.2 for ordinary summer thunderstorms (Figure 2.3.2h) and for the tropical monsoon (Figure 2.3.2e). 3.

METEOROLOGICAL CONDITIONS SUPPORTING THUNDERSTORMS

A surprisingly wide range of meteorological situations exhibit thunderstorms: air mass convection, cold frontal convection, warm frontal convection, mesoscale convective complexes, winter snow­ storms, arctic hurricanes, monsoon convection, typhoons, and hurricanes. This circumstance has often prompted the suggestion that many different mechanisms for lightning production are at work in the earth’s atmosphere. An alternative interpretation of the observations (and the one favored by the author) supports a different view; one mechanism is operating, enabled by three common features: conditional instability with CAPE as an energy source, a lifting mechanism to release the energy, and an ice phase. The necessary lifting of air parcels to the cloud condensation

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figure 2 .2 .1 0 Shape of the CAPE for a wide variety of meteorological situations ranging from small values of CAPE to large values. A pseudoadiabatic process is assumed. The wet bulb adiabat is determined on the basis of surface parcel characteristics. The scale for all plots is identical, (a) Condition prior to the passage of an arctic hurricane over the Bering Sea. (Adapted from Businger, S. and J.-J. Baik. (1991). Moo. Weather Rev., 119, 2293.) (b) New Mexico thunderstorm on July 31, 1984. (Modified from Ziegler, C.L. et al. (1991). ). Geophys Res., 96, 12833.) (c) A thunderstorm in Cambridge, Massachusetts on June 30, 1988 showing a 7-km maximum radar echo top and flash rate of 5-10 flashes per minute, (d) Proximity sounding for a microburst-producing thunderstorm in Huntsville, Alabama on July 20, 1987 (Wakimoto and Bringi, 1988; Tuttle et al., 1989). (e) Mean sounding for the hurricane season for the West Indies. (After Jordan, C.L. (1958). J. Meteoro/., 15, 91.) (0 Monsoon conditions on November 30,1988 in Darwin, Australia (12°) (Rutledge etal., 1992; Williams et al., 1992). The radar depiction of the vertical structure of precipitation is shown in Figure 2.3.2f. (g) Premonsoon (break period) conditions on November 10,1988 prior to development of the giant tropical thunderstorm shown in Figure 2.3.2I (From T.D. Keenan and K. Glasson, personal communication, 1989.) (h) Sounding in Portland, Maine ahead of New England hailstorm whose vertical crossection is shown in Figure 121. (i) Sounding prior to a hailstorm near Miles City, Montana on August 1,1981 in CCOPE. (From Rasmussen, R.M. and A.J. Heymsfield, 1987. i. A tm os Sc/., 44, 2764. With permission.) (j) Sounding preceding the Oklahoma hailstorm on May 23, 1981. (Based on Keighton, SJ. et al. (1991). Mon. Weather Rev., 119,1533. With permission.) (k) Severe tomadic thunderstorm near Plainfield, Illinois on August 29, 1990 (Seimon, 1993; MacCorman and Burgess, 1994). The maximum radar top reached 18 km. (I) Composite sounding for storms in the central U.S. producing hailstones with 4-in. (D = 10 cm) diameter. (After Fawbush and Miller, 1953; Moore and Pino, 1990.)

M eteorological Aspects o f Thunderstorms

Figure 2.2.10

43

(Continued)

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Figure 2.2.10

(Continued)

level and their subsequent movement along some approximation to a moist adiabat is accom­ plished in a variety of ways, as illustrated in Figure 2.3.1; the different meteorological situations are essentially distinguished on the basis of these different lifting mechanisms and the vertical air motions that are achieved to influence the microphysical growth of particles. Observations suggest that the electrical activity in these various meteorological conditions as measured, for example, by lightning flash rate is strongly influenced by the quantity of ice-phase precipitation (i.e., graupel and small hail). Foremost among these observations is radar, which is quite sensitive to the large precipitation particles in a storm (Battan, 1973); these, in turn, appear to be strongly influenced by CAPE as discussed in the previous section. Figure 2.3.2 illustrates specific examples of radar vertical cross sections in the various meteorological conditions discussed below and for which information on lighting activity is available. All illustrations include contours for radar reflectivity in dBZ in 10-dB intervals, and a horizontal line indicating the 0°C isotherm. The dBZ values provide a logarithm compression of the reflectivity scale (dBZ = 10 log Z, with reflectivity z in units of mm6 m-3. 3.1.

AIR MASS THUNDERSTORMS

The most prevalent thunderstorm type in the earth’s atmosphere develops in conditions of mod­ erate wind shear and with CAPE values of order of 1000 J kg-1. This form of convection is initiated over land areas (where thunderstorms are more prevalent than over water), by thermals over hot spots on the ground (Figure 2.3.1), but more frequently by low level convergence lines (Figure 2.3.1). These latter features are miniature fronts with a contrast in thermodynamic prop­ erties (e.g., 0„) quite modest in comparison with fronts at the mesoscale and synoptic scale. These fronts are set up by the lateral spread of colder, denser air from an adjacent body of water (the seabreeze) or by the surface outflow from a distant storm. These near-surface perturbations are not detectable with route meteorological surface observations, and usually require either a special mesonet array of meteorological sensors (Wilk and Barnes, 1988) or a narrow-beam Doppler radar, which can detect the motions of insects or other debris in the planetary boundary layer prior to the formation of cloud. The general absence of such detailed information on the structure of the boundary layer lends considerable difficulty to the prediction of air mass thunderstorms. It is now generally recognized that while air mass thunderstorms appear to develop in random fashion, their underlying origin is probably quite deterministic but requires for prediction purposes this more detailed meteorological information. The first comprehensive study of air mass thunderstorms (called the Thunderstorm Project) was conducted in Ohio and Florida in the late 1940s (Byers and Braham, 1949). The general

WARM FRONT Cold

Air (L o w 8W) ./^ " gS yw w .

Warm Air (High 0W)

Illustration of various means for lifting of air parcels, an essential initial step in the release of condi­ tional instability. Figure 2.3.1

description of storm evolution derived from this study appears to pertain to air mass thunderstorms around the world, as many subsequent studies have shown. Three major phases of cloud devel­ opment (following the initiating lifting stage discussed earlier) are the cumulus phase, the mature phase, and the dissipating phase. These three phases are illustrated in Figure 2.3.3. The cumulus phase is characterized by upward growth of the cloud by virtue of positively buoyant cloudy air parcels above the CCL (Figure 2.2.4) and the initial formation of precipitation within the cloud, sometimes by the collision-coalescence mechanism (mainly in the tropics) and sometimes by the Bergeron process (mainly at higher latitude). The initial radar echo signifying the appearance of precipitation is observed during this phase. Substantial increases in electric field

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RANGE (tun)

Figure 2 3 .2 (a-d) Radar depict ions of the vertical development of precipitation in a wide variety of meteoroiogic conditions, with the corresponding electrical activity increasing through the sequence. All radar cross sections show contours of radar reflectivity in dBZ with I O-dB intervals, with reflectivity greater than 40 dBZ shaded. The position of the 0M isotherm is also shown, (a) Marginal warm cloud convection in Huntsville, Alabama, July 1987 (MIT Radar Data Archive). No lightning activity. 5 g n r 3 at —20°C), indicating that sufficient rimer surface must continue to grow even at high EW to cause net positive chaiging by this mechanism. This is consistent with the results of Avila and Caranti (1991, 1992), who find both signs of charge transfer, with one sign being dominant, in a series of individual particle collisions.

Thunderstorm Electrification

85

The analysis of the contact potential mechanism shows that the rimer charges negatively because its contact potential is more negative than that of the ice crystals. The fact that in the ice crystal experiments, below the reversal temperature, negative charge transfer was independent of temperature is consistent with the results that below about —20°C the contact potential tends to a steady value. Thus the mechanism can account for the negative charging in Region 1 of Figure 3.3.6. Increasing EW does not change the rime contact potential but the contact potential of rime formed at a higher temperature is reduced, which permits a positive charging process to dominate in Region 2. In the dislocation-driven charging mechanism, the rimer surface grows more rapidly than the ice crystals and thus has a higher concentration of positively chaiged dislocations. During contact, the rimer surface charges negatively following the mass transfer of a region of positive disloca­ tions. With increase in temperature or LWC, the droplet freezing time increases and therefore the rimer dislocation concentration decreases and the mechanism becomes less effective. The mech­ anism is included here because dislocation charges and concentrations on single ice crystals, measured by X-ray topography, show that there is sufficient charge available to account for the observed charge transfers. It is not clear, however, why the positive dislocations in the ice lattice do not become surrounded by negative charges that would also be available for transfer during particle contact. The classic temperature gradient theory, as enumerated by Latham and Mason (1961), is inadequate to account for the observed charge transfers. The enhanced temperature gradient mech­ anism of Caranti et al. (1991) is unproven; proof that the mass transfer of charged surface can occur presents a formidable experimental problem. The concentrations and charges on dislocations on atmospherically realistic ice crystals and graupel are unmeasured. The controlling factors in the mechanism of charge transfer may simply be the availability and freezing time of supercooled droplets on the rimer surface. At relatively high temperatures the droplets freeze slowly and have time to bathe the surrounding area with vapor, whereas at low temperatures higher freezing rates limit the vapor available. The situation is made more complicated by the heat released from the freezing droplets; the heat diffuses through the rimer surface and in turn controls the vapor diffusion rate to areas of the surface surrounding the freezing droplets. These ideas warrant a considerable research effort to resolve the outstanding problem of the mechanism of thunderstorm charge generation. 4.

EFFECTS OF THUNDERSTORM ELECTRIC FIELDS

The electric fields developed in thunderstorms reach values of the order of 100 kV m_l, which is sufficiently high to influence the behavior of cloud and precipitation particles. For example, the collection efficiency of 260-pm cloud drops for 15-pm droplets was increased by 20% in a field of 50 kV n r 1 with further increases at higher fields (Latham, 1969). Similarly, the aggre­ gation of freely falling 50-pm columnar ice crystals increased by up to 30% in a field of 100 kV m 1 (Saunders and Wahab, 1975). A small hail pellet was found by Latham and Saunders (1970) to increase its collection efficiency for ice crystals by over 30% in electric fields of 100 kV n r 1. Latham (1969) noted that fields above about 100 kV n r 1 increased the growth rate of ice crystals by collision with supercooled droplets. The growth rate of ice crystals by diffusion from the environmental vapor is also increased in fields above approximately 500 kV n r 1 according to Crowther and Saunders (1973). These field effects all require substantial values of electric field to influence the cloud particle behavior. High fields are only achieved in the mature stages of thunderstorm development, and these effects, although interesting, do not have a profound effect on cloud physical behavior. The electric field strength at which lightning is initiated is considerably below the field value required to initiate an electrical dischaige in a dry, particle-free environment. It has been suggested that lightning may be initiated by corona discharges from electrically stressed particles. Richards

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and Dawson (1971) levitated water drops in a wind tunnel and applied a vertical electric field that caused drop distortion. They observed that the critical field for the drop to become sufficiently unstable to emit corona was radius dependent. For a drop of 3-mm radius, the critical field was around 900 kV n r 1 which is still high relative to the field strengths measured in thunderstorms. Griffiths and Latham (1972) showed that at the 500-mbar pressure level, the critical field reduces to 550 kV m_l. Drops in thunderstorms will carry electric charge, and this may reduce the required critical field still further. Griffiths and Latham (1974) noted that ice crystals in high fields at realistic pressures release corona above critical fields o f400 kV m_l. Lower critical field strengths for corona discharge are evident when pairs of drops interact, particularly when their line of centers lies along the vertical field direction. Latham and Roxburgh (1966) noted critical fields well below the observed field maxima during the close approach of pairs of small drops, and such discharges have been photographed (Sartor, 1967). The lowest critical fields were noted by Crabb and Latham (1974), who collided pairs of water drops of 2.7- and 0.65-mm radius at a relative velocity of 5.8 m s-1. They detected corona in fields as low as 250 kV m_l, which shows that the interaction of particles can initiate lightning. The electric field in thunderstorms is able to modify the fall velocity of charged particles and can lead to particle levitation. Gay et al. (1974) found, for example, that 100-pm drops carrying a typical charge of - 3 0 fC could be levitated in a field of 100 kV m_l. There is visual evidence from thunderstorm observations of the change in orientation of charged ice crystals associated with a lightning dischaige: when the levitating or orienting field releases the crystals, their sub­ sequent movement may be seen as a change in intensity of scattered or reflected light from the upper portion of the cloud. A precipitation particle being charged by the inductive process may eventually achieve a sufficiently high charge to be levitated in the field, at which time the rate of particle interactions decreases; thus precipitation and field development are reduced, as shown by Scott and Levin (1975). Following a lightning stroke, the levitated particles are free to fall and the precipitation rate is enhanced. Rain gushes occurring at the ground a few minutes after a lightning stroke have been observed (Moore et al. 1964), and are attributed to the rapid coalescence of particles charged by the capture of ions released by the lightning dischaige. 5,

CONCLUDING REMARKS

Despite the considerable efforts that have been made in recent years to solve questions concerning thunderstorm electrification, there are still outstanding problems. Laboratory studies of the charging of riming graupel pellets during ice particle collisions give results that are specific to the experimental techniques used; therefore, to ensure that the experiments simulate the real cloud situation as closely as possible it is important to feed information back from field studies con­ cerning particle types, concentrations, locations, velocities, temperatures, and liquid water con­ tents. The heat balance of a riming graupel pellet needs laboratory and theoretical work to ascertain the detailed behavior of the riming surface where the impacting ice crystals transfer charge. Is there evidence that surface material, which may carry charge, is transferred during the contact process? The inductive charging of graupel pellets by means of supercooled water droplets and ice crystals, although ruled out in the past because it is unable to account for observed electrifi­ cation in the early stages of thunderstorm development, may be important in the later stages. Another problem to be accounted for is the observation by Curran and Rust (1992) that low precipitation thunderstorms produce mostly positive lightning strokes to ground. The storms have narrow drop size distributions and low liquid water contents, yet the positive lightning originates in regions of high radar reflectivity associated with the presence of large hail. Recent work using instrumented balloons by Marshall and Rust (1991) has revealed an extremely complex thunder­ storm charge structure, and there are observations of both positive and negative lightning at various stages of the development of tornadoes and mesoscale and supercell storms (MacGorman and Nielsen, 1991; Hunter et al., 1992). There is need here for further studies of thunderstorm charge

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distributions to find the time scale of their development, to locate the charge transfer events, and to test charging theories and the validity of laboratory experiments. The use of numerical models provides an increasingly important tool in the achievement of these aims. Recent numerical models of the electrification of thunderstorms have used storm observations as a template on which to build the electrical development. For example. Dye et al. (1986), Latham and Dye (1989), and Norville et al. (1991) have used a well-studied CCOPE cloud in Montana to test electrification by means of crystal/graupel collisions in a one-dimensional model. Helsdon and Farley (1987) have used the same cloud in a three-dimensional dynamic model that includes charging by many processes. Ziegler et al. (1986, 1991) have used a New Mexico mountain thunderstorm in one- and three-dimensional kinematic models and have included lab­ oratory crystal/graupel charge transfer data together with droplet/graupel charging by the inductive mechanism. Although the early models disagreed on the timing of the electrical development and the location of the charge centers, all the model results show that charging by particle collisions is adequate to account for thunderstorm electrification; however, many assumptions have been made. The latest models use the charge transfer data of Keith and Saunders (1990) to include the dependence of charge transfer on ice crystal size. No models yet take detailed account of the collection efficiency of ice crystals for graupel, for which some data are available (Keith and Saunders, 1989). All the modelers note that the sign of crystal/graupel charging is dependent on temperature and liquid water content, but this is taken into account only in a limited way at present. For example, Ziegler et al. (1991) have used specific charge sign reversal temperatures of - 1 0 and —20°C for the storm studied and find that a reversal temperature of - 10°C matches the cloud observations. Future modeling studies will be able to use the formulations of Saunders et al. (1991) to relate the reversal temperature to the specific cloud conditions. The proponents of the convective mechanism for the charging of thunderstorms have shown that the artificial release of negative charge from the ground can influence the local electric field and produce positive lightning; however, they have not shown that convective charge transport can electrify thunderstorms whose bases are not close to the ground. Experimental proof of this concept is perhaps impossible, but it should be feasible for the process to be tested in numerical models. It is certainly true that convective motions in clouds play an important role in moving regions of charged particles (as shown by Weinheimer, 1987 and Ziegler et al., 1991), and thus convection currents are also involved in precipitation-based charging mechanisms. There is need for more detailed study of the air motions in and around thunderstorms by means of Doppler radar studies of precipitation particles. Chaff released into the cloud can be detected by radar to trace air motions in the early stages of storm development and to trace entrainment and mixing processes at the cloud top and edges. Further airborne and balloon studies are needed, along with advanced ground-based remote sensing techniques, to expand our knowledge of the distribution of charge throughout a thunder­ storm, and to determine the characteristics of the particles in those regions of thunderstorms where there is strong evidence that electrification is taking place.

REFERENCES Aufdermaur, A. N. and Johnson. D. A. (1972). Charge separation due to timing in an electric field, Q. J. R. Meteorol. Soc.. 98, 369. Avila, E. A. and Caranti, G. M. (1991). Charge transfer during individual collisions in ice growing by riming. Int. Aerospace Ground Conf. Lightning Static Electr., Cocoa Beach, NiCG, I09A-1-109A 14. Avila. E. A. and Caranti, G. M. (1992). A laboratory study of static charging by fracture in ice growing by riming, Proc. 9th Int. Conf. Atmos. Electr., St. Petersburg, Russia, 100,103.

Baker, B., Baker, M. B„ Jayaratne, E. R., Latham. J., and Saunders, C. P. R. (1987). The influence of difhisional growth rates on the charge transfer accompanying rebounding collisions between ice crystals and soft hailstones, Q. J. R. Meteorol. Soc.. 113, 1193.

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Baker, M. B. and Dash, J. G. (1989). Charge transfer in thunderstorms and the surface melting of ice, J. Crystal Growth, 97,770. Beard, K. V. and Ochs, H. T. (1986). Charging mechanisms in clouds and thunderstorms, in The Earth’s Electrical Environment, Studies in Geophysics, National Academy Press, Washington, D.C., 114. Blakeslee, R. J , Christian, H. J., and Vonnegut, B. (1989). Electrical measurements over thunderstorms, J. Geophys. Res., 94, 13135. Breed, D. W. and Dye, J. E. (1989). The electrification of New Mexico thunderstorms D. Electric field growth during initial electrification, J Geophys Res., 94, 14841. Bringi, V. N., Seliga, T. A., and Aydin, K. (1984). Hail detection with a differential reflectivity radar, Science, 225. 1145. Brook, M„ Nakano, M„ Krehbiel, P., and Takeuti, T. (1982). The electrical structure of the Hokuriku winter thunderstorms, J. Geophys. Res., 87, 1207. Brooks, I. M. and Saunders, C. P. R. (1992). 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Geophys Res, 90,6041. Caranti, G. M., Avila, E E , and Re, M. A (1991). Charge transfer during individual collisions in ice growing from vapor deposition, / Geophys Res., 96, 15365. Chiu, C.-S. and Klett, J. D. (1976). Convective electrification of clouds, J. Geophys Res, 81, 1111. Christian, R , Holmes, C. R., Bullock, J. W., Gaskell, W., Illingworth, A J.. and Latham, J. (1980). Airborne and groundbased studies of thunderstorms in the vicinity of Langmuir Laboratory, Q. J. R Meteoroi. Soc., 106, 159. Church, C. R. (1966). The Electrification of Hail, Ph. D. thesis. University of Durham, U.K., 55. Ctabb, J. A and Latham, J. (1974). Corona from colliding drops as a possible mechanism for the triggering of lightning, Q. J. R. Meteoroi. Soc., 100, 191. Cross, J. D. and Speare, P. A (1969). Electrical aspects of the evaporation of ice, Br. J. Appl. Phys, (J. Phys D), 2,1021. Crowther, A G. and Saunders, C. P. R. (1973). Ice crystal growth in electric fields, J. Meteoroi. Soc. Jpn., 51, 318. Cupal, J. J., Kale, N. R., Wechsler, P. J , and Vali, G. (1989). An instrument for the simultaneous measurement of the image and electric charge of hydrometeors, J. Atmos Oceanic TechnoL, 6 , 697. Curran, E B. and Rust, W. D. (1992). Positive ground flashes produced by low-precipitation thunderstorms in Oklahoma on April 26, 1984. Mon. Weather Rev., 120, 544. Dash, J. G. (1989). Surface melting. Contemp. Phys, 30,89. Dong, Y. and Hallett, J. H. (1992). Charge separation by ice and water drops during growth and evaporation, / Geophys. Res. 97. 20361. Dye, J. E , Jones, J. J„ Winn, W. P., Cemi, T. A-, Gardiner, B„ Lamb, D., Pitter, R. L , Hallett, J., and Saunders, C. P. R. (1986). Early electrification and precipitation development in a small, isolated Montana cumulonimbus, J. Geophys. Res, 91, 1231. Dye, J. E , Jones, J. J , Weinheimer, A J., and Winn. W, P. (1988). Observations within two regions of charge during initial thunderstorm electrification, Q. J. R. Meteoroi. Soc., 114, 1271. Dye, J. E , Jones, J. J , Weinheimer, A J , and Winn, W. P. (1992). Reply to comments by C. B. Moore and B. Vonnegut further analysis of two regions of charge during initial thunderstorm electrification, Q. J. R. Meteoroi. Soc., 118,401. Dye, J. E , Winn, J. P., Jones, J. J„ and Breed, D. W. (1989). The electrification of New Mexico thunderstorms. 1. Rela­ tionship between precipitation development and the onset of electrification. J. Geophys. Res, 8643-8656. Elster, J. and Geitel, H. (1913). Zur Influenztheorie der Niederschlagselektrizitat, Phys. Z , 14, 1287. Feng, H. and Winn, W. P. (1990). Screening layers of charge at the boundaries of electrified clouds, EOS. 71, 1239. Furulcawa, Y., Yamamoto, M„ and Kutoda, T. (1987). Ellipsometric study of the transition layer on the surface of an ice crystal, J. Crystal Growth, 82, 665. Gardiner, B„ Lamb, D., Pitter. R. L , Hallett, J , and Saunders, C. P. R. (1985). 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Gaskell. W. and Illingworth, A. J. I. (1980). Charge transfer accompanying individual collisions between ice particles and its role in thunderstorm electrification, Q. J. R Meteorol. Soc., 106, 841. Gay, M„ Griffiths, R. F„ Latham, J„ and Saunders, C. P. R. (1974). The terminal velocities of charged raindrops and cloud droplets falling in strong electric fields, Q. J. R. Meteorol. Soc., 100, 682. Gish, O. H. and Wait, G. R. (1930). Thunderstorms and the earth's general electrification, J. Geophys. Res., S3, 473. Goodman, S. 1., Buechler, D. E , and Wright, P. D. (1989). Polarization radar and electrical observations of microbuist producing storms during COHMEX, Preprints 24th AMS Conf. Radar Meteorol., Tallahassee, FL, 109. Grenet, G. (1947). Essai d’explication de la charge electrique des nuages d’orages, Extrait Ann. Geophys., 3, 306. Griffiths, R. F. G. and Latham, J. (1972). The emission of corona from falling drops, J. Meteorol. Soc. Jpn., 50, 416. Griffiths, R. F. 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Jayaratne, E R., Saunders, C. P. R., and Hallett, J. (1983). Laboratory studies of the charging of soft-hail during ice crystal interactions, Q. J. R Meteorol. Soc., 109, 609. Jayaratne, E R., and Saunders, C. P. R. (1984). The “ raingush", lightning and the lower positive charge center in thun­ derstorms, 89, 11816. Jayaratne, E R., and Saunders, C. P. R. (1983). Thunderstorm electrification: the effect of cloud droplets, J. Geophys. Res., 90. 13063. Jennings, S. G. (1975). Charge separation due to water droplet and cloud droplet interactions in an electric field, Q. J. R. Meteorol. Soc., 101, 227. Jonas, P. R. (1990). Observations of cumulus cloud entrainment, Atmos. Res., 25. 105. Keith, W. D. and Saunders, C. P. R. (1988). Light emission from colliding ice particles. Nature (London), 336, 362. Keith, W. D. and Saunders, C. P. R. (1989). The collection efficiency of a cylindrical target for ice crystals, Atmos. Res., 83. Keith, W. D. and Saunders, C. P. R. (1990). Further laboratory studies of the charging of graupel during ice crystal interactions, Atmos. Res, 25,445. Krehbiel, P. R. (1981). An Analysis of the Electric Field Change Produced by Lightning, Ph.D. thesis. University of Manchester Institute of Science and Technology, U.K. Krehbiel, P. R., Brook, M., and McCtoty, R. A. (1979). An analysis of the charge structure of lightning discharges to ground, J. Geophys. Res., 84, 2432. Krehbiel, P. R. (1986). The Electrical structure of thunderstorms, in The Earth's Electrical Environment, Studies in Geo­ physics, National Academy Press, Washington, D.C., 90. Krehbiel, P., McCrary, S., Chen, T., Rison, W„ Gray, G., Blackman, T„ and Brook, M. (1991). Dual-polarization radar observations of electrical particle alignment in storms near Kennedy Space Center, Florida, Am. Geophys. Union Fall Meet, San Francisco, EOS October 29,93. Krider, E P. and Musser, J. A. (1982). Maxwell currents under thunderstorms. J. Geophys. Res., 87, 11171. Krider, E. 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Latham, J. (1969). Experimental studies of the effect of electric fields on the growth of cloud particles, Q. J. R Meteorol. Soc., 95, 349. Latham, J. and Roxburgh, 1. W. (1966). Disintegration of pairs of water drops in an electric field, Proc. R. Soc A, 295,84. Latham, D. (1991). Lightning flashes from a prescribed fire-induced cloud. JGR 96, 17151. Latham, J. (1963). The electrification of frost deposits, Q. J. R Meteorol. Soc., 89, 265. Latham, 1. (1981). The electrification of thunderstorms. Q. J. R. Meteorol. Soc., 107. 277. Latham, J. and Mason, B. J. (1961). Electric charge transfer associated with temperature gradients in ice, Proc. R Soc. A, 260, 537. Latham, J. and Mason, B. J. (1962). Electric charging of hail pellets in a polarising electric field, Proc. R. Soc., 266A, 387. Latham, J. and Saunders, C. P. R. (1970). Experimental measurements of the collection efficiencies of ice crystals in electric fields, Q. J. R. Meteorol. Soc., 96, 257. Latham, J. and Dye, J. E (1989). 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Chapter 4

Lightning Currents TosJiio Ogawa

CONTENTS 1. Introduction...........................................................................................................................94 2. Charge Structure of ThunderstormClouds.......................................................................... 94 3. Ground Discharge................................................................................................................ 97 3.1. Preliminary Breakdown in the Cloud....................................................................... 97 3.2. Stepped Leader.........................................................................................................101 3.3. Attachment Process..................................................................................................104 3.4. Return Strokes...........................................................................................................105 3.5. J Process and K Changes......................................................................................... 105 3.6. Continuing Current and M Component...................................................................107 3.7. Dart Leader...............................................................................................................109 3.8. Summary of Ground Discharge Processes.............................................................. 109 4. Modeling of Return Stroke Current................................................................................. 111 4.1. Bruce-Golde Model..................................................................................................113 4.2. Transmission Line Model........................................................................................ 114 4.3. Electromagnetic Radiation from Lightning Channel.............................................115 4.4. Lin et al. M odel........................................................................................................117 4.5. Recent Modification of the M odels.........................................................................120 5. Positive Lightning...............................................................................................................120 5.1. Upward Lightning....................................................................................................120 5.2. Winter Lightning......................................................................................................122 5.3. Triggered Lightning.................................................................................................. 122 6. Special Lightning................................................................................................................ 122 6.1. Ribbon Lightning...................................................................................................... 123 6.2. Ball Lightning........................................................................................................... 123 6.3. Bead Lightning......................................................................................................... 123 6.4. Volcanic Lightning................................................................................................... 123 6.5. Lightning from Large Fires..................................................................................... 124 6.6. Lightning from Nuclear Detonation.........................................................................124 7. Lightning Parameters.......................................................................................................... 124 8. Cloud Discharge.................................................................................................................. 127 9. Physical Properties of theLightning Channel.....................................................................129 9.1. Temperature and Electron Density...........................................................................129 9.2. Diameter of Lightning Channel................................................................................132 9.3. Channel Orientation.................................................................................................. 132 10. Concluding Remarks.......................................................................................................... 133 References.................................................................................................................................... 133

0-8493-8647-O/95/SO.00+S.50 O 1995 by C R C Preii. Inc.

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1.

INTRODUCTION

The thunderstorm cloud on earth is produced from water vapor and develops in the atmosphere. The water changes its phase in the cloud depending on altitude/temperature from water vapor to water drops, supercooled water droplets, snow crystals, graupel, hailstones, and ice crystals. Electrification of the thunderstorm cloud is caused by mutual contact, friction, and breakup of such water in various phases in the cloud. The electric field grows due to charge generation and separation in the cloud, with lightning resulting. Lightning is a large-scale electrical discharge occurring in the atmosphere. Lightning has immeasurable effects on all things that exist not only near the lightning, but also far from the lightning, even at the opposite point on the globe, as well as far above the globe. The thunderstorm cloud varies in size on different areas of the globe and in different seasons. The specific factors regulating the cloud size and its character are latitude, topography, and season. Accordingly, lightning shows a variety of different characteristics depending on those factors. Artificially triggered lightning offers a different aspect of lightning. Lightning has a long channel with many branches that extend to several kilometers vertically as well as horizontally. The lightning channel acts as an effective radiation antenna for electro­ magnetic waves over a wide frequency range. Such a large-scale antenna cannot be built artifi­ cially. Thus, the lightning discharge provides us with a valuable test of electrical discharges. The radiated electromagnetic (EM) waves propagate around the globe, giving a number of interesting features. Lightning has been investigated using photography, optics, electromagnetics, and acoustics, or a combination of two or three of these. Great success has been made by the combination of photography and electromagnetics. Some results of such lightning research are presented in this chapter. Refer to Uman (1987) for another aspect of lightning currents. 2.

CHARGE STRUCTURE OF THUNDERSTORM CLOUDS

This topic has been discussed in Chapter 1/3, but an average picture of the charge structure of thunderstorm clouds is briefly given here for help in understanding lightning currents, their oc­ currences, and their mechanisms. Thunderstorm electricity consists of swarming main positive and negative charges with a small positive charge. The main positive charge is scattered in the upper portion of the cloud, and the main negative charge crowds in the lower portion of the cloud. The small positive charge, which is oflen called the positive pocket charge, is located under the negative main charge near the cloud base. A model charge distribution in an average medium-size thunderstorm cloud and the typical electric field change observed on the ground are shown in Figure 4.2.1a and 4.2.1b, respectively (Ogawa, 1993). Three different kinds of charges, Q+, Q_, and q+ are produced by two kinds of current sources, /„ and I* The kinds of charge carriers, water in different phases, and air motion in and around the cloud are also shown with height and temperature in Figure 4.2.1, which is based on many references. Charge carriers in the cloud are ice crystals, rimed and unrimed snow crystals, graupel, hail­ stones, supercooled water droplets, and water drops. They are distributed from the upper portion to the bottom of the cloud, respectively. Various precipitation particles acting as the charge carriers are shown in Figure 4.2.2 and are reproduced from the photographs of Figure 11 in Magono (1980). Suppose a group of thunderstorm charges is a point chaige. This assumption is roughly valid for most clouds. The electric field, £(/), on the ground due to three different kinds of charges in the cloud, Qj (i = 1, 2, 3), are given by: «rt = — W

V

M

M

l

4 7 ^ , _ , M t ? + y i( t ? + z tO ? )3*

m { )

Lightning Currents

95

Figure 4.2.1 A model of electrified thundercloud (a) and the typical electric field change pattern measured on the ground (b). Two kinds of source currents, /„ and td, and the associated three kinds of charges, Q ., Q ., and qt are shown with height and temperature. (From Ogawa, T. (1993)./ Atmos. Etectr., 13, 21. With permission.)

v tL # *

(Q)

1mm

& (e)

(f) 5mm

_ 0 .1mm

Ftgure 4.2.2 Various precipitation particles as charge carriers reproduced from photographs in Magono (1980). (a) Snow crystal fragments, (b) rimed snow crystal, (c) graupel, (d) cross section of hailstone, (e) falling water drop, and (f) ice pellet.

where Eo is permittivity of free space; *,(/), y,(/), Zj(t) are the position coordinates of the charges

Figure 4.3.9 Electric field changes observed with slow antenna (upper) and fast antenna (lower) at the intermediate distance approximately 8 km from the lightning dischaige to ground.

to that expected from the positive J streamer theory by Malan and Schonland (1951a, 1951b) in which the positive streamer progresses upward, slowly making a new channel during the J period. Against this theory the present K change, which consists of a large part of field change in the J period, returns back to the channel already made. The roll of the new channel-making streamer has been played by the positive streamer that occurs just after the return stroke, usually being included in the last phase of the return stroke, or the continuing current process. In conclusion, the J process between successive return strokes is not essentially the process of positive junction streamer that proceeds upward slowly in a fresh charged region, but the process of a series of K streamers or K strokes that proceed downward along the channel already made in the short duration just after the preceding return stroke. The positive upward streamer associated with the previous return stroke forms a new channel, making branches into the negatively charged fresh region in the cloud. Sometimes the return stroke associated positive streamer appears as a continuing current. 3.6.

CONTINUING CURRENT AND M COMPONENT

The continuing current was investigated in detail by Kitagawa et al. (1962) and Brook et al. (1962). They discussed the luminous portion that lasts more than 40 msec after the return stroke, and attributed it to the continuing current flowing from the ground to the cloud portion of con­ centrated negative charges. The lowest limit of the duration of the continuing current was defined as 40 msec, the average return stroke interval, but the continuing luminosity of the duration shorter than 40 msec occurs as well. The distribution of the duration of continuing luminosities after the return strokes was exam­ ined (Ogawa, 1971). The duration of continuing luminosity was read as low as 5 msec, and 210 luminosities in total were divided every 40 msec. The histogram of the number of occurrences of the duration of continuing luminosity is shown in Figure 4.3.10a Out of 210 strokes, 90 were found with the duration of luminosity less than 40 msec. These strokes were again divided by the luminosity duration every 7 msec, and the histogram of the number of occurrences is shown in Figure 4.3.10b. The types of distribution of the luminosity durations in Figures 4.3.10a and b are the same. It is suggested from this fact that every return stroke is followed more or less by the continuing luminosity of different duration. The return strokes not counted above may be followed by the luminosity of the duration less than 5 msec. The current of 100 A, the same order as that for the defined continuing current, flows during the period after the return stroke and before the J period. During this period the positive streamer

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DURATION OF CONTINUING LUMINOSITY Figure 4.3.10 Distribution of numbers of occurrences of the duration of continuing luminosities after return strokes, (a) Divided every 40 msec, (b) Divided every 7 msec.

progresses like tree branches into the new negative charge region. The channels thus made are readily followed by the K streamers from the tips of the channel. A large K streamer appears as the next dart leader. The continuing current occurs often after the final return stroke of a flash with a few strokes, or after the small single return stroke. The J process that occurs after the final return stroke is often called the F process. During the continuing current enhancements of luminosity occur, which are caused by a momentary increase in the supply of current from the ground. They are associated with small electric held changes observed on the ground. They are called M components. Thottappilli et al. (1990) reported that the M change duration was 0.9 msec in the geometric mean for 80 samples and that the M change interval was 2.1 msec for 48 samples. A detailed examination on the electric field pulses in K and M changes was made by Rakov et al. (1992a). A portion of the electric field record for a flash that occurred at Kennedy Space Center (KSC) on August 11, 1984 is shown in Figure 4.3.11, where the digital record is 5 psec moving-averaged. Fourth and fifth return strokes in the flash and their leaders as well as K changes (K| through K4) and M changes (Mt through M4) following the fourth stroke are indicated. Seen in Figure 4.3.11 are four M changes occurring in the continuing current period and four K changes occurring in the J period. The deflections of the K, M, and dart leader held changes are all in the same negative direction. The J period field change is thus negative. Note that the field changes in the periods between successive K changes are of the same order of magnitude as in the K

109

Lightning Currents

18:57:05 UT AUGUST 11.19 8 4 KSC

TIME

•—— • 12 ms

Figure 4.3.11 A portion of the electric field record for a flash. Four M changes and K changes occurred between the fourth and fifth return strokes. (Adapted from Rakov, V A et al. (1992a). J. Geophys. Res., 1992 Copyright by the American Geophysical Union, 97,9935. With permission.)

changes. This means that during the periods the continuous currents flow along the K streamer channel. 3.7.

DART LEADER

A strong K change current flows from the densely concentrated negative charge region into the preceding return stroke channel, and it acts to trigger the subsequent strokes to the first return stroke. It travels fast like a dart, and is called the dart leader. The dart leader re-creates ionization of the lightning channel and draws the cloud potential toward the ground again. In the dart leader a luminous portion of about 50 m in length runs toward the ground at the speed of about 2 x 106 m s~'. The dart leader current is of the order of 1 kA, and carries less charge than the stepped leader. The dart leader sometimes shows a steplike luminosity. There are two types of such dart leaders. The first has short steps all along the channel following the previous channel. The second has long steps in the lowest portion of the channel, but is a different channel from the previous one. These two types of dart leaders are called dart-stepped leaders. The sketches of the two types of dart-stepped leaders are shown in Figure 4.3.12 (Maian, 1963). In the second case the lowest portion of the previous return stroke channel might not be conductive enough to guide the dart leader, because the previous channel is deionized with time during the interval between the former and following return strokes. The dart leader has a sufficiently large negative potential and can create a new stepped leader in the fresh air. To draw a dart leader without steps, the old channel made by the previous return stroke should be kept conductive enough. Such physical characters of the channel as temperature, electron density, and conductivity have been investigated and will be discussed in Section 9. 3.8. SUMMARY OF GROUND DISCHARGE PROCESSES The ground discharge processes including the preliminary breakdown process discussed above

are schematically shown in Figure 4.3.13 (Ogawa, 1993). This is different in the J process from

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110

Figure 4.3.12 Dart steeped leaders, (a) Short steps all along the channel, (b) Long dart stepped leaden in the lowest portion of the channel. (Adapted from Malan, DJ. (1963). Physics o f Lightning, English Universities Press, London.)

CLOUD BASE

+ -+ PRELIMINARY BREAK DOWN (INITIAL)

(a)

+ + + PRELIMINARY BREAK DOWN (LAST)

(b)

+ + +

+++

+++

++ +

STEPPED LEADER

RETURN STROKE

i PROCESS

OART LEAOER

(c)

(d)

(e)

GROUNO SECOND RETURN STROKE

(f)

Figure 4.3.13 Ground discharge processes from preliminary breakdown (a) and (b) to second return stroke (g). The actual channel inside the cloud is horizontal as well as vertical. (From Ogawa, T. (1993). J. Atmos. Electr., 13,121. With permission.)

that defined by Malan (1963) and Schonland (1964), who assumed the slowly proceeding streamer into the fresh negative charge region. The J process in Figure 4.3.13e is the process of K recoil current returning from the tips to the trunk of the channel inside the cloud. Note that the lightning channel in Figure 4.3.13 looks more or less vertical, but this is for the sake of convenience to draw six channels in one figure. The actual channel is sometimes more horizontal than vertical (Ogawa and Brook, 1969). In the initial stage of the preliminary breakdown process (PBI:a) the positive continuous streamer proceeds from the positive pocket charge to the negative main charge region distributing positive charge on the channel. In the last state of the preliminary breakdown (PBL:b) the recoil streamer runs back to the channel from the branch tips neutralizing the positive charge on the

Lightning Currents

111

channel, and fills the channel with negative charge resulting in a high negative potential at the lowest part of the channel. When the electric field just below the channel reaches the breakdown field, about 6000 kV m_l, the negative leader streamer begins to proceed downward. The leader appears in a steplike fashion (SL:c). When the stepped leader approaches the ground, the return current streamer runs back, neutralizing the negative charge distributed on the channel (RS:d). The electric charge transferred by the return stroke is supplied from the ground, so that it is continuously supplied as far as there is a potential difference between the breakdown streamer tip and the precedent leader channel upward. When the return stroke breakdown current tip reaches the end point of the previous stepped leader, the potential of the tip is that of the ground, though not exactly, so that the electric field between the tip and the remaining negative charge region gets very high and the electrical break­ down occurs between them. This breakdown process occurs usually during a few milliseconds soon after the return stroke, as discussed in Section 3.5. During this period, the continuous streamer proceeds into the new negative charge region branching like a tree. The streamer proceeds about 600 m on average vertically as well as horizontally. This process is usually included in the preceding return stroke phase, but sometimes appears as the long continuing current process. Through this process a large amount of positive charge is supplied from the ground accumulating near the tip of the branched channel; then the strong electric field arrives between the tip and the negative charge region left. The recoil current then runs back toward the trunk channel just like in the last stage of the preliminary breakdown (PBL.b). This process occurs intermittently with several K streamers as discussed above. The K streamers neutralize the positive charge distributed on the precedent return stroke-associated positive streamer channel. During this period the positive charge deposited on the lower portion of the return stroke channel dissipates with time. The electric field near the lower end of the K streamer channel increases to a very large value (e). About 40 msec (on average) after the preceding return stroke event, the temperature of the channel is still kept at about 3000 K and the electron density of the channel is on the order of 1023 m-3 (Orville, 1968) so that the channel is barely a conductor. The rapid dart leader streamer runs down along the preceding return stroke channel (f). When the dart leader streamer approaches the ground, the second return stroke occurs (g). Proctor et al. (1988) proposed a model of a ground flash as shown in Figure 4.3.14, based on VHF radio pictures of lightning flashes to ground. In this model the return strokes overshoot the previously active regions. It is interesting to see in this model that the greatest height of the channel is attained at the end of the first or second strokes. Thereafter, the vertical streamers, which occur at the end of the return strokes and during interstroke processes, diminish in extent; however, horizontal progression continues with each stroke and with each interstroke process.

4.

MODELING OF RETURN STROKE CURRENT

If the spatial distribution and the temporal variation of the currents energizing the lightning channel were known, then the electric and magnetic fields radiated from the channel could be calculated as a function of time and distance. The mean current waveforms of the lightning currents for the first and subsequent return strokes measured on Mt. San Salvatore, Switzerland (Berger et al., 1975) are shown on two different time scales in Figure 4.4.1. The current amplitudes are nor­ malized to 1.0. Note that the occurrence time of the peak value of the subsequent stroke is about 4 times faster than that of the first stroke. For the sake of comparison the waveforms of positive stroke currents measured in the same location as in Figure 4.4.1 are shown in Figure 4.4.2 (Berger et al., 1975). The positive strokes are characterized by larger charges and slower fronts than their negative counterparts. This topic will be discussed in Section 5.

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112 SL

J

2 -3

STROKE 1

J

1 -2

3RD STROKE

2ND STROKE

STROKE N

Figure 4.3.14 Model of a ground flash by Proctor et al. SL denotes the stepped leader and ] is the interstroke processes. Ground level is 1.4 km above mean sea level (msl). (From Proctor, D.E. et al. (1988). J. Geophys. Res., 93,12,683. 1988 Copyright by the American Geophysical Union. With permission.)

z

UJ CE CE

3 O Q ILI M

80 (a)

160 240 320 FIR S T STROKE

400 p s A

< 2 tr

o z

20 40 60 80 100 p s A (b) SUBSEQUENT STROKE Ftgure 4.4.1 Mean current waveforms for negative first and subsequent strokes on two different time scales (A and B) measured on Mt. San Salvatore, Switzerland. Current amplitudes are normalized to 1.0. (Adapted from Berger, K. et al. (1975). Etectra, 80, 23. With permission.)

Lightning Currents

113

figure 4.4.2 Current waveforms for four different positive strokes on two different time scales measured on Ml. San Salvatore, Switzerland. Current amplitudes are normalized to 1.0. (Adapted from Berger, K. et al. (1975). Etectra. 80, 23. With permission.)

4.1.

BRUCE-GOLDE MODEL

The first successful lightning return stroke current model was given by Bruce and Golde (1941), who suggested a double exponential expression of the form: I, = I„ (* -- - e-P)

(9)

The current in this model is instantaneously uniform from ground to the return stroke tip. This tip ascends at a velocity of u. Then the current moment at a time f is given considering the image current by 2I,P0X)dt, from which the radiated field can be calculated. Bruce and Golde (1941) found that based on the direct measurements at the ground end of the channel the average values of Ia c l , and P to be about 30 kA, 4.4 x 104 s ' 1and 4.6 x 10s s_l, respectively. The first return stroke velocity was represented from the photographic data by: o, = u0 e -w

(10)

where u„ is 8 x 107 m s_l and q is 3 x 104 s_l. The velocity for subsequent strokes in a multiple flash is relatively constant. Because the peak current for the subsequent strokes is about half that of the first return stroke, an average current model for the subsequent strokes is given by: /, = ( / ^ X e - -

0

GO

Pierce (1977) gave the model values of these parameters as a = 2 x 104 s_ l, P = 2 x 106 s-1, I* = 20 kA, u0 = 108 m s ' 1, and q = 3 x 104 s_ l. Calculating the lightning return stroke currents using Equations 9 and 11 they become small for times larger than a few hundred microseconds, that is, the currents become much less than 1 kA. In practice, a current of the order of 1 kA or so usually flows for a few milliseconds. Cianos and Pierce (1972) suggested the intermediate current of another double exponential form: I ^ l o i i e - y ' - e - * 1)

(12)

where /„ = 2 kA y = 103 s_l 6 = 104 s_l The resultant current models for the first and subsequent return strokes are then, respectively: I„ (*'“' - e »0 + /„ (e-y< - e-*0

(13)

(//2 )(e 'a' - e-»0 + /„ (e~v - e~tr)

(14)

and

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TIME, Ftgure 4 .4 .3

ms

First and subsequent return stroke currents with time calculated from Equations 13 and 14.

The current waveforms are calculated by using Equations 13 and 14 for /„ = 20 kA and /„ = 2 kA, and the results are shown in Figure 4.4.3. 4.2. TRANSMISSION LINE MODEL In the Bruce-Golde model, the return stroke current at any given time is assumed to be uniform with height below the return stroke wavefront, and zero above. The current in the channel below the wavefront is identical to the current at the ground level, that is: Kz. t) = 1(0, t) Kz. t) = 0

z5 8

(15)

z> £

The current that characterizes the Bruce-Golde model is schematically shown in Figure 4.4.4 (Lin et al., 1980). The Bruce-Golde model has been much used for analytical computations. However, it is not physically reasonable for the return stroke current to be uniform instantaneously with altitude. Dennis and Pierce (1964) modified the Bruce-Golde model to correct this deficiency. They sug­ gested that thecurrentwavetravels up the channelwith a velocity that isnotlargerthan the velocity of the Bruce-Golde model. This concept of a traveling wave of current regards the channel as a quasi-transmission line that is charged by the preceding leader process and then discharged by the return stroke. In this transmission line model the current waveform at ground level is assumed to propagate up the channel as it would propagate along an ideal transmission line: Kz, t) = /(/ - z/u) Kz. 0 - 0

z< 6 z> 8

(16)

where the return stroke velocity u is assumed constant. Because the transmission line model requires the same current to propagate across any height of the channel, as schematically shown in Figure 4.4.4, no leader corona charge can be removed from the return stroke channel during the return stroke propagation time, charge being transferred wily from the top to the bottom of the channel.This transmission line return stroke model has beenwidely used by Uman and co­ workers (1970b, 1973a, 1973b), Lin and Uman (1973), Leise and Taylor (1977), and Price and Pierce (1977) to find a typical current waveshape and return stroke velocity from the measured electric and magnetic fields produced by lightning within about 200 km. Thus we have come to study the characteristics of any lightning in different geographic locations and under variable

Lightning Currents

115

t

Height, 2

Bruce-Golde model

t

Height, 2

21*Vt, tz . Transmission Line model

Figure 4.4.4 et al. (1980). /.

Return stroke current distributions for the Bruce-Golde and transmission line models. (From Lin, Y.T.

Geophys. Res., 85,

1571. 1980 Copyright by the American Geophysical Union. W ith permission.)

meteorologic conditions. The lightning has no more need to discharge to the special instrumented tower than it does to discharge to any natural landform. 4.3.

ELECTROMAGNETIC RADIATION FROM LIGHTNING CHANNEL

Uman and co-workers (1969, 1970a, 1970b, 1975a, 1975b), McLain and Uman (1971), and Lin et al. (1979,1980) have developed a general theory of the electromagnetic radiation from a finitelength antenna, which is regarded as an assumed lightning channel, and have applied it to a large number of experimental data. Consider a straight vertical antenna of height H above a perfect-conducting ground plane as an idealized lightning channel. Geometry of the antenna with self-explanatory notations is shown in Figure 4.4.5. Boundary conditions at the plane are satisfied by adding the image antenna shown dashed in Figure 4.4.5. The radius of the antenna cross section is assumed to be very small compared to the wavelength of any radiation under consideration. The current at any height is assumed to be an arbitrary continuous function, i(z, /), which is zero everywhere at t = 0. Consider an infinitesimal vertical current dipole of length dz having a current /(& /) on the antenna as shown in Figure 4.4.5. The electric and magnetic fields at an observation point on the plane, a horizontal distance D from the antenna base, are the sum of the fields from the real and the image dipoles.

116

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kji i i i i ■i i i ■-1 Figure 4.4J> Geometry of an idealized lightning return stroke channel.

The vertical component of the electric field and horizontal component of the magnetic field as a function of time t and distance D from the lightning are obtained as follow, respectively:

(17)

Ho fw sin8 dijz. t - Rlc) 2ji J o cR dt where Eo and \io = the permittivity and permeability of free space, respectively H = the height of the antenna R = (D2 + lP )m The first term on the right of Equation 17 is the electrostatic field, the second term is the induction electric field, the third term is the radiation electric field. The first term on the right of Equation 18 is the induction magnetic field and the second term is the radiation magnetic field. Note that there is no static component in the magnetic field. Also note that the electrostatic field in Equation 17 is proportional to the charge quantity that is the integration of the current, and inversely proportional to the cube of the distance. The induction fields in Equations 17 and 18 are proportional to the current and inversely proportional to the square of the distance. The

Lightning Currents

117

radiation fields in Equations 17 and 18 are proportional to the current derivative and inversely proportional to the distance. By using the above theory, the electric and magnetic field waveforms can be calculated. From a comparison between the calculated and the measured waveforms, various parameters that char­ acterize the lightning current can be estimated. Lin et al. (1979) made simultaneous measurements of Florida lightning return stroke electric and magnetic fields at two stations, one station being within 15 km of the lightning and the other being either approximately 50 or 200 km from the lightning. The first and subsequent stroke electric and magnetic fields, chosen as typical from more than 100 simultaneous measurements, are shown as a function of distance in Figures 4.4.6a and b. Note that the electric and magnetic field waveforms are similar to each other at the distance of 50 km and exactly identical at 200 km. It is suggested from these facts that the radiation component from the lightning channel becomes predominant at a distance of about 100 km. 4.4.

LIN ET AL. MODEL

The Bruce-Golde model and the transmission line model represent two extreme cases of what might be expected to occur in the return stroke channel. Lin et al. (1980) tested these two most commonly used lightning return stroke models for subsequent stroke electric and magnetic field waveforms measured simultaneously at two stations near and distant from the lightning, and showed that these models do not fit very well to the experimental data. Lin et al. (1980) then proposed a return stroke model, which is schematically shown in Figure 4.4.7. The model is composed of three separate current components: 1.

2.

A breakdown pulse current propagates upward at the return stroke wavefront. It will traverse the channel with the return stroke wavefront velocity and is treated by the transmission line model. The velocity cannot be determined by the model and is assumed to be constant, 108 m s-1. The current pulse is assumed to be responsible for the initial peak of the electric and magnetic radiation fields. A uniform current may already be flowing (leader current) or may start to flow soon after the return stroke begins. To determine the uniform current, /„, the slope of the electric field, dE/dt, is measured near the lightning in the linear ramp region when the field is primarily electrostatic. Then /„ is computed from the time rate of change of the relation between a point or spherical charge located at the top of the channel and the resultant electrostatic field:

■

3.

2jcU H * + I?)*1 dE(D, t) H dt

{

)

where D is the distance between the lightning and the observing station, and H is the height of the subsequent stroke channel. Lin et al. (1980) assumed that H is 7.5 km. Corona current is caused by the radially inward and then downward movement of the charge initially stored in the corona sheath around the leader channel. The corona current is idealized as a number of current sources distributed along the channel. Each source is turned on when the peak of the return stroke breakdown pulse current reaches the altitude of the source. At each height the corona current waveshape injected into the channel is assumed to be identical, but its magnitude decreases exponentially with height The corona current is assumed to flow into the channel and to ground with the speed of light

An example of two-station data analyzed by Lin et al. (1980) using their model is shown in Figure 4.4.8. Matching of the model fields to the data is considered adequate. The calculated

100

/**

0 • 5.0 km

50

0 ■2 0 km

150170 D • 5.0 km

MAGNETIC FLUX DENSITY

FIELD IN TEN SITY _j_

0 ■ 2 0 0 km

ELECTRIC

D • 2 0 0 km

0 ■ 50 km

4—

I k O '8 Wbftn*

T

Wb/m2

MAGNETIC FLUX DENSITY

J. Geophys. Res., 84, 6307. Copyright

1979 by the American Geophysical Union. W ith permission.)

Figure 4.4.6 Typical return stroke electric and magnetic field waveforms measured simultaneously at two stations in Florida. (From Lin, Y.T. et al. (1979).

0

Initial peak

FIELD INTENSITY

D * 1.0 km

ELECTRIC

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Lightning Currents

Figure 4.4.7

Res., 85,

119

Return stroke current distributions for the Lin et al. model (From Lin, Y.T. et al. (1980).

J. Geophys.

1 5 7 1 .1 9 8 0 Copyright by the American Geophysical Union. W ith permission.)

CLOSE ELECTRIC FIELD

Figure 4.4.8

CLOSE MAGNETIC F IE L D

DISTANT R A D IA TIO N F IE L D

C U R R E N T AT GROUND

/is

/is

An example erf the Lin et al. model fit to two-station electric and magnetic field measurements. KSC

is the Kennedy Space Center and G N V stands for Gainesville, Florida. (From Lin, Y.T. et al. (1980). J.

Geophys. Res.,

85, 1 5 7 1 .1 9 8 0 Copyright by the American Geophysical Union. W ith permission.)

subsequent return stroke current waveforms agree reasonably well with those obtained by the direct measurement as illustrated in Figure 4.4.6. The properties of the current for subsequent return strokes derived from this model were presented for 101 samples for the peak current, the uniform current, the charge transfer by break­ down pulse current, the charge transfer by corona current, and the total charge transfer. The mean value of the subsequent return stroke peak current estimated is 23 ± 10 kA and the median value

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120

is 20 kA, which is a factor of 2 higher than the 12-kA median of Berger et al. (1975). The mean of the uniform current for subsequent return strokes is 3.2 ± 1.8 kA and the median is 2.3 kA. The origin of the uniform current can be considered the continuation of dart leader current. Because the dart leader lasts for about 1 msec, the median charge transfer is about 2.3 C. The mean of charge transfer by the breakdown pulse current for subsequent return strokes is 0.093 ± 0.055 C. The majority of breakdown pulse currents contain the charge less than 0.1 C. The mean charge of corona current is 0.56 ± 0.38 C and the median is 0.45 C. The total charge transferred by the return stroke in the first 100 psec is the time integral of the sum of the breakdown pulse current, the corona current, and the uniform current The mean of total charge transfer is 0.95 ± 0.056 C and the median is 0.85 C. As described above, the model of lightning return stroke current presented by Lin et al. (1980) is physically plausible and has reproduced reasonably acceptable lightning characteristics. The major disadvantage of the model may be the need to choose arbitrarily the value for return stroke velocity. 4,5.

RECENT MODIFICATION OF THE MODELS

Since Lin et al. (1980) presented the model for the subsequent return stroke current there have been many studies on this topic (Willett et al., 1988, 1989; Leteinturier et aL, 1990; Rachidi and Nucci, 1990; Thottappilli et al., 1991; Farrell and Desch, 1992; Rakov et al., 1992b). Among those, Diendorfer and Uman (1990) proposed an improved return stroke model with specified channel base current. The current at the channel base is specified, and a time-dependent dis­ charging of the charge stored on the leader channel determines the channel current as a function of height and time. The discharging process is separated into two processes: (1) the exponential discharge of the leader head and leader core with a relatively short time constant, less than 1 psec, which they call the breakdown time constant; and (2) the exponential discharge of the charge stored around the leader core with a longer time constant, on the order of microseconds. They showed that if a typical measured channel base current is assumed and if the discharge time constants are properly chosen, electric and magnetic field waveshapes calculated with the model exhibit all the significant characteristics of measured fields. An example of the comparison of measured and calculated fields for a triggered stroke is given in Figure 4.4.9. The current of the stroke was split into the two components, iao and io as shown in Figure 4.4.9a. The best discharge time constants were chosen as tbo = 0.1 psec and tc = 6 psec. From a peak current of 11 kA and the observed maximum current derivative of 120 kA/ psec in Figure 4.4.9b, a current rise time constant T| = 0.07 psec was obtained. The comparisons of measured and calculated field and field derivative at a distance D = 5160 m are shown, respectively, in Figures 4.4.9c and d where h = 5 m is the lightning strike height. The numerically calculated field derivative is a factor of approximately two higher than the measured, and the full width at half maximum is approximately one-half of the measured. The authors discussed the discrepancy in detail. Nucci et al. (1990) made a review and comparison of the lightning return stroke current models with specified channel base current. They concluded that all models produce fields that are rea­ sonable approximations of the available measured lightning fields for the first 5 or 10 psec and that all models except the transmission line model are also reasonable approximations of those fields for up to 100 psec, but none of the models can reproduce the fine structure observed in the measured fields. Nature is not easy to duplicate, even in science. 5. 5.1.

POSITIVE LIGHTNING

UPWARD LIGHTNING

Lightning to the Empire State Building in New York City (McEachron, 1939, 1941; Hagenguth and Anderson, 1952) and to the towers on Mt. San Salvatore (e.g., Berger 1967,1977) was found

Lightning Currents

121

v * 150 «/us Too- 0.1 US rc - 6.0 ps h - 5 a

^calculated v - 150 «/us Th,- 0.1 us tc - 6 . 0 us h - 5 ■

■easured

5

10

is

Tiae in us figure 4 .4 .9

0.4

0.6

O.S

Tiae in us

Measured triggered lightning current, current derivative, and electric field and calculated field and

derivative. (From Diendotfer, G . and Uman, M .A . (1990).

j. Geophys. Res., 95,

13,621. 1990 Copyright by the

American Geophysical Union. W ith permission.)

§ 3

Figure 4.5.1

Sketches of the upward-moving negative stepped leader from film (a) and still photograph (b) taken

by Berger (1977) on Mt. San Salvatore, Switzerland.

to be initiated by the upward-moving leader. The upward-initiated lightning has no fiist return stroke of the type always observed in normal downward-initiated lightning, but is followed by the continuing current when the leader reaches the cloud. Later, the lightning has often been followed by combinations of the dart or dart-stepped leaders and the return strokes similar to the subsequent return strokes in normal ground discharges. A sketch of photographs of the upwardmoving leader from a metal tower on Mt. San Salvatore, Switzerland is shown in Figure 4.5.1. The lightning current and the charge transfer to the ground of positive flashes are considerably larger than those of negative flashes. It is shown in Figure 4.5.2 that several positive lightning parameters are compared to those of normal negative lightning: the peak current, the transferred charge, the maximum dildt, the stroke duration, and the flash duration (Berger et al., 1975). The

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122

x NEGATIVE SUBSEQUENT STROKES ® NEGATIVE FLASHES A PO SITIVE FLASHES ♦ EXCLUDING SIN G LE-STRO KE F LA S H E S

Ftpire 45 J2 Comparison of parameters for positive and negative return strokes and flashes. (Data are from Berger, K. et al. (1975). Ekxtra, 80, 23.)

parameters are shown for those values, which 50% of cases exceed. The peak currents, the charges, and the stroke durations in positive flashes are much larger than those in negative flashes. 5.2. WINTER LIGHTNING

The majority of ground lightning in summer thunderstorms brings negative charges to ground, while in winter thunderstorms positive charges are quite often brought to ground. The winter thunderstorm cloud is small in size compared to the summer thunderstorm cloud, and is charac­ terized by the low level cloud top as well as the low level cloud base. The strong wind shear makes the dipole charge distribution tilted, and the upper positive charge is shifted downwind relative to the negative charge beneath it The positive flashes are initiated from the upper positive charge, and are generally composed of single strokes followed by a period of continuing currents. Winter lightning has been studied on the Japan Sea Coast (e.g., Brook et al., 1982). Brook et al. (1982) reported 26 positive and 37 negative ground flashes out of 264 total flashes, including cloud flashes, in eight winter thunderstorms. 5.3. TRIGGERED LIGHTNING

Artificially triggered lightning using a small rocket with a conducting string is very often initiated by the upward-moving leader. This is similar to the lightning from the tall towers on the ground such as those at the Empire State Building and Mt. San Salvatore. This topic will be discussed in Chapter 1/6. The three types of positive lightning (upward lightning, winter lightning, and triggered light­ ning) have this in common: the occurrence frequency of the positive flash apparently increases with increasing latitude and with increasing land elevation above sea level or the low-level cloud base. 6. SPECIAL LIGHTNING

Lightning sometimes appears as special types of ribbon, ball, and bead lightning. Thunderstorms and lightning occur in big fires. Lightning also occurs during volcanic eruptions, nuclear deto­ nations, large earthquakes, and (rarely) during sandstorms. Many people have experienced earth­ quake lightning, but there is no scientific confirmation as yet.

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123

6.1. RIBBON LIGHTNING

The lightning channel sometimes looks broad in width. This type of lightning is called ribbon lightning, and it is known to be caused by the wind. In this case, the component strokes move downwind in a strong wind. Therefore, the type of ribbon depends on the strength of the wind and the angle between the observer’s eyes and the wind direction. Photographs of examples of ribbon lightning are found in Salanave (1980). 6.2. BALL LIGHTNING

Ball lightning is a strange type of lightning. It has been seen by very few people but is discussed often (Uman, 1969; Singer, 1971; Barry, 1980). Ball lightning is reported to be a luminous sphere of 10 ~ 20 cm in diameter. The diameter of the ball varies from 2 cm to 2 m depending on the reports. It will appear after a flash to ground and moves along the ground surface or moves as a fireball in the air. Its shape is sometimes reported as oval. Its color is described as white, red, yellow, and blue, depending on the reporters. It will disappear silently or it will explode with sound when it contacts trees, houses, etc. Its duration is usually only a few seconds, but sometimes it can last for several minutes. Classical drawings show that it sometimes enters a building and rolls around. Its speed of movement varies from walking speed to running speed. Ball lightning may be a gas plasma sphere. There is a research group that creates ball lightning experimentally in the laboratory. The mechanism of its generation will be discussed in Chapter 1/7. 6.3. BEAD LIGHTNING

The lightning channel sometimes looks like a band of luminous dotted or long connected beads. This is called bead lightning. The bead lightning channel lasts for a long duration and can be photographed. It occurs only in heavy rain. The channel first seems to be an ordinary channel, and with time the channel luminosity becomes faint, with beadlike luminosity remaining. There may be two types of bead lightning. One is due only to an optical illusion. If the direction of parts of the channel are toward or away from the observer and if the brightness of the channel decreases, the brightness of those parts of the channel will be integrated and seen as more lu­ minous. On the other hand, when parts of the channel are perpendicular to the observer’s eyes, then the luminosity will decrease, and the parts appear dark. Lightning channels also have bright spots that are not associated with beads. This mechanism is not understood (Malan, 1963). The literature on ball lightning and bead lightning is reviewed by Barry (1980). 6.4. VOLCANIC LIGHTNING

During a volcanic eruption, light arrows of various lengths run here and there around ash smoke. They appear in the violent outflow of ashes from the crater. Volcanic lightning is seen outside the surface of the ash volume, or through the halls in the ash volume. Strong electrification of the volcanic cloud is associated with the high-speed ejection of volcanic ashes from the crater. The thunder is usually short. A systematic electric field due to volcanic smoke was observed, and the charge distribution of the volcanic ash cloud is estimated to have positive polarity in Asama Volcano in Kanto, Japan (i.e., positive charge in the upper portion and negative charge in the lower portion of the ash cloud). On the other hand, negative polarity was observed during the eruption of Aso Volcano in Kyushu (Hatakeyama, 1970). To test the charge generation with ash particles, laboratory ex­ periments were made and it was found that the volcanic charges are generated by friction between smaller and larger grains of ash particles. The sign of charge on the ash particles depends on the kind of volcano. The ash particles fall when they are transported downwind. The larger and heavier particles fall down faster than the smaller and lighter particles. Then the upper portion of the cloud is filled with smaller ash particles, and the lower portion is filled with larger particles. Violent lightning was observed in the volcanic cloud over the Surtsey Submarine Volcano near Iceland in December 1963. When clouds of water vapor and finely broken rock were spouted.

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they became electrified, usually with a strong positive charge. They were apparently electrified by the violent action of melted lava in contact with seawater. Discussions are found in Anderson et al. (1965) and beautiful photographs of lightning are shown in Salanave (1980). 6.5. LIGHTNING FROM LARGE FIRES

Growth of thunderstorm clouds and the occurrence of associated lightning has often been reported in large fires. In Japan, examples are the big fire in Tokyo during the Great Kanto Earthquake of 1923, the large fires during the air raids of World War n (especially on the occasion of the atomic bomb explosion in Hiroshima in 1945), etc. In Hiroshima, black rain as well as lightning occurred. 6.6. LIGHTNING FROM NUCLEAR DETONATION

In 1952 a 10.4-megaton hydrogen bomb was tested in the experiment named Ivy-Mike in the Pacific, and lightning was generated within 10 msec after the detonation (Uman et al., 1972). The explosion occurred in a hemispheric fireball. Lightning occurred on the ground around the fireball and progressed branching along the surface of the ball. Later, a laboratory simulation was made to prove that the lightning is triggered at the point on the ground where the electric field was large, and it traveled upward through the region of greatest negative charge.

7. LIGHTNING PARAMETERS

There are many lightning parameters that characterize the properties of lightning discharges. Lightning parameters of the ground discharge are especially important because they are needed when planning a lightning protection scheme. Those parameters often referred to are • • • • • • • • • • • •

Number of return strokes per flash (IV) Duration of flash (Tg) Return stroke intervals (Ts) Return stroke peak current (//>) Charge quantity per flash (C4) Charge quantity per stroke (C,) Time to peak current (Tp) Rate of current rise (/,) Time to current half-value (Th) Duration of continuing current (7V) Continuing current (/c) Charge in continuing current (Cc)

Such lightning discharge parameters vary over a wide range just like other geophysical parameters. Most of the instruments that enable us to collect such data have been designed to measure an average or a moderate example of lightning quantity. As a result, the extreme values in both larger and smaller regions have been deleted from the data obtained. Giant lightning was often overscaled in the records, and miniature lightning was usually neglected in the analysis. It is necessary to remember, therefore, that the overall picture of lightning available in the literature is representative usually of moderate lightning characteristics and not necessarily of all lightning. The probability of occurrence of these parameters is often statistically given by the log-normal form. The log-normal distribution is a normal distribution in which the variables are given by logarithm, and the probability density function P[x) is given by: P(x) = (l/oV 2n ) exp{—(x - x)2/2a2)

(20)

125

Lightning Currents 10A

103

Tg (ms)

103

10z

102

10

Ts (ms)

Tc Th Tp (ms)(us) (us) Ic Ip (A) (kA) 102

10

b *

1

It (kA/us) Cg (C) Cc (C) 10

i—i—r

-

E -

0.1

2

5 10 20 30 50 70 80 90 95 98 7. > ORDINATE

Figure 4.7.1 Model distributions of lightning parameters: duration of flash ( Tg), return stroke interval ( T,), return stroke peak current (/,), charge quantity per flash {Cg), time to peak current ( TP), rate of current rise (/,), time to current half-value ( Th), duration of continuing current ( Tc), continuing current dr), and charge in continuing current (Cc). (Data are from Cianos, N. and Pierce, E.T. (1972). Technical Report 1, Stanford Research Institute, Menlo Park, CA.)

where a is the log of the standard deviation (SD) and x is the mean. The log-normal distribution is to be expected for any process that consists of a number of independent contributing factors. Cianos and Pierce (1972) have collected data for lightning parameters and have made statistical model distributions of these parameters. The model values are tabulated where the values of the parameters for cumulative frequencies at 2, 10, 50, 90, and 98% are given. Using these values the cumulative frequency distributions of all parameters are plotted together in Figure 4.7.1. The cumulative probability distribution function is given by: (21 )

The parameter with the largest range of distribution is the charge quantity per flash (Cg), and the parameter with the smallest range of distribution is the duration of the continuing current (Tc). The parameters are representative, but recent measurements do not necessarily agree with all these distributions. Numerical data for ground discharges are given in Table 4.7.1. The lightning return stroke velocity is another important parameter for modeling of lightning current. Boyle and Orville (1976) measured two-dimensional return stroke velocities within 1 km up from the ground using a multislit channel isolator with narrow vertical and wide horizontal fields of view on a high-speed streaking camera. Measurements of 12 strokes in three multistroke flashes yielded return stroke velocities, which range from 2.0 x 107 to 1.2 x 10s m s_l with an estimated systematic error of 30 to 60%.

Handbook o f Atm ospheric Electrodynam ics, Volume /

126 Table 4.7.1

Numerical data for ground discharge

Parameter

Stepped leader Length of step, m Time interval between steps, psec Avenge velocity of propagation of stepped leader, m s_l Charge deposited on stepped leader channel, C Dart leader Velocity of propagation, m s' 1 Charge deposited on dart-leader channel, C

Minimum

3 30 1.0 x 10s

3 1.0 x 106 0.2

Typical

30 50 3.0 x 10s 5 2 .0 x 106 1

Maximum

200

125 2.6 x 106 20

2.1 x I07 6

Return stroke Velocity of propagation, m s*1 Current rate of increase, ItA psec-1 Time to peak current, psec Peak current, kA Time to half of peak current, psec Charge transferred excluding continuing current, C Temperature, K Electron density, m~] Channel length, km

1 10 0.2 0.8 x 10* 1 x 10 “ 2

Continuing current Duration of continuing current msec Peak continuing current, A Charge in continuing current, C

50 30 3

150 150 25

500 1600 330

1

3 40

26 380

Lightning flash Number of strokes per flash Time interval between strokes in absence of continuing current, msec Time duration of flash, s Charge transferred including continuing current, C

2.0 x 107 1

0.5

3 0.01

1

5.0 x 107 10 2

30 40 2.5 2 x 10* 3 x 10“ 5

03 20

2.0 x 10* 210

30 250 250 20

3.6 x 10* 3 x 10“ 14

2

400

Idone and Orville (1982) measured two-dimensional return stroke velocities for 63 strokes by using high-speed streaking photographic techniques during the summers of 1977 and 1978 in the Thunderstorm Research International Program (TRIP) at the Kennedy Space Center (KSC), Florida and at the Langmuir Laboratory near Socorro, New Mexico during the summer of 1979. The mean return stroke velocity near ground (channel length s 1.3 km) was found to be 1.1 x 10® m s_l with a maximum error of 35% or less, most frequently at 9 x 107 m s- '. The minimum and maximum values are 2.9 x 107 and 2.4 x 108 m s_l, respectively. The mean velocity for the 17 first return strokes is 9.6 x 107 m s_l and for 46 subsequent strokes is 1.2 x 10s m s_l. The velocity decreased with height, reducing by 25% more in the upper channel lengths than near the ground. Mach and Rust (1989) used a mobile photoelectric device to measure two-dimensional return stroke velocities from 130 strokes. The average velocities are (1.3 ± 0.3) x 108 m s_l for 86 natural negative return strokes, (1.2 ± 0.3) x 108 m s_l for 41 triggered return strokes. They also found that the velocities decrease with height. Jordan et al. (1992) observed dart leader speeds and found that (1) the dart leader speed increases with an increase in the following return stroke field or current peak, and (2) there is a weak but statistically significant tendency for lower leader speeds to be associated with longer preceding interstroke intervals.

Lightning Currents

127 8.

CLO UD DISCHARGE

Lightning occurs within clouds, between clouds, and between clouds and air. These three dis­ charges are considered to be essentially of the same mechanism. We call them intracloud dis­ charge, or simply, cloud dischaige. The cloud dischaige occurring within clouds illuminates the whole cloud. More than half of all lightning flashes are such discharges. The discharge path is not usually seen but sometimes appears between portions of clouds. This type of discharge is called the intercloud or cloud-tocloud discharge. The discharge path also sometimes appears outside the cloud, probably toward the transparent space charge accumulated region. This type of dischaige is called the air discharge. These two types of discharges provide us opportunities to see details of cloud dischaige channels. Ogawa and Brook (1964) investigated the mechanism of cloud discharge using the photographs of the extended channels outside the cloud and the electric fields measured on the ground. The usual cloud discharge begins with the slow positive streamer from the upper portion of the boundary region between positive and negative main charges in the cloud. This initial streamer extends downward as well as horizontally depending on the charge distribution. The streamer continues for about half the total duration, about 250 msec, with the velocity on the order of 104 m s_l. The current of the streamer is of the order of 100 A. The streamer distributes positive charge along the tree branchlike paths. This process is similar to the initial breakdown process in the ground discharge. As the space charge in the region where the streamer leaves becomes scanty, the recoil streamers start from the tips of the positive streamer and run back along the channels already made by the positive streamer and neutralize the distributed positive charge. The electric field change produced by these recoil streamers are called K changes. The K change streamers occur intermittently and have a speed of the order of 106 m s_l and neutralize the charge of about 1 C distributed along the channels by the initial streamer. As the duration of the K change is about 1 msec, the corresponding current is of the order of 1 kA. Recognizable K changes in the electric field record repeat several times during the latter half of the total duration. A time series of cloud discharge field change data from an isolated thunderstorm is shown in Figure 4.8.1 where the field changes are classified into four groups as near (1 and II), intermediate (ID), and distant (IV) flashes (Ogawa and Brook, 1964). The field changes show different curves from each group. The measured electric field change due to the thundercloud that produced the cloud discharges, and the occurrences of each type of cloud discharge are also shown in Figure 4.8.1. The magnitudes of the cloud discharge field changes (A£) are obtained in Figure 4.8.2. The maximum AE is about 700 V m_l for near discharges and about 200 V m_l for distant discharges. Approximate flash distances are also obtained in Figure 4.8.2. From the detailed analysis of these field change data Ogawa and Brook (1964) concluded that the cloud discharge is the combination of the initial positive streamer process and the series of recoil current K change processes as discussed above. Detailed examination of the time-lapse photograph of the cloud-to-air discharge channel showed that each branched channel has a few streaks parallel to the channel. The relative brightness of the streaks offered evidence that the K streamer starts at the tip of the branched streamer and recoils back toward the main trunk of the initial streamer as described above. This process repeats a few times from each branch tip. The speed of the K streamer is of the same order as that of the dart leader in the ground discharge. Smith (1957) reported from two-station electric field measurements that the initial streamer goes upward from the lower negative charge toward the upper positive charge. Takagi’s (1961) statistical result suggested the positive initial streamers. Liu and Krehbiel (1985) analyzed four intracloud flashes and found that the discharges were initiated by the upward motion of negative charge. Proctor (1981) obtained VHF radio pictures of cloud flashes in South Africa using 253

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128

TYPES OF POTENTIAL GRADIENT CHANGES IN CLOUD DISCHARGES

I

1900

I

I

I

1930

I

I

I

2000

I

I

I

1—

2030 0

LOCAL TIME

I_________I_________»

200

»________ L

400

-i

600

MILLISECONDS

SEPT. 28,1961

figure 4.8.1 Types of electric field changes in cloud discharges observed near (I and II; approximately 4 to 7 km), intermediate to (III; 6 to 9 km), and distant from (IV; a ~ 1 0 km) the cloud discharges. The thundercloud electric field and the distribution of the occurrences of each type of cloud flash are also shown. (From Ogawa, T. and Brook, M. (1964).,/. Geophys. Res., 69, 5141.1964 Copyright by the American Geophysical Union. With permission.)

SEPT 28,1961

TIME MST

Figure 4.8.2 Thundercloud electric field if], cloud discharge field changes (AjD, and estimated flash distances observed on September 28, 1961 in Socorro, New Mexico. (Adapted from Ogawa, T. and Brook, M. (1964). J. Geophys. Res., 69, 5141.1964 Copyright by the American Geophysical Union. With permission.)

MHz of the center frequency and found two types of radiation pulses. One class on the order of 103 pulses per second progressed at speeds that ranged from 0.9 x 105 to 2.1 x 10s m S'1. Hie second class was on the order of typically 10s pulses per second in which streamer speeds ranged from 2.7 x 106 to 4.6 x 107 m s_l. It was found that the pulses originated in regions near the

Lightning Currents Table 4.8.1

129

Numerical data for velocities of streamers in doud discharges'

Initial streamer

Recoil streamer

0.5 x 10s

13 x 106 6 x 105

6 x 10*

0.5 x 105 2 x 10* IO*-2 10*-4 7.8 x 1.4 x 7.5 x 1.5 x *

3 x 10M x 10s 106 or more 2 x 106

x 10* x 10* 10s (5.6 x 10M.1 x 10*) 10* (1.5 x I0M 05) 10* 105 (0.6 x lO’-S x 105)

23 x 10M.4 x 107

Ref.

Sourdillon (1952) Schonland (1956) Hewitt (1957) Ishikawa (1961) Takagi(1961) Ogawa and Brook (1964) Takeuti (1965) Krider (1974) Brantley et al. (1975) Taylor (1978) Krehbiel et al. (1979) Proctor (1981a)

Measured in m s~'.

streamer tips and that the pulses were associated with initial ionization. The line charge densities were near 10~3 C m_1, and the average currents were between 89 and 210 A. The first class pulses corresponded to the slow streamer in the initial stage of the cloud discharge, and the second class pulses accompanied rapid recoil streamers of K changes. From five case studies, four positive K changes and one negative K change were observed. Most cloud flashes were horizontal. The apparently contradictory results of the polarity of the cloud discharges show possibilities of initiation of the streamer from either positive or negative cloud charge regions. The positive initial streamer may start from ice crystals occurring in the upper portion of the cloud. The negative initial streamer may start from graupel occurring in the lower portion of the cloud. The choice of either possibility depends on the complex distribution of charges. The initiation mechanism of the streamer from such precipitation particles of solid state is not clear and offers an interesting future field of investigation. The numerical data for cloud discharge progression in the initial streamer and the recoil streamer observed so far are listed in Table 4.8.1. 9. 9.1.

PHYSICAL PROPERTIES OF THE LIGHTNING CHANNEL

TEMPERATURE AND ELECTRON DENSITY

The determination of temperature and electron density of the lightning channel is important for discussing the discharge mechanism, especially its multiplicity of strokes. If the lightning channel maintains sufficiently large conductivity after the return stroke, it can draw the next dart leader current along the preceding return stroke channel. The temperature and the electron density to determine electrical conductivity of the channel can be determined from the analysis of the optical spectrum of the channel. The spectroscopic study of lightning has been performed for over a century, but the lightning spectra obtained before 1960 gave only time-integrated effects of whole lightning. Since Salanave (1961) succeeded in having separate spectra for each stroke, Salanave et al. (1962), Krider (1965), Orville (1966), etc. developed their own spectrometers and obtained many data from lightning channels. These data enabled us to study the physical properties of the lightning channel, and thereafter, the discharge mechanism. Using these techniques, Prueitt (1963) obtained the channel average temperature of 24,000 to 28,000 K. Uman et al. (1964a, 1964b) obtained the channel electron density of 3 x 1024 m~3. The electrical conductivity of the channel calculated by Uman (1964) was 1.8 x 104 S n r 1.

Uman and Orville (1964) determined the electron density by using Stark broadening of the spectral line of Ha in the Balmar series. From the results obtained for three return strokes the

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Handbook o f Atm ospheric Electrodynam ics, Volume /

Figure 4.9.1 Return stroke temperature as a function of time for two strokes. Horizontal dashed lines indicate the time resolution and vertical bars indicate the error limits. (Adapted from Orville, R.E. (1968).). Atmos. Sci., 25,852. With permission.)

electron density was determined to be 1 x 1023 to 5 x 1023 m-3. These values are more reliable than the value obtained above by using the Saha equation. Orville (1968) obtained the temporal variation of temperature for the return stroke with the time-resolved spectrum. Figure 4.9.1 shows the results of average temperature for the 50 psec during which the exposure was made. The typical maximum temperature is about 30,000 K. The temperature reaches a maximum within the first 10 psec and decreases steadily thereafter. Orville (1968) also estimated the channel electron density as a function of time calculated from the measured half width of the Ha line. The result is shown in Figure 4.9.2. The electron density was of the order of 1024 n r 3 in the initial 5 psec of the return stroke and decreased to 1 x 1023 m-3 during the next 25 psec; then it stayed at a rather constant value for 50 psec, after which the temperature decreased. If the channel temperature and the electron density are known as a function of time as given above, then the pressure and other properties of the channel can be calculated. Orville (1968) showed the channel pressure to be of the order of 10 atm at a temperature of 30,000 K and an electron density of 1024 n r 3. As the channel pressure exceeds that of the surrounding air, the channel expands until the pressure equilibrium will be attained. From Figures 4.9.1 and 4.9.2 one can see that the channel pressure approaches the atmospheric pressure in about 20 psec. Most lightning flashes consist of more than one stroke. For the second and later strokes to progress along the same channel as the first stroke, they need to keep the preceding channel in a state of relatively high ionization/conductivity during several tens of milliseconds before the next dart leader starts. Brook et al. (1962) discussed the possibility that a current with an amplitude of approximately 10 A may flow during that period, keeping the channel conductive. Loeb (1966) suggested ionization waves due to K changes, which has not yet been photographed. Uman and Voshall (1968) calculated the cooling rate of the channel in the case without energy input They calculated the temperature decay as a heat transfer problem. They solved the following four equations simultaneously: (1) the energy balance equation, (2) the momentum transfer equa­ tion, (3) the mass conservation equation, and (4) the equation of state. They assumed that these four equations hold for in the discharge channel as well as for in the surrounding air.

Lightning Currents

131

’E > 5) 2

O lii

TIME.ms Figure 4.9.2 Return stroke electron density as a function of time calculated from the measured half-width of H a line. (Adapted from Orville, R.E. (1968)./ Atmos. Sci., 25, 852. With permission.)

TIM E, ms Figure 4.9.3 Decrease of the temperature for return stroke channel radii of 1, 2, 4, and 8 cm. The initial central temperature is 8 x 103 K. (Adapted from Uman, M.A. and Voshall, R.E. (1968). /. Geophys. Res., 73, 497. 1968 Copyright by the American Geophysical Union. With permission.)

An example of the calculated results is shown in Figure 4.9.3. Assuming an initial temperature of 8000 K at the moment when the return stroke current stopped, the temperature at the center of the channel is shown taking the channel radius as a parameter. The calculated temperature does not decrease as much during the average duration of 40 msec between successive strokes.

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At 4000 K the electron density and the conductivity of dry air are 1019 m-3 and about 1 S m_l, respectively; then the air is conductive. At 2000 K the electron density is 10'3 m-3 and the conductivity is 10-6 S m_l, which means nonconductive air (Yos, 1963). The channel at the temperature between 2000 and 4000 K (as shown in Figure 4.9.3) is therefore in a state between a conductor and an insulator, but may be conductive enough to draw the next dart leader. Because

of these physical properties of the channel, the lightning shows multiplicity with several com­ ponent strokes. 9.2. DIAMETER OF LIGHTNING CHANNEL Measurements of the lightning return stroke channel diameter have been made in basically two ways: (1) from measurements of channel images in photographs and (2) from measurements of the size of the region of interaction of lightning and material objects. Besides these, theoretical calculations of the return stroke parameters lead to estimates of the current-carrying core of the channel. Estimated results are summarized by Orville et al. (1974) and show that the luminous diameter of the channel is of the order of 10 cm while the current flowing diameter is of the order of 1 cm. 9.3. CHANNEL ORIENTATION The orientation of the lowest part of the lightning channel to the ground can be studied with photography. The visual portion looks more or less vertical with some sideward branches. The visible channel is, however, not the entire channel, because the channel inside the cloud cannot be seen. The lightning channels hidden within clouds are studied by electrical and electromagnetic methods. An electrical study was made earlier by Malan and Schonland (1951a, 1951b). They found that the negative charge lowered to the ground in a flash-to-ground is distributed in a vertical column extending up to 6 km in length in the cloud. Hacking (1954) supported this result for South African storms; however, Pierce (1955), using the J change-slope analysis given by Malan and Schonland (1951b), concluded that most return strokes are oriented at roughly the same height, i.e„ the intervening streamers between successive return strokes traveled horizontally, suggesting a horizontal distribution of negative charge. Using a network of eight field change simultaneous recordings. Workman et al. (1942) con­ cluded that horizontal separation of intracloud discharges was on the average more than three times larger than the vertical separation. Reynolds and Neill (1955), in a study similar to that of Workman et al. (1942), also found that the negative charges brought to the ground in successive strokes were displaced horizontally. Ogawa and Brook (1969), based on a study of electric field changes measured at two stations, concluded that the horizontal component of the in-cloud channel of the ground discharges on the average exceeds the vertical component. The negative charge involved in lightning flashes to ground is distributed in a manner strongly dependent on the direction of the movement of the storm. A nonelectrical method for determining the lightning channel orientation was reported by Teer and Few (1974) from an analysis of thunder recorded by an array of microphones. Lightning channel reconstructions derived by them indicated that the horizontal lightning structures are persistent and much extended. A typical ratio was 3:2:1 of long horizontal axis:short horizontal axis:vertical axis in their ellipsoid model of intracloud lightning and the intracloud portions of ground lightning. All channels analyzed by them aligned along the same direction and perpen­ dicular to the direction of storm motion. Nakano (1976), with the thunder technique, discussed the relationship between the channel direction and the storm characteristics and showed that the ground discharge channel inside the cloud is tilted toward downstream of the free atmospheric wind.

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The horizontal nature of lightning discharges was determined using the polarization of the electromagnetic radiation from lightning. Proctor (1971, 1981a, 1981b, 1983, 1991) and Proctor et al. (1988) made space-time mapping of lightning discharge processes by using the VHF tech­ nique in South Africa, and reported that most cloud flashes were horizontal. Taylor (1978), using a similar technique in Florida, showed that most lightning activity occurred about 5 to 6 km high and near the —10°C temperature level; considerable movement of discharge centers occurred as the lightning processes permeated the thunderstorm volume at the progression speed of about 50 to 150 km s_l. Much work has been done since then (e.g., Weidman and Krider, 1979). Proctor et al. (1988) proposed a model of a ground flash as shown in Figure 4.3.14 in which the discharge channel inside the cloud extends horizontally. As discussed above, the intracloud lightning discharge channel and the portion within the cloud of the lightning channel to ground are considerably inclined. The horizontal extent of the channel is usually more than the vertical extent. Furthermore, the in-cloud part of the ground discharge may be composed of more than one channel. The nature of lightning channel orientation makes modeling of lightning current and associated radiation electric and magnetic fields complex. No theory may be applicable to the actual lightning current if such nature is taken into account. 10.

CONCLUDING REMARKS

Lightning and thunderstorms provide us many interesting geophysical phenomena on fair-weather atmospheric electric fields and various kinds of atmospherics in a wide frequency range (such as whistlers, tweeks, and Schumann resonances). In this chapter, however, the topics are limited to the direct properties of lightning currents as an origin of those phenomena. Lightning and thun­ derstorms are old subjects for study, but they always give us new interests. This is because of their mysterious nature, and because they produce admiration rather than fear.

REFERENCES Anderson, R., Bjomsson, S., Blanchard, D.C., Gathman, S., Hughes, J., Janasson, S., Moor, C.B., Survilas, HJ., and Vonnegut, B. (1965). Electricity in volcanic clouds. Science. 148, 1179. Baity, J.D. (1980). Ball Lightning and Bead Lightning, Plenum Press, New York. Beasley, W., Uman, M.A., and Rustan, Jr., Pi.. (1982). Electric fields preceding cloud-to-ground lightning flashes, J. Geophys. Res., 87,4883. Berger, K. (1967). Novel observations on lightning discharges: results of research on Mount San Salvatore, J. Franklin Inst.. 283,478. Berger, K. (1977). The earth flash, in Lightning, Vol. 1, Golde, R.H., Ed., Academic Press, New York, 119. Berger, K., Anderson, R.B., and KrOninger, H. (1975). Parameters of lightning flashes. Electro, 80, 23. Boyle, J.S. and Orville, R.E. (1976). Return stroke velocity measurements in mulristroke lightning flashes, J. Geophys. Res., 81. 4461. Brantley. R.D., Tiller, J.A., and Uman, M.A. (1975). Lightning properties in Florida thunderstorms from videotape records, J. Geophys. Res., 80, 3402. Brook, M. (1992). Breakdown electric fields in winter storms. Res. Lett. Atmos. Eiectr., 12, 47. Brook, M. and Ogawa. T. (1977). The cloud discharge, in Lightning, Vol. 1, Golde, R.H., Ed., Academic Press, London, 191. Brook, M., Kitagawa, N., and Workman, EJ. (1962). Quantitative study of strokes and continuing currents in lightning discharges to ground, J. Geophys. Res., 67,649. Brook, M., Nakano, M., Krehbiel, P., and Takeuti, T. (1982).The electrical structure of the Hokuriku winter thunderstorms, J. Geophys. Res., 87. 1207. Bruce, C.E.R. and Golde, R.H. (1941). The lightning dischaige, J. Inst. Eiectr. Eng. Part 2, 88, 487. Cianos, N. and Pierce, E.T. (1972). A ground-lightning environment for engineering usage. Tech. Report 1, Stanford Research Institute, Menlo Park, CA.

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Clarence, N.D. and Malan, DJ. (1957). Preliminary discharge processes in lightning flashes to ground, Q. J. R. Meteorol. Soc.. 83, 161. Dawson, G.A. (1969). Pressure dependence of water-drop corona onset and its atmospheric importance, J. Geophys. Res., 74,6859. Dawson, G.A. (1970a). The Reyleigh instability of water drops in the presence of external electric fields, J. Geophys. Res., 75,701.

Dawson, G.A. (1970b). Electrical corona from water-drop surfaces, J. Geophys. Res.. 75,2153. Dawson, G.A. (1970c). Initiation of cloud-to-ground lightning strokes, J. Geophys. Res., 75, 5858. Dennis, AS. and Pierce, ET. (1964). The return stroke of the lightning flash to earth as a source of VLF atmospherics. Radio Sci.. 68 D, 777. Diendorfcr, G. and Uman. M.A (1990). An improved return stroke model with specified channel-base current, J. Geophys. Res.. 95. 13,621. Farrell, W.M. and Desch, M.D. (1992). Cloud-to-stralosphere lightning discharges: a radio emission model, Geophys. Res. Lett., 19, 665. Griffiths, R.F. and Phelps, C.T. (1976). A model of lightning initiation arising horn positive corona streamer development, J. Geophys. Res., 81, 3671. Hacking, C.A. (1954). Observations on the negatively-charged column in thunderclouds, J. Geophys. Res., 59, 449. Hagenguth, J.H. and Anderson, J.G. (1952). Lightning to the Empire State Building, Trans. Am. Inst. Electr. Eng., Part 3, 641. Hatakeyama, H. (1970). Science o f Thunderstorm and Lightning, Kawadeshobo-shinsha, Tokyo (in Japanese). Hewitt, FJ. (1957). Radar echoes from interstroke processes in lightning, Proc. Phys. Soc. B, 70,961. Idone, V.P. and Orville, R.E (1982). Lightning return stroke velocities in the thunderstorm Research International Program (TRIP). J. Geophys. Res., 87,4903. Ishikawa, R (1961). Nature of lightning discharge as origins of atmospherics, Proc. Res. Inst. Nagoya Univ., 8 A 1. Jordan, DAI., Idone, VP., Rakov, V A , Uman, M.A., Beasley, W.H., and Jurenka, H. (1992). Observed dart leader speed in natural and triggered lightning, J. Geophys, Res., 97, 9951. Kitagawa, N. and Brook, M. (1960). A comparison of intracloud and cloud to ground lightning discharges, J. Geophys. Res., 65. 1189. Kitagawa, N., Btook, M., and Workman, EJ. (1962). Continuing currents in cloud-to-ground lightning discharges, J. Geophys. Res., 67, 637. Krehbiel, P.R., Brook, M., and McCrory. (1979). An analysis of the charge structure of lightning discharges to ground, J. Geophys. Res., 84, 2432. Krider, EP. (1965). Time-resolved spectra emissions from individual return strokes in lightning discharges, J. Geophys. Res., 70, 2459. Krider, EP. (1974). An unusual photograph of an air lightning discharge. Weather, 29, 24. Kuettner, J. (1950). The electrical and meteorological conditions inside thunderclouds, J. Meteorol., 7,322. Leise, JA. and Taylor, W L (1977). A transmission line model with general velocities for lightning, J. Geophys. Res., 82, 391. Leteinturier, C , Weidman, C., and Hamelin, J. (1990). Current and electric held derivatives in triggered lightning return strokes, J. Geophys. Res., 95, 811. Lin, Y.T. and Uman, MA (1973). Electric radiation fields of lightning return strokes in three isolated Florida thunderstorms. J. Geophys. Res., 78, 7911. Lin, Y.T., Uman, M A , and Standler, R.B. (1980). Lightning return stroke models, J. Geophys. Res., 85, 1571. Lin, Y.T., Uman, M A , Tiller, JA., Brantley, R.D., Beasley, W.R, Krider, EP., and Weidman, C.D (1979). Character­ ization of lightning return stroke electric and magnetic fields from simultaneous two-station measurements,/ Geophys. Res., 84, 6307. Liu. X and Krehbiel, P.R. (1985). The initial streamer Of intracloud lightning flashes, / Geophys. Res., 90, 6211. Loeb, LB. (1966). The mechanism of stepped and dart leaders in cloud-to-ground lightning strokes, / Geophys. Res. 71, 4711. Mach, D.M. and Rust, W.D. (1989). Photoelectric return-stroke velocity and peak current estimates in natural and triggered lightning. / Geophys Res., 94, 13,237. Magono, C. (1980). Thunderstorms, Elsevier, Amsterdam. Malan, DJ. (1963). Physics o f Lightning, English Universities Press, London. Malan, DJ. and Schonland, B. (1951a). The electrical processes in the intervals between the strokes of a lightning discharge, Proc. R Soc. London, Ser. A., 206, 145. Malan, DJ. and Schonland, B. (1951b). The distribution of electricity in thunderclouds, Proc. R Soc. London, Ser. A. 209, 158. McEachron, K.B. (1939). Lightning to the Empire State Building, / Franklin hat.. 227, 147. McEachron, XB. (1941). Lightning to the Empire State Building, Trans. A1EE 60, 885. McLain, D.X and Uman, M A (1971). Exact expression and moment approximation for the electric field intensity of the lightning return stroke, J. Geophys. Res, 76,2101.

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Nakano, M. (1976). Characteristics of lightning channel in thunderclouds determined by thunder, J. Meteorol. Soc. Jpn., 54,441. Nucci, CA., Diendorfer, G., Uman, M.A, Rachidi, F., Ianoz, M., and Mazzetti, C. (1990). Lightning return stroke current models with specified channel-base current: a review and comparison, J. Geophys. Res., 95, 20,395. Ogawa, T. (1971). Discharge processes in lightning to ground, Proc. Atmos. Electr. Jpn, 4, 46 (in Japanese). Ogawa, T. (1973). Analyses of measurement techniques of electric fields and currents in the atmosphere, Contr. Geophys. Inst. Kyoto Univ., 13, 111. ■ Ogawa, T. (1993). Initiation of lightning to ground, J. Atmos. Electr., 13, 121. Ogawa, T. and Brook, M. (1964). The mechanism of the intracloud discharge, J. Geophys. Res., 69, 5141. Ogawa, T. and Brook, M. (1969). Charge distribution in thunderstorm clouds. Q. J. R Meteorol.Soc., 95, 513. Ogawa, T. and Sakaguchi, F. (1983). Electrification of the winter minor showerclouds (Shigure), J. Meteorol. Soc. Jpn., 61,313. Orville, R.E. (1966). High-speed, time-resolved spectrum of a lightning stroke. Science, 151, 451. Orville, R.E. (1968). A high-speed time-resolved spectroscopic study of the lightning return stroke. III.A time-dependent model, J. Atmos. Sci., 25, 852. Orville, R.E, Helsdon. J.H., Jr., and Evans, W.H. (1974). Quantitative analysis of a lightning returnstroke for diameter and luminosity changes as a function of space and time, J. Geophys. Res., 79, 4059. Pierce, E.T. (1955). Electrostatic field-changes due to lightning discharges, Q. J. R Meteorol. Soc., 81,211. Pierce, E.T. (1977). Atmospherics and radio noise, in Lighming, Vol. 1, Golde, R.H., Ed., Academic Press, London, 351. Price, G.H. and Pierce, E.T. (1977). The modeling of channel current in the lightning return stroke, Radio Sci., 12, 381. Proctor, D.E (1971). A hyperbolic system for obtaining VHF radio pictures of lightning, J. Geophys. Res., 76, 1478. Proctor, D.E (1981a). VHF radio pictures of cloud flashes, J. Geophys. Res., 86 , 4041. Proctor, D.E (1981b). Radar observations of lightning, J. Geophys. Res., 86 , 12109. Proctor, D .E (1983). Lightning and precipitation in a small mulhcellular thunderstorm, J. Geophys. Res., 88, 5421. Proctor, D.E (1991). Regions where lightning flashes began, J. Geophys. Res., 96, 5099. Proctor, D.E, Uytenbogaardt, R., and Meredith, B.M. (1988). VHF radio pictures of lightning flashes to ground, J. Geophys. Res, 93, 12683. Prueitt, M L. (1963). The excitation temperature of lightning. J. Geophys. Res. 68 , 803. Rachidi, F. and Nucci, CA. (1990). On the Master, Uman, Lin, Standler and the modified transmission line lightning return stroke current models, J. Geophys. Res, 95, 20389. Rakov, V.A, Thottappillil, R., and Uman, M.A. (1992a). Electric field pulses in K and M changes of lightning ground flashes, J. Geophys Res., 97, 9935. Rakov, V A , Thottappillil, R., and Uman, M.A. (1992b). On the empirical formula of Willett et al. relating lightning retum-stroke peak current and peak electric field, J. Geophys. Res., 97, 11327. Reynolds, S.E and Neill, H.W. (1955). The distribution and discharge of thunderstorm charge-center, J. Meteorology, 12, 1.

Richards, C.N. and Dawson, G.A (1971). The hydrodynamic instability of water drops falling at terminal velocity in vertical electric fields, J. Geophys. Res, 76, 3445. Salanave, E E (1961). The optical spectrum of lightning. Science, 134, 1395. Salanave, L E (1980). Lightning and Its Spectrum, University of Arizona Press, Tucson, AZ. Salanave. E E , Orville, R.E., and Richard, C.N. (1962). Slitless spectra of lightning in theregion from 3850 to 6900 Angstroms, J. Geophys. Res., 67, 1877. Schonland, B.FJ. (1956). The lightning dischaige, Handb. Phys., 22, 576. Schonland, B.FJ. (1964). The Flight o f Thunderbolts, 2nd ed., Clarendon Press, Oxford. Singer, S. (1971). The Nature a f Ball Lightning, Plenum Press, New York. Smith, EG. (1957). Intracloud lightning discharges, Q. J. R Meteorol. Soc., 83, 103. Sourdilkm, M. (1952) foude k la Chambre de Boys de I'&lair dans I'air et du coup de foudreit rimehorizontale, Ann. Geophys, 8 , 349. Takagi, M. (1961). The mechanism of discharges in a thundercloud, Proc. Res. Inst. Atmos. Nagoya Univ., 8 B, 1. Takeuti, T. (1965). Studies on thunderstorm electricity. I. Cloud discharge, J. Geomagn. Geoelectr., 17, 59. Taylor, W.L (1978). A VHF technique for space-time mapping of lightning dischaige processes, J. Geophys. Res, 83, 3575. Teer, T E and Few, A A (1974). Horizontal lightning, J. Geophys Res, 79, 3436. Thottappilli, R., McLain, D.K., Uman, M.A., and Diendorfer, G. (1991). Extension of the Diendorfer-Uman lightning return stroke model to the case of a variable upward return stroke speed and a variable downward dischaige current speed, J. Geophys. Res, 96, 17143. Thottappilli, R., Rakov, V.A, and Uman, M.A. (1990). K and M changes in close lightning ground flashes in Florida, J. Geophys. Res., 95, 18,631. Uman, M.A. (1964). The conductivity of lighming. J. Atmos. Terr. Phys., 26,1215.

Uman, M.A. (1969). Lighming, McGraw-Hill, New York. Uman, M.A. (1987). The Lighming Discharge, Academic Press, Orlando, FL.

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Uman, M.A. and McLain, D.K. (1969). Magnetic field of lightning return stroke, J. Geophys. Res., 74. 6899. Uman, M.A. and McLain, D.K. (1970a). Radiation field and current of the lightning stepped leader, J. Geophys. Res., 75, 1058. Uman, M.A. and McLain, D.K. (1970b). Lightning return stroke current from magnetic and radiation field measurements, J. Geophys. Res., 75, 5143. Uman, M.A. and Orville, R.E (1964). Electron density measurement in lightning from Stark-broadening of Ha, J. Geophys.

Res.. 69,5151. Uman, M.A. and Voshall, R.E. (1968). Time interval between lightning strokes and the initiation of dart leaders, J. Geophys. Res., 73.497. Uman, M.A., McLain, D.K., and Krider, EJP. (1975). The electromagnetic radiation from a finite antenna, Am J. Phys., 43, 33. Uman, M.A., Orville, R.E, and Salanave, L_E. (1964a). The density, pressure, and particle distribution in a lightning stroke near peak temperature, J. Atmos. Sci., 21, 306. Uman, M.A., Orville, RE., and Salanave. L.E. ( 1964b). The mass density, pressure, and electron density in three lightning strokes near peak temperature, J. Geophys. Res, 69, 5423. Uman, M.A., Brantley, R.D., Lin, Y.T., and Tiller, J.A. (1975). Correlated electric and magnetic fields from lightning return strokes, J. Geophys. Res.. 80, 373. Uman, M.A., McLain, D.K., Fisher, RJ., and Krider, E.P. (1973a). Electric field intensity of the lightning return stroke, J. Geophys. Res, 78,3523, Uman, M.A., McLain, D.K., Fisher, RJ„ and Krider, E.P. (1973b). Currents in Florida lightning return strokes, J. Geophys Res, 78, 3530. Uman, M.A., Seacotd, D.F., Price, G.H., and Pieree, ET. (1972). Lightning induced by thermonuclear detonations, J. Geophys Res, TJ, 1591. Weidman, C.D. and Krider, EE. (1979). The radiation fields wave forms produced by intracloud lightning discharge processes, J. Geophys. Res, 84, 3159. Workman, EJ„ Hoizer, R.E, and Pelser, G.T. (1942). The electrical structure of thunderstorms. Technical Notes National Advisory Committee on Aeronautics, No. 864. Willett, J.C., Bailey, J.C., Idone, VP., Eybert-Berard, A^ and Barret, L (1989). Submicrosecond interoomparison of radiation fields and currents in triggered lightning return strokes based on the transmission-line model, J. Geophys Res. 94, 13275. Willett, J.C, Idone, VP., Orville, R.R, Leteinturier, C„ Eybert-Berard, A., Barret, L , and Krider, EP. (1988). An exper­ imental test of the “transmission-line model” of electromagnetic radiation from triggered lightning return strokes, J. Geophys Res, 93, 3867. Yos, J.M. (1963). Transport properties of nitrogen, hydrogen, oxygen, and air to 30,000 K, Tech. Mem. RAD-TM-63-7, Avco Corp., Wilmington. MA.

Chapter 5

Lightning Detection from Ground and Space Richard E. Orville

CONTENTS 1. 2.

Introduction........................................................................................................................ 137 The Lightning Flash...........................................................................................................138 2.1. Intracloud Lightning............................................................................................... 138 2.2. Cloud-to-Ground Lightning: First Return Strokes.................................................138 2.3. Cloud-to-Ground Lightning: Subsequent Lightning Strokes................................ 139 2.4. Lightning to Surrounding Air Air Discharges......................................................139 3. Lightning Detection from Ground......................................................................................139 3.1. Magnetic Direction Finding....................................................................................139 3.2. Time of Arrival....................................................................................................... 140 3.3. Combined Magnetic Direction Finding and Time of Arrival............................... 142 4. Lightning Detection from Space.........................................................................................144 4.1. The DMSP Satellites............................................................................................... 144 4.1.1. DMSP Scanners.......................................................................................... 144 4.1.2. DMSP Global Lightning Observations...................................................... 147 4.2. The Lightning Imaging Sensor............................................................................... 147 References ........................................................................................................................ 149

1. INTRODUCTION

The worldwide distribution of lightning remains an unknown despite the advancement of groundbased and space-based lightning detection systems. Progress is being made, although we do not have better estimates than 100 flashes per second based on calculations made by Brooks (1925) in the early part of this century. Brooks arrived at his estimate by combining the results of his climatological survey of thunderstorm frequencies with a flashing rate observed by Marriott (1908) during a thunderstorm at West Norwood, England on June 4, 1908. Doubtless, Marriott would have been surprised to see the role played in the meteorologic literature by his observations over a single 28-min period. We are now on the brink of making the first continuous measurements of lightning on earth. Ground-based networks cover much of the land area, and the first of several satellites to measure lightning will be launched within the next few years. Only part of the land is now covered by lightning detection networks; and the first satellites to measure lightning will be in low orbit, thus measuring only part of the global lightning. Nevertheless, satellites will observe lightning over the land and over the oceans without bias and thus give us the most reliable estimates of global lightning. It is the purpose of this chapter to present the current technology in measuring lightning from the ground and from space. Our present best results for global lightning measurements will be summarized, based on both ground and satellite observations. First, however, it is important to review a few fundamentals of the lightning flash.

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THE LIGHTNING FLASH

Regions of net charge develop in clouds that are produced by charge separation processes believed to require the presence of supercooled liquid water, ice, and updrafts and downdrafts to ensure the interaction of particles. The buildup of the electric field continues in a cloud until the dielectric strength of the air is exceeded. At this time, breakdown occurs within the cloud. Discharges exclusively in the cloud are intracloud flashes, those leaving the cloud and contacting the ground are called cloud-to-ground flashes, and those ending in the air surrounding the cloud are termed air discharges. The most common lightning flash occurs within the cloud, followed by flashes to ground. The least common flashes are the air discharges that end in the surrounding air. These include the lightning flashes that have been observed recently to propagate from the top of clouds to the stratosphere. 2.1.

INTRACLOUD LIGHTNING

Lightning occurs most irequently within clouds. Observations indicate that the cloud is luminous for approximately 0.5 s. Breakdown occurs within the cloud and a leader propagates to a region of opposite charge within the cloud. Pockets of charge are probably encountered during the propagation of the leader, resulting in momentary enhancements of the luminosity that last about 1 msec. The amount of charge transferred in an intracloud flash is estimated to be 20 C, but ranges from 0.3 to 100 C (Workman et al., 1942). Propagation of the breakdown process is relatively slow, moving at about 1 x 104 to 2 X 104 m s-1. Electrical currents have not been directly measured, but the measured radiation fields suggest that the peak currents are of the order of 1000 to 4000 A. Strikes to instrumented aircraft suggest that the peak currents are no more than a few thousand amperes, and the rise to peak current amplitude is a few milliseconds. The energy in intracloud flashes is unknown. A detailed discussion of the intracloud flash is given by Brook and Ogawa (1977). 2.2.

CLOUD-TO-GROUND LIGHTNING: FIRST RETURN STROKES

The most familiar lightning occurs from the cloud to the ground. Easily measured and observed, data have been accumulated over the decades to give us a description of this type of discharge. Initiation of this type of discharge is manifested by a stepping process that is recorded as radiation steps and as optically pulsating emissions. Called the stepped leader, it moves in luminous steps toward the ground at an average speed of 1.5 x 10s m s~' and carries a current on the order of a few hundred amperes. When contact is made with the ground, the 5 C of charge deposited on the channel flows to ground. The resulting intense luminosity is called the return stroke and moves toward the cloud base at one third to one half the speed of light. Median peak currents for first strokes lowering negative charge are 30,000 A and median peak currents for strokes lowering positive charge are 45,000 A. During the return stroke phase, about 104 to 10s J n r 1are dissipated within the channel. The energy is divided among the dissociation, ionization, excitation and kinetic energy of the particles, energy of expansion of the channel, and radiation. Spectroscopic meas­ urements reveal that the air molecules, principally nitrogen, oxygen, and water molecules, are split into their respective atoms and that, on the average, one electron is removed from each atom. The conversion from air molecules to a singly ionized plasma in a section of the channel occurs in less than a few microseconds. The resulting optical emissions are principally from ionized nitrogen and oxygen atoms with one strong neutral emission line from hydrogen at 656.3 nm (H-alpha). In the near infrared region, from 700 to 900 nm, the spectrum is entirely dominated by neutral emission from nitrogen and oxygen atoms. Beyond 900 nm, the spectrum has been measured by Weidman et al. (1989) and shows emissions from neutral nitrogen out to 1350 nm. Peak temperatures in the lightning channel have been calculated to reach 30,000 K. The return stroke emissions may last a few hundred microseconds, and at the end the stroke is over and also perhaps the flash. There is frequently, however, a subsequent stroke.

Lightning Detection from Ground and Space

0

40

80

139

120

160

200

MICROSECONDS 5.3.1 The radiation field signatures produced by a typical lightning discharge to ground at a distance of about 60 km. The top trace (a) shows a cloud discharge impulse that preceded the first return stroke (b) and a subsequent return stroke (c). (From Krider, E. P. et al. (1980). Bull. Am. Meteorol. Soc., 61, 980. With permission.) Figure

2.3.

CLOUD-TO-GROUND LIGHTNING: SUBSEQUENT LIGHTNING STROKES

If a subsequent stroke occurs, it will usually do so in about 40 to 70 msec after the previous stroke. A short length of light, appearing as a dart of light, is recorded to propagate down the previous channel. Carrying a thousand or so amperes, the dart propagates from the cloud base to the ground in about 2 msec. Once again, the cloud is short-circuited to ground and another return stroke occurs. On the average, two to four strokes occur in lightning flashes to ground covering a total time of 100 to 200 msec. 2.4.

LIGHTNING TO SURROUNDING AIR: AIR DISCHARGES

Lightning discharges have been observed to propagate outside a cloud and end in the surrounding air. Called air discharges, these comprise a small percentage of the total lightning. An even rarer air discharge has been reported recently. Winckler et al. (1993) report on luminous events observed above thunderstorms. These are reported to be transient luminous events extending from the top of the cloud toward the stratosphere. Rarely seen by the eye, they have been recorded by sensitive photometric telescopes equipped with photomultipliers. The rarity and weak luminosity of these discharges suggest that they will not be detected by the present lightning location systems or those that are planned for near future. 3.

LIGHTNING DETECTION FROM GROUND

A discussion of the previous lightning types has said nothing about the ways in which we are slowly solving some of the problems associated with lightning. Most of the advances in the last two decades have been in the general area of lightning location. These advances have been pursued in response to answering the question, “Where is the lightning?” To understand this, it is nec­ essary to examine the radiation waveforms that are fundamental to magnetic direction finding and to the time-of-arrival method of locating lightning. 3.1.

MAGNETIC DIRECTION FINDING

The electromagnetic radiation pulses from lightning are many, but only a few key ones are used in locating the source of a ground strike. Figure 5.3.1 shows the electric radiation field signatures from typical lightning discharges at a range of 60 km. Figure 5.3.1a is a cloud discharge, 5.3.1b is a first return stroke, and 5.3.1c is a subsequent return stroke. Using appropriate electronics, instrumentation has been developed to pass only the waveform characteristic of return strokes (Figure 5.3.1b and c) and to reject waveforms characteristic of cloud discharges (Krider et al., 1976,1980). The result is that over a period of a decade, lightning networks have been developed

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140

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L || - Lo c a k o a CoM pH tsd Iran i O F j ta d O F j

Figure 53J2 The pairs of intersections are shown for this three-DF network. An optimal location algorithm is used to minimize the azimuthal errors. (Adapted from Cummins, K. L et al. (1993). Precise Measurements in Power Conf., Arlington, VA, October 27-29. With permission.)

to cover the U.S. (Orville, 1991). These networks now provide us with estimates of location, time, polarity, peak currents, and multiplicity of ground strokes. The principal of the magnetic direction finding networks is shown in Figure 5.3.2. A direction finder (DF) sensor consisting of two orthogonal magnetic loop antennas and associated electronics measures the azimuth to the lightning stroke. When two direction finders detect a lightning stroke, an intersection can be plotted. When three or more direction finders detect a lightning stroke, then three locations can be plotted and an optimal estimate can be obtained. The optimization mini­ mizes the angle disagreement among the three direction finders. Conditions can exist in which very poor locations of lightning are obtained. This can happen, for example, if only two direction finders detect a lightning stroke and the stroke is near the baseline joining the two direction finders. These are called baseline errors. The azimuth errors can be large, resulting in a poor determination of the location. Consequently, most direction finding networks have three or more sensors. One result of a direction finding network operating in the U.S. is,shown for the year 1989 (Orville, 1991) in Frgure 5.3.3. Over 13.4 million lightning flashes are plotted and contoured. A detection efficiency of 70% is assumed; thus the measured lightning values are multiplied by 1.4 before the contouring routine is applied. 3,2.

TIME OF ARRIVAL

The time-of-arrival (TOA) technique can use either a relative time difference or an absolute TOA method. In both cases, we are interested in the time that the peak of the radiation wavefront passes a sensor. In Figure 5.3.4a, three sensors have detected a lightning radiation waveform. Each sensor measures the arrival time of the lightning radiation waveform. The sensors allow the measurement of the relative time difference between arrival times at multiple sensors. Thus, each pair of sensors, for example, SI and S2, yield a hyperbolic curve describing the set of possible locations that satisfy the time difference measurement Two such curves produce an intersection. Under some conditions. Figure 5.3.4b, three sensors will produce curves that have two intersections. Conse­ quently, four sensors are required for an unambiguous location.

Figure 5.3.3 Lightning flash density for the contiguous U.S. in 1989. The total number of lightning flashes contoured is 13.4 million flashes. The contours assume a detection efficiency of 70%; thus, all measured values were increased by a factor of 1.4, and then contoured. (From R. E. Orville, (1991). Mon. Weather Rev., 119, 573. With permission.)

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fipjre 5.3.4 (a) Hypetboiic intersection method for locating lightning strokes using three sensors, (b) An example of an ambiguous location for a three-sensor hyperbolic intersection. (Adapted from Cummins, K. L. et al. (1993). Precise Measurements in Power Conf., Arlington, VA, October 27-29. With permission.)

If the absolute arrival time of the radiation waveform is known, such as from the use of the global positioning satellite (GPS), then a set of sensors can be used to measure the location and time of the lightning stroke. The GPS clocks have the advantage of providing the time to an accuracy of 300 nsec. Each sensor establishes the range from the lightning stroke, thus producing a circle locus of possible locations. The radius of each circle is based on the difference between the estimated time of the discharge and the measured time of its arrival at the sensor site (see Figure 5.35). The location of the lightning stroke is determined by selecting the position and time of the discharge that causes all the circles to intersect When more than three sensors detect a stroke, the method of circular intersections can produce an optimized solution by employing an iterative algorithm similar to the ones used in magnetic direction finding. Circular intersections are readily generalized to include angle measurements, i.e., they provide an excellent way to combine TOA methods and magnetic direction methods. 3.3.

COMBINED MAGNETIC DIRECTION FINDING AND TIME OF ARRIVAL

The optimum lightning location system uses both the magnetic direction finding (MDF) and the time of arrival (TOA) techniques simultaneously. This is now possible and has been in use in a

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figure 53 J Circular intersection method for locating lightning strokes using four sensors and absolute timing. (Adapted from Cummins, K. L. et al. (1993). Precise Measurements in Power Conf., Arlington, VA, October 27-29. With permission.)

Figure 5.3.6 Advanced lightning direction finder with both MDF and TOA capability. The GPS antenna, in this research lightning sensor, is located 10 m away. Current sensors integrate the GPS antenna within the instrument. This lightning sensor was located on Kapingamarangi Atoll from November 1992 to July 1993.

research mode for over a year (see Figure 5.3.6). A three-sensor network has been operating in the remote Western Pacific Ocean with sensors located on Kapingamarangi Atoll, and in the cities of Rabaul and Kavieng, Papua New Guinea (Orville et al., 1994). This three-direction finder network uses absolute timing from the GPS satellites and has operated without problems since its establishment in late 1992. Similar instrumentation is now being installed in the U.S. and can be expected to improve the real-time locating of lightning to an accuracy of less than 500 m. The network operates as follows. The MDFs provide the azimuth information and the TOA instrumentation provides the ab­ solute arrival time with the inherent range information. Employed simultaneously, the method of circular intersections is used to determine the optimal estimate of the lightning stroke location, employing all the available information. This combined method avoids the problem inherent in each of the location methods of MDF and TOA, while taking advantage of the strengths inherent in each method. Consider a lightning

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Figure 5.3.7

This illustrates the combined MDF and TOA method for locating a lightning stroke on the baseline between two sensors. (Adapted from Cummins, K. L et al. (1993). Precise Measurements in Power Conf., Arlington, VA, October 27-29. With permission.)

stroke to ground between the sensors shown in Figure 5.3.7. The stroke location can be located exactly by using the azimuth vectors and range circle information. In this figure, the azimuth information for sensor SI is the angle 0 1 , and the range value, based on the absolute arrival time is rl. There are four measured parameters in this example, two angles and two arrival times. These measurements produce three estimate parameters: latitude, longitude, and time of the stroke. Thus, there is redundant information in this example, allowing for optimization to be used. It should be noted that the MDF and TOA combination outperforms the individual methods in location accuracy and in the probability of detection. This combined technique is less likely to produce erroneous flash locations. In addition, the lightning location accuracy should be on the order of 500 m. Undoubtedly, this will lead to more useful applications of the lightning infor­ mation to meteorologic problems. 4.

LIGHTNING DETECTION FROM SPACE

Methods of detecting lightning from space are now concentrating on optical techniques. This is primarily the result of the superior spatial resolution offered by these techniques, which were pioneered by the Defense Meterological Satellite Program (DMSP) series during the last 15 years. 4.1.

THE DMSP SATELLITES

This system of satellites was initiated in the 1970s by the U.S. Air Force and consists of satellites in sun-synchronous polar orbit around the earth; that is, the orbit processes around the earth once a year and passes overhead near the same local time each day. The orbit is circular with an altitude of 830 km and is inclined 98.7° to the equator on the northbound pass (Figure 5.4.1). The orbital period is 101.56 min, and the highest latitude reached by the subpoint track is 81.3°. 4.1.1.

DMSP Scanners

The primary sensor on the DMSP satellites consists of high-resolution scanners that produce visible- and infrared-spectrum photographs. It was discovered soon after the launch of the block 5C satellites in 1973 that the high-resolution visible scanner has the capability of detecting light­ ning during the nighttime portion of the orbit To understand this, we should first consider the characteristics of the detector. The DMSP high-resolution detector has a 4.56-mrad field of view, which at 830 km corre­ sponds to an area 3.8 km in diameter on the earth’s surface. A rotating mirror with a frequency of 1.8 Hz reflects light from the scanned area into the detector, and a photograph is composed line by line as the satellite moves in its orbit (Ftgure 5.4.2). The mirror points toward the earth during part of each rotation, which amounts to 111° of each minor rotation (360°). Therefore, the detector scans the earth 31% of the time and covers approximately 3000 km in each scan line. The time resolution, that is, the length of time a surface point is scanned, and the field of view at the surface vary as a function of scan angle. The angular frequency of the scanning mirror is 11.2 rad s_l, which produces, at nadir, a ground speed of 9.3 x 103 km s_l. For a distance of 3.8 km on the ground, this corresponds to a time resolution of 4 x 10 4 s.

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Figure 5.4.1 DMSP cubital inclination (not drawn to scale). (From Orville, R.E. (1982). Handbook o f Atmospherics, Vol. II, Volland, H., Ed., CRC Press, Boca Raton, FL. With permission.)

Figure 5.4.2 Geometry of DMSP scan line. A series of scan lines will produce photographs such as those repro­ duced in Figure 11. (From Orville, R.E. (1982). Handbook o f Atmospherics, Vol. II, Volland, H„ Ed., CRC Press, Boca Raton, FL. With permission.)

Figure 5.4.3 Normalized DMSP sensor response for a simulated solar radiation source. (From Orville, R.E. (1982). Handbook o f Atmospherics, Vol. II, Volland, H., Ed., CRC Press, Boca Raton, FL. With permission.)

The high-resolution detector is a silicon photodiode with the response curve shown in Figure 5.4.3. Gain controls allow the satellite to photograph the surface under illumination from full daylight to one quarter moonlight. A change in gain changes the saturation threshold of the system. At night the threshold is low enough so that cities, gas and brush fires, and lightning flashes saturate the system.

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\

i

40°N

30°N

20°N

figure 5.4.4 DMSP photograph of the eastern part of the U.S. Horizontal streaks produced by lightning are visible off the coast of Florida. A gas flare is visible at the bottom in the oil fields of the Yucatan. (From Orville, R.E. (1982). Handbook o f Atmospherics, Vol. II, Volland, H., Ed., CRC Press, Boca Raton, FL. With permission.)

One example of a DMSP image is shown in Figure 5.4.4, which contains cities, gas fires, and lightning. The cities are those in the eastern U.S. and Mexico. The gas fire is from flare gas burning in the oil fields of the Yucatan, and the lightning appears as horizontal streaks off the East Coast of Florida.

Lightning Detection from Ground and Space 4.1.2.

147

DMSP Global Lightning Observations

The reduction of lightning data on DMSP positive transparencies has been accomplished by Orville and Henderson (1986). The lightning streaks on 365 consecutive days of recordings were transferred by hand to maps and then digitized. The error in the lightning location was estimated to be 1°, corresponding to approximately 100 km. Over 32,000 flashes were digitized. The results have been published by Orville and Henderson (1986); several examples are shown here. Figure 5.4.5a shows the results for an entire year, 365 days, of coverage by the DMSP satellite. Over 32,000 lightning locations are plotted, indicating where the local midnight lightning occurs on earth. The geometry of the scan line and the small amount of time that the satellite sensor is viewing the earth results in detecting, we estimate, only 1 in 105 lightning flashes that occur. Nevertheless, the observations are totalled over the entire year to give an accurate distribution of the local midnight lightning on earth. Figures 5.4.5b and c show the distribution of midnight lightning in two seasons, summer in the Northern Hemisphere and summer in the Southern Hemisphere. The shift in the lightning locations is dramatic in the two figures. In addition, note that more lightning is detected in the summer Northern Hemisphere (9368 flashes) vs. the summer Southern Hemisphere (7221 flashes). 4.2.

THE LIGHTNING IMAGING SENSOR

A major program is now underway to develop an instrument to detect lightning from space. Sponsored by the National Aeronautics and Space Administration (NASA), the plan is to launch a series of satellites to monitor the optical signatures from lightning on a nearly continuous basis. One of the first descriptions of this program was published by Christian et al. (1989). The lightning imaging sensor (LIS) will locate lightning with an accuracy on the order of 10 km over a large region of the earth. Intracloud and cloud-to-ground lightning will be detected by the LIS. There will be no discrimination between these types of lightning. The instrument will image a scene similar to a television camera, but the technique to process the transient nature of the optical source, the lightning, is more complicated. A wide field-of-view lens will be used and combined with a narrowband interference filter. The image will be focused on a small, high-speed photodiode focal plane. The resulting signal must then be read from the focal plane into the real-time data processor. Resulting data are then formatted and transmitted to the ground. Characteristics of the space lightning detector are dictated by the need to record the flash against a background of daylight. It is necessary to select a method to extract the lightning signal from the bright illumination of day. Four methods are used to do this (Christian et al., 1989). First, spatial filtering is used to match the view of each detector element to the typical cloud top area illuminated by a lightning flash, generally on the order of 10 km. This produces the optimal sampling of the lightning area relative to the background. Second, and perhaps most important, spectral filtering with a narrowband interference filter centered on the neutral oxygen line at 777.4 nm is used to isolate one of the most intense lines in the lightning spectrum. This maximizes the signal against the bright background. Third, the LIS will use filtering of the temporal signal to take advantage of the pulse duration, typically 400 psec vs. the background illumination that is constant on the order of seconds. Technological limitations require that integration times only as short as 2 msec be used in the LIS design. Even with these filtering techniques, the signal-tobackground illumination may be only 0.02. Therefore, a fourth technique is necessary to improve the signal detection. A frame-to-frame background subtraction will be used to remove the slowly varying background illumination coming off the LIS focal plane. A real-time processor is an important part of the LIS. It will produce a background estimate of the scene imaged at each pixel of the focal plane array. The background signal will be compared to the off-the-focal-plane signal on a pixel basis. When the difference is above a certain threshold, the signal will be identified as a lightning event.

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□MSP MIDNIGHT S A T B J-IT E OBSERVATIONS

Figure 5.43

(a) O ne year of local midnight lightning is plotted to show the distribution of lightning flashes on the

earth. Note the high number of flashes over land relative to the oceans. The land:ocean ratio for lightning is ap­ proximately 10:1. (b) Distribution of local midnight lightning for the summer season in the Northern Hemisphere, June, July, and August (c) Distribution of local midnight lightning for the summer season in the Southern Hem i­ sphere, December, January, and February.

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149

The performance criteria of the LIS are as follows: Pixel IFOV Field of view Scene duration Wavelength Threshold Signal-to-noise ratio Array size Dynamic range Detection efficiency False alarm rate Weight Power Telemetry data rate

8.5 km 75° x 75° square FOV 180s 777.4 run 4.7 J m 2 sr_l

6 128 x 128 >100

>90% for all events and are as previously defined. Estimates of Me and 7> have generally been obtained using two different models for the dissipation of the discharge energy. One assumes that the energy dissipation process is dominated by the hydro­ dynamic rapid expansion of the discharge tube by a shock wave (see, for instance, Chameides et al., 1977 and Chameides, 1979a, 1979b). The other assumes that the energy dissipation occurs by a slower ohmic heating process using a turbulent hot channel model (see Hill et al., 1980). Values obtained for both approaches are listed in Table 8.1.1. An interesting contrast to the theoretical calculations described above is provided by a few more empirical estimates of p(NO) derived using data from laboratory experiments. These ex­ periments employ an apparatus similar to that shown in Figure 8.3.1, in which air is allowed to pass through a simple, electrostatic spark, and the NO concentration is measured using standard chemiluminescent techniques (see Chameides et al., 1977; Levine et al., 1981; and Peyrous and Lapeyre, 1982). The value of p(NO) is then related to the energy of the spark and to the change in the concentration of NO in the air before and after exposure to the spark. While these exper­ iments have the obvious advantage of being straightforward and thus easy to interpret, they do have the potentially serious drawback of requiring an extrapolation of size and energy density from a laboratory spark to a lightning discharge. If the NO production mechanism varies nonlineariy with discharge characteristics (e.g., radius, energy), these laboratory results would not represent an appropriate surrogate for NO production by lightning. A somewhat different approach was adopted by Borucki and Chameides (1984). These in­ vestigators used the results of the high energy discharge experiments of Picone et al. (1981) to obtain values for the cooling time constant of the hot channel, which allowed for the determination of Tf and f%Q (7», and for the ratio of ME(TF) to Ef. These values were then used to calculate p(NO) using Equation 4. Interestingly, this approach yielded a value for p(NO) that is quite similar to that found in the other laboratory studies (see Table 8.3.1).

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196

E LECTR O STA T IC G EN ERATO R

3 5 kV fig u re 8.3.1

Schematic diagram demonstrating the type o f apparatus used in laboratory studies to determ ine N O ,

m olecular production due to a spark discharge. (From Chameides, W .L. et al. (1977). J. Atmos. Sci., 3 4 ,1 4 3 . W ith permission.)

Table 8.3.1 summarizes the p(NO) values obtained by previous investigators using each of the methods described above. Note that in spite of the widely varying approaches adopted, the NO yields obtained are all generally consistent, ranging from a minimum of about 2 x 1016 to a maximum of about 13 x 1016 molecules of NO per joule of discharge energy. 3.2.2.

Energy per Flash

The energy per flash, Ef, is essentially the sum of the energy dissipated in each of the individual strokes that make up the flash. Values used in previous studies have tended to be in the range (1 to 20) x 10s J flash-1 (see Table 8.1.1). No doubt this large range of values reflects, at least in part, the large variability in the actual energy of lightning flashes in the earth’s atmosphere (see Uman, 1969). Perhaps the most reliable value available for lightning flash energy dissipation is that from Borucki and Chameides (1984), derived by considering six studies of electrical measurements and six studies of optical measurements. Adjusting the values to account for 1.75 equivalent return strokes per flash, they obtain an average of (4 ± 2) x 10® J flash-1 for the optical measurements, and (4 ± 3) x 10s J flash-1 for the electrical measurements. An energy of 4 x 10s J flash-1 will thus be used later in this chapter in converting from NO production per unit energy to NO production per flash. 3.3.

DETERMINATION OF NO YIELD PER FLASH: FIELD OBSERVATIONS

Direct field observations represent a third method of estimating the lightning fixation rate of nitrogen for use in Equation 2; in these studies, P(NO) is typically directly estimated, rather than its component parts p(NO) and iy (Equation 3). As indicated in Table 8.1.1, four major estimates using field observations along with the FEA have been made. The obvious advantage of this approach is that it represents a direct measurement and does not require knowledge of the flash energy, a parameter that appears to be subject to a high degree of variability and uncertainty. On

Lightning and Atm ospheric Chem istry Table 8.3.1

197

Review of previous estimates of the NO molecular production rates: /HNO) and /"(NO)

p i NO) (10“ N O )-')

4 (bomb) 12

Ref.

/’(NO) — Normalized1 (10“ NO flash"1) Theoretical

1.1 (flash)

1.6, 1.1

—

4-5.2

Tuck (1976) Grifftng (1977)

5

If)

1.2-2.8

Chameides et al. (1977)

13

26

Chameides (1979a)

—

1.2b 0.8

3.2-6.8 1.2 0.8 1.6

Dawson (1980) Bhetanabhoda et al. (1985)

—

Average

/»(NO) (10“ NO flash ')

—

1.6

8.5 ± 4 .7

6.7 ± 10

H ill et al. (1980)

2.1 ± 1.4

Laboratory 6 ± 1, 8 ± 4

1 4 , 3.2

12, 16

Chameides et al. (1977)

(low and high energy sparks, resp.) 5± 2

0.5

2

Levine et al. (1981)

1.6

3.2

0.6

Pcyrous and Lapeyie

9 ± 2

3.6

3.6

Borucki and Chameides

5.9 ± 2.8

7.0 ± 6 .6

2.4 ±

(1982) (1984) Average

12

Field Observations ____

10

___

Noxon (1976, 1978)

—

25

—

Kowalczyk and Bauer

—

10-100

—

—

300

—

Drapcho et al. (1983) Franzblau and Popp (1989)

—

92 ± 122

—

(1982)

Average

Note:

Average values given with ±1 SD.

PiN O ) calculated assuming a uniform

*

Normalized

6

Inferred following method o f Borucki and Chameides (1984).

£( = 4 x

10* J flash"1 (see text).

the other hand, the approach is not without its own set of problems. A major source of uncertainty for all field measurements of this kind relates to the representativeness of the observations; it is extremely difficult to determine whether the particular event observed is representative of events on a global scale. Moreover, as will be seen below, the interpretation of the observations generally requires the adoption of several fairly arbitrary assumptions. Given the varying nature of the field observations, a brief account of each is presented below. The first direct observations of enhanced NO* concentrations in the vicinity of lightning flashes were made by Noxon (1976, 1978), who used a spectrometer to measure NO2 concentrations below the cloud base of active thunderstorms. The observed increase in NO2 as the storm passed over the area of observation, along with estimates of the flash rate within the vicinity of the storm from visual observations and assumptions with regard to the volume of the storm and the relative abundances of NO and NO2, where then used to estimate /*(NO). Kowalczyk and Bauer (1982) attempted to improve upon Noxon’s estimates for P(NO) by correcting for the fact that Noxon’s measurements primarily represented production from CG, while most flashes are actually IC. Because of their assumption that IC are some ten times less energetic than CG, Kowalczyk and

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Bauer’s estimate for P(NO) was significantly smaller than that originally obtained by Noxon (see Table 8.1.1). Drapeho et al. (1983) used a chemiluminescent analyzer to measure NOx concentrations fol­ lowing a CG lightning flash that occurred about 700 m from the analyzer. The production of NO from this one flash was then estimated assuming that, on reaching the measurement site shortly after the flash occurrence, the NO from the flash was uniformly dispersed in a cylinder of 700 m in radius and 3 km in height. Franzblau and Popp (1989) adopted a combination of the Noxon and the Drapcho et al. approaches: they used an NOz spectrometer, along with commercial local lightning frequency data, to compute an NO, molecular production rate per flash from two distant storms, as well as from measurements of enhanced NO2 in the vicinity of a single CG flash. These authors’ final value for P(NO) was taken to be the average of the three values thus obtained. 3.4.

SUMMARY OF VALUES DERIVED FOR NO YIELD PER FLASH

A summary of all values obtained for p(NO) and P(NO), the NO yields per unit energy or per flash, respectively, is presented in Table 8.3.1. A remarkably good agreement is seen between the theoretical and laboratory values, while a significant inconsistency appears to exist between these values and those obtained from field observations. The average theoretical and laboratory values for p{NO) are seen to be (8.5 ± 4.7) x 1016 and (5.9 ± 2.8) x 1016 molecules J-1. If a uniform flash energy of 4 x 108 J flash-1 (see Section 3.2.3) is applied to these p(NO) values, an average P(NO) of (2.1 ± 1.4) x 1025 and (2.4 ± 1.2) x 1025 molecules flash-1 is derived from the theoretical and laboratory results, respectively. By comparison, the average P(NO) from the field studies is (92 ± 122) x 1025 molecules flash-1. The high average value for P(NO) from the field observations is primarily caused by the yields obtained by Franzblau and Popp (1989) and Drapcho et al. (1983). Note that the NO yield of Kowalczyk and Bauer (1982), derived from Noxon’s data in conjunction with an assessment of the IC and CG differences, is in excellent agreement with the theoretical and laboratory averages. There are several reasons for being suspicious of the NO yields of the two anomalous studies. In the case of the Drapcho et al. (1983) estimate it should be kept in mind that the P(NO) value was derived from a single flash, which may or may not have been very representative. Moreover, measurements were made in an urban area where background NO, concentrations were relatively large (from 3 to 24 ppbv) and quite variable. As a result, quantitative conclusions about lightning production based on these authors’ observations of elevated NO, concentrations of about 15 ppbv should be taken with caution (Franzblau and Popp, 1989). In the case of the Franzblau and Popp (1989) estimate, there appears to be some question as to the accuracy of the local flash frequency data used. The authors themselves demonstrate that the data are likely low by about a factor of two; such an error in the flash frequency would cause an overestimate in their global production estimate. Further, lightning in New Mexico, where the measurements were made, has been found to have on an average of 6.5 return strokes (Kowalczyk and Bauer, 1982), compared to a more typical global average of 2 to 3 return strokes (Uman, 1969). Thus, the lightning discharges observed by these authors may have been more energetic than those that would be expected in most other regions of the globe. These uncertainties, along with the uncertainties implicit in deriving a P(NO) value from an observed enhancement in ambient NO, or NO2 concentrations, could easily account for over an order of magnitude uncertainty in these estimates, and perhaps explain the discrepancy between them and the other values listed in Table 8.3.1. 3.5.

RECALCULATION OF THE GLOBAL NO PRODUCTION RATE USING THE FLASH-EXTRAPOLATION METHOD

Discussion in the previous sections indicates that a large portion of the disparities found among the previous estimates for G(NO) using the FEA can be attributed to: (1) differences in the value used for the flash rate, f/, (2) differences in the value used for the flash energy, f y and (3) two apparently anomalous estimates of the NO yield from field observations. From the values adopted

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in the preceding sections, we can now recalculate the value for G(NO) using the FEA. Taking ff to be 100 (70 to 150) s-1, as per Section 3.1, and taking P(NO) to be 2.3 (1 to 7) x 1025 molecules flash 1, based on Table 3, the resulting value for G(NO) is 2 (1 to 8) Tg (N) year-1. It is interesting to note that this value is more than an order of magnitude smaller than the global production rate of 81 Tg (N) year-1 recently obtained by Liaw et al. (1990) through a similar review and nor­ malization of previous estimates of the global nitrogen fixation rate. The difference between our value and that of Liaw et al. can be attributed primarily to the high value for Ef adopted by Liaw et al., along with their inclusion of the anomalously high values obtained by Drapcho et al. (1983) and Franzblau and Popp (1989). 4.

OTHER ESTIMATES OF GLOBAL FIXATION RATE BY LIGHTNING

While the discussion in the previous section indicates a fairly high degree of consistency between different estimates of the global rate of nitrogen fixation by lightning using the FEA, it is important to bear in mind that this method is not without potential flaws. As noted earlier, the method requires a fairly large extrapolation from the amount of NO produced from a single representative flash to the total production from all flashes. Such an extrapolation assumes, at the very least, a linear relationship between flash energy and channel volume and NO production, which may not be strictly correct. To address this problem, estimates of the fixation rate by lightning using different and independent approaches are needed. As indicated in Table 8.1.1 and described below, two such estimates may be found in the literature. The first such estimate (by Chameides et al., 1987) was based on an extrapolation of the amount of NO produced by a single thunderstorm rather than of the amount produced by a single lightning flash. The amount of NO produced by a thunderstorm was estimated from airborne measurements of elevated NO concentrations in the anvil regions of two active cumulonimbus clouds (Davis et al., 1987), along with evaluations of the NO, concentration from the photostationary state equations and the typical advective flow rate out of the tops of thunderclouds. This quantity was then multiplied by the number of active thunderclouds over the earth at any time to obtain a G(NO) of 7 Tg (N) year-1, a value within the range of the bounds obtained in Section 3.5 of this study using the FEA. An interesting feature of the Chameides et al. (1987) estimate is that it does not assume a priori that lightning flashes are the only electrical source of NO in thunderclouds, and thus includes contributions from other discharges, such as corona that com­ monly occur in electrified clouds. Another relatively independent estimate for G(NO) is that obtained by Tuck (1976), who estimated the global nitrogen fixation rate by lightning via analogy to a similar value obtained from nuclear blasts determined theoretically by Taylor (1950). By comparing the heated channel of a lightning stroke to the blast area of a nuclear bomb and by arguing that because lightning involves extranuclear processes, it should be twice as efficient at producing NO, as a nuclear blast. Tuck arrived at an estimate for G(NO) of 5.6 Tg (N) year-1, a number also in good agreement with that obtained in Section 3.5. In spite of the fact that these two additional estimates, like those obtained from the FEA, are subject to significant uncertainties, they are generally consistent with the FEA estimates. This overall consistency across essentially independent methods lends credence to all three methods and thus suggests that the global fixation rate by lightning is indeed of the order of 1 to 10 Tg (N) year-1. In the next section we discuss the probable impact of this source on the global distribution of reactive nitrogen in the earth’s troposphere. 5.

THE ROLE OF LIGHTNING IN THE BUDGET OF TROPOSPHERIC REACTIVE NITROGEN

l The total rate of production of reactive nitrogen in the troposphere is estimated to be about 20 to 100 Tg (N) year-1 (see Table 8.1.2). On this basis it might be concluded that lightning, estimated

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200

10.0

g

i

-1 5 0

i

i

-1 2 0

20.0

i

i

-9 0

i 10.0

i

40.0

i

-6 0

i

i

-3 0

i

i

i

0

1 -. . T r ~ 20.0

80.0

40.0

1

i

30

i

100.

60

i

»-• 60.0

i

90

i

i

120

i

l

i

150

□ 100.

Figure 8.5.1 (A) Percent o f the annually averaged N O , concentration as a function o f latitude and longitude cal­ culated to arise from the production of N O by lightning at the surface (990 m bar) and (B) in the m idtroposphere (500 m bar). Results based on the three-dim ensional chem ical transport m odel o f Kasibhatla et a l. (1993) w ith a 2 Tg (N ) y e a r’ source strength assumed for lightning.

here to produce some 1 to 8 Tg (N) year-1, must play a relatively minor role in controlling the abundance and concentration of reactive nitrogen in the troposphere. Such a conclusion, however, would not be strictly connect. Reactive nitrogen is relatively short-lived in the atmosphere, having a residence time against removal by rain and dry deposition of the order of days to weeks (Logan, 1983). As a result, its concentration is highly variable, being highest in uiban-industrial areas where anthropogenic emissions dominate and lowest in remote locations and in the upper tro­ posphere where the impact of surface sources such as combustion is minimal. In these regions the production of reactive nitrogen by lightning can have its greatest impact This impact is illustrated in Figure 8.S.1, where the results of a simulation of the global atmospheric nitrogen cycle using the three-dimensional chemical transport model (CTM) of Kasibhatla et al. (1993)

Lightning and Atm ospheric Chem istry

201

are illustrated. Inspection of the figure reveals negligibly small contributions from lightning in the lower atmosphere of the continents, where production from fossil fuel burning, biomass burning, and soil emissions dominate. However, in the remote tropical marine atmosphere and the mid- to upper troposphere, lightning makes a significant and in some cases a dominant contribution. 6.

CONCLUSIONS

The global magnitude of NOx production by lightning is an important subject of debate among the atmospheric chemistry community. In contrast to recent indications of a dominant role for lightning in global tropospheric NO* chemistry (Franzblau and Popp, 1989; Liaw et al., 1990), a range of 1 to 8 Tg (N) year-1 — accounting for less than 20% of the global tropospheric NO* budget — is derived using the FEA in this review. This value is in good agreement with two independent estimates of NO* production, as well as the magnitude of the known sinks of NO*. Much research remains to be done before a consensus can be reached regarding the role of lightning in the global NO* budget Further, the role of lightning needs to be examined on a more region-specific basis, rather than simply on a coarse global budget basis, with particular attention being paid to the remote ocean and the upper troposphere. In closing, a few remarks on what appear to be the most pertinent research needs are appropriate. More field observations in regions other than the western U.S., particularly in remote tropical regions, are needed. Fieldwork-based calculations such as those of Chameides et al. (1987), which represent estimates based on thun­ derstorm activity rather than single lightning stroke production, are strongly encouraged. Research to obtain greater confidence in values for lightning energy dissipation and global flash frequency is also needed. A better assessment of the sinks for NO, may allow an ostensible upper bound to production estimates to be established more rigorously. Finally, continued theoretical work may help to determine the differences in the mechanisms of lightning production by cloud-toground and intracloud lightning, and thus may shed light on the vertical distribution and overall global significance of lightning in tropospheric NO* chemistry. ACKNOWLEDGMENT

This work was performed in part with support from the National Science Foundation under Grant ATM-8905901, Grant ATM-9213653, and a National Science Foundation Graduate Fellowship (to MGL); and from the U.S. Environmental Protection Agency under Cooperative Agreement CR-816963-0100. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation or the U.S. Environmental Protection Agency.

REFERENCES Bhetanabhotla, M . N ., B. A . Crowell, A . Coucouvinos, R. D . H ill, and R. G Rinker. (1985). Simulation o f the trace species production by lightning and corona discharge in moist air, Atmos. Environ.. 19, 1391. Borocki, W . J. and W . L . Chameides. (1984). Lightning: estimates o f the rates o f energy dissipation and nitrogen fixation.

Rev. Geophys. Space Phys., 22, 363. Atmospheric Electricity, Academic Press, New York, 515 pp.

Chalmers, J. A . (1967).

Chameides, W . L (1979a). Effect o f variable energy input on nitrogen fixation in instantaneous linear discharges. Nature

(London), 277, 123. Geophys. Res. Lett., 6, 287, April. The Earth's Electrical Environment,

Chameides. W . L . (1979b). The implications o f C O production in electrical discharges, Chameides, W . L . (1986). The role o f lightning in the chemistry o f the atmosphere, in National Academy Press, Washington, D .C ., 70.

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Chameides, W . L and D. D. Davis. (1982). Chemistry in the troposphere, Chem.

Eng. News, 60, 38. Geophys. Res., 78,8751.

Chameides, W . L . and J. C . G. W alker. (1973). A photochemical theory o f tropospheric ozone, J.

Chameides, W . L., D . H. Stedman, R. R. Dickerson, D. W . Rusch, and R. J. Cicerone. (1977). N O , production in lightning, 7. Atmos. Sci., 34, 143. Chameides, W . L ., D . D. Davis, J. Bradshaw, M . Rodgers, S. Sandholm, and D. B. Bai. (1987). An estimate o f the N O , production rate in electrified clouds based on N O observations from the G T E /C ITE 1 Fall 1983 field operation,

J.

Geophys. Res., 92,2153. Crutzen, P. J. (1973). A discussion o f the chemistry o f some minor constituents in the stratosphere and troposphere.

Pure

Appi. Geophys., 106-108, 1385. Davis, D . D „ J. D . Bradshaw, M . O . Rodgers, S. T . Sandholm, and S. KeSheng. (1987). Free tropospheric and boundary layer measurements o f N O over the Central and Eastern North Pacific Ocean, J. Geophys. Res., 92, 2049. Dawson, G. A . (1980). Nitrogen fixation by lightning, J. Atmos.

Sci.. 37, 174. The Biosphere, A Scientific American Book, W .H . Freeman, 69. Drapcho, D. L , D . Sisterson, and R. Kumar. (1983). Nitrogen fixation by lightning in a thunderstorm, Atmos. Environ., Delwiche, C . G. (1970). The Nitrogen Cycle, in 17, 729. Ehhalt, D. H . and J. W . Drummond. (1982). The tropospheric cycle o f N O ,, in

Chemistry of the Unpolluted and Polluted

Troposphere, D . Reidel Publishing, 219. Ehhalt, D . H ., F. Rohrer, and A . Wahner (1992). Sources and distribution o f N O , in the upper troposphere at northern mid-latitudes, J.

Geophys. Res., 97,3725.

Franzblau, E and C . J. Popp. (1989). Nitrogen oxides produced from lightning, J.

Geophys. Res., 94, 11089. Geophys. Res., 82,943. H ill, R. D ., R. G . Rinker, and H. Dale Wilson. (1980). Atmospheric nitrogen fixation by lightning, J. Atmos. Sci, 37, 179. Hutchinson, G . E (1954). The biogeochemistry o f the terrestrial atmosphere, in The Earth as a Planet, G. P. Kuiper, Ed.,

Griffing, G . W . (1977). Ozone and oxides o f nitrogen produced during thunderstorms, J.

University o f Chicago Press, Chicago, 371. Kasibhatla. P. S., H. Levy, H. and W . J. Moxim. (1993). Global N O ,, H N O j, PAN, and N O , distributions from fossil fuel combustion emissions: a model study, J.

Geophys. Res., 98, 7165.

Kotaki, M ., I. K uriki, C. Katoh, and H. Sugiuchi. (1981). Global distribution o f thunderstorm activity observed with ISS-b, /

Rad Res. Lab., 28, 49.

Kowalczyk, M . and E Bauer. (1982). Lightning as a source o f NOx in the troposphere. Technical Report FAA-EE-82-4, Inst, for Defense Anal., Alexandria, V A , 76 pp. Levine, J. S., R. S. Rogowski, G . L . Gregory, W . E Howell, and J. Fishman. (1981). Simultaneous measurements o f N O ,, NO . and O j production in a laboratory discharge: atmospheric implications, Geophys. Res. Lett., 8, 357. Levy, H. (1971). Normal Atmosphere: large radical and formaldehyde concentrations predicted. Science, 173, 141. Liaw, Y . P., D . E Sisterson, and N . L M iller. (1990). Comparison o f field, laboratory, and theoretical estimates o f global nitrogen fixation by lightning, J.

Geophys. Res, 95, 22489. Chem. Phys. 35, 329.

Liebig, J. von. (1827). Une note sur la nitrification, Ann.

Logan, J. A. (1983). Nitrogen oxides in the troposphere: global and regional budgets, J. Noxon, J. F. (1976). Atmospheric nitrogen fixation by lightning, Geophys Noxon, J. F. (1978). Tropospheric N Q 2. J.

Geophys Res, 88. 10,785. Res. Lett., 3,4 63.

Geophys. Res, 83, 3051.

Orville, R. E and D . W . Spencer. (1979). Global lightning flash frequency, Mon.

Weather Rev., 107, 934.

Penner, J. E , C S. Atherton, J. Dignon, S. J. Ghan, J. J. Walton, and S. Hameed. (1991). Tropospheric nitrogen: a three­ dimensional study o f sources, distributions, and deposition, J.

Geophys. Res, 96,959.

Peyrous, R. and R .-M . Lapeyre. (1982). Gaseous products created by electrical discharges in the atmosphere and conden­ sation nuclei resulting from gaseous phase reactions, Atmos.

Environ., 16, 959.

Picone, J. M ., J. P. Boris, J. R. Grieg, M . Rayleigh, and R. F. Femsler. (1981). Convective cooling o f lightning channels,

/ Atmos. Sci., 38, 2056. Prentice, S. A . and D . Mackerras. (1977). The ratio o f cloud to cloud-ground lightning flashes in thunderstorms, J. Appi.

Meteorol., 16, 545. Salanave, L . E (1961). The optical spectrum o f lightning. Science, 134, 1395.

Biogeochemistry: An Analysis of Global Change, Academic Press, San Diego. R Soc., A201, 159. Tuck, A. F. (1976). Production o f nitrogen oxides by lightning discharges, Q. J. R Meteorol. Soc., 102, 749. Turman, B. N . (1978). Analysis of lightning data from the DM SP satellite, J. Geophys. Res, 83,5019. Schiesinger, W . H. (1991).

Taylor, G . I. (1950). The formation o f a blast wave by a very intense explosion, Proc.

Turman, B. N . (1984). Comparison o f lightning flash rates from the PBE sensor streak counting from the DM SP satellite, paper presented at VD International Conference on Atmospheric Electricity, American Meteorological Society, Albany, N Y . June 3 -8 . Turman, B. N . and B. C. Edgar. (1982). Global lightning distributions at dawn and dusk, J. Uman, M . A . (1969).

Geophys Res., 87, 1191.

Ughming, M cG raw -H ill, New York, 264.

W ofsy, S. G , J. C . McConnell, and M . B. McElroy. (1972). Atmospheric C H * CO , and C O 2, J. Zel'dovitch, Y . B. and Y . P. Raizer. (1966). Academic Press, New York, 445 pp.

Geophys. Res., 77,4477. Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena,

Chapter 9

Lightning within Planetary Atmospheres K . Rinnert

CONTENTS 1. 2.

3.

Introduction........................................................................................................................204 Remote Lightning Search................................................................................................. 205 2.1.Optica] Emissions........................................................................................................205 2.2. Radio Wave Emissions..........................................................................................205 Lightning on Other Planets...............................................................................................206 3.1. Mercury ................................................................................................................ 206 3.2. Venus.................................................................................................................... 207 3.2.1. Venus Atmosphere.................................................................................... 207 3.2.2. Venus Lightning Search............................................................................ 209 3.2.2.1. Optical Search.............................................................................. 209 3.2.2.2. Radio Frequency Wave Search...................................................210 3.2.3. Venus Lightning Summary....................................................................... 214 3.3. Mars........................................................................................................................ 214 3.3.1. Mars Atmosphere...................................................................................... 214 3.4...... Jupiter.................................................................................................................... 215 3.4.1. Jupiter Atmosphere.................................................................................... 215 3.4.2. Jupiter Lightning Search........................................................................... 217 3.4.2.1. Voyager 1, 2 Imaging.................................................................. 217 3.4.2.2. Voyager 1 Plasma Wave Analyzer............................................. 218 3.4.2.3. I o ...................................................................................................219 3.4.3. Jupiter Lightning Summary.......................................................................219 3.5....... Saturn.....................................................................................................................219 3.5.1. Saturn Atmosphere.................................................................................... 219 3.5.2. Saturn Lightning Search............................................................................221 3.5.2.1. Voyager Imaging..........................................................................221 3.5.2.2. Plasma Wave Analyzer................................................................ 221 3.5.2.3. Planetary Radio Astronomy Instrument.......................................221 3.5.2.4. Titan.............................................................................................. 223 3.5.3. Saturn Lightning Summary.......................................................................224 3.6. Uranus.................................................................................................................... 224 3.6.1. Uranus Atmosphere....................................................................................224 3.6.2. Uranus Lightning Search........................................................................... 225 3.6.3. Uranus Lightning Summary...................................................................... 226 3.7. Neptune...................................................................................................................226 3.7.1. Neptune Atmosphere...................................................................................226 3.7.2. Neptune Lightning Search..........................................................................226 3.7.2.1. Voyager Imaging..........................................................................226 3.12.2. Planetary Radio Astronomy Instrument.......................................227 3.7.2.3. Plasma Wave Analyzer................................................................ 228

0-8493-8647-O/95/SO.00+S.50 O 1995 by C R C Preti, Inc.

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3.7.3. Neptune Lightning Summary

3.8. Pluto................ 4. Concluding Remarks Acknowledgment............... References......................... 1.

228 228 228 229 229

INTRODUCTION

Lightning on planet Earth is primarily associated with thunderstorms, i.e., with convective, pre­ cipitating cumulonimbus clouds. In addition, natural lightning, or lightning-like electrical dis­ charges, are sometimes generated in active volcanic eruptions and in sandstorms and snowstorms, and they have been observed during earthquakes. In the following, lightning is again defined as a high-current electric discharge that dissipates a substantial amount of energy. (See also Chapters II/3 and 1/4 and, e.g., Uman, 1987.) The discharge channel is a region of high temperatures (several thousand degrees Kelvin) where a host of chemical reactions can take place that are not possible in an environment in thermochemical equilibrium. During the cooling of the expanding discharge channel many syn­ thesized compounds are frozen out Thus, lightning may play an important role in atmospheric chemistry (see Chapter 1/8) and in the origin of life. Bar-Nun (1975) suggested that strong light­ ning activity on Jupiter might account for the high acetylene abundance. Some two decades of planetary space missions also yielded information relative to possible lightning on other planets, and general reviews have been presented by Williams et al. (1983), Levin et al. (1983), Rinnert (1985), Uman (1987), and Russell (1993). Because lightning is such a complex phenomenon and the available information is so incomplete, only estimates of lightning activity in other atmos­ pheres can be given. In terrestrial lightning the cloud-to-ground discharges are the most intensively studied, and this is a type of lightning that is not expected to occur in other planetary atmospheres. The requirements for the production of lightning within an atmosphere are the following: (1) a sufficient abundance of appropriate material for electrification, (2) the operation of a microscale electrification process to produce classes of particles with different signs of charge and (3) a mechanism to separate and to accumulate particles according to their charge. For the purpose of (1) above, particles larger than tens of micrometers, such as crystals, droplets, or aerosol particles, are necessary. Thus, the concentration of each substance has to exceed the saturation level to condense and form dense clouds and precipitation. Water, as drops, snowflakes, or hail, is an excellent substance for electrification but probably not the only possible one. In reference to (2) above, there is a variety of possible processes such as ion capture, friction, riming, phase changes, mixed-phase interactions, thermoelectric effects, collision with polarized particles (inductive process), etc. The specific properties of each atmosphere (see Chapter 1/3) would determine which of these is the most important process. Cloud particles exposed to an ambient electric field are polarized, and the rebounding of polarized particles falling with different velocities may result in charge transfer. This inductive process tends to augment the ambient field. Initially the inductive process may not be the prime process, but as the electric field is enhanced it seems to be dominant for charging a cloud to high potentials (Levin et al., 1983; Tzur and Levin, 1981). The induction mechanism is more effective for larger values of the polarizability, or the dielectric constant e, of the cloud particles. Table 9.1.1 gives static e values of some liquids that are found as cloud-forming substances in planetary atmospheres. In reference to (3) above, the electrified particles must be sorted by the sign of their charge, separated to distances of the order of kilometers (on Earth) and accumulated (to tens of coulombs) until the electric field exceeds the dielectric strength. There must be a dissimilarity in mass (or size) or mobility depending on the polarity of the particles. Updrafts together with gravity are capable of performing such large-scale charge separation.

205

Lightning within Planetary Atmospheres Table 9.1.1 Substance E

Dielectric constants of some doud-forming substances H ,S04

H2Q

NH,

SO,

H,S

CH,

CO ,

110

SO

25

17

9

1.7

1.6

To summarize, for the generation of lightning, convective motions within dense clouds of material appropriate for electrification are required. Lightning can be expected if these conditions are fulfilled. In Section 2, brief comments on optical and radio frequency observations are given, and in Section 3, the present information on possible lightning on the other planets of the solar system is surveyed including brief descriptions of planetary atmospheric properties relevant to lightning generation. For Earth lightning see the relevant chapters in this volume or Uman (1987). 2, 2.1.

REMOTE LIGHTNING SEARCH

OPTICAL EMISSIONS

The discharge current heats the channel to some thousand degrees Kelvin. Because of this very high temperature, the molecules are dissociated and the atoms are ionized (or in highly excited states). The spectra of lightning discharges show continuum radiation and line emissions de­ pending on the composition of the atmosphere. Only about 0.1 to 1% of the energy dissipated by lightning is emitted in the visual (Krider et al., 1968; Uman, 1987; Borucky and McKay, 1987). A terrestrial cloud-to-ground dischaige (return stroke) typically produces a lightning flash of some hundred microseconds in duration, while intracloud discharges (K changes) produce less intense but longer optica] emissions. Borucki et al. (1983) conducted laboratory discharge exper­ iments to simulate Venus lightning and found strong radiation in the 600- to 900-nm band with bright lines of oxygen and carbon (spectra of terrestrial lightning contain bright lines of oxygen and nitrogen). Optical lightning searches from spacecraft have to consider the scattering and absorption of the clouds, which depends on mass loading, particle size, and phase. Thomason and Krider (1982) have modeled the cloud effects and found that the high reflectivity of even thin cloud layers will prevent almost all the light produced behind the clouds from reaching the detector. However, since the total absorption tends to be small, the time-integrated fluxes from light sources in the optical center of the cloud are almost the same as if the cloud were not there. With appropriate instrumentation, optical lightning measurements can provide information on the dissipated energy if the cloud influence can be well estimated. Earth-based optical searches for lightning on other planets has, so far, been negative. On the outer planets, the bright sunlit disks are seen and there is no chance to detect lightning. A faint glow is occasionally observed, termed ashen light, on the nightside of Venus. This was originally attributed to lightning; however, this was ruled out by more recent observations: Slanger and Black (1978) found that this glow is molecular emission from about an 80-km altitude. Important information on extraterrestrial lightning, especially on the energetics, is available from optical observations from space probes. 2.2.

RADIO WAVE EMISSIONS

The high-current dischaige radiates electromagnetic waves corresponding to the time derivative of the discharge current or the second time derivative of the electric dipole moment. Typical average radio frequency (RF) spectra of terrestrial lightning peak at about 10 kHz and decay as /-*• Any planetary body with a dense atmosphere, where lightning could be expected, also has an ionosphere with an electron density peak above the potential lightning source region. Electromagnetic waves cannot propagate in a plasma with frequencies below the plasma fre­ quency fp = 9000 • y/rif (n, is the electron density per cubic centimeter). Thus radio waves.

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excited by lightning, cannot cross the ionosphere at frequencies /below the maximum plasma frequency fp n , corresponding to the maximum electron density nrnw ina horizontally stratified ionosphere. If the ionosphere is highly inhomogeneous, with blobs, holes, and patches, RF waves may penetrate by partial reflection and scattering (Singh and Russell, 1986). In case of a planetary magnetic field there is a wave mode, the whistler mode, which can propagate at frequencies below fp. The refractive index n is then given by:

where f c = 28 • B is the cyclotron frequency (B is the magnetic field in nT). As the wave group 2c velocity is \)gr = — (c is the velocity of light) and n can be large, a signal is dispersed along its propagation path. ”The Eckersley law 1( 1

D — t„ \ I describes the frequency-dependent time

= —j

1 f

delay. The dispersion parameter D depends on the propagation path with D = — J y

fp

hi

a frequency-time display, the whistler trace appears as a unique curve of descending frequency with time. For more details see Chapter H/7.

3.

LIGHTNING ON OTHER PLANETS

The inner planets of the solar system—Mercury, Venus, Earth, and Mars—are often referred to as the Terrestrial Planets. They all have well-defined surfaces but their atmospheres are very different in density, composition, structure, and dynamics. Among the outer planets, Jupiter, Saturn, Uranus, and Neptune are often referred to as the Giant Planets. These planets have no defined surfaces, but they do have similarities in the structure and composition of their atmospheres. Dense cloud decks define their visual disks. Toward the planetary center, the atmosphere (mainly hydrogen) increases in temperature and pressure, and deep down (thousands of kilometers) the hydrogen becomes liquid. Pluto, the outermost planet, is a cold body and is assumed to have different characteristics. In the following, the planetary atmospheric conditions are outlined briefly insofar as they appear to be relevant to lightning generation. For more details see Atreya et al. (1989). The various indications of the existence of lightning are presented and discussed. Venus and the Giant Planets are all candidates for possible lightning activity. On Venus, the cloud deck with a width of ca. 15 to 20 km is located about 50 km above the surface. This large distance together with the dense lower atmosphere makes cloud-to-ground discharges unlikely. The Giant Planets do not have distinct surfaces. Thus, if there is lightning in the other planetary atmospheres, it is of the intracloud or cloud-to-cloud type. In 1978, the Venera 11 and 12 probes delivered the first indications of lightning on other planets. This interpretation of RF bursts started a lively discussion in this field of research. Other missions (Venera, Pioneer Venus, and Voyagers 1 and 2) gathered more information and evidence of the existence of planetary lightning. The Galileo spacecraft is on its way to Jupiter. A descent probe will enter the Jovian atmosphere in December 1995, and this carries a lightning and radio emission detector (Lanzerotti et al., 1992). 3.1.

MERCURY

Statistics include Ru = 2439 km, rotation period = 176 d, revolution period = 87.97 d (1 Mercury day lasts 2 Mercury years = 176 Earth days), surface gravity = 3.7 m s-2, and magnetic field (equator) = 350 to 400 nT.

Lightning within Planetary Atmospheres

207

WIND SPEED U [ms'1] 0

20

40

60

80

100

-1----- 1------ 1____ 1____I____

0

1 -2

200

*

-

1

400

1

*

120

600

160

160

800

1------ 1------ 1------ *------1 0 1 2

LOG PRESSURE P [bar]

Figure 9.3.1

Sketch of Venus atmospheric properties.

The U.S. spacecraft Mariner 10 encountered Mercury, the innermost planet, twice in 1974 and once in 1975 (Vilas et al., 1988). The planet exhibits a heavily cratered surface, similar to that of the moon, with no evidence of recent volcanic activity. Mercury has a very thin atmosphere of hydrogen and helium with a surface pressure of about 10"12 bar (1 bar = 105 Pa). Within such an atmosphere the particle collisions are negligible and there are no chemical reactions, no winds, no weather, and therefore no lightning. 3.2. VENUS Statistics include Rv = 6050 km, rotation period (retrograde) = 243 d, revolution period = 224.7 d (day-night cycle = 116.75 d), magnetic field (crustal remanence) — 3 to 10 nT, and surface gravity = 8.87 m s-2. 3.2.1. Venus Atmosphere Venus is about the size of Earth and has a similar surface structure with mountains, highlands, and valleys, except that there is no surface water. The dense atmosphere consists predominantly of carbon dioxide. The surface temperature is about 750 K, and the surface pressure of about 90 bar is almost 100 times that of Earth. Since 1962, many spacecraft flybys, orbiters, and about 20 descent probes, including 2 bal­ loons, made the Venus atmosphere the most extensively investigated extraterrestrial atmosphere. For a detailed review, see the book Venus edited by Hunten et al. (1983) and The Venus Inter­ national Reference Atmosphere (VIRA) edited by Kliore et al. (1985). Figure 9.3.1 sketches some properties of the Venus atmosphere derived from Venera and Pioneer Venus measurements. There is a dense global cloud cover between about 45 and 70 km

Handbook o f Atm ospheric Electrodynam ics, Volume /

208 Table 9.3.1

Venus doud properties

Clouds

Altitude (km)

Temperature 3 pm, uncertain as separate mode, sulfur-coated sulfuric acid (?), solid (?).

From Ragen et «L, 1985; Esposito etal., 1983; Knollenberg and Hunten. 1979._____________________________

above the surface. Three cloud layers can be distinguished: upper, middle, and lower. Drops of sulfuric acid have been identified as cloud particles. Three modes of particle size have been found (Knollenberg and Hunten, 1979). Pressure and temperature at the cloud altitude are comparable with Earth conditions. The lapse rate was found to be subadiabatic between 30 and SO km; thus the atmosphere is statically stable against overturning in this region. Above and below, especially in the middle cloud layer, there may be a tendency to instability. There are haze layers above and below the cloud system. These conditions were found to be very similar at the different descent locations in latitude and longitude and time. Zonal winds reach their maximum at the cloud top with westward wind speeds of more than 120 m s_1. At the surface, the wind speeds are low, too low to raise dust and sand. From the orographic features it is evident that there was volcanic activity in the past. The measured variation of SO2 was attributed to still-active volcanoes; how­ ever, no ejected material was found, and the lower atmosphere was clear when the space probes descended. Thus volcanic eruptions should be rare. The cloud layers seem to be stable. The two Vega balloons floated more than 45 h from midnight to the morning sector and found only low vertical velocities mainly around 1 m s~' (maximum 3 m s -1 downward). The light sensors measured fluctuations in the backscattered light, indicating cloud inhomogeneities, but found no breaks in the cloud deck. Levin et al. (1983) expect a larger probability of updrafts downwind of the subsolar point but this region has not yet been probed. In general, the atmosphere seems to be stable against overturning, without major convection. The clouds consist of very small particles and have low mass loading (Table 9.3.1). They appear to be more like stratiform than cumuliform clouds. The potential for drizzle and mist is there, but heavy precipitation is extremely unlikely (Knollenberg and Hunten, 1979). Global circulation models assume decoupled convection cells, one within the cloud region and another above the surface. The global cloud circulation does not seem to be affected by topo­ graphic features, but it is related to the subsolar point Although the atmosphere of Venus seems to be unfavorable for efficient electrification, it was the first planetary atmosphere where strong evidence of the existence of lightning was discovered. Venus has no intrinsic magnetic field and therefore its atmosphere and ionosphere are directly exposed to the solar wind. The dayside ionosphere is controlled by the solar zenith angle with a maximum electron density of about 7 x 105 cm-3 at about 140 km altitude (Bauer et al„ 1985). The discovery of a nightside ionosphere was a surprise in view of the long Venusian night of ~58 d. This ionosphere is assumed to be formed by the ionizing flux of electrons of several tens

Lightning within Planetary Atmospheres

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of electron volts and by transport from the dayside. The nightside ionosphere, with a peak electron density of up to 2 x 104cm- 3 around 140-km altitude, is extremely structured patchy and variable. The ionosphere is magnetized by the interplanetary magnetic field (IMF) as well as by currents driven in the lower ionosphere depending on the solar wind dynamics. The magnetic field strength may reach the order of 100 nT and is highly variable. 3.2.2. Venus Lightning Search The first indications of lightning on Venus were the radio frequency pulses received by the Soviet Venera 11 and 12 descent probes in December 1978 (Ksanfomality, 1980). Subsequendy, optical pulses detected by Venera 9 were interpreted as being due to lightning (Krasnopolsky, 1983a). Bomcki et al. (1981 and 1991) evaluated the U.S. Pioneer Venus star sensor data but found no positive evidence of lightning-generated signals. The Vega 1 and 2 balloons equipped with optical detectors also failed to find light pulses. Impulsive low frequency signals, measured by the Pioneer Venus Orbiter Plasma Wave Detector (OEFD), were interpreted as lightning whistlers (Taylor et al., 1979). Subsequent evaluation and discussion of these data led to considerable knowledge of possible lightning on Venus. The most recent positive indication came from the Galileo flyby in 1990. A review of Venus lightning evidence has been recendy given by Russell (1991). 3.2.2.1. Optical Search The middle clouds are the most probable source region of lightning at some 50 km above the surface; because of the high dielectric strength of the dense CO2 atmosphere, it is unlikely that cloud-to-ground discharges occur. The influence of the clouds on the transmission of light pro­ duced by lightning has been modeled by Williams et al. (1982) and by Williams and Thomason (1983) using a Monte Carlo program by Thomason and Krider (1982). It was found that the fraction of visible light that escapes into space is 0.36, 0.41, and 0.64 for flashes in the lower, middle, and upper clouds, respectively. The fraction is less for blue photons. Bomcki et al. (1983) showed with laboratory simulations that Venus lightning can be expected to radiate strongly in the 600- to 900-nm band. Venera 9 Spectrometer. Krasnopolsky (1980, 1983a, 1983b) reported irregular optical pulses observed with the Venera 9 scanning spectrometer for a period of 70 s. The pulse rate was ~ 100 s_l with a characteristic duration of 0.25 s. He argues that these pulses are real and attributes them to lightning. (No pulses were recorded when the instrument was pointing into space.) The spectrometer searched an area of 3.5 x 107 km2 on the nightside of Venus in the latitude range ±32°, and the area showing optical pulses was 5 x 104 km2. This gives an occurrence rate of 2 x 10' 3 km"2 s_l or about 0.1 km-2 min-1, which is comparable to localized Earth thunder­ storms. Because the spectrum was rather flat, it was concluded that the source was within the clouds; otherwise the spectrum should have fallen off at wavelengths below 5000 A because of absorption if the source were below the clouds. The spectral power in the visible was 2.6 x 104 W A-1. Thus, a received burst is indicative of about 3 x 107 J of optical energy or, with an efficiency factor of 3 x 10“3, of about 1010 J of total dissipated energy of the source (typical values for the Earth are 108to 109J). The spectrometer did not resolve individual strokes; however, from the instrument characteristics, it was concluded that strokes are spaced by 20 to 30 msec and that a flash consists of 20 to 30 strokes. If lightning is confined to latitudes between ±32°, the global rate would be 45 km-2 y ea r 1 or 15 X 10“7 km 2 s_l. Note that these conclusions are based on a single period of activity; also, Williams et al. (1983) find it difficult to understand the deduced high burst rate and energy dissipation due to lightning, in view of the Venus meteorology. Pioneer Venus Star Sensor. The Pioneer Venus Orbiter navigation star sensor has been used by Borucki et al. (1981) to search for lightning. The star sensor was not designed to search for lightning, and the Ashen light (airglow) saturates the instrument when it views the dark side of Venus directly. Therefore, in the lightning search mode, the star sensor was operated so that only light from the dark side that is scattered by the optical system reaches the detector element. The

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instrument has the potential to measure the frequency and amplitude of the optical radiation as well as the spatial distribution of Earthlike lightning. Comparisons of received pulses from the Venus nightside with those received when the star sensor pointed into deep space (false alarm rate due to energetic particle impacts) showed no statistical difference, however. These data, from orbits 300 through 345, set an upper limit of 30 flashes km-2 year*1 assuming that the amplitude distribution of the optical pulses and the attenuation by the clouds are not substantially different from those on Earth. Thus, if there is lightning activity on Venus, it cannot be much greater than on Earth and therefore has no significant importance in atmospheric chemistry. Borucki et al. (1991) repeated this investigation in 1988 and 1990. Because the periapsis altitude had increased, the star sensor viewed a much larger area on Venus than during the earlier search, but again no optical evidence for lightning activity on the nightside of Venus was found. A reexamination of the sensor characteristics in this specific mode, a more reliable consideration of the cloud influence, and the larger database led to a reduction of the earlier upper limit of lightning activity by a factor of 10 to about 3 flashes km*2 year-1 or 1 x 10*7 flashes km*2 s- ' (less than the global flash rate on Earth) and a total energy dissipation rate of 2 x 10~5 W m~2. Vega I, 2 Balloons. On June 11 and 15, 1985, respectively, the Vega 1 and 2 spacecraft each released a balloon into the Venus atmosphere (Sagdeev et al., 1986 a, 1986b). Both balloons were inserted at midnight at 7°N and 7°S of the equator. They drifted westward into the sunlit hemi­ sphere at an altitude of about 53 km, which is in the middle cloud region. Data were received for about 46 h. The gondolas carried instruments to measure the ambient illumination and to detect transient light events (lightning). No reliable lightning flashes were detected and no obvious breaks in the cloud deck were observed. Vertical winds were measured to be mainly of the order of 1 m s_l, but both balloons encountered downdrafts of maximum 3 m s*1. 3.2.2.2. Radio Frequency Wave Search The Venus dayside ionosphere can be described to a first order by a Chapman layer controlled by the solar zenith angle (VIRA Model Ionosphere by Bauer et al., 1985). The electron density profile peaks at ~140-km altitude with a number density of about 7 x 10s cm-3. The nightside ionosphere is characterized by its high variability; it appears to be patchy, it may almost disappear, and it may have structured layers around 150-km altitude with peak electron densities up to 2 x 104cm-3. The magnetic field depends on the solar wind dynamics and the IMF; it is also highly variable in field strength and direction, especially at the nightside. Thus, lightning-generated RF signals with frequencies below a few megahertz are below the ionosphere at daytime but may escape into space at nighttime. Very low frequencies (a few hundred hertz) may propagate in the whistler mode (see Section 2.2 and Chapters D/7 and D/13). Venera 11, 12, 13, and 14. The Soviet Venera 11, 12, 13, and 14 descent probes carried the groza instruments (groza meaning thunderstorm) to detect and analyze RF noise in the atmosphere of Venus below 60 km (Ksanfomaliti, 1980; Ksanfomaliti et al., 1983). Each instrument consisted of a loop antenna to respond to the magnetic component of RF signals, a receiver with narrowband channels centered at 10, 18, 36, and 80 kHz, and a wideband channel. The Venera 11 and 12 instruments detected impulsive low-frequency signals with varying intensity during the 1-h de­ scents on December 21 and 25, 1979. The profiles of the registered RF noise were very different for the two probes, which landed in the same area but 4 d apart Venera 11 observed maximum intensity between 30- and 15-km altitudes with measured field strengths up to 100 pV m 1 Hz_l/2 in the 10-kHz channel, some variations below, and a decay to zero at the surface. Between 13 and 10 km the noise bursts were grouped in clusters or modulated with a period of 50 s. Figure 9.3.2 represents signals received by the groza instrument on Venera 11 between 13 and 9 km altitude. During the Venera 12 descent the overall activity was much less, with some activity in the 50- to 30-km height interval and a maximum below 9 km, again decreasing toward the surface. Venera 12, however, detected a burst of about 150 pulses in an 8-s measuring interval after landing. These low-frequency RF pulse bursts have characteristics of sferics and were attributed

Lightning within Planetary Atmospheres

211

E

>

150-i

O _! ut

-1-------1-------1-------1-------r

0606 0607 0608 0609 0610 0611 0 6 1 2 ' EARTH RECEIVED TW E

figure 9.3.2 The field intensity in the altitude interval of 9 to 13 km for Venera 11 had the appearance of periodic pulse packets. The sequence is abruptly interrupted near 6:11. The decrease in modulation with frequency rise is related to distortions of the beam pattern at 36 and 80 kHz (Ksanfomaliti et al., 1983). (Reprinted from Hunten, D.M. et al., Eds. (1984). Venus (Space Science Series). University of Arizona Press, Tucson, AZ. Copyright 1984. With permission.)

to lightning. It is possible, however, that some or all of the signals observed were due to electro­ static discharging of the probes (triboelectric charging of the spacecrafts with the ambient). There­ fore, the Venera 13 and 14 probes carries additional devices to monitor electrostatic discharges. Venera 13 and 14 entered the Venus atmosphere on March 1 and 5, 1982 and again measured different noise profiles with activity similar to that found by Venera 12. No discharge currents from the probes were detected. The average impulse rate was about 30 s-1 but reached as high as 55 s_l; the spectral index describing the frequency dependence varying as f was about - 2 for Venera 11 and - 1 for Venera 12. Ksanfomaliti et al. (1983) explain these observations as signals from localized and distant lightning with both short- and long-term temporal variations. The intensity modulation observed by Venera 11 is regarded as an effect of spacecraft and antenna rotation. With this hypothesis they estimate the angular diameter of the source to be about 5°. Applying the empirical AustinCohen formula (Austin, 1926) they derive distances of 700 to 1000 km and, for another period, 1250 to 1500 km for a storm region of about 120 to 150 km in extent. With these estimates Ksanfomaliti et al. (1983) find a flash density of 1.5 x 10' 3 km-2 s~1. Obviously, these deductions can only give an estimate because neither the spectrum at the source nor the propagation path is known. Pioneer Venus Orbiter. The Pioneer Venus Orbiter carried a plasma wave instrument, the orbiter electric field detector (OEFD). The instrument uses an electric antenna and monitors the

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wave power in four narrow-ftequency bands centered at 100 and 730 Hz, and 3.4 and 30 kHz. Taylor et al. (1979) and Scarf et al. (1980) reported the detection of impulsive signals in the 100Hz channel near periapsis at nighttime. These bursts were seen when the magnetic field was strong enough for the gyroftequency ft to exceed the lower frequency limit of the OEFD (fs = 28 x B > 100 Hz). Furthermore, the radial orientation of the local magnetic field at the moment of detection confirmed the possibility of whistler mode propagation from a source in the atmo­ sphere of Venus. The evaluation of 1185 orbits (Scarf and Russell, 1983) resulted in the detection of 567 individual events. Tracing the signals back from the Orbiter along the magnetic field led to a clustering in the midlatitude highlands, especially in Beta Regio and Atla Regio, which are assumed to be of volcanic origin (Masursky et al., 1980). The OEFD is only sensitive enough on the nightside when the solar panel noise and antenna interference are low. The attribution of these signals to lightning was based on: (1) the signals are intense and highly impulsive; (2) they are detected in the 100-Hz channel only, and (3) the magnetic field configuration allowed whistler wave propagation from a source below. Figure 9.3.3 illustrates the received signals together with plasma density and electric field strength. Taylor et al. (1985, 1987) and Taylor and Cloutier (1987,1992) questioned this interpretation and attributed the detected signals to plasma instabilities, locally generated in the ionosphere (ion acoustic waves or current-driven plasma instabilities). They found that many of the pulses coincide with ion density depletions (troughs), occurrence of superthermal ions, and magnetic field gra­ dients. Taylor et al. (1987) also argued against the clustering in areas of supposedly volcanic origin and showed that the spatial distribution reflects the observational coverage of the surface of the planet These controversal interpretations started a lively ongoing discussion but also ini­ tiated further extended data analyses. The later analyses also included impulsive signals at the higher frequencies, if these exceeded certain thresholds, as it is believed that waves with f > f g may well leak through the inhomogeneous and patchy nighttime ionosphere (Singh and Russell, 1986). Because of the large attenuation in the ionosphere, the high-frequency signals are believed to be generated relatively close and thus allow good estimates of the source location, whereas the 100-Hz whistler waves may have traveled over longer distances. The correlation of the occurrence rates of bursts at 0.73, 5.4, and 30 kHz with local time (LT) shows a well-defined maximum around 21 LT (Russell et al., 1988a, 1988c, 1989; Russell and Scarf, 1990). The actual maximum of pulse generation may be earlier (for terrestrial lightning there is a maximum of occurrence around 16 LT), and the observed maximum is a product of the time dependences of occurrence and ionospheric attenuation. A correlation with topographic features may also exist However, a connection with volcanic activity is not really strong. A study of the polarization of the 100-Hz pulses showed that the wave electric field is polarized perpendicular to the ambient magnetic field (Scarf and Russell, 1988; Strangeway, 1991; Russell and Strangeway, 1992). Destabilized plasma waves would be more likely to have electric polar­ ization parallel to the ambient magnetic field. Such plasma instabilities (ion acoustic waves or current-driven plasma instabilities) propagate with low-phase velocity, and therefore the signal would also be Doppler-shifted into higher frequency bands. Because this is not observed. Scarf and Russell (1988) conclude that the wave-phase velocity is high. The Doppler-shifted frequency i s / = / x (1 + o (0rMer) x cos fl/Ujph**)). This velocity ratio can easily be 10 for plasma waves but is < 0.1 for electromagnetic waves. The dependence of the occurrence rate vs. altitude below 400 km exhibits a significant dif­ ference between the 100-Hz bursts and those of higher frequencies ( f > fg). There is essentially no variation with altitude at 100 Hz, but the occurrence rate falls off with a scale length of about 30 km at 730 Hz and at 5.4 kHz and about 10 km at 30 kHz. Russell et al. (1988b, 1990) attribute this to the fact that whistler waves can propagate almost unattenuated (if B > 15 nT, within the whistler mode cone), whereas the higher frequency waves ( / * < / < / ) are heavily damped in

213

Lightning within Planetary Atmospheres Al (Dopptof)

nr

• V - 10, » 1. 8. 7. 5A 4.5 kHi

P IO N E E R V E N U S

I

O R B IT 66 I ORE

E L E C T R IC F IE L D . /2 V / m ( H l)

104 D E N S IT Y . IO N S / c m 3

fp* ( H i) 3

1660 1175 750 5 25

102

M A G N ET IC F IE L D . GAMMA

0 U T :2 0 :0 4 :0 0 A L T (k m ): 4 6 8

2 0 :0 6 :4 5 2 17

2 0 :0 6 :3 0 148

2 0 :1 2 :1 6 2 73

2 0 :1 5 :0 0 573

Figure 9.3.3 Electric field amplitude of the OEFD channels, the plasma density and magnetic field strength near periapsis. The Doppler shifts shown at the top of the figure, expected if these waves were electrostatic, are not observed (Scarf arid Russell, 1988). (Reprinted from Russell, C.T. (1991). Space Sci. Rev., 55,317. By permission of Kluwer Academic Publishers.)

the ionosphere. This behavior at higher frequencies is also indicative of a source below 150 km. An updated evaluation by Ho et al. (1991) results in an average burst rate of 0.14 s~‘ at 5.4 kHz during the observed maximum around 21 LT; assuming a search area of 31.400 km2 for the instrument (radius of 100 km), this yields an estimated flash rate of 140 krrr2 year-1. Thus, Scarf, Russell, and co-workers feel sure that the impulses are electromagnetic radiation, that a subset of these signals observed in the 100-Hz channel is whistler waves (Ho et al., 1991, 1992), and that atmospheric lightning is responsible for them. Strangeway (1992) investigated plasma instabilities in the Venus ionosphere and found no explanation for the detected pulse bursts. Galileo Spacecraft Flyby. During the Galileo flyby of Venus on February 10,1990, the plasma wave instrument was used to search for impulsive radio signals from lightning (Gumett et al., 1991). A total of nine events were detected in the frequency range from 100 kHz to 5.6 MHz; these events exhibit all the characteristics that one would expect from terrestrial lightning at an equivalent distance. The authors have no other acceptable interpretation than lightning.

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214 Table 9.3.2

Summary of indications of lightning on Venus Observations

Instrument Venera 11, 12, (13, 14), Grow instrument, magnetic loop: 10, 18. 36, 80 kHz and windband

Pioneer Venus Otbiter, Plasma Wave Experiment, electric field detector (OEFD): 0.1,0.73,5.4, and 30 kHz

Venera 9, spectrometer

Pioneer Venus Orbiter, star sensor

Vega 1, 2 balloons, light sensor

Galileo (Venus flyby), plasma wave instrument

3.2.3.

Inference

Bursts of RF pulses, average rate: Localized storms, one 120-150 km ~30 $"■ (maximum 55 *■'), some across and 1,200-1,500 km away, burst rate: 1.5 x 10 3 km*2 s" 1 received within 5° azimuth sector, max intensity in 10-k-Hz channel of (storm area) (Ksanfomaliti et al., 100 (lV m_l H z'w, spectral index: 1983) - 1 to —2, —150 pulses after landing RF impulses (on nightside presumably Signals originating from below the whistler waves) in 100-Hz channel, ionosphere, clustered within ±30° at higher frequencies: max around latitude (topographic relation not 21 LT with 0.14 s-' at 5.4 kHz excluded), maximum rate: 140 km ' 2 y e a r 1 or 45 x 10' 7 km' 2 s' 1 (Russell and Scarf, 1990), alternative: plasma instabilities in the ionosphere (Taylor et al„ 1987) For 70 s, optical bursts of 0.25 s Rate: 2 x 10~3 km-2 S' 1 (storm area), duration, 100 s_l in 5 x 10* km2 3 x 107 J per burst in the visible, 1010 storm area from 3.5 x 107 km2 total J total energy, source in the clouds, observed, ±32° latitude. 2.6 x 10* flash consists of 20-30 strokes, W A-' (4,500-7,500 k \ flat global rate (within ±32° latitude): up spectrum to 45 km-2 y e a r 1 (Krasnopolsky, 1983b) No positive identification of light Flash rate less than 3 lo ir 2 y e a r 1 flashes (or 10~7 km*2 s '1) of Earth-like lightning (Borucki et al., 1991) No identification of light flashes No lightning within range of sight during about 46 h of floating time (Sagdeev et al„ 1986b) ( 11.000 km) for each balloon from midnight to dayside at 7°N and 7°S 9 Impulsive events above ionospheric Lighming is the most likely source propagation cutoff in 100 kHz-5.6 (Gumett et al., 1991) MHz range___________________

Venus Lightning Summary

The atmospheric conditions on Venus, known from several descent probe measurements, do not favor strong lightning activity. The middle cloud region (around a 55-km altitude) in the afternoon may have the potential for lightning generation. There is evidence from the Venera probes and the Pioneer Venus Orbiter radio wave detector for surprisingly strong lightning activity, all of which detected RF pulse bursts that were highly variable in time as might be expected to be for weather-related sources. Although there is still no real verification of the existence of lightning on Venus, lightning is the best explanation for the observed impulsive radio wave bursts. Table 9.3.2 summarizes the findings; however, note that the derived rates depend on many assumptions. 3.3.

MARS

Statistics include RM = 3393 km, rotation period = 24.62 h, revolution period = 687 d, and surface gravity = 3.72 m s-2. 3.3.1.

Mars Atmosphere

Mars, the outermost Terrestrial Planet, has also been the subject of several space missions, such as the U.S. Mariner and Viking and the Soviet Mars missions. Further missions are in preparation (Russian Mars 96). The Viking landers VL1 and VL2 measured height profiles of atmospheric conditions during descent and continued the observations after landing.

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In Figure 9.3.4, some of the Martian atmospheric properties relative to lightning generation are presented. Hie thin atmosphere with surface pressure of 5 to 10 mbar is composed mainly of CO2 (0.95), N2 (0.027), and Ar (0.01) with O2, CO, and H20 as trace constituents. Although there seems to be plenty of water as subsurface water ice and in the polar ice caps, the atmosphere is dry with a column of about 10 pm precipitated water. There is morning haze in valleys and temporary clouds up to an altitude of 50 km. The cirrus-like upper clouds presumably consist of C 02-ice and the lower clouds of water ice (maximum mass loading ~ 2 mg mr3). Wave structures are sometimes seen in the lee of mountains. There are also diurnal and seasonal variations in pressure, temperature, and composition. The adiabatic lapse rate is ~2.5 K k m 1, whereas the Viking landers observed a prevailing subadiabalic lapse rate of ~1.6 K k n r1 down to 10 km and adiabatic below (Seiff and Kirk, 1977). Thus, the atmosphere is stable against overturning at least above 10 km. Although there is some weather (clouds, winds, dynamics, and global flows), the Martian atmosphere does not satisfy the requirements for lightning generation mentioned in the introduc­ tion. The largest volcano known, Olympus Mons with a 25-km altitude, is on Mars, but there is no evidence of recent volcanic activity. Normally the surface wind speeds of less than 20 m s' 1 are too calm to raise dust and sand. During planetary perihelion, dust storms starting locally may grow to global storms lasting for weeks (Briggs et al., 1977). Dust can be raised up to 40 km, the optical depth approaches values of 10, and wind speeds of 150 m s~’ have been observed at the fronts of such storms. It is possible that electrification occurs under such conditions (Eden and Vonnegut, 1973; Kamra, 1972). On Earth, dust storms and snowstorms are known to exhibit electric activity and may produce light­ ning-like discharges, but these are rare events. On the other hand, the dust particles are small (~ 5 pm) and the number density of the order of 5 cm-3 make the particles essentially noncolliding (Kondratyev and Hunt, 1982). Thus, it is very unlikely that efficient electrification and charge accumulation to high potentials can occur. Except for a slight possibility of electrical discharges in sandstorms, there are no thunderstorms on Mars. 3.4.

JUPITER

Statistics include Rj = 71,400 km, rotation period = 9 h 55.5 min, revolution period = 11.86 Earth years, gravity at 1-bar level = 23.5 m s~2, and magnetic field =5 G at 1 bar level (equator). 3.4.1.

Jupiter Atmosphere

After Pioneer 10 and 11 passed Jupiter on December 5, 1973 and on December 3, 1974, respec­ tively, Voyager 1 and 2 flew by on March 5, and on July 9, 1979. Figure 9.3.5 sketches the Weidenschilling and Lewis (1973) model cloud system based on solar abundance and thermal equilibrium. This model predicts an ammonia cloud near 0.5 bar, an NH4SH cloud near 3 bar, and a massive water cloud from 4 to 6 bar, this cloud probably also contains some liquid ammonia. More recent cloud models, deduced primarily from spacecraft optical measurements, contain only an optically thin (if any) NH4SH cloud. These models assume aerosol haze layers above the ammonia cloud top (Sato and Hansen, 1979; West and Tomasko, 1980; Marten etal., 1981;Orten et al., 1982). The analysis of Voyager infrared spectra led Bjoraker et al. (1986) to conclude that the water is depleted by a factor of 50 relative to solar abundance in the 2- to 6-bar level. Such a depletion of water would significantly reduce the massive lower water cloud of the Weiden­ schilling and Lewis model. This deduced water (and oxygen) depletion could be explained using Stoker’s moist convection model (1986). She constructed a model of localized updrafts to describe the Jovian equatorial plumes. Starting at the 5-bar level (water clouds), upwelling moist gas becomes saturated, framing precipitation, and the release of latent heat drives the gas further upward. At roughly the 2-bar level, overturn of the plume occurs and the dry gas descends. If

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0

100

f

I

-5

11 1 I I I l l |

200 I

f"T T T T T lt

-4

300 I

^ I I I I 11|

-3

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LOG PRESSURE P [bar] figure 9.3.4

Sketch of Mars atmospheric properties with occasionally occurring clouds and dust storms.

LOG CLOUD DENSITY [g l'1]

-3 -2 -1 ---------1___________ i___________ I JUPITER ATMOSPHERE

100 -,

SOLAR COMPOSITION: 88.6% H„ 11.2% He, 0.2% (HjO, CH* NHj, HjS, Ar, ..) OPT. DEPTH: ~10 TRANSPARENT

-100

0

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TEMPERATURE T IK] 200 300

11-1 11— i 11 i . | — >-■ -*■ ■ ■.] 0.1

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PRESSURE P [bar] figure 9 3 3 Jupiter model cloud system, adapted from Weidenschilling and Lewis (1973), together with pressure and temperature profiles.

such localized plumes occupy only 2% of the area, the dry regions would explain the infrared measurements without changing the global water abundance (Lunine and Hunten, 1987). Such a system, with strong updrafts and heavy precipitation, would be an ideal lightning generator. The plumes are seen near the equator, but they could exist also at higher latitudes. (Lightning seems

Lightning within Planetary Atmospheres

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to be concentrated at latitudes of 50° and 60°.) Another analysis of Voyager infrared data (Carlson et al., 1992) showed that the abundance of water in the Jovian atmosphere must be at least 1.5 times solar (1.38 x 10~3 relative to H2). Thus, the difficult composition problem is not yet settled, and the assumption of solar composition is a reasonable model. All models predict an upper cloud composed of ammonia with an optical depth of 5 to 10. Jupiter’s atmosphere is characterized by the alternating zonal bands. These are produced by vertical gas convection due to the heat flux from the interior in the fast rotating planet The ratio of emitted power to absorbed power (energy balance) is 1.67. The light warmer zones are due to upwellings; and the dark, colder belts are due to downwellings. The global zonal winds change with latitude in strength and in direction and appear to maximize at about 120 m s*1 between ±10°. The zonal jets disappear, together with visual banded structure, at latitudes higher than about ±50°. These mean zonal winds appear to have been remarkably stable during the four months between the two Voyager flybys (Smith et al., 1979; Limaye, 1986). Besides the “Great Red Spot” there are numerous smaller spots, eddies, wave trains, and other turbulent features, espe­ cially in the shear regions between zones and belts. There are still many questions concerning the structure, dynamics, and composition of the Jovian atmosphere. Some of these will be resolved when the Galileo descent probe, which also carries a lightning detector instrument (Lanzerotti et al., 1992), enters the atmosphere in 1995. The presence of strong convection and heavy clouds makes the Jovian atmosphere a good candidate for lightning generation. 3.4.2. Jupiter Lightning Search Sagan et al. (1967) concluded that, with strict thermodynamic equilibrium, the coloration of the Jovian clouds cannot be explained by organic molecules. High local temperatures that occur in lightning discharge channels give rise to a wide range of complex colored substances in significant amounts; Ponnamperuma (1966) and Woeller and Ponnamperuma (1969) verified experimentally the synthesis of brightly colored compounds as well as several organic molecules of biological significance. The detection of enhanced nonequilibrium amounts of acetylene led Bar-Nun (1975) to suggest that intense lightning activity could account for this observation, and he deduced a rate of Earth-like lightning as high as 5.3 x 104 km*2 year*1 (104 times larger than on Earth). The first real evidence of Jovian lightning was gained by Voyager 1 in 1978 (Cook et al., 1979), although lightning was expected to exist on Jupiter long ago. 3.4.2.1. Voyager 1, 2 Imaging Cook et al. (1979) reported the detection of 20 bright spots attributed to lightning on the nightside of Jupiter. Further evaluations by Borucki et al. (1982) yielded an optical energy per flash of (2.5 ± 1.9) x 109 J and a total dissipated energy per flash of (1.7 ± 1.3) x 10'2 J. Borucki and coauthors have used an optical efficiency factor of l .5 x 10*3, which corresponds to the efficiency factor derived by Krider et al. (1968) for terrestrial lightning and is adapted to the bandwidth of the Voyager imaging system (380 to 580 nm). These energy values are about 1000 times larger than those of terrestrial lightning. Only very rare events, the so-called superbolts, have comparable energies (Turman, 1977). A global flashing rate of 4 x 10*3 flashes km*2 year' follows from the total exposure time of 319 s and the viewed area of 109 km2. These rates are lower limits because dimmer flashes are not seen and the recorded events are probably the high energy end of the energy distribution of all flashes. Magalhaes and Borucki (1991) found a striking alignment of the bright features detected by Voyager 1 and 2 at about 5tTN, with an apparent periodicity in longitude of about 30°, but no unusual cloud feature could be associated with this activity. Only a few light features were seen at 14°N, and these could be associated with cloud disturbances in that region. The southern hemisphere high latitude was not sufficiently covered by the cameras. Assuming that the full spectrum of the emission is given by the Balmer series of hydrogen.

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WHISTLERS

£ JC

TIME (SEC) 0

5

10

15

VOYAGER-I, START TIME, DAY 64, 0912:48.53 UT (SCET) R * 5.80 R j, LT ■ 16.4 HR, ^ (1965) * 201.0*, Xm * 5.45* Figure 9.3.6 Frequency-time spectrogram from the Voyager 2 wideband receiver showing two whistlers. (Re­ printed from Dessler, A.D. (1983). Physics o f the Jovian Magnetosphere, Cambridge University Press. With permission.)

MagalhSes and Bonicki (1991) derived a total energy of 2 X 10'° — 4 x 10" J per feature. It is not clear whether this clustering of the most energetic lightning at 50°N reflects the global distribution of lightning or that of cloud opacity. Borucki and Williams (1986) concluded that the lightning occurs in the 5-bar level where Weidenschilling and Lewis (1973) predicted massive water clouds. They have modeled the lu­ minosity distribution in the bright spots seen in the Voyager images depending on various param­ eters of the cloud system and the flash location. The best agreement is obtained when the lightning is assumed to be at 5 bar. The 5-bar level is about 80 km below the visible ammonia cloud deck, and this can also be the reason that the lightning is not associated with cloud top features. The observed light intensity can be converted into real total energy (Borucki and McKay, 1987). Dividing the total energy in each image by the area and by the exposure time lead to average energy dissipation rates of 510 and 710 W km-2 for Voyager 1 and 2, respectively (absorption in the upper clouds is not included). The corresponding value for the Earth is 78 W km-2 (Borucki and Chameides, 1984). The observed bright spots are the cumulation of many flashes in extended storms rather than individual flashes. Therefore no information on discharge duration and impulse structure can be obtained. 3.4.2.2. Voyager 1 Plasma Wave Analyzer Scarf et al. (1979) reported the detection of whistlers originating from Jupiter lightning. A detailed summary has been given by Kurth et al. (1985). The whistlers can only be detected in the wideband waveform analyzer channel (40 Hz to 12 kHz) by their unique frequency-time structure. The gain of this channel is controlled by the background. When the waveform analyzer was sensitive enough, whistler signals were recorded. This happened on three occasions during closest approach, in or close to the Io plasma torus. Out of a total of 167 detected whistler signals, 90 had bandwidths large enough to derive the dispersion D. Figure 9.3.6 shows two examples of whistler traces in the frequency-time diagram. The dispersions of these whistlers are about 300 s Hz1/2. Each of the three groups (A, B, and C) had characteristic dispersions. For the largest group, B around 5.4 I?, at the inner edge of the Io toms, D was about 60 s Hz1/2. Hie earlier shorter period and smaller group A from north of the Io torus, close to the L = 6 fieldline, had D about 300 s Hzl/2, and group C, from south of the Io torus, had D about 500 s Hz,/2. Using ray tracing, Menietti and Gumett (1980) confirmed that these whistlers originate from Jupiter high latitudes (magnetic shell L = 6). Tokar et al. (1982) concluded, from the dispersion and the geometry, that the sources for the A-group whistlers are in the southern hemisphere (60°S) and for the B- and C-groups in the northern hemisphere (55° to 75°N).

Lightning within Planetary Atmospheres

219

On the average, one whistler was recorded every 8 s, but the frequency was very variable (in one 48-s frame as much as 32 whistlers were identified). The source area is difficult to estimate, and Scarf et al. (1981) derived an upper bound to the lightning flash rate of 40 flashes km-2 y ea r1. Based on terrestrial experience, they assumed that an area of 106 km2 illuminates the foot of an appropriate fieldline to the spacecraft and that one flash out of ten launches a detectable whistler. This rate refers to the active latitude bands at about 60°, as seen by the imaging, but it is uncertain as to what extent it holds for the entire globe. A representative detected whistler amplitude was E — 5 x IO-5 V m~'. Scarf et al. (1981) traced the signal back and computed a corresponding signal amplitude £b = 0.85 V m_l at a distance of 10 km from the source. Thus Voyager detected only whistlers with power levels at least 10 times greater than typical terrestrial whistlers. 3.4.2.3. to Io, the innermost of the so-called Galilean satellites, is included in this review because it is unique with respect to its volcanic activity (Smith et al., 1979). Io has a rare atmosphere, primarily SQj, with a surface pressure and temperature of 10-7 to 1 0 12 bar and about 100 K, respectively. The volcanoes are high-speed flows of SO2 gas forming umbrella-shaped plumes from a vent entering a near-vacuum environment. The material is ejected 100 km and higher and hundreds of kilo­ meters wide. The SO2 condenses and falls back as SO2 snow along ballistic trajectories. There is no evidence of turbulence within these plumes. The prerequisites of lightning generation are not satisfied. 3.4.3.

Jupiter Lightning Summary

The detection of both whistlers and luminous spots is an indication, or can even be accepted as proof, of the existence of strong lightning in the Jovian atmosphere. All deduced characteristics, however, include large uncertainties. What is the occurrence frequency distribution vs. energy? Obviously the bright spots are due to extremely energetic lightning. What is the spatial distribu­ tion? Is there a band of high lightning activity (50°N) or of high cloud transparency? Is there lightning, maybe less energetic lightning, everywhere? To estimate the source area from whistler observations is difficult. The latitude of the aligned luminous spots is within the prospective region, but how large is it and what is the efficiency for launching whistlers? The planetary radio as­ tronomy (PRA) instrument did not detect impulsive signals at frequencies above the ionospheric critical frequency of about 1 MHz attributable to electrostatic discharges, as it did for Saturn and Uranus. Both the imaging and the whistler observations are indicative of Jovian lightning being more powerful than terrestrial lightning. The lack of detection of high-frequency signals by the PRA is not a contradiction if the RF spectrum falls off at least as f~ 2. The derived rates and energies, summarized in Table 9.3.3, are uncertain by probably more than an order of magnitude. 3.5.

SATURN

Statistics include Rs = 60,000 km, rotation period = 10 h 39.4 min, revolution period = 29.5 Earth years, gravity at 1-bar level = 9.05 m s~2, and magnetic field (axis nearly aligned with rotation axis) B = 2 x 104 nT at 1-bar level (equator). 3.5.1.

Saturn Atmosphere

Pioneer 11 encountered Saturn on September 1, 1979, Voyager 1 on November 12, 1980, and Voyager 2 on August 26, 1981. A comprehensive review of the Saturn system is presented in the book Saturn, edited by Gehrels and Matthews (1984). To a first order, the Saturn atmosphere is similar in composition, structure, and dynamics to that of Jupiter. H2, He, CH4, HN3, and PH3 have been identified in solar abundance. Given NH3, and probably H20 and H2S, one can expect to find a series of condensation clouds. Figure 9.3.7

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220 Table 9.3.3

Summary of indications of lightning on (upiter

Instrument

Observations

Inference

Voyager 1 and 2, imaging

Bright spots primarily aligned at ~ 5 < m 15 x 10» J optical per feature, total exposure time: 319 s, viewed area: 1CP km2

Lightning at 5-bar level about 1,000 times more energetic than typical Earth lightning, total energy: -1 .7 x 1012 J per feature (Borucki et al.. 1982), 2 x 10'°-4 x 10" J per feature (MagaMes and Borucki, 1991), global rate: - 4 x MH flashes km-2 year*1 (lower limit), energy dissipation rate: 500-700

Voyager I. Plasma wave analyzer, wideband receiver SO Hz to 14 kHz

167 Whistlers in 2-7-kHz range between 5.4 and 6 Rj. dispersion between 45 and 500 (typically 60) s Hzl/2, detection rate: 0.12 *-2

Lightning in high latitudes ±—60“ (Toicar et aL, 1982), global rate: up to 40 km-2 y e a r1, about 10 times more energetic than typical terrestrial whistlers (Scarf et al., 1981)

Wknr2

LOG C10U0 DENSITY |gl',l •4

-3

-2

-1

0

100

200

300

400

i________i________i________i------------1

0 !----

-2

■ ‘ . . . m l---- ml------------- r * ......... I---- ■ ............I

-

1

0

1

2

LOG PRESSURE P [borl

Figure 9.3.7

Saturn model cloud system adapted from Weidenschilling and Lewis (1973).

sketches the model cloud layers of Weidenschilling and Lewis (1993), assuming solar abundance and thermochemical equilibrium. The faint coloring, however, must be a product of nonequilib­ rium reactions. Prinn et al. (1984) believe that lightning is not an important factor in the chemistry compared to ultraviolet radiation. The dense top cloud layer probably consists of ammonia-ice. Because the gravity is less than on Jupiter, the scale height is larger and the cloud system is more extended in altitude. The energy balance (ratio of emitted power to absorbed power) is 1.78.

Lightning within Planetary Atmospheres

221

There is a heat flux from the interior of about 2 W m-2, which drives convective motion between the 1- and lO^bar level (Prinn et al., 1984). On the fast rotating planet such convective flows lead to the visible banded structure. Saturn is different from Jupiter in that the visual contrast is lower and there are fewer features (spots, eddies, vortex trains, etc.). The wind speed at equatorial latitudes is much larger, however, with a maximum of about 500 m s~' eastward at 5°N (Smith et al., 1981, 1982; Ingersoll et al., 1984). Smith et al. (1982) found numerous unstable features (probably connected to upwellings) in regions where the zonal wind speed was close to zero. On the other hand, Sanchez-Lavega et al. (1991) reported the seasonal evolution of Great White Spots near the equator. Compared to Jupiter the Saturn atmosphere appears to be less turbulent, dom­ inated by the strong zonal flow, but it probably has the characteristics necessary for lightning activity. The ionospheric plasma density is deduced from radio occultation experiments during the Pioneer and Voyager flybys. There exist a few average electron density profiles with maximum electron density of some 104 cm*3 at about a 2000-km altitude (Atreya et al., 1984). 3.5.2.

Saturn Lightning Search

3.5.2.1. Voyager Im aging The detection of flashes on the nightside was impossible because of sunlight scattered from the rings (Smith et al., 1981). 3.5.2.2. Plasm a Wave A nalyzer Gumett et al. (1983) and Scarf et al. (1983) reported the detection of impulsive signals from Voyager 2 close to the ring plane, but these did not have the dispersion characteristics of whistlers generated by lightning. Similar pulses had also been observed from Voyager 1, but none were found on Jupiter. It was concluded that this noise was produced by impacts of micrometer-size particles on the spacecraft From the absence of whistlers in the kilohertz band it can be concluded that there was no Earth-like or Jupiter-like lightning at latitudes corresponding to L > about 3. 3 .5 .2 .3 . Planetary Radio A stronom y Instrum ent The Voyager 1 Planetary Radio Astronomy (PRA) instrument recorded strong, discrete, unpo­ larized, broadband bursts of radio emissions that were termed Saturn electrostatic discharges (SEDs) (Warwick et al., 1981; Zarka and Pedersen, 1983). Figure 9.3.8 illustrates SED detection. SEDs appear as vertical streaks because the receiver sweeps through the entire frequency range in a stepping mode. The signals were detected from 20 kHz up to the maximum PRA frequency of 40 MHz with a flat spectrum, presumably extending to 100 MHz. The bursts lasted 15 to 400 msec with a mean value of 55 msec and were made up of many short pulses (< 1 msec). Warwick et al. (1981) concluded that the source might not be larger than 50 km. The bursts were grouped into episodes with period of about 10 h 10 min. Each episode lasted about 7 h, during which the number of SEDs grew to a structured maximum and then fell back to the background level, which then persisted for the next 3 h. The intensity increased as the spacecraft approached Saturn, reaching maximum at closest approach and then decreasing with distance from the planet About twice as many episodes were identified during post-encounter as compared to pre-encounter. During the Voyager 2 flyby 9 months later, the SEDs were observed again with the same characteristics. However, the intensity was only about one third, and the grouping into episodes was less pronounced. No similar signals were detected from Jupiter. Only two regions in the Saturn system exhibit the SED periodicity: in the B-rings at 1.8 Rs where the Keplerian revolution period equals 10 h 10 min and in the equatorial atmosphere where the high wind speed causes superrotation. Warwick et al. (1981) and Evans et al. (1982) feel that

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222

SKR

I MHz • - ; * T '{*1

I .

.

» .,•

* * > • " » j* *•

•' .•

.1.

J*

•» .

•• i

.,» i

- a)d3x = 0 if AV does not

contain x = a, or 1 if AV does contain x = a (Jackson,1975). Then the total density of particles is just thesum over species, for example, a sum over positive and negative charge carriers as N(x, v, t) = 2 n s( x, v, t). An exact solution for the evolution of the plasma may be obtained S

by taking the time derivative of the density and using the Lorentz force equation: — > d V i(t)

— 1dt

Q % -*

-»

-♦

-»

-*

= — Em[Xj(t), t] + qsV,(t) x B-fXid), t] + g m,

(2)

where g is the local gravitational acceleration and the superscript m indicates that Emand Bmare the superposition of those microscopic fields produced self-consistently by the other particles together with the external fields. Note that Equation 2 includes all neutral fluid interactions because the fields are the microscopic fields including those responsible for momentum transfer between neutral particles. For most of plasma physics the gravitational acceleration can be neglected (however, we will need to use it later to treat the neutral gas species). Neglecting gravity the exact time evolution of the density is given by the Klimontovich equation (Klimontovich, 1967; Nicholson, 1983):

dt

^ • (vNs) + % ■f — (Em + v x Bm)Ns) = 0 Vm, /

(3)

In this equation the three-dimensional gradient operators are defined as Vx = d/dx and = d/dv. Note that in this six-dimensional phase space the configuration space coordinate x and the velocity space coordinate v are independent variables. The Klimontovich Equation 3 taken to­ gether with Maxwell’s equations (see Section 2.1) constitute an exact descriptionof the plasma. In a plasma it isnot practical to determine the exact location and velocity of eachparticle at any time t Furthermore, we need a smooth function that tells us how many particles are to be found in a small volume AxAv of phase space rather than one that has an infinite density at the location of each charge. Therefore, we introduce the distribution function f where f$(x, v, t) = the ensemble average of a large number of possible states. The distribution function f j ) t, v, t) is proportional to the probability of finding a particle with velocity between v and v + Av at within a volume Ax of x at time t We now replace the microscopic fields by the ensemble average plus some small perturbations or departures from the average, i.e., Nj(x, v, t) = f,(x^v, t) + 5Ns(x, v, t), E“(x, v,_t) = E(x, v, t) + 5E(x, v, t) and Bm(x, v, t) = B(x, v, t) + 8B(x, v, t) where B = < B m> , E = , and < 8N ,> = < 8E > = < 8B >

Quasistatic Electrom agnetic Phenomena in the Atmosphere and Ionosphere

239

= 0. Now we can write the Klimontovich Equation 3 in terms of the smooth functions and fields on the left-hand side and all the discrete effects on the right-hand side: afs(X‘ V, ~ + Vx • (vfs) + Vv • (E + v x B)fs ) = dt Vms /

ms

Vv • ((5E + v x 8B)8NS)

(4)

This is called the plasma kinetic equation or the Boltzmann equation. When the right-hand side is zero, it is called the Vlasov equation or collisionless Boltzmann equation. 2.1.

COMPLETE DESCRIPTION OF THE CONDUCTING FLUID

Schematically we will write the plasma kinetic Equation 4 as:

at

+

+ *

•(? « + ?.

dt

(5)

Here the right-hand side is composed of two terms representing the change in the distribution function with time due to collisional effects and the change due to sources and sinks (such as the case for ionization or recombination). Note that Equation 5 includes the physics of neutral species where the charge qs = 0 and therefore the macroscopic E and B fields have no influence (but the collision term on the right-hand side is important). The full set of equations to describe the plasma and neutral fluid is then composed of this plasma kinetic Equation 4 or 3 and Maxwell’s equations: V • E(x, t) = £ Eo

(6)

V • B(x, t) = 0

(7)

_» dB V x E(x, 0 = —— -»

(8)

at

-» dE V x B(x, t) = poJ + MoEo— at

(9)

with p(x, t) = < p m> =

v, t)dv = charge density

( 10)

S

J(x, t)

= ^ q ,< n > s/v f s(x, v, t)dv = current density

(11)

S

ns(x, t) = < n > J ‘f5(x, v, t)dv = number density of species s

( 12)

where < n > , = Nso/V the total number of particles of species s in volume V. This sets the normalization of f$. 2.2.

COLLISION-DOMINATED PLASMAS

For many problems in space plasma physics the Vlasov equation (Equation 5 with the right-hand side = 0) is a useful description of the collisionless environment above about 250-km altitude.

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240

Below this altitude collisions become increasingly important as the neutral density increases. Nevertheless, the equations of motion are still simplified because collisions between the electrons and ions, the two primary charge carriers, are generally elastic because of the vast difference in mass. In such a case the equations for ions and electrons can be decoupled because there is relatively little momentum exchange between the species. This cannot be done in the atmosphere below about 70 km where the dominant charge carriers are positive and negative ions. The attachment coefficient for free electrons on neutral molecules is high enough that free electrons are relatively few below 60 km. Thus, below a 250-km altitude where collisions become increas­ ingly important as one descends in altitude, the description of the plasma becomes more com­ plicated in many ways. The standard approach to determining the form of the collision term of the plasma kinetic Equation 5 — is given by the Krook model (cf. Krall and Trivelpiece, 1973). The collision term dt c for each species is exactly equal to the change in the distribution function divided by the interaction time t( v) of the collision and can be approximated by: fo ~ f(v, v, t) d t |r

f0 - f(x, v, t)

t(v)




Here the velocity-dependent interaction time t(v) is replaced with a constant average collision time


=~ ~

< v > the collision frequency. There is a separate equation like Equation

13 for each species. Note that, in this theory, the largest collision frequency or shortest collision time is used. For instance, for a high neutral density, weakly ionized plasma, the collision fre­ quency between ions and neutrals Vj„ will be the dominant collision frequency. Thus, neglecting the source terms the plasma kinetic Equation S becomes:

m + V ,. ( % E + ? X

+ V. ■ dt

g )f,) =

\tlls

J

« * • * '> - f-

(14)

Ts

where t , = 1/. This equation indicates that the distribution tends to relax toward an equi­ librium value f„ due to collisions. Also note that this model eventually brings the distribution to rest and thus requires the momentum of species s to be absorbed by another species to conserve momentum. One can use the Krook model (Equation 13) to determine the electrical conductivity of a weakly ionized plasma such as the lower atmosphere (following Krall and Trivelpiece, 1973). For example, beginning with a Maxwellian distribution for negative charge carriers (such as negative ions or electrons e):

*eo

\2jtkTe/

g-nvtokT,

(15)

we apply a weak electric field E = EjZ so the distribution function becomes perturbed from the Maxwellian by a small amount fe = f^, + fei where f«, > f*i. We then use the Krook model to • dfl write — = -Vne(fe - feo) = -v„efei where v,* = 1 / t c is the collision frequency of negative dt charge carriers with neutrals. We assume that we have a spatially homogenous plasma so that

Q uasistatic Electromagnetic Phenomena in th e A tm osphere a n d Ionosphere

241

= /fdv = 1. Applying this to the plasma kinetic Equation 5 in the steady state with

sources balancing the sinks and neglecting second-order terms involving Ej and fd, we have: -eEzdfeo = -V„efel m* d \z

(16)

so that the total distribution function is: fc = feo + —

^

IHeVne dv2

(17)

Now from Equation 11 for the total conduction current density we have: h = - e n j 1Vjfjdv = —— L ne/v z^ 2dv tTWVne dV2

(18)

This can be integrated by parts (see Krall and Trivelpiece, 1973), and using the normalization that Jf«,dv = 1 we have: J, - ^

(19)

If we assume a linear relationship between current density Jz and electric held Ej as is the case for Ohm’s law, we have that the conductivity o for a single species of charge carrier, in this case negative charge carriers or electrons, is given by: n*e2 oe = - S meV*

(20)

This isalso referred to as the Spitzer conductivity in a resistive medium under the influence of a weakelectric held. The total conductivity is the sum over species of theconductivity for each species, which can be written in terms of the mobility Kj = qs/nvVns as o =

2

^

s n> sVns

2.3.

= 2 n5q5K, s

MAGNETIC FIELD EFFECTS ON CONDUCTIVITY

Moving up to higher altitudes such as the lower ionosphere, we must add the effects of a magnetic held, which we take here in the 2 direction, and then proceed from the plasma kinetic Equation 5 as we did to derive Equation 19: J = XihcjsVs = ^ - ^ - ( E + v, x B) s

(2 1 )

s ^ s^ n s

— ♦ For each species we have an equation linking the velocity and the fields asm^v^Vj= q^E + vs X B). If we combine the terms with the velocity on the left-hand side, we have a vector equation for the velocity v: Vsm^ - qsv5 x B = qsE

(22)

Then for each species we can write the contribution to the current density as: Js = nsqsvs = 8 • E

(23)

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242

From Equation 22 we can write out three equations in three unknowns (v„, vy, v*) and solve for the components of the species conductivity tensor 8S so that Ohm’s law becomes:

T=

£ a s. g

(24)

Evaluating individual tensor components using Equations 22 to 24, the conductivity tensor for the whole plasma is then:

o = 2 j Os =

0

Op

Oh

- o H

Op

0

0

0

o„

(25)

where we use the gyrofrequency w* = q,|B |/m, in the definitions for the Pederson conductivity Op and the Hall conductivity o Has:

Op

iwq^vn

(26)

- s

and

and the (2 2] component of o is just the Spitzer term: is satisfied £2 = the local conductivity scale height at y = hi.

(

)

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286

The transition altitude typically occurs at 45 to 50 km, in the lower D-region. At altitudes y » hi, the wave vector is nearly vertical, and because of the condition Oi » e0w, the wavelength is very much shorter than within the cavity at altitudes y < h \. The altitude hi > h\ is where the local scale height approximately equals the inverse wave number of the mode, at y = 75 to 90 km. Both hi and h2 depend logarithmically on frequency in the two-scale height model. Most of the Joule dissipation of the modes occurs within a few scale heights above and below the char­ acteristic altitudes h\ and h2. Using the two-scale-height model it can be shown (Sentman, 1990a) that the complex eigenfrequencies of the cavity are approximately:

Mil

+

—i—u - i- L ii

10 -3

i o ’2

i____i

i m ill

io '1

Relative Values

10

10

Figure 11.5.4 Average field amplitudes and foule dissipation profiles of Schumann resonances for an exponential conductivity profile. Here, the solid curves show the amplitudes of the radial electric component E„ the transverse electric component £,, and the azimuthal component of the magnetic field B, averaged over all angular distances from a source, as a function of height. Also shown are the corresponding Joule dissipation profiles for the radial and tangential electric components, and their sum. The total dissipation profile exhibits two relative maximums at heights corresponding to A, and A2, respectively. Most of the dissipation in the system occurs within a few local conductivity scale heights about A, and A2.

290

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has focused attention on quantitative issues related to the interpretation of the resonances as unique signatures of global lightning. While a general theoretical understanding of the principal features of the Schumann resonances has been achieved (e.g., Wait, 1972; Galejs, 1972; Bezrodny et al., 1977; Bliokh et al., 1980a), additional observations and theoretical work are needed in several key areas to establish the strength of the thunderstorm-resonance link, and the attendant errors in such a description. Ongoing work in this direction is discussed in the next three sections. 6.1.

EFFECTS OF IONOSPHERIC HEIGHT VARIATIONS

First-order perturbation techniques using only the TMq normal modes of spherically symmetrical cavity as zeroth-order basis functions are not able to model lateral height variations in the cavity, such as the day-night asymmetry. Sentman and Fraser (1991) partially compensated for the effects of the local time variation in the ionospheric height by using an energy argument that applies to the spectrum when integrated in frequency across all the modes. However, interpretations of the data involving comparison of intensities between different modes require a more detailed descrip­ tion than is provided using integrated intensities. It is therefore desirable to obtain normal mode solutions for each mode separately for the case of an ionosphere possessing a lateral height variation. 6.2.

EFFECTS ON THE EIGENFREQUENCIES FROM TRANSIENT PERTURBATIONS TO THE IONOSPHERE

Transient, large-scale ionization perturbations occur in the upper D-region and lower E-region ionosphere during and after major solar flares. These effects occur from solar cosmic rays and X-rays, and energetic particles, principally relativistic electrons and energetic protons, precipitating from the magnetosphere at mid- to high latitudes. Major disruptions of communications systems by the effects of such events on the ionosphere suggest that large-scale distortions in the upper boundary of the earth ionosphere cavity may also produce corresponding effects on Schumann resonances. An assessment is needed, both observationally and theoretically, of the effect of such ionospheric perturbations on the resonances. 6.3.

CONTRIBUTION FROM EXCITATION SOURCES OTHER THAN CLOUD-TO-GROUND LIGHTNING

A third area in need of improved theoretical description, as well as observations, is in assessing the importance of ELF excitation of the cavity by sources other than cloud-to-ground lightning. Such sources might include: (1) the vertical current component of intracloud and intercloud dis­ charges—a partitioning of the effects on the Schumann resonance spectrum between these dis­ charges on the one hand, and from cloud-to-ground discharges on the other hand, is needed; (2) a fluctuating auroral electrojet with total current ~1 MA that flows horizontally within the upper boundary of the cavity at altitudes of approximately 100 km and that may be modulated at ELF by magnetospheric Alfv6n waves (Abbas, 1968); (3) ELF whistlers, which extend downward in frequency from —200 to at least 60 Hz, and possibly into the Schumann band (Heacock, 1974; Sentman and Ehring, 1994)—these narrowband signals are believed to originate as plasma drift waves in the dayside magnetosheath and enter the earth-ionosphere cavity through the polar cusps; (4) currents associated with the recently observed upper atmospheric optical flashes (Vaughan and Vonnegut, 1989; Franz et al., 1990; Vaughan et al., 1992; Sentman and Westcott, 1993; Lyons and Williams, 1994) associated with mesoscale thunderstorm systems—these flashes may indicate the breakdown of the middle atmospheric dielectric, and the resultant electrical current between the cloud tops and the ionosphere could constitute a potential electric dipole excitation source of the earth-ionosphere cavity. ACKNOWLEDGMENTS

The author has benefited from discussions concerning Schumann resonances with numerous individuals over the years. These include D.N. Baker, P.V. Bliokh, PJ. Coleman, Jr., F.R. George,

291

Schumann Resonances

D.L. Jones, C.F. Kennel, MJ. McCarrick, C. Polk, MJ. Rycroft, C.T. Russell, JJ. Sweeney, E.R. Williams, and A.Y. Wong.

REFERENCES Abbas, M. (1968), Hydromagnetic wave propagation and excitation of Schumann resonances. Planet. Space Sci., 16, 831. Balser, M. and Wagner, C.A. (I960). Observations of earth-ionosphere cavity resonances. Nature (London), 188, 638. Balser, M. and Wagner, C.A. ( 1962a). Diumal power variations of the Earth-ionosphere cavity modes and their relationship to worldwide thunderstorm activity, J. Geophys. Res., 67,619. Balser, M. and Wagner, C.A. (1962b). On frequency variations of the earth-ionosphere cavity modes, J. Geophys. Res., 67,4081. Balser, M. and Wagner, C.A. (1963). Effect of a high-altitude nuclear detonation on the earth-ionosphere cavity, J. Geophys. Res., 68,4115. Bannister, P.R., Ed. (1987a). Scientific and Engineering Studies Series, Vol. 1. Simplified Expressions for the Electro­ magnetic Fields of Elevated, Surface, or Buried Dipole Antennas, Naval Underwater Systems Center, New London, CT. Bannister, P.R., Ed. (1987b). Scientific and Engineering Studies Series, Vol. 2, ELF System Parameter Variations, Naval Underwater Systems Center, New London, CT. Bannister, P.R., Ed. (1987c). Scientific and Engineering Studies Series, Vol. 3, ELF Propagation Measurements and interpretations, Naval Underwater Systems Center, New London, CT. Bannister, P.R. (1987d). Scientific and Engineering Studies Series, Quasi-Static Electromagnetic Fields, Naval Underwater Systems Center, New London, CT (available from National Technical Information Service, U.S. Department of Com­ merce, Springfield, VA 22161). Bannister, P.R. (1987e). Scientific and Engineering Studies Series, Extremely Low Frequency (ELF) Propagation, Naval Underwater Systems Center, New London, CT (available from National Technical Information Service, U.S. Depart­ ment of Commerce, Springfield, VA 22161). Bashkuev, Yu. B., Haptanov, V.B., and Buyanova, D.G. (1989). The Natural Electromagnetic Field in Central Asia, in Proc. 8th Int. Wroclaw Symp. on Electmmagn. Compat., Wroclaw, Poland. Bashkuev, Yu. B., Haptanov, V.B., Buyanova, D.G., and Mitkinov, E.M. (1990). Global Electromagnetic Resonances of Earth-ionosphere Cavity in Middle Latitudes of Asia, in Proc. IOth Int. Zurich Symp. Electmmagn. Compatibility, Zurich. Beamish, D. and Tzanis, A. (1986). High resolution spectral characteristics of the Earth-ionosphere cavity resonances, /. Atmos. Terr. Phys., 48, 187. Behroozi-Toosi, A.B. and Booker, H.G. (1983). Application of a simplified theory of ELF propagation to a simplified worldwide model of the ionosphere, Space Sci. Rev., 35,91. Bezrodny, V.G., Nickolaenko, A.P., and Sinitsin, V.G. (1977). Radio propagation in natural waveguides, J. Atmos. Terr. Phys., 39,661. Bliokh, P.V., Nikolaenko. A.P.. and Filippov, Yu. F. (1980a). Schumann Resonances in the Earth-ionosphere Cavity, Peter Peregrinus, London. Bliokh, P.V., Nikolaenko, A.P., and Filippov, Yu. F. (1980b). Diumal variations of the eigenfrequencies of the earthionosphere cavity due to the eccentricity of the geomagnetic pole, Geomagn. Aeron., 8 , 250. Budden, ICG. (1962). The Waveguide Mode Theory o f Wave Propagation, Prentice-Hall, Englewood Cliffs, NJ. Burke, C.P. and Jones, D.L.I. (1992a). Radiolocation in the lower ELF Frequency Band, in Proc. 50th AGARD-EPP Symp., Radiolocation Techniques, London, 41-1. Burke, C.P. and Jones, D.L.I. ( 1992b). An experimental investigation of ELF attenuation rates in die earth-ionosphere duct J. Atmos. Terr. Phys., 54, 243. Burrows, M L (1978). ELF Communications Antennas, Peter Peregrinus, London. Cannon, P.S. and Rycroft, MJ. (1982). J. Atmos. Terr. Phys., 44, 201. Chapman, F.W. and Jones, D.L.I. (1964). Earth-ionosphere cavity resonances and the propagation of extremely low frequency radio waves. Nature (London), 202, 654. Clayton, M.D., Cooper, W„ Etzold, H., and Polk, C. (1972). Absolute calibration of antennas at extremely low frequencies. Report EE 4041/2, University of Rhode Island, Kingston. Clayton, M. and Polk, C. (1974). Diumal Variation and Absolute Intensity of World-Wide Lightning Activity, September 1970 to May 1971, in Proc. Corf. Electrical Processes in Atmospheres, Garmisch-Paitenkirohen, Germany. Dolezalek, H. (1972). Discussion of the fundamental problem of atmospheric electricity. Pure Appi. Geophys., 100,8.

Egeland, A. and Larsen, T.R. (1968). Fine structure of the earth-ionosphere cavity resonances, J. Geophys. Res., 73,4986. Franz, R.C., Nemzek, RJ., and Winckler, J.R. (1990). Television image of a large upward electrical discharge above a thunderstorm system. Science, 249, 48.

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Galejs, j. (1961a). Terrestrial extremely low frequency noise spectrum in the presence of exponential ionospheric conduc­ tivity profiles, J. Geophys. Res., 66 , 2787. Galejs, J. (1961b). ELF waves in the presence of exponential ionospheric conductivity profiles, IRE Trans. Antennas Propag., AP-9, 554. Galejs, J. (1962). A further note on terrestrial extremely low frequency propagation in the presence of isotropic ionospheric with an exponential conductivity height profiles, J. Geophys. Res., 67, 2715. Galejs, J. (1964). Terrestrial extremely-low-ffequency propagation, in Natural Electromagnetic Phenomena Below 30 KC/S, DP. Bleil, Ed., Plenum, New York. Galejs, J. (1965a). Schumann resonances. Radio Sci. J. Res. NBS, 69D, 1043. Galejs, J. (1965b). On the terrestrial propagation of ELF and VLF waves in the presence of a radial magnetic field. Radio Sci J. Res. NBS. 69D, 705. Galejs, I. (1968). Propagation of ELF and VLF radio waves below an anisotropic ionosphere with a dipping magnetic field, J. Geophys. Res., 73, 339. Galejs, I. (1972). Terrestrial Propagation o f Long Electromagnetic Waves, Pogamon Press, New York. Griefinger, C. and Greifinger, P. (1968). Theory of hydromagnetic propagation in the ionospheric waveguide, J. Geophys. Res., 73, 7473. Greifinger, C and Greifinger, P. (1973). Wave guide propagation of micropulsation out of the plane of the geomagnetic meridian, J. Geophys. Res., 78,4611. Greifinger, C. and Greifinger, P. (1978). Approximate method for determining ELF eigenvalues in the earth-ionosphere cavity. Radio Sci., 13, 831. Greifinger, C. and Greifinger, P. (1979). On the ionospheric parameters which govern high-latitude ELF propagation in the earth-ionosphere cavity. Radio Sci, 14, 889. Greifinger, C and Greifinger, P. (1986). Noniterative procedure far calculating ELF mode constants in the anisotropic earth-ionosphere waveguide. Radio Sci, 21,981. Heacock, R.R. (1974). Whistler-like pulsation events in the frequency range of 20 to 200 Hz, Geophys. Res. Lett., 1,77. Holtham, P.M. and McAsldll, BJ. (1988). The spatial coherence of Schumann activity in the polar cap, J. Atmos. Terr. Phys., 50, 83. Holzer, R.E. and Deal, D.E. (1956). Low audio frequency electromagnetic signals of natural origin. Nature (London), 177, 536. Holzer, R.E. (1958). World thunderstorm activity and extremely low frequency spherics, in Recent Advances in Atmospheric Electricity, L.G. Smith, Ed., Pergamon Press, New York. Huzita, A. (1969). Effect of radioactivity fallout upon die electrical conductivity of the lower atmosphere, in Planetary Electrodynamics, S. Cororuti and J. Hughes, Eds., Gordon & Breach, New York. IEEE J. Oceanic Eng. (1984). (Special issue on long range communication at ELF), Vol. QE-9. Johler, J R. and Berry, L.A. (1962). Propagation of terrestrial radio waves of long wavelength—theory of zonal harmonics with improved summation techniques, J. Res, Nat. Bur. Stand Sect. D, 66 ,737. Jones, D U . (1964). The calculation of the Q-factors and frequencies of earth-ionosphere cavity resonances for a twolayer ionospheric model, J. Geophys. Res, 69,4037. Jones, D U . (1967). Schumann resonances and ELF propagation for inhomogeneous isotropic ionospheric profiles, J. Atmos. Terr. Phys, 29, 1037. Jones, D U . (1970a). Numerical computations of terrestrial ELF electromagnetic wave fields in the frequency domain. Radio Sci, 5, 803. Jones, D U . (1970b). Propagation of ELF pulses in the earth-ionosphere cavity and application to slow tail sferics. Radio Sci, 5, 1153. Jones, D U . (1970c). Electromagnetic radiation from multiple return strokes of lightning. J. Atmos. Terr. Phys, 32, 1077. Jones, D U . (1974). Extremely low frequency (ELF) ionospheric radio propagation studies using natural sources, IEEE Trans. Comm., COM-22, 477. Jones, D.L.L (1985). Sending signals to submarines. New Sci, July 4,37. Jones, D U . and Burke, C.P. (1990). Zonal harmonic series expansions of Legendre functions and associated Legendre functions, J. Phys A: Math. Gen., 23, 3159. Jones, D U . and Buike, CP. (1992). An experimental investigation of ELF attenuation rates in the Earth-ionosphere duct, J. Atmos. Terr. Phys, 54, 243. Jones, D U . and Joyce, G.S. (1989). The computation of ELF radio wave fields in the earth-ionosphere cavity, J. Atmos. Terr. Phys, 51,233. Jones, D U . and Kemp, D.T. (1970). Experimental and theoretical observations of Schumann resonances, J. Atmos. Terr. Phys., 32, 1095. Jones, D U . and Kemp, D.T. (1971). The nature and average magnitude al the sources of transient excitation of the Schumann resonances. J. Atmos Ten. Phys, 33,557. Kemp, D.T. (1971). The global location of large lightning discharges from single station observations of ELF disturbances in the earth-ionosphere cavity, J. Atmos. Ten. Phys, 33,919.

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Kemp. D.T. and Jones, D U. (1971). A new technique for the analysis of transient ELF electromagnetic disturbances. J. Atmos. Terr. Phys., 33, 567. Kdnig, H. (1959). Atmospherics geringster Frequenzen, Z Agnew. Phys.. 11(7), 264. Landau, L.D. and Lifshitz, E.M. (1984). Electrodynamics o f Continuous Media. 2nd ecL, Pergamon, Oxford. Large, D.B. and Wait, J.R. (1967). Resonances of the thin-shell model of the earth-ionosphere cavity with a dipolar magnetic field. Radio Sci., 2, 695. Large, D.B. and Wait, J.R. (1968a). Theory of electromagnetic coupling phenomena in the earth-ionosphere cavity, J. Geophys. Res., 73, 4335. Large. D.B. and Wait, J.R. (1968b). Influence of a radial magnetic field on the resonances of a spherical plasma cavity. Radio Sci., 3, 663. Larsen, T.R. and Egeland, A. (1968). Fine structure of the earth-ionosphere cavity resonances, J. Geophys. Res., 73,4986. Lyons, W.A. and Williams, ER. (1994). Some characteristics of cloud-to-stratosphere "lightning" and considerations for its detection. Symposium on the Global Electrical Circuit, Global Change and the Meteorological Applications o f Lightning Information, American Meteorological Society, Nashville, TN. January. Madden, T. and Thompson, W. (1965). Low-frequency electromagnetic oscillations of the earth-ionosphere cavity. Rev. Geophys., 3, 211. Nelson, P.H., (1967). Ionospheric Perturbations and Schumann Resonance Data, Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA. Nikolaenko, A.P. and Rabinovich (1982). Possible global electromagnetic resonances on the planets of the solar system. Cosmic Res., 20, 67. Ogawa, T„ Miura, T„ Owaki, M , and Tanaka, Y. (1966a). ELF noise bursts and enhanced oscillations associated with the solar-flare of July 7, 1966, Rep. lonos. Space Res. Jpn., 20, 528. Ogawa, T., Miura, T„ Tanaka Y„ and Yasuhara. M. ( 1966b). Observations of natural ELF and VLF electromagnetic noises by using ball antennas, J. Geomag. Geoelectr.. 18, 443. Ogawa, T., Fraser-Smith, A.C., Gendrin, R., Tanaka, Y., and Yasuhara. M. (1967). Worldwide simultaneity of occurrence of a Q-type ELF burst in the Schumann resonance frequency range, J. Geomag. Geoelectr., 19, 377. Ogawa, T„ Tanaka, Y„ and Yasuhara, M. ( 1969a). Schumann resonances and worldwide thunderstorm activity, in Plan­ etary Electrodynamics, S. Coroniti and J. Hughes, Eds., Gordon & Breach, New York, 2, 85. Ogawa, T., Tanaka, Y„ and Yasuhara, M. (1969b). Schumann resonances and worldwide thunderstorm activity—diumal variations of the resonant power of natural noises in the earth-ionosphere cavity, I-power, J. Geomagn. Geoelectr., 21,

1. Ogawa, T. and Tanaka, Y. (1970). Q-factors of the Schumann resonances and solar activity. Spec. Contrib. Geophys. Inst. Kyoto Univ., 10, 21. Ogawa, T. and Murakami. Y. (1973). Schumann resonance frequencies and the conductivity profiles in the atmosphere. Spec. Contrib. Geophys. Inst. Kyoto Univ., 13, 13. Ogawa, T., Kozai, K., and Kawamoto. H. (1979). Schumann resonances observed with a balloon in the stratosphere, J. Atmos. Terr. Phys., 41, 135. Orville, R.E. and Henderson, R. (1986). Global distribution of midnight lightning: September 1977 to August 1978, Mon. Weather Rev., 114,2640. Pierce, E.T. (1963), Excitation of earth-ionosphere resonances by lightning flashes, J. Geophys. Res., 68 , 4125. Polk, C. (1969). Relation of ELF noise and Schumann resonances to thunderstorm activity, in Planetary Electrodynamics, S. Coroniti and J. Hughes, Eds., Gordon & Breach, New York, 2,55. Polk, C. (1982). Schumann resonances, in CRC Handbook o f Atmospherics. Vol. 1, H. Volland, Ed., CRC Press, Boca Raton, FL. Polk, C. (1983). Natural and man-made noise in the earth-ionosphere cavity at extremely low frequencies (Schumann resonances and man-made ‘interference’). Space Sci. Rev., 35. 83. Polk. C. and Fttchen, F. (1962). Schumann resonances of the earth-ionosphere cavity: extremely low frequency reception at Kingston, J. Res. NBS Radio Sci., 66 D, 313. Raemer. E.T. (1961). On the extra low frequency spectrum of the earth-ionosphere cavity response to electrical storms, J. Geophys. Res, 66 , 1580. Raina, B.N. and Raina, R.C. (1988). Diumal variation of some fair weather electrode effect parameters at Guimarg, J. Atmos. Terr. Phys., 50, 1. Row, R.V. (1962). On the electromagnetic resonance frequencies of the earth-ionosphere cavity, IRE Trans. Antennas Propag., AP-10, 766. Ryctoft, MJ. (1965). Resonances of the earth-ionosphere cavity observed at Cambridge, England, Radio Sci. J. Res. NBS, 69D, 1071. Sao, K. (1971). Day to day variation of Schumann resonance frequency and occurrence of Pci in view of solar activity, J. Geomagn. Geoelectr., 23, 411. Sapagova, N.A. and Kontorovich. V.M. (1971). The application of group theory to an investigation of the removal of degeneracy in a spherical resonator, Izv. VUZ Radiofiz. 14, 1869.

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Schumann, W.O. (1952a). Ober die strahlungslosen Eigenschwingungen einer leitenden Kugel, die von einer Luftschicht und einer Iooospharenhiille umgeben ist, Z Naturforsch, 7a, 149. Schumann, W.O. (1952b). Ober die DSmpfung der elektromagnetischen Eigenschwingungen des Systems Erde-Luftkmosphare, Z Naturforsch., 7a, 250. Schumann, W.O. (1952c). Ober die Ausbreiwng sehr langer electrischer Wellen und der Blitzentladung um die Eide, Z Agnew. Phys., 4(12), 474, 1952. Schumann, W.O. (1954). Ober die Oberfelder bei der Austneitung langer, electrischer Wellen im System Erde-Luftlonosphare und 2 Andwendungen (horizontaler und senkrechter Dipol). Z Agnew. Phys., 6(1), 35, 1954. Schumann, W.O. and Kdnig, H. (1954). Ober die Beobachtung von Atmospherics bei geringsten Ftequenzen. Naturwissenschajien, 41, 183. Schumann, W.O. (1957). Ober elektrische Eigenschwingungen des Hohlraumes Erde-Luft-Ionosphare, erregt dutch Blitzentladungen, A. Agnew. Phys., 9,373. Sentman, D.D. (1983). Schumann resonance effects of electrical conductivity perturbations in an exponential atmospheric/ ionospheric profile, J. Atmos. Terr. Phys., 45, 55. Sentman, D.D. (1987a). Magnetic elliptical polarization of Schumann resonances. Radio Sci, 22, 595. Sentman, D.D. (1987b). PC monitors lightning worldwide, Comput. Sci., 1,25. Sentman, D.D. and George, F.R. (1988). A microcomputer-controlled, real-time data acquisition and analysis system for Schumann resonance studies. Institute of Geophysics and Planetary Physics Technical Repot 88-001, University of California, Los Angeles. Sentman, D.D. (1989). Detection of elliptical polarization and mode splitting in discrete Schumann resonance excitations, J. Atmos. Terr. Phys., 51, 507. Sentman, D.D. (1990a). Approximate Schumann resonance parameters for a two-scale-height ionosphere, J. Atmos. Terr. Phys., 52, 35. Sentman, D.D. (1990b). Electrical conductivity of Jupiter’s shallow interior and the formation of a resonant pianetaryionospheric cavity, Icarus, 88, 73. Sentman, D.D. and Fraser, BJ. (1991). Simultaneous observations of Schumann resonances in California and Australia: evidence for intensity modulation by the local height of the D region, J. Geophys. Res., 96,15,973. Sentman, D.D. and Wescott, E.M. (1993). Observations of upper atmospheric optical flashes recorded from an aircraft, Geophys. Res. Lett., 20,2857. Sentman, D.D. (1944). A critical comparison of Schumann resonance theory and observations. Symposium on the Global Electrical Circuit, Global Change and the Meteorological Applications o f Lightning Information, American Meteor­ ological Society, Nashville, TN January. Sentman, D.D. and Ehring, D.A. (1994). Midlatitude detection of ELF whistlers. J. Geophys. Res., 99,2183. Stefant, R. (1963). Application d'un magnetometer &(’induction It la detection des frequences de resonance de la cavite tore-ionosphere. Arm. Geophys., 19, 250. Sukhorukov, AJ. (1991). On the Schumann resonances on Mars, Planet. Space Sci, 39, 1673. Sukborukov, AJ. (1993). Approximate solution for VLF propagation in an isotropic exponential Earth-ionosphere wave­ guide, J. Atmos. Terr. Phys., 55, 919. Sweeney, J J. (1989). An Investigation of the Usefulness of Extremely Low-Frequency Electromagnetic Measurements for Treaty Verification, Report No. UCRL-53899, Lawrence Livermore National Laboratory, Livermore, CA. Turman, B.N. (1977). Detection of lightning superbolts, J. Geophys. Res., 82, 2566. Turman, B.N. (1978). Analysis of lightning data from the DMSP satellite, J. Geophys. Res., 83,5019. Tzanis, A. and Beamish, D. (1987a). Audiomagnetotelluric sounding using the Schumann resonances, J. Geophys., 61, 97. Tzanis, A. and Beamish, D. (1987b). Tune domain polarization analysis of Schumann resonance waveforms, J. Atmos. Terr. Phys., 49,217. Uman, M.A. (1987). The Lightning Discharge, International Geophysical Series, Vol. 39, Academic Press, Orlando, FL. Vaughan, Jr., O.H., and Vonnegut, B. (1989). Recent observations of lightning discharges from the top of a thundercloud into the clear air above, J. Geophys. Res., 94, 13179. Vaughan, Jr., O.H., Blakeslee, R., Boeck, WJ_, Brook, M., McKune. Jr., J , and Vonnegut, B. (1992). A cloud-to-space lightning as recorded by the space shuttle payload-bay TV cameras, Mon. Weather Rev., 120, 1459. Volland, H. (1982). Low frequency radio noise, in CRC Handbook o f Atmospherics, Vol. 1, H. Volland, Ed., CRC Press, Boca Raton, FL. Wait, J.R. ( 1960a). Mode theory and propagation of ELF radio waves, J. Res Sect. Nat. Bur. Stand, Sect. D, 64, 387. Wait, J.R. (1960b). On the propagation of ELF radio waves and the influence of a non-homogeneous ionosphere, J. Geophys Res, 65. 595. Wait, J.R. (1962). On the propagation of VLF and ELF radio waves when the ionosphere is not sharply bounded, J. Res Nat. Bur. Stand, Sea. D., 66,53. Wait, J.R. (1965a). Earth-ionosphere cavity resonances and the propagation of ELF radio waves. Radio Sci, 69D, 1057. Wait, J.R. (1965b). Cavity resonances for a spherical earth with a concentric anisotropic shell, J. Atmos. Terr. Phys, 27, 81.

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Wait, J.R., Guest Ed. (1963). Special issue on electromagnetic waves in the earth, IEEE Trans. Antennas Propag., AP-11. Wait, J.R. (1972). Electromagnetic Waves in Stratified Media, 2nd ed., Pergamon Press, New York. Wait, J.R., Ed. (1974). Special issue on extremely low frequency communications, IEEE Trans. Antennas Propag., COM22.

Wait, J.R. (1992). On ELF transmission in the earth-ionosphere waveguide, J. Atmos. Terr. Phys., 54, 109. Williams, EL, Blasch, K., Boldi. B„ and Sentman, D. (1994). Extraction of information on global lightning activity from single-station measurements in the Schumann band. Symposium on the Global Electrical Circuit, Global Change and the Meteorological Applications o f Lightning Information, American Meteorological Society, Nashville, TN, January. Williams, E.R. (1992). The Schumann resonance: a global tropical thermometer. Science, 256, 1184.

Chapter 12

Low-Frequency Radio Noise Antony C. Fraser-Smith

CONTENTS 1. Introduction......................................................................................................................... 297 1.1. Typical Low-Frequency Radio Noise.................................................................... 298 1.2. The /^Frequency Variation...................................................................................299 1.3. Surveys of ELF/VLF Radio N oise.........................................................................300 1.4. Electric and Magnetic Field Units...........................................................................301 2. Natural Radio Noise at 50 or 60 H z ................................................................................. 301 3. Low-Frequency Radio Noise Statistics............................................................................. 302 3.1. Average Noise Amplitudes..................................................................................... 302 3.2. Voltage Deviation Vd ...............................................................................................303 3.3. Antenna Noise Factor Fa ........................................................................................ 304 3.4. Amplitude Probability Distributions....................................................................... 305 4. Summary............................................................................................................................. 308 Acknowledgments....................................................................................................................... 308 Appendix 1: Conversion Between Electric and Magnetic Noise Amplitudes........................ 308 References....................................................................................................................................309

1.

INTRODUCTION

The description low-frequency radio noise covers a multitude of different radio noise sources and noise phenomena. However, a number of these sources and phenomena are discussed in other chapters. The low-frequency radio noise considered here is restricted to the noise observed on the earth’s surface in the extremely low frequency (ELF)/very low frequency (VLF) range (fre­ quencies in the range 3 Hz to 30 kHz), which includes both the ELF range (frequencies in the range 3 Hz to 3 kHz) and the VLF range (frequencies in the range 3 to 30 kHz). Thus this chapter does not include discussion of phenomena in the ultralow frequency (ULF) range (frequencies less than 3 Hz); these ULF phenomena are covered in Chapter 11/14. Of the phenomena occurring in the ELF/VLF range, whistler waveforms are covered in Chapter D/7, and high latitude forms of noise that originate above the ionosphere (hiss and chorus) are discussed in Chapter n/13. Schumann resonances (also known as the earth-ionosphere cavity resonances), which occupy the lowest part of the ELF range (7 to 40 Hz), are discussed in Chapter 1/11. A major component of radio noise in the ELF/VLF range is noise of human origin. This chapter will only be concerned with natural ELF/VLF noise; however, man-made noise, in par­ ticular power line harmonic radiation, is of great significance. There are two reasons for this significance. First, man-made noise is making it difficult to measure the natural background ELF/VLF noise all over the world, no matter how remote (Fraser-Smith and Bowen, 1992), and second, it may subtly influence the generation and propagation of some forms of natural noise. Man-made noise at power line frequencies and their harmonics (frequencies less than about 4 kHz) are discussed in Chapter n/10. The upper part of the ELF/VLF range is also severely impacted by man-made noise, in this case by VLF transmissions from a variety of navigation and communication stations around the world. Although the signals from these stations carry useful 0-8493-8647-0/95/50.00+$. 50 e 1995 by C R C Press, Inc.

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298 AH

1 9 . Inn 9 3

I f l O .S l lT

Figure 12.1.1 Typical spectrum of ELF/VLF radio noise. The measurements were made at Arrival Heights, Antarc­ tica, starting at 1805:00 UT on June 19, 1993.

information, they nevertheless make it nearly impossible for measurements to be made of the natural background noise, and in the context of such measurements they can also be considered a form of noise. Unfortunately, the interference to measurements of the natural background noise by power line harmonic radiation and VLF transmissions has been growing steadily over the years, and lacking protected frequency ranges, it may be impossible to write a chapter on natural radio noise in the ELF/VLF range in the future, because measurements will have become im­ possible. To illustrate the difficulty, when my group began a survey of ELF/VLF radio noise in 1984 (Fraser-Smith et al., 1985,1988, 1991,1994), a search of the frequency range 16 to 60 kHz for frequencies at which a 5% bandwidth filter could be placed for measurements of the radio noise amplitudes at whose frequencies resulted in the surprising finding that there was only one frequency (32 kHz) that was not impacted by radio transmissions of some kind. What remains when all these other noise sources and phenomena are removed? It is sferics, the strongest and most pervasive form of ELF/VLF radio noise. Generated by the lightning in up to 2000 thunderstorms in progress around the world at any time (e.g., Chalmers, 1967), these sferics so completely dominate the natural ELF/VLF noise spectrum that the long-term statistics of the noise (some of which are presented in this chapter) contain essentially no contribution from the other forms of natural ELF/VLF radio noise (e.g., Watt, 1967). An exception is at high latitudes, where the noise statistics for the frequency range 0.5 to 1.5 kHz may have a significant contribution from polar chorus. 1.1.

TYPICAL LOW-FREQUENCY RADIO NOISE

Figure 12.1.1 shows an illustrative spectrum of the low-frequency radio noise measured at Arrival Heights, Antarctica. With comparatively minor variations, similar spectmms would be observed all over the earth. As noted above, at high latitudes the 0.5 to 1.5 kHz band quite often contains additional activity, an example erf which is shown in Figure 12.1.2. This activity was originally referred to as polar chorus by Ungstrup and Jackerott (1963), but following more recent devel­ opments in terminology it would probably be more accurately referred to as a form of hiss, because it consists predominantly or solely of hiss at most times and at most locations. The horizontal lines at frequencies of 16 kHz and above in Figure 12.1.1 correspond to manmade VLF radio transmissions, which are usually intended to be used for communications. Below about 4 kHz the horizontal lines also have a man-made source, in this case the power lines in and around Arrival Heights. Their frequencies are all harmonics of 60 Hz in this case; at other locations they could well be harmonics of 50 Hz. In the range 10 to 14 kHz the broken horizontal

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-10

-15

0

10

20

30

Time (sec)

ref 50 dBQ df 5 1 Hz

Figure 12.1.2 Spectrum of ELF/VLF radio noise during the occurrence of polar chorus. The measurements were made at Sondrestromfjord, Greenland, starting at 1005:02 UT on November 13,1986, and quasiperiodicity of the hiss around 1.0 kHz is clearly evident.

lines are produced by the various transmitters making up the worldwide omega navigation system. Note that the horizontal line at 10 kHz is not typical of the normal radio noise environment; it is introduced by the measurement system that recorded the data shown in the figure to provide a phase and frequency reference. The remaining signals, essentially all vertical lines, are natural; they are the sferics produced by lightning. The sferics that can be seen in Figures 12.1.1 and 12.1.2 are the most ubiquitous form of radio noise in the ELF/VLF range. They extend down in frequency to about 4 kHz, below which they generally disappear, but they often reappear again around 1 kHz and extend down to frequencies in the lowest part of the ELF range. The gap in the approximate range 1 to 4 kHz is the result of a waveguide cutoff for the propagation of the sferic electromagnetic waves in the earthionosphere waveguide. Some of the sferics can be seen to extend completely through the fre­ quency range corresponding to the cutoff, with little or no attenuation. These sferics are obviously little affected by the cutoff, and thus they must have originated close to the measuring system. In general terms, the strongest sferics are produced by the nearest lightning flashes, and the weakest come from the most distant lightning. Interestingly, if a quiet section of the spectrogram shown in Figure 12.1.1 is selected in which few sferics are evident (for example, the section between 1908:42 universal time (UT) and 1805:44 UT), and a fresh spectrogram is prepared for that particular section with greater amplification and with the time scale expanded, it will be found that the quiet section in the original spectrogram actually contains many (weak) sferics. The process can be repeated until finally the spectrograms will become more or less uniformly blackened, at which time the noise being displayed corre­ sponds to the internal noise of the measurement system. 1.2.

THE 1/f FREQUENCY VARIATION

An important general property of radio noise in the ELF/VLF band, and for some decades of frequency on either side of the band, is an overall approximate inverse relation between the noise amplitude and frequency, or equivalently, an overall approximate inverse square relation between the noise power and frequency. Figure 12.1.3, taken from Lanzerotti et al. (1990), shows this tendency specifically for data measured in the ten-decade frequency range IO-5 to IO5 Hz. Other data presented in the same reference suggest that the inverse tendency persists, at least up to frequencies as high as IO8 Hz. If the frequency dependence of the noise amplitudes is written

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f. Hi Figure 12.1.3 Monthly average 3-hour amplitude spectrums for magnetic field fluctuations measured at Arrival Heights, Antarctica (near McMurdo Station), during June 1986. (Taken from lanzerotti, L. J. et al. (1990). Geophys. Res. Lett., 17,1593. With permission.)

/■", the exponent n measured by Lanzerotti et al. (1990) lays in the range 1.0 to 1.5, with a best lit value of 1.25. Thus the relationship between amplitude and frequency was only approximately inverse. However, the value of n appears to vary considerably, depending on the particular study and on the form of the noise measurements, and until there are more definitive measurements, it is probably sufficient for most purposes to assume a roughly inverse relation. Knowledge of this tendency for the noise amplitudes to decline approximately inversely with frequency is important from a practical point of view, because it implies that communication is likely to be easier at higher frequencies, given a communication signal with an amplitude that can only be increased up to some limiting value. The knowledge is also important from a scientific point of view, because, as pointed out by Lanzerotti et al. (1990) it provides information about the spatial and temporal variations of natural electromagnetic emissions and their source mech­ anisms. There is also an interesting implication to the Iff amplitude variation that follows from general considerations of noise. If it is remembered that white or Johnson noise is random, with no correlation between the amplitudes at any one moment and those that follow, and with no relation between amplitude and frequency (the amplitude varies as Iff0), the Iff amplitude vari­ ation of ELF/VLF noise implies substantial correlation between successive amplitude measure­ ments. Some such correlation might be expected because of the thunderstorm source of the sferics. Nevertheless, it must be pointed out that it is not understood at this time why the approximate inverse relation between noise amplitude and frequency exists, either in the ELF/VLF range, or over the much broader frequency range considered by Lanzerotti et al. (1990). 1.3.

SURVEYS OF ELF/VLF RADIO NOISE

As mentioned above, the STAR Laboratory at Stanford University began a survey of low fre­ quency (ELF/VLF) radio noise in 1984, and many of the data that are presented here originated in that survey. Previous surveys of radio noise in the ELF/VLF range or measurements covering the ELF/VLF range as part of a broader survey of radio noise have not been extensive, but there are some useful and important data available.

Low-Frequency Radio N oise

301

The principal source of information on the characteristics of atmospheric radio noise in general, and on ELF/VLF radio noise as a component of that general description, is a series of reports published by the International Radio Consultative Committee (CCIR, an acronym derived from the French title of the Committee) (CCIR, 1964,1978,1988). These reports draw on many sources of information on radio noise, but the most extensive series of measurements that were incor­ porated were obtained by the U.S. National Bureau of Standards (NBS) from 16 stations distrib­ uted over the earth’s surface (see Crichlow et al., 1955; Crichlow, 1957). Unfortunately, in the most comprehensive of these reports, the data were limited to frequencies above 10 kHz, and therefore they do not provide information about ELF noise or about VLF noise in the lower part of the VLF band. Two useful papers repotting on extensions of the NBS work are those by Watt and Maxwell (1957a, 1957b). Watt (1967) incorporates some of the results described in these papers into a later comprehensive review of atmospheric radio noise. Two additional papers that are particularly relevant to this review of ELF/VLF radio noise are those by Maxwell and Stone (1963) and Maxwell (1966). A review by Soderberg (1982) gives access to many different measurements of ELF radio noise. More recently, a mini-review by Flock and Smith (1984) presents a selection of radio noise data in compact form. 1.4.

ELECTRIC AND MAGNETIC FIELD UNITS

Even though most measurements of electric and magnetic fields are now reported in International System (SI) units, there is still some variation in the units that are used for the electric and magnetic fields of radio noise. Typically, the basic electric field unit that is used is the volt per meter (V/m), but on occasion the electric field is reported either in decibels (dB), or more fully in the form of decibels relative to 1 V n r 1 (often 1 mV m~1or 1 pV m~' are used instead of 1 V n r', because the electric fields in electromagnetic radiation are rarely as large as 1 V n r 1). The basic magnetic field unit is the tesla (T), but the units most commonly used for the magnetic fields of radio noise are the picotesla (pT; 1 pT = 10-12 T) or the femtotesla (fT; 1 fT = 10-15 T). Because radio noise is spread over a wide range of frequencies, measurements of the noise are dependent on the frequency bandwidth of the measurement system, and the measurements are most completely reported in the form of spectral densities. By analogy with white noise, where the measured noise power is proportional to the bandwidth of the measurement (i.e., the noise amplitude is proportional to the square root of the bandwidth), radio noise amplitudes are usually reported in units of picotesla per square root of hertz (pT/VHz) for example, or in related electric field units. It must be remembered, however, that low frequency radio noise is not white noise, and whereas white noise has equal power at ail frequencies, ELF/VLF noise has proportionately greater power at low frequencies. It is most unusual for simultaneous measurements to be made of the electric and magnetic fields of radio noise. Instead, the measurements are usually made on either the electric or the magnetic field. It is then common practice to convert between the electric and magnetic fields by assuming that the noise reaches the measurement system as plane electromagnetic waves. The conversion between the electric and magnetic field units is then quite straightforward (Appendix 1). Unfortunately, at the lowest frequencies in the ELF/VLF range it is not always certain that the electric and magnetic fields reaching the measurement system are doing so as the components of a plane-polarized electromagnetic wave. Under these circumstances the conventional conver­ sion between electric and magnetic field units is not necessarily valid, and the converted field amplitudes should be regarded only as estimates. This is an area in which more research is needed to establish the validity of the conventional conversion process.

2. NATURAL RADIO NOISE AT 50 OR 60 Hz Very few measurements have ever been made of the natural background levels of 50 or 60 Hz radio noise, for the obvious reason that the natural activity is now widely contaminated by power

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302

line noise at those frequencies. Nevertheless, it is important that the natural levels be measured because of the growing concern over the possible hazard to human health of the magnetic fields associated with electric power distribution systems or with the use of electric power as whole. As pointed out by Fraser-Smith and Bowen (1992), the significance of the power line fields is sometimes assessed by comparing them with the earth’s steady magnetic field, which can be misleading due to the fact that the earth's field is steady, whereas the other fields are not More relevant is a comparison with the natural background fields at the same frequencies and locations. By making measurements of the radio noise at frequencies just above and below the power line fundamental frequencies and interpolating, Fraser-Smith and Bowen (1992) were able to derive the natural amplitudes of 50 or 60 Hz radio noise at a number of locations around the world. Typically, the amplitudes lay in the range of 150 to 600 flYy/Hz, and it is likely that this range would remain typical for most locations on the earth's surface and for most seasons. In general, power line and electric appliance magnetic fields are substantially greater (by many orders of magnitude) than the corresponding background field levels. To illustrate, if a 1-Hz frequency bandwidth is taken at 60 Hz, the above natural field amplitudes imply that a maximum magnetic field amplitude of 600 fT will be measured in the 1-Hz band. A typical 60-Hz magnetic field near an electric appliance is 10 pT, which is more than 107 times greater than the corresponding natural field level. 3.

LOW-FREQUENCY RADIO NOISE STATISTICS

There are a number of statistical measures that are used to define the properties of low-frequency radio noise. Only the most common of these quantities will be discussed here: the average am­ plitude; the voltage deviation Vd (the descriptive term has lost significance, but Vd, being a measure of the impulsiveness of the noise, is still a very useful quantity); the antenna noise factor Fa, which is widely used to characterize radio noise, particularly in the CCIR reports; and amplitude probability distributions, or APDs, which give important information about the amplitudes that can be expected. Although they are less often quoted, statistical distributions of the time between pulses of the atmospheric noise envelope have considerable practical application. This is because weak radio transmissions can often be easily detected between sferic occurrences, even though they may be completely lost when the sferics are occurring. A communication system designed with redundancy based on the statistics of the time between pulses may provide adequate infor­ mation even during times that would be considered very noisy. 3.1.

AVERAGE NOISE AMPLITUDES

Some information on these particular noise statistics has already been given in Section 1.2 and in Figure 12.1.3, in particular, where the variation of the ELF/VLF noise amplitudes shown for June 1986 is typical. Figure 12.3.1, taken from Fraser-Smith et al. (1991), provides an expanded view of these Arrival Heights monthly average ELF/VLF noise amplitudes for a number of different months in the interval January 1986 through January 1988. The dip in the noise ampli­ tudes in the frequency range 1 to 4 kHz, corresponding to the earth-ionosphere waveguide cutoff, is distinctive and it can be recognized in all statistical data covering the average amplitudes of ELF/VLF radio noise. It will be noted that there is surprisingly small variation in the noise amplitudes at frequencies below 1 kHz, whereas a clear seasonal variation is evident at the higher frequencies. The noise measurements at Arrival Heights, an Antarctic location, are not typical of those made at lower latitudes, because most thunderstorm activity is concentrated in a comparatively narrow band of latitudes centered on the equator (e.g., Uman, 1987). Figure 12.3.2 compares monthly average ELF/VLF noise amplitudes at three different locations during northern hemi­ sphere summer months. Two locations are at high latitudes (Arrival Heights and Sondrestromfjord), and the third is at a low latitude (Kochi, Japan; latitude 33°N). The amplitudes at Kochi are substantially higher than those for the two high latitude stations.

Low-Frequency Radio N oise

303

N

a

E

•
£o

where w = 2 n /ra d s_1 Co = 1/(36 n x 109) F n r 1

’P = the angle between ground and the incident ray as shown in Figure 13.4.1a. Also put Z=

(32)

Er~jX

Then the reflection coefficient for vertically polarized waves is: „ Z sin ¥ - J Z - cos2^ . , Rv —-----------, — \Rv\ Cxt Z sin ¥ + J Z — cos2'!'

(33)

and for horizontally polarized waves it is: _

sin 'P - J Z - cos2'?

Rh =

sin 'P + J Z - cos2^

.

... .

7=

. =

.

**

Z ct

(3 4 >

Then adding the electric field of the direct ray to that of the ground-reflected ray yields, for vertically polarized waves:

(

p~j&81 —

2+« )\

+ w

-

*

- )

l3 5 )

where E\ is the amplitude of the electric field at unit distance and R\ and R2 are the path lengths of the direct- and ground-reflected rays, respectively and P = 2Jt/X (a in radians). The inclusion of R\ and R2 in the phase term is important, whereas the denominators can usually have a common term. Et may be scaled from normalized data, quoted for a range of 10 km. A similar equation applies for horizontal polarization, in which /?* replaces Rv. Figures 13.4.1b and c show plots of the magnitude and phase of Rv and Figure 13.4. Id shows how ET varies with distance for given heights of source and receiver antenna Notice that the amplitudes of pulses received from low sources are reduced selectively when the height of the receiving antenna is low. The foregoing is based on an assumption that the surface is smooth. The reflection coefficient changes if the surface becomes rough, particularly at the higher frequencies where the depths of penetration are small. Goodman (1992) shows curves for additional transmission losses introduced by rough seas, specified in terms of wind speed. In nearly all cases, transmission losses increase with roughness. These would be cases in which the ground-reflected wave interfered construc­ tively, or where the roughness affected the surface wave. Attenuation is increased by vegetation. 4.4. SURFACE WAVES The division into spacewave and surface wave components is somewhat artificial. Unless the surface wave is attenuated, the groundwave for vertically polarized waves should always sum to

Handbook o f Atm ospheric Electrodynam ics, Volume /

324 Table 13.4.1

Relative signal strengths at three frequencies propagated over a distance of 360 Ian 1 ,000

10,000

Conductivity S/m

Dielectric Constant

0.05

6

1

28 58

29 103 125

5 2 5 x 1(H 3 x 10- 3

70 15 5

Frequency (kHz)

100

Sea Good earth Poor earth

4

Note: Units are decibels below signal propagated over plane, perfect ground.

2 E\!dL Below the pseudo-Brewster angle, the spacewaves tend to cancel, but the surface wave is strong. Above the Brewster angle, the surface wave falls off, and the spacewaves tend to make up for its loss. The formula for adding the space and surface waves is of the form: E — (1 + R) X fqncewavc "F (1 — /?) X £jurf*ct wave

(36)

There can be no horizontally polarized surface wave. Calculation of the surface wave follows the procedure set out by Norton (1936,1937a,b). The procedure is not unduly complicated but it does necessitate consulting various graphs. It is given also byTerman (1943) and Jordan (1950). Various models and computer programs have been developed for this purpose (see Goodman, 1992). If the surface wave field is givenseparately, then it may be added to the spacewave to give:

E = Et + £,(1 - Rv)(\ — ii2 + u*cos*lr)F——

i

(37)

where F is the attenuation factor (see Norton, 1936 or Terman, 1943) and where: u2 = 1/(6, + jx)

(38)

The formula for Er is given above. Table 13.4.1 lists relative magnitudes of surface waves that traveled 360 km over sea, and good and bad ground. Further details are given by Causebrook (1989). 4.5.

THE IONOSPHERE

There are four layers where concentrations of free electrons reach local maxima in the upper atmosphere. In order of increasing height, they are the D, E, F(, and F2 layers. They are embedded in a sea of free electrons, ions, and neutrals called the ionosphere. They form as a result of ionizing radiation, nearly all of which originates in the sun. See also Chapters n/8 and D/9. For detailed descriptions of this intriguing and complex subject, see Davies (1990), Goodman (1992), Hall and Barclay (1989), and McNamara (1991). Radio waves accelerate the free electrons in the ionosphere, causing them to oscillate. Some of these electrons strike neutral atoms or ions and therefore lose their energy as heat, and cause the incoming wave to be attenuated. Others reradiate electromagnetic waves, and these have the same frequencies as the incoming waves, but their phases change with height so that the reradiated wavefronts have been rotated slightly. Many texts give the derivation for the plasma frequency:

(39)

Radio N oise Above 300 kH z Due to Natural Causes

325

/ /

Figure 13.4.2

Vertical plane showing ray reflected by ionosphere. The virtual height is Hv.

where q = electronic charge m = electronic mass N = number of electrons per meter cubed The refractive index, rt = c / v p is a measure of the phase speed which, in the ionosphere, is higher than the speed of light c. The Appleton formula relates rt2 to the plasma frequency; in the absence of collisions and magnetic fields:

•-is■ '- '

-

m

-

For the derivation of this see Budden (1961) or Kelso (1964). When rt = 1, there is no refraction. Maximum refraction occurs when n tends to 0, for real values of n. At rt = 0, the wave is reflected and / = f N. The wave is reflected also when rt becomes complex. The Appleton equation also shows that as/increases, rt tends to unity; i.e., low frequency waves are refracted more than highfrequency waves. The angle through which the incoming waves must be rotated for reflection to occur is greatest at normal incidence, i.e., when the incoming wave is directed vertically. The frequency at which a vertically propagated wave just fails to be reflected is called the critical frequency f c and has a special significance. Below f c waves of any angle of incidence are reflected. Obliquely incident waves of frequencies higher thanf c are also reflected if their angles of incidence are large enough. There is a frequency fmat which the angle through which the ray can be refracted by a particular layer is a maximum. In Figure 13.4.2 the angle is (180 - 2 ®). Therefore, ® is a minimum at that frequency. The region TR is known as the skip distance, and stations between T and R will not receive waves from T via that layer of the ionosphere at frequency f m, or at frequencies higher than f m. The frequency f m is termed the maximum usable frequency (MUF) for that distance TR. The distance TR increases as the frequency is increased. There is no skip distance at frequencies below the critical frequency. In the simplified case where the earth’s surface and the ionosphere are represented by planes: sec® = I 1 + I — I

»

-

n

(41)

m

An ionogram is a radar map of virtual heights of the reflecting layers displayed to a base of frequency. If the transmission frequency f„ and the transmission distance D are known, a curve,

Handbook o f Atm ospheric Electrodynam ics, Volume I

326 800 700 600 £

•* 500 X

o

uj 400 X

3 300

t­ a

> 200

100

0

I

2

3

4

5

6

7

8

9

10

II

12

13

f. MHz

Figure 13.4.3 A family of curves derived from Equation 41 plotted onto a simplified ionogram. The distance D is a constant 2000 km. The curve for f0 = 18 MHz intersects the ionogram at b and b' indicating virtual heights of 460 and 350 km for the two rays. (Taken from Davies, K. 11990]. Ionospheric Radio, Peter Peregrinus, London. With permission.)

representing Equation 41 can be plotted on the ionogram as shown in Figure 13.4.3. Virtual heights corresponding to the reflections, can then be read from the ordinate scale. For example, the curve for 14 MHz cuts the ionograms for the Fr , and the Fr layers twice, and also cuts the ionogram for the E-layer at least once. The inference is that the F|- and the Frlayers each reflect two rays, called the high-angle and the low-angle rays, respectively. There would be five or six paths between the two stations, T and R. The earth’s magnetic field causes the incident waves to split into two components, the ordinary and the extraordinary waves, ellipdcally polarized in opposite senses. Parts of the ionograms then split into two, and these would cause even more paths to form. Even when transmission occurs via only one layer, say the E-layer, many paths are possible simultaneously at frequencies below the critical frequency. Multihop transmission occurs when waves are reflected more than once. Noise from lightning is essentially impulsive. The multipath propagation can cause the received pulses to be elongated. Usually the differences in transmission times along the various paths exceed the durations of the pulses, and then the multipath conditions proliferate the numbers of pulses received. Some pulses are inverted. In summary, the ionosphere causes noise to be transmitted over long distances. It can modify the polarization of the radiated noise. There are skip distances where the higher frequency com­ ponents will be absent Multipath conditions cause pulses to be repeated. The ionosphere is effective, complicated, and variable. 4.6.

SCATTER MODES

Distances over which noise is propagated are increased by tropospheric scatter and reflections and by ionospheric scatter, and by transient reflections from meteor trails and lightning. Tropo­ spheric propagation is treated by Hall (1979) and by CCIR Report 718. Ionospheric scatter is discussed by JTAC (1960). Signals received by virtue of scatter are usually considerably weaker than HF signals reflected via the ionosphere under optimum conditions. Tropospheric scatter is effective at VHF and above, i.e., at frequencies not normally reflected by the ionosphere. Strengths

Radio N oise Above 300 kH z Due to Natural Causes

327

of signals scattered by the ionosphere increase as the frequency decreases according to a power law: /= /- “

(42)

where 6.9 < a < 7.8. Diurnal variation amounted to some 20 dB apart from occasional peaks, ascribed to specular reflections from meteor trails, and median signal strengths were some 90 to 110 dB below power calculated using the square of the inverse distance. Multistation observations of lightning by Proctor (1993) showed that noise from lightning is often attenuated severely by intervening lightning channels. See the examples in Section 5.1.5. 5. 5.1.

NOISE OF ATMOSPHERIC ORIGIN

RADIO NOISE FROM LIGHTNING

For a description of lightning and its various component processes, see Chapter 1/4. There are also texts by Uman (1969, 1987), Golde (1977), Malan (1963), and Schonland (1956). The intensities of radio noise from lightning vary considerably with frequency. For this reason, their magnitudes are found conveniently by consulting their spectra, or curves of measured peak amplitude vs. frequency. Examples are given in Section 5.1.2. Spectra of individual events differ from the spectra of noise emitted by a chorus of many flashes, such as may be heard on the MF and HF bands. For this reason. Section 5.1.2 gives spectra of individual processes, as well as data concerning atmospheric noise, or static, received on the various bands. A distribution of measured amplitudes of pulses at 10 MHz from a single stepped leader has been published by Oetzel and Pierce (1969). The bandwidth lay in the region 100 to 300 kHz. The distribution was roughly lognormal with a standard deviation (SD) of 6 dB. Homer and Bradley (1964) provide information on the ranges of SD of amplitudes at frequencies between 6 kHz and 11 MHz. At 500 kHz their best estimate was 4.4 dB, and at 11 MHz it was 4.6 dB. The variation in standard deviations for noise at 11 MHz received from ten storms was 2.6 dB. 5.1.1.

Waveforms and Sources of Lightning Noise

Noise from lightning begins as a sequence of pulses. Receivers having bandwidths that exceed approximately 0.1 MHz reproduce these pulses as separate entities. When received in a 10-MHz bandwidth, the pulses have durations that range 0.1 to 3 psec, and they appear to have been sequences of pulses of even shorter duration that were smeared together by the receiver whose bandwidth was not adequate to respond to each separately. See Figure 13.5.1. The pulses are associated with steps. Proctor (1981) showed that the initial streamers of cloud flashes also extend by a process of stepping. After the flash has extended fully, it emits a succession of separate bursts, or trains of noise. Individually, they appear continuous for durations whose decile values are 40 and 400 psec and whose median value is 80 psec. These waveforms usually begin and end gradually, as shown in Figure 13.5.1, and they are emitted at irregular intervals for some tens of milliseconds after the cessation of the pulses. Whereas the pulsed emission predominates during phases that Kitagawa and Brook (1960) defined as initial and very active (VA) phases, the second type of noise occurs almost exclusively during the J-type or final phase of the flash. The same pattern of behavior is to be found with flashes to ground, with the exception that the pulsed emission is ended abruptly by contact with ground and the return stroke follows immediately. On the other hand, cloud flashes produce a delay of 1 or 2 msec between the cessation of pulses and start of the recoil streamer. When the noise is displayed to a slow time base, the pulsed emission appears to be continuous, and the bursts of continuous noise appear as short and quite separate pulses, which are variously called solitary pulses, burst pulses, and Q-noise. This noise may occur occasionally also during the earlier phases of a flash, but it is far more frequent during

Handbook o f Atm ospheric Electrodynam ics, Volume /

328

R

GROUND FLASH

CLOUD FLASH

J “type

PHASE EFC

e

100 ms

Figure 133.1 Electric field changes produced by (a) ground flashes and (b) cloud flashes. The occurrence of radio noise and its waveforms are also shown.

the later stages. It accompanies some first return strokes and dart leaders, and it precedes and follows first and subsequent strokes. It accompanies a gradual retrogression by which the flash extends backward from its origin at an overall speed near 2 x 10* m s-1. It is usual for subsequent strokes not to emit noise at HF and above. Noise associated with subsequent strokes occurs before and after the return stroke. Sources active immediately before the stroke are located at the far or top end of the channel; sources of the noise that become active at the end of the stroke indicate that the return stroke extended the channel. All the results obtained hitherto are consistent with the belief that radio noise generated by lightning at HF, VHF, and ultrahigh frequency {IMF) (and probably also at microwave frequencies) accompanies ionization of virgin air. When the same pulses are received at widely spaced stations, they are seen to have different durations. This is a temporal manifestation of the Doppler effect It appears as though an array of radiators become activated by a wave so that they radiate briefly in succession. When this wave is directed away from a receiver, the pulse received from the assembly becomes elongated, and in extreme cases appears as a succession of separate impulses. On the other hand, when the wave is directed toward a receiver, the intervals between the instants when the contributors are activated become foreshortened, and the overall pulse is compressed in time. By timing the arrival of pulses received at widely spaced stations, it is possible to locate points associated with the leading and trailing edges of the pulses. The directed line segment joining these two points is termed a pulse-width vector (FWV). It is possible to calculate the source lifetime, length, speed at which it formed, and orientation. Proctor (1981) reported that pulses formed at speeds whose average was near the speed of light. A few superiuminal speeds were supposed at first to be in error. Lifetimes were close to 1 psec. Extents of sources of the longer pulses averaged 270 to 300 m. The median extent of sources active in the lower flashes were estimated to be 60 m by

Radio N oise Above 300 kH z Due to Natural Causes

X , km

329

X,km

Figure 133.2 Two plan views of the same horizontal segment of a high lighting channel. On the left-hand version, the circles have a radius equal to the rms error of measurement, and the arrows are the horizontal components of the pulse-width vectors, which represent the in-pulse activity. Vector V had zero measured extent. The right-hand version shows the time sequence in which the sources became active. Times stated at the top had elapsed after the start of the flash. (Taken from Proctor, D. E. [1981]. J. Geophys. Res., 86(C5), 4041. With permission. Copyright 1981 ACU.)

supposing they formed at the mean speed. The resolution afforded by the system described by Proctor (1971,1981) allowed the PWVs of the longer sources to be found with sufficient accuracy, but this was not true for sources 60 m long. PWVs of the longer pulses in any one flash appeared to lie on the surface of a cone. There was some evidence to suggest that the axis of the cones were affected by the earth’s magnetic field, but the resolution was not adequate for a definite decision to be taken. Although this information concerns processes that generate the radio noise, which are unknown, the matter was dropped, and the emphasis of the work was directed toward a macroscopic view of lightning. Figure 13.5.2 shows PWVs plotted onto a radio picture of a short length of channel. The map has been duplicated on the right so as to show the erratic sequence in which the sources became active. Statistics of step lengths between successively active (high) sources have been given by Proctor (1981). Lightning causes charges to move, and this changes the electric field at ground. Waveforms of electric field change (EFC) and their magnitudes provide useful information concerning light­ ning. Processes such as leaders and return strokes produce characteristic waveforms, which can be recognized on recordings of EFC. Simultaneous recordings of noise and EFCs reveal associ­ ations between these processes and the waveforms of noise that they generate. Recordings of light output have also been used for this purpose. Figure 13.5.1 shows examples of these waveforms and Figures 13.5.3 and 13.5.4 show pulses from stepped leaders and cloud flashes, recorded at baseband, i.e., in bands that extend from DC to the lower portions of the HF band. Figures 13.5.3 and 13.5.4 show responses of linear wideband amplifiers, which incorporated neither tuned circuits nor detectors; the pulse polarities have been reproduced faithfully. In this respect they differ from waveforms of Figure 13.5.1 (later in Figure 13.5.6), which are the responses of envelope detectors that succeeded tuned RF amplifiers, with logarithmic amplitude transferences. The envelope de­ tectors destroyed the polarity information. Figures 13.5.3 and 13.5.4 show pulses that are essen­ tially unipolar, having a large excursion followed by a small and slow overshoot. The “narrow, positive, bipolar pulses” reported by Willett et al. (1989) are likewise essentially unipolar, but were endowed with an overshoot whose magnitude amounted to 20% of the positive excursion. Krider and Radda (1975) and Krider et al. (1975) show histograms of the pulse widths and intervals for flashes in Florida and Arizona. They also distinguish between pulses that occurred early in the leader process (labeled early in Table 13.5.1), and those near ground (late). Their

Handbook o f Atm ospheric Electrodynam ics, Volume /

330

i— r

1 — i— i— i— i— i— i

E(V/m) 30 20 ■ 10 0

40

_

Ftgure 1 3 3 3 Waveforms of noise from lightning ground flashes recorded in a band 0 to 2 3 MHz by Krider et al. The sequence of pulses is shown twice: the top trace is inverted and has been expanded to 8 psec per division; the lower trace is 40 psec per division. L denotes stepped leader pulses. R is noise due to first return strokes. (Re­ produced from Krider, £. P. et al. [1977]. J. Geophys. Res., 82(6), 951. With permission. Copyright American Ge­ ophysical Union.) B x io * (W b/m 2 )

*>■■4 it j

&— i r Jo

Ar n fc

At

wU

& r ~Ao- ~ A o " Ao

B X O * (W b/m 2 )

■"Ae1■*

o— i— A A A

c

'A~ A

A

A

A

MICROSECONDS Ftgure 133.4 Pulses from first leaders in cloud flashes recorded in a baseband from 0 to 3.5 MHz. (Reproduced from Krider, E. P. et al. [1975]./ Geophys. Res., 80(27), 3801. With permission. Copyright American Geophysical Union.)

Table 13.5.1

Widths and intervals between pulses' in cloud flashes and stepped leaders

SL widths SL widths SL intervals SL intervals CF widths CF widths CF intervals CF intervals

Early Late Early Late Arizona Florida Arizona Florida

N

Mean

SD

145 165 119 92 358 346 744 627

33 23 75 13.7 0.74 0.74 5.1

1.8

13 47 4.8 0.23 0.26

6.1

3.1

1.8

Note: Units are microseconds. * Stranger pulses recorded by linear receiver at baseband by Krider and Radda (1975) and Krider etal. (1975).

331

Radio N oise Above 300 kH z Due to Natural Causes TM E 1618-1620 DATE SEPTEMBER 12,1975 LOCATOR: ATLANTA, GA. 3 MHz (VERTICAL)

-H-p •*•»(

))< |

i R - 9 )■ ■ « • < » )♦■■ «.> 4 . ;

3 0 MHz(VERTOAL)

139 MHz (VERTOAL) 295 MHz (VERTOAL)

|.. o f f H f f | m + f

< llf f *■*«♦« >*■

dE/dtrecorded by

74 first return strokes is shown as a

solid line. The dashed line concerns 55 subsequent strokes, and the dotted line was calculated for 18 characteristic pulses. The 0 dB corresponds to 1 V 2 r r r 2 H z -2 at a distance of 50 km. The record length, or window , W = 5.12 psec. (Reproduced from W illett, J. C. et al. [1990]. J.

Geophys. Res., 95(D 12), 20,367. W ith

permission. Copyright

American Geophysical Union.)

have been the subject of papers by Homer and Bradley (1964), Iwata and Kanada (1967), Kimpara (1965), Kosarev et al. (1970), Preta et al. (1985), Serhan et al. (1980), Weidman et al. (1981), and by Weidman and Krider (1986), to mention just a few. See also Section 2.2.2 and Chapter 1/14. 5.1.3.

Polarization of Radiation from Lightning

There appears not to have been any publication regarding measurements of polarization of radio waves generated by lightning at high frequencies. Measurements of this kind might prove to be very interesting. 5.1.4.

Noise Received When Thunderstorms Are Directly Overhead

High electric fields cause corona discharges from antennas and from other conductors. When these are nearby they produce noise of great intensities. Charged raindrops that strike the receiver antenna cause intense noise, known as rain static, to be received. Fortunately, the duration of these disturbances seldom exceed a few minutes. Lewis (1982) estimates the spectral density of antenna noise at 200 MHz due to corona to be 1.5 X 10'16 W Hz-1, which is equivalent to an antenna temperature near 107 K. 5.15.

Radio Images of Lightning

A few examples of radio pictures are given here. Figure 13.5.10 is a picture of a flash having an open structure in which its filamentary nature is cleady evident. This was a high flash. The flash shown in Figure 13.5.11 also consisted of filamentary branches, as shown by detailed plots and by plots of separate coordinates X, Y, Z vs. time. Branches were so entwined as to present an apparently solid obstacle. Waves emitted by sources on the far side of this flash were attenuated by the intervening lightning. Figures 13.5.10 and 13.5.11 are maps of source position obtained using long baselines. Figure 13.5.12 is a two-dimensional picture of a flash recorded using short baselines.

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334

FREQUENCY

CMHz)

Figure 13.5.8 The averaged energy spectrum for 65 leader steps of stepped leaders (solid line) and from 15 steps of dart-stepped leaders (dashed curve). The dotted line replicates the curve for first return strokes shown in the previous figure. Here W = 1.28 psec. All curves have been normalized to a range of 50 km. (Reproduced from Willett, J. C. et al. 11990). / Geophys. Res, 95(D12), 20,367. With permission. Copyright American Geophysical Union.)

m T3

ui 2

UJ

o

< EC

CL

L0

CC

lli 2

o

0.

FREQUENCY

(M Hz)

Figure 13.5.9 Average power spectral density of 15 so-called chaotic leaders recorded during three storms less than 35 km distant (solid curve). The dashed curve concerns 18 narrow positive bipolar pulses recorded by Willett et al. (1989). W = 5.12 psec for the solid curve and 2.56 psec for the dashed curve. Both curves have been nor­ malized to a range of 50 km. The 0 dB corresponds to 1 V2 m_I Hz_J. (Reproduced from Willett, J. C. et al. [1990|. i. G eophys Res, 95(012), 20,367. With permission. Copyright American Geophysical Union.)

Radio N oise Above 300 kH z Due to Natural Causes

335

Figure 133.10 Radio picture recorded at 355 MHz of the upper branches of a high cloud flash. The plan view is shown here. Sources have been mapped with alphabetical symbols that increment for every 10 msec. Sources were located by timing the arrivals of leading edges of the pulses, which were emitted at rates approximately one or two per millisecond, while new channels extended. The filamentary structure is clearly evident. Errors in the three co­ ordinates of each point are 25, 25, 200 m rms.

Previous reviews of radio noise from lightning have been given by Homer (1964), Oetzel and Pierce (1969), Pierce (1977), and Lewis (1982). 5.2.

NOISE DUE TO THE CONSTITUENTS OF THE ATMOSPHERE

The classic article on this subject is by Hogg (1959), and the matter also has been treated by Smith (1982), whose data appear also in CCIR report 720-2. This noise is a strong function of elevation angle and is a minimum at the zenith. It is due to molecular oxygen and to water vapor. The noise due to oxygen occurs in a band (of 43 lines) between 50 and 70 GHz and at 118.74 GHz. There are three components due to water vapor one at 22.2 GHz, one at 183.3 GHz, and another at 325 GHz. Data from Smith (1982) have been published in CCIR 720-2. The curves show noise temperatures plotted to a base of frequency for various elevation angles, and for three values of water vapor density. These curves indicate that at 5° elevation and at 22.5 GHz, the brightness temperature is 118 K when the water vapor concentration was 3 g m 3 near ground, and 265 K when the concentration was 17 g nrr3. See also curve I in Figure 14.2.3 of Chapter 1/14. Radio emissions from hydrometeors are discussed in CCIR 720-2. Attenuation increases with frequency to the millimeter region, and there are no resonant effects. Only the absorption affects radiation, whereas both scattering and absorption contribute to the attenuation. Brightness tem­ perature, Tb for an upward-looking antenna may be estimated from: T„ = Tm(\ - 10-*>°) + Tsky/L

(43)

L = expOW 4.34)

(44)

where

L is the loss factor due to the absorbing medium and A is the one-way attenuation in decibels. A can be obtained from curves in CCIR 719-3 for atmospheric gases and in CCIR 721-3 for hydrometeors and sand. 7"^ is the extraterrestrial background brightness temperature. This ra­ diation is important at frequencies above 2 GHz, as shown by Figure 14.2.3 of Chapter 1/14. For

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336

t—

i— i— |— i— i— i— i— |— i— i— r— i— |— i— i— i— i— |— i— r 16 S 3 2 6 . SS

84 1 6 24

FLASH NQ.

—i— i— i— I— i— i— i

-1 0

i

I i

i

i

-5 X

i

1 i

0

> i

151

« I « i

5

KM.

figure 13.5.11 Elevation (top) and plan views of a radio picture of a flash to ground. The height coordinate Z measured with respect to ground 1430 m above sea level. Detailed plots, and time-based graphs of the separate coordinates showed the filamentary nature of this flash, whose ionized channels are densely packed and effectively obscure radiation emitted by sources on the far side. Lightning flashes also reflect radio waves and permit intermittent viewing of distant TV. (After Proctor, D. E. et al. (1988|.y! Geophys. Res., 93(D10), 12,683. With permission. Copy­ right American Geophysical Union.)

further information, see Chapter 3 of Hall (1979), the CCIR reports mentioned above. Crane (1971), Ippolito (1971), and Decker and Dutton (1970). Charged raindrops that fall onto a receiver antenna cause very strong noise as noted in Section 5.1.4. Ionospheric thermal noise has been received at 2 MHz by Pawsey et al. (1951) using a dipole antenna. The noise originated in the D-layer, and the noise temperature is a few hundred degrees Kelvin. See curve E of Figure 14.2.3, Chapter 1/14. The intensity of this noise is negligible compared with the noise from lightning. The noise has diagnostic value. Hsieh (1966) has derived an expression from which the power per unit bandwidth may be calculated. The Earth’s auroral kilometric radiation (AKR) is shielded from the ground by the ionosphere, but can be detected in space. Active periods last 30 to 90 min, and this noise is received when the north magnetic pole is inclined toward the receiver. It is most intense when the observer’s local time is near midnight, is slightly less intense at dusk, and is —20 dB down at dawn and midday. At 1 astronomical unit (AU) distance its peak intensity is 10 23 W m-2 Hz-1. The source

Radio N oise Above 300 kH z Due to Natural Causes

337

Azimuth, deg. Figure 133.12 Two-dimensional radio picture recorded by X.-M. Shao, P. R. Krehbiel, and R. Thomas in 1992 using a short baseline interferometer. Angular accuracy of each point approximately 1.5°. (Reproduced from Kreh­ biel, P. R. [1992], Private communication. With permission.)

power is 2 to 3 X 107 W. Its spectrum extends below 10 kHz and above 500 kHz. It peaks near 178 kHz, where it fills a cone of some 3.5 sr. This left-hand circularly polarized x-mode radiation originates at local depletions in electron density and just above the local cutoff frequency. See Kaiser and Desch (1984) and Benson and Calvert (1979). 6.

RADIO NOISE FROM THE SOLAR SYSTEM

The sun, the Earth, the moon, and the planets all radiate noise. The strongest is the disturbed sun, followed at HF by Jupiter, at VHF the quiet sun is next. All radiate noise that is strongly dependent on frequency and that varies with time. In recent years many of the planets have been observed at close range by instrumented spacecraft that have provided us with a wealth of information, a little of which is reported in this section. 6.1.

THE SUN

The sun may be quiet; a term that is used to describe regions where its radio emissions are relatively constant and less intense than those emitted by disturbed regions where sunspots and active regions occur. The term disturbed has both a spatial and a temporal connotation. The sun’s visible surface, called the photosphere, has a diameter of 1.4 x 109 m. The photosphere is surrounded by the relatively cool reversing layer a few hundred kilometers thick. A very extensive atmosphere overlies this shell. The lower portion of this atmosphere, the chromosphere, is about 20 Mm thick. The higher portion is the corona, whose visible height exceeds 109 m, but its more tenuous regions envelop the orbit of the earth (mean radius 1.5 x 1011 m) and more. In one sense, the earth is endowed with two atmospheres. Localized magnetic fields (~0.4 T) that emerge from the photosphere (and return to another area of the surface) cause cool surface regions called sunspots to appear in pairs, which rotate with the sun (sidereal period 25 d at the equator and 27.5 d at latitude 45°). Sunspot durations vary from 1 d to several months. Sunspots change in number almost cyclically with a variable period almost 11 years (22 years if their alternating magnetic polarity is taken into account). Sunspots form on the photosphere at the bases of centers

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338 Table 13.6.1

Brightness temperatures of the quiet sun

Frequency (MHz) 200 600 3.000 24.000

Wavelength (cm) 150

50 10

Brightness Temp, (degrees K)

1,000,000 500,000 55.000

10.000

Taken from Piddington, J. H. (1961). Radio Astronomy, Hutchinson & Co., London. With permission.

of activity, which precede, accompany, and outlive the sunspots. Sudden increases in luminosity occur in localized regions adjoining sunspots. These flares, which last fractions of an hour to several hours, are usually accompanied by huge explosions, which eject vast quantities of gas, amounting to 1010 tons or more, into the chromosphere and beyond. The gas drags magnetic fields into space at speeds near 106 m s-1. Some particles ejected by the explosions attain speeds near 1.5 x 10s m s-1. The explosions cause strong, transient, radio emissions called bursts. At the peaks of sunspot activity, several small flares may occur within an hour and one large flare may occur during the course of 50 h. Much more information about the sun is provided by Foukal (1990) and Stix (1991). Noise from the sun is radiated over a wide range of frequencies, although the spectra of the stronger components are sometimes relatively narrow, as the following paragraphs will describe. The intensity of solar noise is low in the microwave and VHF regions. At 10 GHz and higher, it follows the Planck curve for a blackbody at 6000 K. Noise intensities increase to high levels near the center of the HF band, where brightness temperatures of the disturbed sun can reach 10'° K. Even the quiet sun produces brightness temperatures near 106 K. The dominant compo­ nents of radio noise from the sun are nonthermal in origin. In the following paragraphs, noise from the quiet sun is treated first and noise radiated by the disturbed sun is discussed in the following section. Noise from the sun has been reviewed by Piddington (1961) and by Kraus (1986). 6.2.

RADIO NOISE FROM THE QUIET SUN

Electron density decreases with height above the photosphere. Allen (1947) published a formula, the Baumbach-Allen formula, derived from observations of optical brightness. At some height H the plasma frequency will be / = /n, as given by Equation 39. Below H, any radiation at/ will be absorbed, and therefore will be attenuated. Above H, the plasma will be transparent to waves of frequency / By Kirchoffs law, plasma above height H cannot radiate efficiently (because it does not absorb effectively.) Therefore waves of frequency / will originate just below H. Fur­ thermore, radio waves that originate at greater heights H, will emerge only if their frequencies are correspondingly lower than f. Between heights of 7 x 10* and 1.7 x 107 m above the photosphere, the temperature increases with height, from 7000 to ~ 2 x 106 K, after which it decreases so slowly with height that it can be considered constant at Iff K to a height near 5 x 109 m. (See Piddington, 1961.) Because the measured brightness temperatures at various frequencies (hence at calculable heights) agree reasonably well with the known electron temper­ atures of the sun’s atmosphere, it follows that the radiation is thermally generated. Measured brightness temperatures vs. frequency and wavelength are shown in Table 13.6.1. Noise from the quiet sun has been described by Rohlfs (1986), Piddington (1961), and Kraus (1986). 6.3.

RADIO EMISSIONS FROM THE DISTURBED SUN

There are two kinds of noise from the disturbed sun, namely: (1) those that vary rapidly, such as bursts, or during storms; and (2) those that vary slowly in intensity.

Radio N oise Above 300 kH z Due to Natural Causes

339

6.3.1. Solar Bursts The classic article on this subject was written by Wild et al. (1963). It was updated by Wild and Smerd (1972). Further information appears in reviews by Dulk (1985), Piddington (1961), and Kraus (1986). Flux density of emissions received from the sun are shown plotted to a base of wavelength in Figure 13.6.1. The strongest radio emissions from the sun occur as intermittent bursts that may last from seconds to tens of minutes. One type called a noise storm may continue for a day or more. Solar noise bursts radiate from 30 GHz to 30 kHz or lower. The earth’s ionosphere obscures this radiation below some frequency in the range 3 to 12 MHz. As the sources of some of these emissions travel out from the photosphere, their frequencies change. Time-resolved spectra of these emissions have been displayed and recorded by devices known as dynamic spectrographs, the first of which was built by Wild et al. (1954) specially for this purpose. Examples of their truly spectacular spectrograms are shown in Figure 13.6.2. Many radio bursts have been classified by their dynamic spectra. Types of bursts are listed in Table 13.6.2. Type I continuum may last from a few hours as a storm continuum, to days or even weeks, when it is called a Type I storm. It causes serious interference to radar and to sensitive receivers that operate at meter wavelengths in a band 50 to 300 MHz. (It was discovered by British radar operators of the Chain-Home system. See Kraus (1986) or Hey (1971)). Circularly polarized components are strong. Type I bursts are narrowband bursts of short duration. Sometimes they are accompanied by Type I continuum. The width of their spectrum is approximately 1% of their center frequency, and they last for a few tenths of a second to 10 s. About half exhibit frequency drift. During periods of intense solar activity, hundreds of these bursts may be received every hour. Type II bursts are also called slow-drift bursts or outbursts, and are the most powerful of the solar bursts. They are associated with large flares and begin some 5 to 20 min after the start of the flare. Dulk (1985) states that although a clear relationship between Type II bursts and visible events could be observed during periods of low solar activity, this association was not always evident when solar activity was high. Type II bursts drift from high to low frequencies at rates as high as 1 MHz s_l. Almost half duplicate their spectral features with equal strength at the second harmonic. No other harmonic is ever observed. Wild and Smerd (1972) discuss four radio images that showed the two sources were displaced laterally, and were equidistant from the flare. They suggest that the second harmonic is due to waves that propagated back toward the sun before being refracted by the corona so that they emerged again. At any instant. Type II emissions occupy narrowbands, often only a few megahertz wide. They exhibit band-splitting in which their spectra split into two or more bands separated some 10% of center frequency. Type II bursts are associated with gas streamers that are ejected at 106 m s-1. Wild and Smerd (1972) discuss two theoretical models, and also provide radio images of the sources. One is shown here as Frgure 13.6.3. About 20% of Type II bursts are followed by Type IV continuum. Type III bursts are fast drift bursts, and they occur more frequently than the Type II. At times of sunspot maxima they occur at an average rate of three per hour, and even more frequently during times of strong activity. They drift rapidly from high to low frequency at ~ 20 MHz s_l, and last for some 10 s. Some Type III bursts occur individually, some successively in groups, and others in persistent storms. Solar flares initiate groups of intense bursts during the course of 1 or 2 min. Their cause is ascribed to fast electrons that are ejected by the explosions and that travel at speeds 0.1 to 0.5 c along open field lines. Wild et al. (1963) state that Type ID have been observed at frequencies as high as 600 MHz. Dulk (1985) sets their low frequency limit below 30 kHz. Sometimes both the fundamental and the second harmonic are present. At fre­ quencies above 100 MHz only the second harmonic is observed. A few show dynamic spectra shaped like inverted Js and inverted Us. Some radiate over only a limited frequency range. Some 10% of Type HI bursts are followed by Type V continuum.

340

Handbook o f Atm ospheric Electrodynam ics, Volume / FREQUENCY Me/*

WAVELENGTH Figure 13.6.1 The intensities of various components of solar emission measured by Wild et al. (1963). (Reproduced from W ild,). P. et al. [19631. Annu. Rev. Astron. Astmphys., 1, 291. With permission. Copyright 1963 by Annual Reviews Inc.)

Figure 13.6.2 Diagram showing some dynamic spectra recorded by Wild et al. (1963). (Reproduced from Piddington,). H. [1961]. Radio Astronomy, Hutchinson & Co., London, copyright 1961. With permission.)

—100% x-mode?

M = MHz; G = GHz; k - kHz; 1 AU = 1.5 x 10" m, R„ = 7 x 10s m.

> I0 13

Low

—107

Minutes to hours

—10 ms burst — 10 min (group)

—10% x-mode

< 10% x-mode —30% x-mode

—0.5-5G/a few M

1-10 G/5 G

1-30G/I0G

100-10 M/50 M 3-30 G/IO G

50-300 M/100 M

60-100% o-mode

IO7-10>

I0 *-I0 " I07-I0»

200-10 M/100 M

200-10 M/> 10 M

200-1 M/10 M 2 harmonics

200-1 M/10 M

50-300 M /-I M burst —100 M (storm) 50M-30 k

Frequency Range/ Bandwidth*

0-40% o-mode?

Fund: 30% Harmonic: 10% o-mode low-high x-mode

Usually unpolarized

50-100% o-mode o-mode

Polarization (Circular)

—IO min

> l min > l min (at I0G)

> 10'

I0M 0 '2

lOMO'MO 15 at —1 M I0 M 0?

lOMO"

-> 10'’

~ > 1010 ~ > I0 9

rb(K)

IO4—IO5 km closed

IO4—105 km closed

104—103 km closed

0.5-2 Rg open? —10* km closed

0.1-0.6 R„ closed?

0.1-1 R,. closed?

0.2-200 R,. open but closed for U or J 0.5 to Few R„ plasmoid

0 .2-200 Ro open

0.6 R„ to 1 AU/open

—

0.1-0.6 R„ closed

Height Range/Magnetic Topology

Reproduced from Dulk, G. A. (1985). Amu. Rev. Astron. Astrophys., 23. 169. With permission. Copyright 1985 by Annual Reviews Inc.

*

Microwave postburst Microwave spikeburst

Microwave IV

—20 min

IV Rare continuum IV Storm continuum V Microwave impulsive

Few hours

—30 min

Few seconds

—> 1 0 min

~ 10- “ • Day 5 x CIO*27 10*27* « Night 3 x 10*2* 2 x 10*25' IO*27'

10 10-u 3 x 10*25 4 x IO* 19

100

1,000

,o-i« io-ii 10*22 2 x 10*21 2 x 10*27 2 x IO*27

—

—

—

10-256

_

_

IO"29 est 6 x 10- 22

— — 2 x IO"22 8 x IO*21

10,000 8 x 10“ 2 x 10“ 5 X IO*27

1-57 io - 27 —

— 4 x IO"21

Note: Units are W n r2 Hz*1. Listed values at 0.1 MHz and at 1 MHz are valid above the ionosphere. 1 AU - 1.47 x 10" m; •

Warwick et at (1979);b Catr et al. (1983);c Warwick et al. (1989);* Can et al. (1981);' Warwick et al. (1981); f Calculated from 106 K and 9.5 I0*10steradians; * Warwick et al. (1986); h Zarka and Pedetsen (1986), 5 x 10*23 at 1 A U;' Calculated for a beam width of 0.1 steradian.

7.1

JUPITER

Its equatorial radius is more than a tenth of the sun’s radius. It has its own source of heat. Its rotational period varies with latitude, and, using its radio emissions, Riddle and Warwick (1976) measured 9 h 55 min 29.71 s for the equatorial region. The orbital period is 11.86 years, but because the Earth’s period is so much shorter, Jupiter’s synodic period is only 399 days. Burke and Franklin (1955) first reported radio noise from Jupiter. The subject has been re­ viewed by Carr et al. (1983) and by Carr and Kraus (1986). Remarkable data were obtained from several spacecraft, including Pioneer 10 and 11, Voyager 1 and 2, IMP-66, RAE-1, and Ulysses. Dynamic spectra were published by Warwick (1963) and by Kaiser and Desch (1984). Jupiter radiates intermittent, strong and fluctuating noise from 1 kHz to almost 40 MHz. It also emits weaker, continuous radiation that extends above 100 MHz to the microwave region, as Figure 13.7.1 shows. Between 1 and 40 MHz its radiation is elliptically or circularly polarized, and its

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344

KILOM^RIC

BAND DESIGNATIONS DECAMETRIC DECIMETRE

HECTOMETRIC

n

3 0 km

1---------- 1---------- 1---------- 1---------- 1---------- 1— i

3km

30 0m

30 m

3m

30cm

3cm

— WAVELENGTH Figure 13.7.1 Average power flux-density spectrum of Jupiter's non thermal magnetospheric radio emissions. Burstcomponent flux densities were averaged over inactive as well as active periods; the instantaneous spectrum may appear considerably different. The highest burst peaks attained values one or two orders of magnitude above the curve. The solid line part of the burst-component curve is from Schauble and Carr (unpublished). Flux densities are normalized to a distance of 4.04 All. (After Carr, T. D. et al. [19831. Physics o f the Jovian Magnetosphere, The Cambridge University Press, Cambridge, U.K., chap. 7. Reproduced with permission.)

nonthermal nature is confirmed by its spectrum. Jupiter emits thermal radiation above 2 GHz. Table 13.7.1 lists some equivalent blackbody temperatures. Kaiser et al. (1979) reported the occurrence of Type HI Jovian bursts and showed a dependence o f reception of HF radiation on the Jovian longitude of the receiver. Measurements at 22 MHz reported by Douglas and Smith (1963) indicated that Jupiter beamed its radiation that could be detected if the beam were directed toward the receiver and if the beam happened to be active. There are at least three such possible beams. They are located in three longitudinal regions, 1, 2, and 3 (also called B, A, and C). A has the highest probability of occurrence (0.3), and is near longitude 225°. B and C have prob­ abilities of occurrence approximately 0.03 and radiate from longitudes near 120° and 300°, re­ spectively. Jupiter’s magnetic axis, tilted at 10P to its rotational axis, leans toward the 220° meridian in the Northern hemisphere (Kaiser et al., 1979). Bigg (1964) analyzed data that had been collected over 4 years by J. W. Warwick and found that the satellite Io played a major role in some of the radiation processes. Decametric radiation is received from source B when the range of longitudes occupied by B lies on the line of centers between Jupiter and the receiver. A second prerequisite is for the orbital phase of Io to be almost 90° from superior geocentric conjunction. The reception of radiation from A or C was likely when their longitudes were on line to the earth, and Io was near 240° from superior geocentric conjunction. Some HF radiation from A was found to be unrelated to Io, as was the radiation below 2 MHz. Emissions were classified as Io A, Io B, Io C, and non-Io A. There are also Io D,

Radio N oise Above 300 kH z Due to Natural Causes

1C

■■ IS

17

C6

tIGHT aSCCHSION

345

as

Figure 13.73. Radio image of Jupiter's emissions at 2 cm. Most of this radiation will have been thermal in nature. Contour values in degrees Kelvin are 1.8 , 5 ,9 ,1 8 , 44, 71, 98,124,151,160,168, and 174. The size of the half­ power beam width is shown. (After de Pater, I. and Dickel, J. R. [19861. Astrophys. J , 308,459. Reprinted with permission.)

non-Io B, and non-Io C. Io’s surface is frosted with solid SO2 (Howell et al., 1984) and volcanoes spew SO2 (Pearl et al., 1979) to produce sulfur, oxygen, and other atoms in an ionized trail called the Io torus (Shemansky, 1987), which has been mapped by Voyager 1 (Warwick et al., 1979). HF radiation consists of L-bursts that last 1 to 6 s, and that repeat randomly during the active interval, which may last several hours. There are also S-bursts that last 5 to 50 msec. Warwick et al. (1979) found that HF dynamic spectra, recorded by Voyager 1, were often curved. Also the spectra showed that the center frequency of the radiation increased, reached a maximum, and then decreased, and that at any instant the noise occupied a band that was often less than 10 MHz. Lecacheux et al. (1992) and Warwick et al. (1977) describe a hectometric (HOM) component, which can be detected from 40 kHz to a few megahertz and which peaks near 1 MHz. Sources occur in auroral regions in both magnetic hemispheres and with opposite senses of circularly polarized waves. This radiation is modulated by the planetary rotation so that there are two peaks in the probability of occurrence per rotation. Lecacheux et al. (1992) report that comparisons between observations made with the two Voyager craft (the RAE-1 and the IMP-6) with those taken on the Ulysses craft, show that the longitudes of the peaks change some 60° as the latitude of the observer varies over some 20°. There are two kilometric components, broadband and narrowband. These are designated bKOM and nKOM and they originate at high latitudes on the daylit side and from another source in the Io torus. The broadband radiation (bKOM) is a bursty radiation, is strongly polarized, and extends from 10 kHz to 1 MHz. Both its intensity and its duration decrease with frequency above 100 kHz. Its probability of occurrence, when plotted to a base of longitude, shows two maxima 180° apart, and it appears in antiphase with HOM. This indicates that it is somehow linked with HOM. Lecacheux et al. (1992) stated that there were indications that bKOM was radiated in two beams, north and south of the Jovian equator.

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•i «

M

•7

Radio image of Jupiter at a wavelength 20.5 cm. Most of the emission will be due to synchrotron radiation. The Central Meridian longitude is 200°. Contour values in degrees K are 119,178, 237, 297, 356,416, 475, 594, 712, 831, 950, and 1070. (After de Pater, I. and Dickel, J. R. 11986]. Astmphys. J., 308,459. Reprinted with permission.) Figure 13.7.3

nKOM is a smooth, narrowband radiation that occurs within a 50-kHz band centered near 150 kHz (Lecacheux et al., 1992). An event may last 2 h and recur after one rotational period. Its source slips with respect to the rotation of the planet, lagging 3 to 5%. Spectral lines of the narrowband radiation are separated by approximately 200 Hz, the gyrofrequency for 10~8 T in the Io torus. de Pater (1990) shows images of Jupiter’s thermal radiation at 2 cm (see Figure 13.7.2) and of synchrotron radiation at 20.5 cm (shown in Figure 13.7.3). The radio images appear to emerge from a region 3 to 5 times the size of the visible disk. Figure 13.7.4 shows a spectrum, published by de Pater (1990), of microwave emission from Jupiter. Between wavelengths of 1 and 6 mm the brightness temperature is approximately 170 K. There is a minimum of 140 K at 1.26 cm. At 20 cm the brightness temperature is —370 K. de Pater et al. (1982) describe thermal emission from Io; and report blackbody temperatures 85 and 90 K at 2 and 6 cm, respectively. The following calculation gives an idea of the intensity of the noise from Jupiter. Figure 13.7.1 gives a flux density of 5 x 106 Jansky at 10 MHz at a distance of 4 AU. Jupiter’s average distance from the earth is near 5 AU. Assume that this radiation is circularly polarized, and that the ionosphere is transparent. A 10-MHz receiver, having a noise factor of 10, bandwidth B, is connected to an antenna of gain 6 with a lobe on Jupiter. The ambient temperature of the receiver is 290 K. The effective capture area of the antenna, A = X2g/4n = 430. The received power is P = BSA = B X (0.5) X (5 X IO"20 X 16/25) X (430) W. The factor 0.5 comes about because we assume that the receiver antenna is linearly polarized. Now kTB = 4 x 10-21 B W. Therefore, the input signal-to-noise ratio (SNR) is 1720. The noise factor is 10, and therefore the output SNR is 172 or 22 dB; and the noise from Jupiter will be received strongly. According to Carr et al. (1983) the highest peaks can exceed these levels by 10 or 20 dB. 7.2.

SATURN

This is another giant Its orbital radius is almost 10 AU. Warwick et al. (1981, 1982) mention two kinds of emission, Saturn’s kilometric radiation (SKR) and Saturn’s electrostatic dischaige

Radio N oise Above 300 kH z Due to Natural Causes

-i

0

A

lo fu iU u n « > v i l a |t h (cm)

347

1-8

Radio spectrum of Jupiter. Superimposed are two model atmosphere calculations. (After de Pater, I. [1990). Annu. Rev. Astrophys., 28, 347. Reproduced with permission. Copyright 1990 by Annual Reviews Inc.)

Figure 13.7.4

(SED). Saturn’s SKR has been received at frequencies below 1.2 MHz. Carr et al. (1981) show a spectrum that peaks near 200 kHz. The SKR radiation is bursty, strongly polarized, and cor­ relates with the rotation period of the planet, 10 h 39.4 min (Desch and Kaiser, 1981). Warwick et al. (1989) state that the burst radiations from Saturn, Jupiter, and Uranus are x-mode. Thieman and Goldstein (1981) describe the arc structure of the dynamic spectra. Sources are situated on the dayside. Sources are variable due to the influences of solar wind and the satellite Dione. Kaiser etal. (1980) quote SKR flux density in the band 60 to 500 kHz as 10-,9 W m-2 Hz-1 at a distance 4.04 AU. Thieman and Goldstein (1981) quote a median level 10-206 W m-2 Hz-1 at 1 AU (= 1.5 x 10" m). Desch and Kaiser (1981) report a 66-h modulation of SKR that is both frequency dependent as well as dependent on the phase of the satellite Dione. Saturn’s SED radiation is unpolarized, extremely impulsive, and very broadband (it was re­ ceived over the entire band of the receiver 20.4 kHz to 40.4 MHz). Kaiser et al. (1983) state that the noise is grouped into episodes that recurred at intervals of 10 h 10 min, rather more frequently than the rotational period of 10 h 39.4 min. de Pater (1990) has published images obtained at wavelengths of 2 and 6 cm. The A and B rings and the Cassini division are discernible in these radio pictures. Microwave emission from Saturn has been reviewed by de Pater (1990) and uses data by Dowling et al. (1987), Grossman et al. (1989), and Briggs and Sackett (1989). This shows almost constant brightness temperature ~130 K between wavelengths of 1 mm and 2 cm, then rising to 310 K at 63 cm. 7.3.

URANUS

Zarka and Pedersen (1986) report that noise from Uranus consists of bursts lasting 100 to 300 msec. It occupied a band 900 kHz to 40 MHz. They publish a spectrum normalized to a distance 1 AU. (The orbital radius is 19.5 AU.) Between 1.3 and 30 MHz the flux density was 10"23 to 10"22 W m-2 Hz-1, and fell to ~ 2 x 10-23 W m-2 Hz-1 at 40 MHz. Average flux densities were

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stated as 6 x 10-24 W m~2 Hz ' at HF and 2 x 10-22 W m-2 H z 1 at LF. They state that the spectra were similar to those of SED and terrestrial lightning. Warwick et al. (1986) report that the emission was modulated with period 17.24 h, which was the rotational period of Uranus’ magnetic held. They publish separate spectra for day and night, both normalized to 1 AU. The former extends 50 to 100 kHz and peaks near 104 Jansky at —80 kHz. The nighttime spectrum extends to 800 kHz, peaking about 5 x 104 Jansky near 90 kHz. de Pater (1990) shows a spectrum of the microwave emission from Uranus. Disk-averaged brightness temperatures taken after 1973 increase almost linearly from 80 K at 1 mm wavelength to 260 K at 20 cm. Temperatures measured before 1973 were cooler as the warm pole was not then in view. The difference at 1 mm was small; however, at 1 cm, the difference in brightness temperature amounted to 100 K. de Pater (1990) also shows radio pictures of Uranus taken at 2 and 6 cm. 7.4.

NEPTUNE

Warwick et al. (1989) received two kinds of noise from Neptune: bursts and smooth emission. Bursts recurred at intervals of 16 h, with some missing episodes. The rotational period of the planet was 16.10 h ± 0.08 h. The burst emissions lasted for an hour or so and were polarized strongly, being left-hand circular both before and after closest approach. Smooth emissions near 100 kHz occurred repetitively at particular subspacecraft longitudes. The spectrum of radiation normalized to a distance of 4 AU, extended from ~ 1 0 -23 W m-2 Hz-1 at 50 kHz, to 2 x 10-26 W m-2 Hz-1 at 900 kHz. Orbital radius is 30.6 AU. de Pater (1990) shows a spectrum of the microwave radiation from Neptune. At 1-mm wave­ length the brightness temperature is —90 K. At 2 cm measured values vary from 140 to 230 K; at 20 cm the brightness temperatures are 230 K. 7.5.

TERRESTRIAL PLANETS

Radio noise from the earth is discussed briefly at the end of Section 5.2. Table 7 includes data concerning microwave radiation from the other terrestrial planets. 7.6.

THE MOON

The moon behaves as a thermal emitter. It is a source of radio waves, not merely a reflector. Its equivalent temperature varies with lunar phase, but its radio brightness is not maximum at full moon; instead it reaches maximum 35 d later. The equivalent temperatures vary much less than the infrared emissions. This behavior has been explained by supposing that the radio emissions originate some depth below the surface, and that two substances, rock and overlying dust, act together to moderate changes in equivalent temperature at radio frequencies. Dicke and Beringer (1946) and Piddington and Minnett (1949) measured lunar emissions at 1.25 cm. Temperatures vary from 200 to 277 K. At 3.15 cm Mayer et al. (1961) measured 188 to 200 K at 8.6-mm wavelength. Gibson (1958) measured 150 to 217 K. Further details are given by Piddington (1961) and by Kraus (1986). 8. 8.1.

NOISE FROM THE GALAXY AND BEYOND

GALACTIC SOURCES

Figure 13.8.1 shows a spectrum of noise from the sky. The temperatures have been averaged so that small-scale spatial variations of temperature and temperature changes due to bright individual objects have been smoothed out. This spectrum shows that the galactic noise predominates be­ tween 20 MHz and 1 GHz, in directions away from the sun and Jupiter. At 30 MHz, the galactic noise is almost as intense as noise from the disturbed sun. At 300 MHz galactic noise is 20 dB weaker, and at 10 GHz it is about 12 dB weaker than noise from the disturbed sun. Figure 13.8.1 shows that between 1 GHz and about 30 GHz the background noise sets a limit of 2.7 K on the

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Wavelength Figure 13.8.1 Antenna noise temperature as a function of frequency and angle from the zenith. A beam width less than a few degrees and 100% efficiency are assumed. The cosmic noise between 10 MHz and 1 CHz after Ko and Kraus (1957); cosmic noise above 1 CHz after Penzias and Wilson (1965); atmospheric noise after Croom (1964) and Radio Explorer Satellite RAE-2; noise-labeled atmospherics after CCIR 322,1964; cosmic noise below 10 MHz after Novaco and Brown (1978). (From Kraus, ). D. (1986). Radio Astronomy, 2nd ed., Cygnus-Quasar Books, Powell, OH. Reproduced with permission.)

sensitivity of radio telescopes. This background noise is independent of direction. Its source envelops the universe. It was discovered by Penzias and Wilson (1965) and is ascribed to the primordial fireball that initiated the universe. It can be measured using special techniques. See Dicke et al. (1965), Wilson (1983), and Uson and Wilkinson (1988). Above 40 GHz, another limit is set by quantum noise whose temperature is: T = hf/k

(45)

where h and A are the Planck and Boltzmann constants, respectively, and / i s the frequency. The spectrum of this photon noise is shown as line K in Figure 14.2.3 of Chapter 1/14. Figure 13.8.1 also shows the limits imposed by atmospheric absorption for three zenith distances (angles from zenith). Also shown are the resulting atmospheric window and the cosmic window. The diameter of the galaxy is approximately 100,000 light years (ly) (1021 m). At optical wavelengths its axial extent is 6,000 to 10,000 ly. The galaxy is shaped like a disk. Radio observations of hydrogen-line emission have shown that the galaxy has a spiral structure that lies in the plane. At other radio wavelengths, the galaxy resembles a spheroid. The axial bulge, evident in the radio part of the spectrum, is called the galactic halo. A similar state of affairs is evident

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for other spiral galaxies, e.g., the Great Nebula in Andromeda, The halo has become the subject of a controversy that has been reviewed by Salter and Brown (1988). At low frequencies, noise from the galaxy partially obscures our view of regions beyond the galaxy. At frequencies above 300 MHz, the galactic noise increases in intensity toward the galactic plane and it is strongest in the direction of the galactic center. Figure 13.8.1 indicates that between frequencies of 10 MHz and —2 GHz, noise from the galactic center is some 10 dB stronger than noise from the galactic poles. At frequencies below 300 MHz, absorption by singly ionized hydrogen, which pervades the galaxy, causes the intensity of the galactic noise to form a local trough in the directions of the galactic plane. For this reason the map drawn from measurements at 15-m wavelength ap­ proximated a negative of one resulting from a survey at 22 cm, and the map at 3.5-m wavelength showed less contrast than the other two. (See, for example, Piddington, 1961.) The galactic plane is tilted roughly 63° from the Earth’s equatorial plane. Figure 13.8.2, a radio map of the galaxy, shows that the galactic plane cuts the equatorial plane at right ascension 18 h 44 min. The galactic center is near right ascension (RA) 17 h 40 min, and —30° declination, in Sagittarius. The sun is some 30,000 ly from the galactic center, situated in one of the spiral arms. A series of maps of radiation below 16.5 MHz has been published by Ellis (1982). Other medium resolution maps have been produced by Caswell (1976) at 10 MHz, Cane (1978) at 30 MHz, Williams et al. (1966) at 38 MHz, Landecker and Wielebinski (1970) at 85 and 178 MHz, Taylor (1973) at 136 and 400 MHz, Droge and Priester (1956) at 200 MHz, Ko and Kraus (1957) at 250 MHz (see Figure 13.8.2), and Berkhuijzen (1972) at 820 MHz; and COR 720-2 shows maps due to Hasiam et al. (1982) at 408 MHz. Authors who published high resolution maps have been cited by Verschuur and Kellerman (1988). To illustrate the magnitude of noise from the galaxy, we consider a receiver, center frequency 30 MHz, bandwidth B, and noise factor F = 3 dB. The receiver is connected to a high-gain antenna of gain = g and effective capture area = A„ and it is linearly polarized. Its beam width is: ft = 4n C\lg steradians

(46)

The antenna views a segment of sky where the average brightness temperature Ts = 1300 K is constant over the beam width. We shall calculate now the ratio of galactic noise received to receiver internal noise at the receiver output, i.e., the output signal-to-noise ratio (output SNR). The ionosphere is transparent at this time. Denote the receiver ambient temperature by T,. We may calculate A, using Equation 2. Using this, and Equations 3 ,4, and 5, we And that; Pr = k Ts B Ci

(47)

Hence the signal-to-noise ratio at the input, in the absence of feeder loss, is: (kT, B C m Tr B) = C, T,ITr

(48)

Now F is defined to be the quotient (SNR at the input of the receiver)/(SNR at the output of the receiver). Here F = 2. Therefore: Output SNR = C, TJ(2 Tr)

(49)

If C, ~ 1, the output SNR ~ 1300/(2 x 290) = 2.24 or 3 5 dB. Notice that Equation 47 is independent of antenna gain. Thus if we were to use an antenna with a wider beam, then toe effective brightness temperature of the sky would be averaged over a wider segment and might therefore be a few decibels less. The precise amount of the reduction would depend on which part of the sky were viewed.

Figure 13.8.2 Radio sky background contours at 250 MHz as observed with 96-helix radio telescope at Ohio State University, after Ko and Kraus (1957), with extension south of -4 0 “ declination after DrOge and Priester (1956). The positions of a number of discrete radio sources are indicated. The dashed line represents the Galactic Equator. The galactic coordinates are new system (bn , 1"). Contours labeled n, are for temperatures 80 + 6 n degrees K. (From Kraus,). D. [1986], Radio Astronomy, 2nd ed., Cygnus-Quasar Books, Powell, OH. Reproduced with permission.)

Right Aactnsion (1950), hrs

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58°35'

58°33'

58°31'

23h

21m

308

23h 21m

108

23h

20m 508 (1950)

figure 13.8.3 Radio contour map of Cassiopeia A recorded at a wavelength of 21 cm by Ryle et al. (1965) in Cambridge, U.K. Their telescope comprised two dishes separated by a fixed distance and a third movable dish, each 60 ft in diameter. Repeated scans at various spacings permitted them to synthesize an aperture 1 mi in diameter. This yielded a resolution 23 sec of arc. The map shows the main optical filaments. Some of the brighter stars in the field of view are mapped with crosses. Contour intervals are 3000 K. This source is a supernova remnant that exploded ca 1700 AD. It is expanding at 5000 m s- '. It is ~ 10 ' 7 m distant. (Reprinted from Ryle, M. et al. [1965]. Nature (London), 205(4978), 1259. With permission, copyright [1965] Macmillan Magazines.)

8.2.

DISCRETE SOURCES

Radio astronomers routinely observe sources of very small angular extent through a background of noise radiated by the galaxy. They even produce highly resolved images of these small sources. An example is shown by Ftgure 13.8.3. How do they detect these sources in the presence of stronger noise from the galaxy? First, we notice that a change to higher frequency reduces the noise contributed by the galaxy, as shown by Figure 13.8.1. A change to high frequency also increases the resolving power of an antenna of a given size, so that more detailed images are possible. Equation 47 shows that the reduction in beam size does not reduce the power received from an extensive source in the field of view. Reducing the beam size until it is less than or equal to the extent of the target source does increase the power received from the source, because the source then contributes more effectively to the average in the beam. Radio astronomers use receivers that generate very little internal noise. Weak sources are detected by averaging their emissions over long times. The number of samples taken in a given interval of time is increased by using wide predetection bandwidths. The accuracy with which intensities are measured is proportional to the square root of the ratio of pre- to postdetection bandwidths. There are also techniques in which the receiver input is switched repeatedly from the antenna feed to a cold resistor, and back again, so that the temperature difference is measured. These techniques permit noise temperatures to be measured in the presence of relatively stronger receiver noise. See, for example. Hey (1971), Kraus (1986), Piddington (1961), Rohlfs (1986), or Verschuur and Kellerman (1988). Pulsars radiate in narrow beams. They also rotate, and therefore their radiation can be received only when the beam is directed toward the receiver. Their emissions are received as pulses whose periods range from 15 msec to 2.5 sec. They radiate at frequencies between 200 MHz and 9 GHz. (There is one that radiates as low as 10 MHz.) The density of free electrons in the galaxy

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is approximately 3 x 10-8 m 3, which is sufficient to cause the medium to be dispersive. Emission from pulsars may be timed at two frequencies, and the difference in time of arrival (sometimes amounting to seconds for frequency differences of 100 MHz at VHF) permits the distance of the source to be estimated. Moreover, their speed of rotation diminishes with time in a manner that permits their age to be estimated from measurements of rotational period. Quasars, or quasi-stellar objects, are thought to be centers of distant galaxies. One is estimated to be 3.5 x 1023 m distant; another’s range is estimated at 1.5 x IO30 m. There are many strange and interesting objects that may be observed in the radio spectrum (see Kraus, 1986). 9.

NOTES ON INSTRUMENTATION

One of the problems associated with recording impulsive noise that is not steady but instead consists of strong bursts that occur at intervals in an otherwise quiet background, arises when AC-coupled circuits are followed by amplifiers that have been biased near cutoff, or if they are followed by devices of other kinds that are endowed with some sort of threshold. Examples are capacitor-coupled amplifiers, tape recorders, or a display screen with a sharp boundary. Consider an interstage coupling network consisting of a series capacitor C and a shunt resistor R. The time constant is given by the product RC. During a quiescent interval a direct voltage V appears across C. A strong positive-going signal is (hen applied to the input The voltage V will gradually adjust so that the average potential of the signal across R is zero. In the process of this adjustment charge flows so that the voltage across C increases. The trouble arises when this is large enough to cut off the following stage, which then responds to only the upper portion of the input wave. Weaker signals that immediately follow may not produce any response from the amplifier. This problem is aggravated by the incorporation of DC restorers. It is avoided by judicious choosing of the time constant, by using direct coupling, or by causing the wave to modulate a carrier, so that a balanced waveform is produced. Such a waveform is usually available at the intermediate frequency (IF) stages of receivers. Tape recorders often avoid these problems by using frequency modulation, which provides an additional benefit that DC levels can be recovered. Track-to-track timing problems can arise in multitrack tape recorders. Even high-quality ma­ chines suffer from these defects, which arise because of tape stretch and because the tape tends to yaw as it passes the head. Fixed delays are caused when tape heads have been staggered along the line of the tape, to permit the required number of heads to be stacked closely. The absolute values of the delays depend on the tape speed, and erratic delays amounting to 25 or 50 psec are typical, unless special deskewing circuitry has been incorporated. It is a simple matter to measure these delays, by recording a series of pulses with a pulsed repetition frequency (prf) of a few kHz and with all tracks connected in parallel, and then observing the replayed pulses on the individual channels using the output of one tape channel to trigger the oscilloscope. Designing suitable deskewing circuitry does not present insuperable problems. Problems can arise when noise is displayed to a base of time on a cathode ray tube. Care must be taken to ensure that the time base speed has been matched to the duration of shorter pulses of high amplitude; otherwise the number of electrons that impinge on the screen may not be sufficient to illuminate the screen during the deflection caused by a large pulse, which then goes undetected. This problem can be alleviated by applying the signal, with appropriate polarity, to the Z axis also. It is necessary to rectify bipolar signals before applying them to the cathode ray tube (crt) grid. The receiver used by the Central Radio Propagation Laboratory (CRPL) to record noise in­ corporated an attenuator in the early stages of the IF amplifier chain. This attenuator was driven by the detected output, so that a constant output voltage was maintained. The attenuator shaft drove a potentiometer that provided a voltage indicative of the attenuator setting, and this voltage was recorded. Homer (1964) has reproduced a block diagram of this receiver. Modem technology makes it possible to devise many elegant variations of that approach. High-speed digitizers are

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available that will permit signals to be stored in computer memory for transfer to bulk storage. Modem computer techniques permit statistics to be computed, perhaps even in real time. ACKNOWLEDGMENTS I am indebted to Dr. George Nicholson for his advice and for providing library facilities. I have benefited from discussions with Professor Duncan Baker, and from correspondence with Dr. Fred Homer. I extend my thanks to all three gentlemen.

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Douglas, J. N. and Smith, H. J. (1963). Decametric radiation from Jupiter, Astron. J., 68 , 163. Dowling, T. E , Muhleman, D. O., and Beige, G. L (1987). Icarus, 70, 506. Drbge, F. and Priester, W. (1956). Z Astrophys., 40, 236. Dulk, G. A. (1985). Radio emission from the sun and stars, in Annu. Rev. Astron. Astrophys., 23, 169. Ellis, G. R. A. (1982). Galactic Radio Emission below 16.5 MHz and the galactic emission measure, Aust. J. Phys., 35, 91. Epstein, E. E (1959). Anomalous continuum radiation from Jupiter, Nature (London), 184, 52. Foukal, P. (1990). Solar Astrophysics, John Wiley & Sons, New York. Gibson, J. E (1958). Lunar thermal emission at 35 KMC, Proc. IRE, 46, 280. Gibson, J. E. and McEwan, R. J. (1959). Observations of Venus at 8.6 mm wavelength, in Paris Symposium on Radio Astronomy, Bracewell, R. N., Ed., Stanford University Press, Stanford, CA, 50. Gkxdmaine, J. A., Alsop, L E , Townes, C. H., and Mayer, C. H. (1959). Observations ofJupiterand Mars at 3 cm wavelength, Astron. J., 64, 332. Gokie, R. H. (1977). Lightning, Vol. 1, Academic Press, New York. Goodman, J. M. (1992). HF Communication Science and Technology, Van Norstrand Reinhold, New York, 192. Grossman, A. W„ Muhleman, D. O., and Beige, G. L (1989). Science, 245, 1211. Hagn, G. H. (1988). HF ground and vegetation constants unpublished lecture notes from AFCEA course 104,Military Uses of the HF Spectrum, Armed Forces Communications and Electronics Association, Fairfax, VA and SRI Inter­ national, Arlington, VA, (see also Goodman. (1992). 192/3). Hall, M. P. M. (1979). Effects o f the Troposphere on Radio Communication, Peter Peregrinus, London. Hall. M. P. M. and Barclay, L W. (1989). Radio Wave Propagation, Peter Peregrinus, London. Hallgren, R. E and MacDonald, R. B. (1963). Atmospherics from lightning 100 to 5600 MHz, Report No. 63-538-89, IBM Federal Systems Division. Haslam, G. T„ Salter, C. J., Stoffel, H., and Wilson, W. E (1982). A 408 MHZ all-sky continuum survey. II. The atlas of contour maps, Astron. Astrophys., Suppl. 47, 1. Hayenga, C. O. (1984). Characteristics of lightning VHF radiation near the time of return strokes, J. Geophys. Res., 89(D1), 1403. Hayenga, C. O. and Warwick, J. W. (1981). Two-dimensional interferometric positions of VHF lightning sources, J. Geophys. Res., 86(C8 ), 7451. Hey, J. S. (1971). The Radio Universe, Pergamon, London. Hogg, D. (1959), Effective antenna temperatures due to oxygen and water vapor in the atmosphere, J. Appt. Phys., 30(9), 1417. Homer, F. (1958). The relationship between atmospheric radio noise and lightning, J. Atmos. Terr. Phys., 13, 140. Homer. F. (1961). Narrow-hand atmospherics from two local thunderstorms, J. Atmos. Terr. Phys., 21, 13. Homer, F. (1964). Radio noise from thunderstorms, in Advances in Radio Research. Vol. 2, Saxton, J. A., Ed., Academic Press, New York, 121. Homer, F. and Bradley, P. A. (1964). The spectra of atmospherics from near lightning discharges, J. Atmos. Terr. Phys., 26, 1155. Howard, W. E , Barrett, A. H„ and Haddock, F. T. (1962). Measurements of microwave radiation from the planet Mercury, Astrophys. J., 136, 995. Howell, R. R., Criukshank, D. P., and Fanale, F. P. (1984). Sulfur dioxide on Io: spatial distribution and physical state, Icarus, 57, 83. Hsieh. H. C. (1966). A theory of ionospheric thermal radiation, J. Atmos. Terr. Phys., 28, 769. Iawata, A. and Kanada, M. (1967). On the nature of frequency spectrum of atmospheric source signals, Proc. Res. Inst. Atmos. Nagoya Univ., 14, 1. Ippolito, E J. (1971). Effects of precipitation on 153- and 31.65-GHz earth-space transmissions with the ATS-V satellite, Proc. IEEE 59(2), 189. ITT, (1973). Reference Data fo r Radio Engineers, Westman, H. P., Karsh, M., Perugini, M. M., and Fujii, W. S., Eds., Howard Sams, New York, 34. Jordan, E G (1950). Electromagnetic Waver and Radiating Systems, Constable & Co., London. JTAC, Joint Technical Advisory Council. (1960). Ionospheric Scatter Transmission, Proc. IRE 48,4. Kaiser, M. E and Desch, M. D. (1984). Radio emission from the planets earth, Jupiter, and Saturn, Rev. Geophys. Space Phys., 22(4), 373. Kaiser. M. E , Desch, M. D., Riddle, A. G . Lecacheux, A., Pearce, J. B., Alexander. J. K., Warwick, J. W„ and Thieman, J. R. (1979). Voyager spacecraft radio observations of Jupiter initial cruise results, Geophys. Res. Lett., 6 (6 ), 507. Kaiser. M. L , Desch, M. D., Warwick, J. W.. and Pearce, J. B. (1980). Voyager detection of non-thermal radio emission from Saturn, Science. 209, 1238. Kaiser, M. E , Connemey, J. E. P., and Desch, M. D. (1983). Atmospheric storm explanation of Satumian electrostatic discharges. Nature (London), 303, 50. Kelso, J. M. (1964). Radio Ray Propagation in the Ionosphere, McGraw-Hill, New York.

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Kimpara, A. (1965). Electromagnetic energy radiated from lightning in Problems o f Atmospheric and Space Electricity, Coroniti, S. C , Ed., Elsevier, Amsterdam, 352. Kitagawa, N. and Brook, M. (1960). A comparison of intracloud and cloud-to-ground lightning discharges, J. Geophys. Res., 65(4), 1189. Ko, H. C. and Kraus, J. D. (1957). A radio map of the sky at 1.2 meters. Sky Telescope, 16, 160. Kosarev, E. L. Zatespin. V. G., and Mitrafanov, A. V. (1970). Ultrahigh frequency radiation from lightnings. J. Geophys. Res., 75(36), 7524. Kraus, J. D. (1986). Radio Astronomy, 2nd ed., Cygnus-Quasar Books, Powell, OH. Krehbiel, P. R. (1992). Private communication. Krider, E P. and Radda, G. J. (1975). Radiation field wave forms produced by lightning stepped leaders, J. Geophys. Res., 80(18), 2653. Krider, E P., Radda, G. J., and Noggle, R. C. (1975). Regular radiation held pulses produced by intracloud lightning discharges, J. Geophys. Res., 80(27), 3801. Krider, E P., Weidman, C. D„ and Noggle, R. G (1977). The electric fields produced by lightning stepped leaders, J. Geophys Res, 82(6). 951. Krider, E. P., Weidman, C. D., and LeVine, D. M. (1979). The temporal structure of the HF and VHF radiation produced by intracloud lightning discharges, J. Geophys Res, 84(C9), 5760. Landecker, T. L. and Wielebinski, R. (1970). The galactic metre wave radiation, a survey between declinations +25° and -25° and the preparation of a map of the whole sky, Aust. J. Phys, Astrophys, Suppl. 16,1. Lawson, J. L. and Uhlenbeck, G. E. (1950). Threshold Signals McGraw-Hill. New York. Le Boulch, M„ Hamelin, J , and Weidman, C. (1987). UHF-VHF radiation from lightning. Electromagnetics 4(3-4). 287. Lecacheux, A., Pedersen, B. M., Zarka, Ph., Aubier, M. G., Desch, M. D.. Farrell, W. M., Kaiser, M. I_ MacDowall, R. J„ and Stone, R. G. (1992). In ecliptic observations of Jovian radio emission by Ulysses. Comparison with Voyager results, Geophys Res. Lett., 19(12), 1307. Le Vine, D. M., Jenkins, H. H., Wilson, B. J., and Wilson, C S. (1976). The structure of lightning flashes HF-UHF: September 12,1975, Atlanta, Georgia, Preprint X-953-76-176, Goddard Space Flight Center, Greenbelt, MD. Le Vine, D. M. and Krider, E P. (1977). The temporal structure of HF and VHF radiations during Florida lightning return strokes, Geophys. Res. Lett., 4(1), 13. Lewis, E A. (1982). High frequency radio noise, in Handbook o f Atmospherics, Vol. 1, Volland, H„ Ed., CRC Press, Boca Raton, FL, 251. Lhermitte, R. and Krehbiel, P. R. (1979). Doppler radar and radio observations of thunderstorms, IEEE Trans. Geosci. Electron., GE-17(4). 162. Maian, D. J. (1959). Radiation from lightning discharges and its relation to the discharge process, in Recent Advances in Atmospheric Electricity, L. G. Smith, Ed., Pergamon Press, New York, 557. Malan, D. J. (1963). Physics o f Lightning. The English Universities Press, London. McNamara, L. F. (1991). The Ionosphere: Communications Surveillance and Direction Finding, Oibit, Krieger Publishing. Malabar, FL. MacLement, W. D. and Murty, R. C. (1978). VHF direction finder studies of lightning, J. AppL Meteoroi., 17, 786. Mayer, C. H. (1964). Thermal radiation from the moon and planets, IEEE Trans. Antennas and Propag., AP-12.902. Mayer, C. H., McCullough, T. P., and Sknnaker, R. M. (1958a). Observations of Venus at 3.15 cm wavelength, Astrophys. J , 127, 1. Mayer, C. H„ McCullough, T. P., and Sknnaker, R. M. (1958b). Observations of Mars and Jupiter at a wavelength of 3.15 cm, Astrophys J„ 127, 11. Mayer, C H., McCullough, T. P., and Sloanaker, R. M. (1961). Planets and Satellites, Kuiper, G. P. and Middlehurst, B. M., Eds., University of Chicago Press, Chicago, chap. 12. Muller-Hillebrand, D. (1962). The magnetic field of the lightning discharge, in Gas Discharges and the Electric Supply Industry, Forrest, J. S., Howard, P. R , and Littler, D. J„ Eds., Butterworths, London, 89. Nanewicz, J. E , Vance, E F„ and Hamm, J. M. (1987). Observation of lightning in the frequency and time domains. Electromagnetics 7, 267. Norton, K. A. (1936). The propagation of radio waves over the surface of the earth and in the upper atmosphere. I. Groundwave propagation from short antennas, Proc. IRE 24(10), 1367. Norton, K. A. (1937a). The propagation of radio waves over the surface of the earth and in the upper atmosphere. 11. The propagation from vertical, horizontal, and loop antennas over a plane earth of finite conductivity, Proc. IRE 25(9), 1203. Norton, K. A. (1937b). The physical reality of space and surface waves in the radiation field of radio antennas, Proc. IRE 25(9), 1192. Novaco, J. C. and Brown, L. W. (1978). Astrophys. J., 221, 114. Octzel, G. N. and Pierce, E T. (1969). Radio emissions from close lightning, in Planetary Electrodynamics Coroniti, S. C. and Hughes, J., Eds., Gordon & Breach, New York, 543. Oh, E L (1969). Measured and calculated spectral amplitude distribution of lightning sferics, IEEE Trans Electromagn. Compat.. EMC 11(4), 125.

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Pawsey, J. L., McCready, L. L., and Gardner, F. F. (1951). J. Atmos. Terr. Phys., 1,261. Pearl, J., Hanel, R„ Kunde, V., Maguire, W., Fox, K., Gupta, S., Ponnamperuma, C., and Raulin, F. (1979). Identification of gaseous SOj and new upper limits for other gases on Io, Nature (LondonJ. 280, 755. Penzias, A. A. and Wilson, R. W. (1965). A measurement of excess antenna temperature at 4080 MHz, Astrophys. J., 142, 419. Piddington, J. H. (1961). Radio Astronomy, Hutchinson & Co., London. Piddington, J. H. and Minnett, H. C. (1949). Microwave thermal radiation from the moon, Aust. J. Sci. Res., A2,63. Pierce, E. T. (1977). Atmospherics and radio noise, in Lightning, Vol. 1, Golde, R. H., Ed., Academic Press, New York, 351. Prcta, Jr., J., Uman, M. A., Childers, D. G., and Lin, Y, T. (1985). Comment on The RF spectra of first and subsequent lightning strokes in the 1- to 200-km range, Radio Sci., 20, 143. Proctor, D. E (1971). A hyperbolic system for obtaining VHF radio pictures of lighming, J. Geophys. Res., 76(6),1478. Proctor, D. E (1981). VHF radio pictures of cloud flashes, J. Geophys. Res., 86(C5), 4041. Proctor, D. E. (1983). Lightning and precipitation in a small multicellular thunderstorm, J. Geophys Res., 88(C9), 5421. Proctor, D. E. (1991). Regions where lighming flashes began, J. Geophys. Res, 96(D3), 5099. Proctor, D. E , Uytenbogaardt, R., and Meredith, B. M. (1988). VHF radio pictures of lightning flashes to ground, J. Geophys. Res., 93(D10), 12,683. Proctor, D. E. (1993). Lightning and its relation to precipitation. Rep. No. 27W1/93, Water Research Commission, Pretoria, South Africa. Rhodes. C. and Krehbiel. P. R. (1989). Interfetometric observations of a single stroke cloud-to-ground flash, Geophys. Res Lett., 16(10), 1169. Richard, P. and Auffiay, G. (1985). VHF-UHF interferometric measurements, applications to lightning discharge mapping, Radio Sci., 20(2), 171. Richard, P., Delannoy, A , Labaune, G., and Laroche, P. (1986). Results of spatial and temporal characterization of the VHF-UHF radiation of lightning, J. Geophys. Res, 91 (Dl), 1248. Riddle, A. C. (1970). Solar Phys.. 13, 488. Riddle, A. C. and Warwick, J. W. (1976). Redefinition of System III longitude, Icarus 27(3), 457. Roberts, J. A and Stanley, G. J. (1959). Radio emission from Jupiter at a wavelength of 31 cm, Puhi. Astron. Soc. Pac., 71, 485. Rohlfs, K. (1986). Tools o f Radio Astronomy, Springer-Veriag, Berlin. Rose, W. K., Bologna, J. M„ and Sloanaker, R. M. (1963). Linear polarization of the 3,200 Mc/sec radiation from Saturn, Phys. Rev. Lett., 10,123. Rust, W. D., Taylor, W. L., Macgorman, D. R„ and Arnold, R. T. (1981). Research on electrical properties of severe thunderstorms in the great plains. Bull. Am. Meteorol. Soc., 62, 9, 1286. Rustan, P. L., Uman, M. A , Childers, D. G., Beasley, W. H., and Lennon, C. L. (1980). Lightning source locations from VHF radiation data for a flash at Kennedy Space Center, J. Geophys Res.. 85(C9), 4893. Ryle, M., Elsmore, B., and Neville, A C . (1965). High resolution observations of the radio sources in Cygnus and Cassiopiea, Nature (London), 205(4978), 1259. Salter, C. J. and Brown, R. L. (1988). Galactic nonthermal continuum emission, in Galactic and Extragalactic Radio Astronomy, Verschuur, G. L. and Kellerman, K. 1., Eds., Springer-Veriag, Heidelberg, 1. Schonland, B. F. J. (1956). The lightning discharge, in Handbuch der Physik, S. Flugge-Marburg, Ed., Springer-Veriag. 22,576. Scott, R. E. (1960). Linear Circuits, Part n, Addison-Wesley, Reading, MA. Serhan, G. 1., Uman, M. A., Childers, D. G„ and Lin, Y. T. (1980). The rf spectra of first and subsequentlightning return strokes in the 1- to 200-km range. Radio Sci., 15(6), 1089. Shemansky, D. E. (1987). Ratio of oxygen to sulfur in the Io plasma torus, J. Geophys Res., 92, 6141. Sloanaker, R. M. (1959). Apparent temperature of Jupiter at a wavelength of 10 cm, Astron. J., 64, 346. Smerd, S. F. (1970). Proc. Astron. Soc. Aust., 1, 305. Smith, E. K. (1982). Centimeter and millimeter wave attenuationand brightness temperature due to atmospheric oxygen and water vapor. Radio Sci., 17(6), 1455. Stix, M. (1991). The Sun, Springer-Veriag, Heidelberg. Takagi, M. (1969). VHF radiation from ground discharges, Proc. Res. Inst. Atmos Nagoya Univ., 16, 163. Takagi, M. and Takeuti, T. (1963). Atmospherics radiation from lightning discharges, Proc. Res. Inst. Atmos. Nagoya Univ.. 10, 1. Taylor. R. E (1973). 136-MHz/4(XTMHz Radio-Sky Maps, Proc. IEEE, 61. 469. Taylor, W. L (1978). A VHF technique for space-time mapping of lightning discharge processes, J. Geophys. Res.. 83(C7), 3575. Terman, F. E (1943), Radio Engineers Handbook, McGraw-Hill, New York. Terman, F. E. (1951). Radio Engineering, 3nd ed., McGraw-Hill, New York. Thieman, J. R. and Goldstein, M. L. (1981). Arcs in Saturn radio spectra. Nature (London), 292,728. Uman, M. A. (1987). The Lightning Discharge, Academic Press, New York.

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Uman, M. A (1969). Lightning, McGraw-Hill, New York. Uson, J. M. and Wilkinson, D. T. (1988). The microwave background radiation, in Galactic and Extragalactk Radio Astronomy, 2nd ed., Versdiuur, G. L. and Kellerman, K L, Eds., Springer-Verlag, Berlin, 602. Vetschuur, G. L. and Kellerman, K. I. (1988). Galactic and Extragalactic Radio Astronomy, 2nd ed.. Springer-Verlag, Berlin. Warwick, J. W. (1963). Dynamic spectra of Jupiter’s decametric emission, 1961, Astrophys. J., 137,41. Warwick, J. W., Pearce, J. B., Peltzer, R. G., and Riddle, A. C. (1977). Planetary radio astronomy experiment for Voyager missions. Space Sci. Rev., 21, 309. Warwick, J. W„ Hayenga, C. O., and Brosnahan, J. W. (1979). Interferometric directions of lightning sources at 34 MHz, J. Geophys. Res., 84(C5), 2457. Warwick, J. W., Pearce, J. B., Riddle, A. C., Alexander, J. K., Desch, M. D., Kaiser, M. U, Thieman, J. R., Cam, T. D., Guilds, S., Boischot, A., Harvey, G G, and Pedersen, B. M. (1979). Science, 204,995. Warwick, J. W„ Pearce, J. B„ Evans, D. R., Carr, T. D., Schauble, J. J., Alexander, J. K„ Kaiser, M. L , Desch, M. D., Pedersen, B. M.. Lecacheux, A., Daigne, G„ Boischot, A., and Barrow, C. H. (1981). Planetary radio astronomy observations (ran Voyager 1 near Saturn, Science, 212,239. Warwick, J. W., Evans, D. R., Rornig, J. R , Alexander, J. K., Desch, M. D , Kaiser, M. L , Aubier, M., Leblanc, Y., Lecacheux, A., and Pedersen, B. M. (1982). Planetary radio astronomy observations from Voyager 2 near Saturn, Science, 215, 582. Warwick. J. W„ Evans, D. R., Romig, J. R , Sawyer, G B., Desch, M. D„ Kaiser, M. L.. Alexander, J. K-, Carr, T. D., Staelin, D. H„ Guilds, S., Poynter, R. L , Aubier, M., Boischot, A., Leblanc, Y., Lecacheux, A , Pedersen, B. M„ and Zatka, P. (1986). Voyager 2 observations of Uranus, Science, 233. 102. Warwick, J. W., Evans, D. R., Peltzer, G. R., Peltzer, R. G„ Romig, J. R , Sawyer, C. B„ Riddle, A C., Schweitzer, A E., Desch, M. D., Kaiser, M. I_ Farrell, W. M., Carr, T. D., de Pater, L, Staelin, D. R , Guilds, S., Poynter, R. L., Boischot, A , Genova, F„ Leblanc, Y., Lecacheux, A et al. (1989). Voyager planetary ratio astronomy at Neptune, Science, 246, 1498. Weidman, C. D., Krider, E. P., and Uman, M. A (1981). Lightning amplitude spectra in the interval from 100 kHz to 20 MHz, Geophys. Res. Lett., 8(8 ), 931. Weidman, C. D. and Krider, E. P. (1986). The amplitude spectra of lightning radiation fields in the interval from I to 20 MHz, Radio Sci, 21(6), 964. Willett, J. G , Bailey, J. C„ and Krider, E. P. (1989). A class of unusual lightning electric field waveforms with very strong HF radiation, J. Geophys. Res., 94(D13), 16,255. Willett, J. G , Bailey, J. C., Leteinturier, G , and Krider, E. P. (1990). Lightning electromagnetic radiation field spectra in the interval from 0.2 to 20 MHz, J. Geophys. Res., 9S(D12), 20367. Wild. J. P„ Murray, J. D„ and Rowe, W. G (1954). Aust. J. Phys., 7,439. Wild, J. P., Smerd, S. F„ and Weiss, A A (1963). Solar bursts, Annu. Rev. Astron. Astrophys., 1, 291. Wild, J. P. and Smerd, S. F. (1972). Radio bursts from the solar corona, Annu. Rev. Astron. Astrophys., 10, 159. Williams, P. J. S., Kendenhne, S.. and Baldwin, J. E. (1966). Mem. R. Astron. Soc., 70, S3. Wilson, R. W. (1983). Discovery of the cosmic microwave background, in Serendipitous Discoveries in Radio Astronomy. Kellerman, K. and Sheets, B., Eds., NRAO, Greenbank, 175. Zatka, Ph. and Pedersen, B. M. (1986). Radio detection of Uranian lightning by Voyager 2, Nature (London), 323,605.

Chapter 14

Atmospheric Noise and Its Effects on Telecommunication System Performance A.D. Spaulding

CONTENTS

1. Introduction......................................................................................................................... 359 2. Worldwide Minimum Environmental Radio Noise Levels (1 Hz to 1 TH z)..................360 2.1. Predetection Signal-to-Noise Ratio and Receiving System Operating Noise Factor....................................................................................................................... 360 2.2. Relationships Among F„ Noise Power, Spectral Density, and Noise Power Bandwidth............................................................................................................... 362 2.3. Estimates of Minimum (and Maximum) Environmental Noise Levels.................363 3. Worldwide Atmospheric Radio Noise Estimates..............................................................364 3.1. Introduction.............................................................................................................. 364 3.2. Definition and Examples of Measured Received Atmospheric Noise Envelope Statistics................................................................................................................... 365 3.3. CCIR Report 322..................................................................................................... 370 3.4. Summary of Mathematical Models for Atmospheric Radio Noise Processes......378 4. Effect of Atmospheric Noise on System Performance....................................................384 4.1. Introduction.............................................................................................................. 384 4.2. General Effects of Atmospheric Noise on System Performance........................... 384 4.3. Means of Improving System Performance in Impulsive Atmospheric N oise.......389 References....................................................................................................................................393 1.

INTRODUCTION

Atmospherics are electromagnetic signals, impulsive in nature, which means they are spectrally broadband processes. The lightning that radiates these atmospherics produces most of its energy at and below high frequency (HF) (3 to 30 MHz). These frequencies are used for long-range communications, because propagation is supported by the earth-ionosphere waveguide. While this means that atmospherics can be used to study this propagation media, the density and location of thunderstorms, and other geophysical phenomena, it also means that long-range communica­ tions systems can receive interference from these atmospherics. At any receiving location, at­ mospherics can be received from the entire earth’s surface (at low enough frequencies). Therefore, the satisfactory design of a radio communications system must take into account the level and other characteristics of this atmospheric noise. It is the purpose of this chapter to treat this nature of atmospherics, i.e., the relationships between atmospheric noise and telecommunication systems. It should also be noted that in spite of satellite systems for long-range communications, the use of systems using the ionosphere to achieve long-range communications is continually increasing. The satisfactory design of a radio communications system depends on consideration of all the parameters affecting operation. This requires not only the proper choice of terminal facilities and an understanding of propagation of the desired signal between the terminals, but also knowledge of the interference environment. This environment may consist of signals that are intentionally radiated, or of noise, either of natural origin or unintentionally radiated from man-made sources. O-8493-8647-O/95/SO.0O+S.50 © 1993 by C R C P m t , Inc.

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360

or various combinations of these. It has long been recognized that the ultimate limitation to a communication link will usually be the radio noise. There are a number of types of radio noise that must be considered in any design, although, in general, one type will be the predominant noise and will be the deciding design factor. In broad categories, the noise can be divided into two types: noise internal to the receiving system and noise external to the receiving antenna. Noise power is generally the most significant parameter (but seldom sufficient) in relating the interference potential of the noise to system performance. Because the noise level often results from a combination of external and internal noise, it is convenient to express the resulting noise by means of an overall operating noise factor, which characterizes the performance of the entire receiving system. Section 2 of this chapter, therefore, defines the receiving system operating noise factor and shows how the internal and external noises must be combined. Section 2 then gives estimates of the minimum (and maximum) environmental noise levels likely at any location on the earth’s surface. The frequency range 1 Hz to 1 THz is covered, and thus the interference potential of atmospheric noise can be compared to that of other external noises (e.g., man-made and galactic). After the broad overview of Section 2, Section 3 goes on in much more detail concerning atmospheric noise, giving its level as a function of time and geographic location. In addition, the required statistical characterizations (in addition to level) are defined and examples given. Finally, in Section 3 a summary of mathematical models for the atmospheric-noise process is given, because quite often proper system design requires more information (obtained by modeling) about the process than can be obtained by measurement alone. The last section (Section 4) summarizes the effects of atmospheric noise on system perfor­ mance and then gives various means of improving system performance in impulsive noise. 2. 2.1.

WORLDWIDE MINIMUM ENVIRONMENTAL RADIO NOISE LEVELS (1 Hz to 1 THz)

PREDETECTION SIGNAL-TO-NOISE RATIO AND RECEIVING SYSTEM OPERATING NOISE FACTOR

As mentioned in the introduction, it is desirable to express the external noise levels in a form that will allow the external noises to be appropriately combined with noise internal to a telecommu­ nications system. In so doing, it is then possible to make decisions concerning required receiving system sensitivity; that is, a receiver need have no more sensitivity than that dictated by the external noise. Also, the noise levels can then be compared to the desired signal level to determine the predetection signal-to-noise ratio (SNR). The predetection SNR is an important system design parameter and is always required knowledge (required but seldom sufficient) when determining the effects of the external noise on system performance. It is useful to refer (or translate) the noise from all sources to one point in the system for comparison with the signal power (desired signal). A unique system reference point exists: the terminals of an equivalent lossless antenna having the same characteristics (except efficiency) as the actual antenna (see CCIR, 1966). Consider the receiving system shown in Figure 14.2.1. The output of block (a) is this unique reference point. The output of block (c) represents the actual (available) antenna terminals to which one could attach a meter or a transmission line. Let s represent the signal power and n the average noise power in watts that would be observed at the output of block (a) in an actual system (if the terminals were accessible). We can define a receiving system overall operating noise factor, f, such that n = fkTob, where k = Boltzmann constant = 1.38 x 10-23 J/K, T0 = the reference temperature in K taken as 288 K, and b = the noise power bandwidth of the receiving system in hertz. We can also define a system overall operating noise figure F= 10 logiof in decibels. The ratio S/N can be expressed: (S/N) = S - N

( 1)

361

Atm ospheric N oise and Its Effects on Telecommunication

(a)

(c)

(t)

fri

f t

%

TC

*a= V

(e)

(r)

fc=

To

Tt >Ktc /T q )

f

f= fQ+ ( / c -|)(T c / T 0) + Figure 14.2.1

l+ ( i^ ~ l)(T j/ Tq)

fr

!)(T j / T q ) +

The receiving system and its operating noise factor, f.

where S = the desired average signal power in decibels (1 W) = 1 0 logios

N = the average system noise power in decibels (1 W) =

1 0 lo g io n

Let us now explore the components of n in greater detail with emphasis on environmental noise external to the system components. For receivers free from spurious responses, the system noise factor is given by:

f = f, + (8c - 1) ^

+ 8c (fi, - l)

(?rj

+ *A (fr - l)

(2)

where f, = the external noise factor defined as:

f ,=

Pn kT„b

F, = the external noise figure defined as F, = 10 log f, p„ = the available noise power from a lossless antenna (the output o f block (a) in Figure 14.2.1) Be = the antenna circuit loss (power available from lossless antenna/power available from actual antenna) Tc = the actual temperature, in K, o f the antenna and nearby ground = the transmission line loss (available input power/available output power) T, = the actual temperature, in K, o f the transmission line fr = the noise factor of the receiver (Fr = 10 log fr = noise figure in decibels)

(3)

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Let us now define noise factors fc and f„ where fc in the noise factor associated with the antenna circuit losses: fc = 1 + (fic- 1 ) ( ^ )

(4)

and f, is the noise factor associated with the transmission line losses: f, = 1 + («, - 1) ( £ )

(5)

If Tc = T, = Tm Equation 2 becomes: f = f, - 1 + fcf,fr

(6)

Note specifically that when fc = f, = 1 (lossless antenna and transmission line), then F ¥■ F. + F„ Relation 3 can be written: P„ = F, + B - 204 dB(lW )

(7)

where Pn = 10 log p„ (p„ = available power at the output of block (a) in Figure 14.2.1, in watts); B = 10 log b; and -2 0 4 = 10 log kT0. For a short (h « X) grounded vertical monopole, the vertical component of the root-mean-square (rms) field strength is given by: E„ = F, + 20 log fwm + B - 95.5 dB (1 pV/m)

(8)

where En is the field strength in bandwidth b and fMHz is the center frequency in megahertz. Similar expressions for E„ can be derived for other antennas (Lauber, 1977). For example, for a halfwave dipole in free space: E„ = F. + 20 log fMHz + B - 98.9 dB (1 pV/m)

(9)

The external noise factor is also commonly expressed as a temperature, t,, where by definition of f,: f, = £

(10)

and T0 is the reference temperature in K and T, is the antenna temperature due to external noise. More detailed definitions and discussions (including the casewithspurious responses) are contained in CCIR Report 413 (1966). Additional discussions on natural noise are given in Section 3 of this chapter and in Chapters 1/12,1/13 and CCIR Report 258-5 (1990). 2.2.

RELATIONSHIPS AMONG F*, NOISE POWER, SPECTRAL DENSITY, AND NOISE POWER BANDWIDTH

Note that f, is a dimensionless quantity, being the ratio of two powers. The quantity f„ however, gives numerically the available power spectral density in terms of kT0 and the available power in terms of kTob. The relationship between the noise power, P„, the noise power spectral density, Pj* and noise power bandwidth, b, are summarized in Figure 14.2.2 (from Spaulding, 1976).

Atm ospheric N oise and Its Effects on Telecommunication

dB(HT0) +67 dB -1 0 log b

+204dB -10 log by

dB(1W) (in b)

+ 7 dB

— 'i\ + 144 dB

+60 dB / \ *474dB /d B (1 /lV ) ' -10 log b /dB(VW/MHi] \CActom500.) - I O I o g b l ( A o o » * 50A ) +30dB dB(lmW) (In b)

Powor

Figure 14.2.2

dBtlmV/

Bandwidth Conversion

Powar Spactral Density

Relationships between power, power spectral density, and noise bandwidth (mns detector).

When F, is known, then P„ or P*) can be determined by following the steps indicated in the figure. For example, if the minimum value of F, = 40 dB and b = 10 kHz, then the minimum value of noise power available from the equivalent lossless antenna is P„ = -1 2 4 dB (1 W). If Cc = 3, then the noise power available from the actual receiving antenna is -128.8 dB (1 W). 2.3.

ESTIMATES OF MINIMUM (AND MAXIMUM) ENVIRONMENTAL NOISE LEVELS

The best available estimates of the minimum expected values of F, along with other external noise levels of interest are summarized in this section as a function of frequency. Figure 14.2.3 covers the frequency range from 1 Hz to 1 THz. On Figure 14.2.3, for frequencies CIO4 Hz, curve B is the minimum expected values of F, (or T,) at the earth’s surface based on measurements (taking into account all seasons and times of day for the entire earth), and curve A gives the maximum expected values. Note that in this frequency range there is very little seasonal, diumal, or geographic variation. The larger variability in the 100- to 10,000-Hz range is due to the variability of the earth-ionosphere waveguide cutoff. For atmospheric noise (f > 104 Hz), the minimum values expected are taken to be those values exceeded 99.5% of the time, and the maximum values are those exceeded 0.5% of the time. For atmospheric noise curves, all times of day, season, and the entire earth’s surface have been taken into account. More precise details (geographic and time variations) can be obtained from CCIR Report 322-3 (1988), which is discussed in Section 3 of this chapter. These atmospheric noise data are average background. Local thunderstorms can cause higher noise levels. Figure 14.2.3 also shows other background noise levels up to a frequency of 1 THz. The atmospheric noise results (A, B, C, and D) are for omni-directional vertically polarized antennas. The average value of F, for directional antennas will be the same if we assume random direction. Studies have indicated that at HF (for example), for atmospheric noise from lightning, there can be as much as 10-dB variation (5 dB above to 5 dB below the average F, value shown) with direction for very narrowbeam antennas. The other noise levels shown on Figure 14.2.3 (E through K) are for very narrowbeam antennas, pointing at the source.

Handbook o f Atm ospheric Electrodynam ics, Volume /

VJiSB above kT«b)

364

Figure 14.2.3

F. vs. frequency (1 to 10” Hz).

Corresponding levels for background man-made noise can be obtained from CCIR Report 258-5 (1990), Spaulding and Disney (1974) and references therein, and Hagn and Shephard (1974). 3. 3.1.

WORLDWIDE ATMOSPHERIC RADIO NOISE ESTIMATES

INTRODUCTION

In the previous section we defined f, (and TJ, the most useful and common way of specifying the external noise level. We also noted that when one is concerned with determining the effects of the external noise (e.g., atmospheric noise) on system performance, more information about the received noise process than just its energy content (level) is almost always required. In Section 3.2 we define these more detailed statistics that are required and show, via examples for atmos­ pheric noise, their general characteristics. With definitions in hand. Section 3.3 discusses CCIR Report 322 (1988), which gives the available worldwide estimates for atmospheric noise; its level, f,; and also the most useful statistic, the amplitude probability distribution of the received noise envelope along with the time, frequency, and geographic variations of these parameters. Because the impulsive atmospheric noise can have serious effects on the performance of communication systems, various techniques can be used to minimize these effects. This means

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that receiving systems must be designed to function as well as possible in impulsive noise. In general, to cany out such system designs, more knowledge about the noise process is required than can be obtained by measurement alone. Therefore, Section 3.4 gives a summary of the mathematical models that have been developed for the atmospheric noise process. In addition to system performance and design problems, some of these models can be used, coupled with measured noise data, to study various geophysical phenomena such as radio wave propagation, thunderstorm occurrence rates, the nature of lightning, etc. 3.2,

DEFINITION AND EXAMPLES O F MEASURED RECEIVED ATMOSPHERIC NOISE ENVELOPE STATISTICS

Atmospheric noise is a random process. The fact that we are dealing with a random process means that the noise can be described only in probabilistic or statistical terms and cannot be represented by a deterministic waveform or any collection of deterministic waveforms. In addition, atmos­ pheric noise is basically nonstationary; therefore, great care must be exercised in planning and making measurements and in interpreting the results. We must measure long enough to obtain a good estimate of the required parameter but be certain that the noise remains stationary enough during this period. This is no small point and is frequently overlooked in the design of measure­ ment experiments. We assume that the random noise process is stationary enough over some required time period for us to obtain the required statistics. Of course, how these statistics then change with time (from day to day), as well as with location, now becomes important. The basic description of any random process is its probability density function (pdf) or distri­ bution function. The first order pdf of the received interference process is almost always required to determine system performance (i.e., always necessary but sometimes not sufficient). Although a random process, X(t), is said to be completely described if its hierarchy of distri­ butions is known, there are other important statistical properties (important to communications systems) that are not immediately implied by this hierarchy. Moments and distributions of level crossings of X(t) within a time interval, moments and distributions of time interval between successive crossings, distribution of extremes in the interval, etc. are typical examples. We now want to define, in a unified way, the atmospheric noise parameters that have been measured and their interrelationships. For analysis of a communication system, the noise process of interest is the one seen by our receiving system. This means that we are almost always interested in narrowband noise processes. A narrowband process results whenever that bandpass of the system is a small fraction of the center frequency, fc and means that the received noise is describable in terms of its envelope and phase as shown on Figure 14.3.1. The noise process, x(t), at the output of a narrowband filter is given by: x(t) = v(t) cos[o»ct + Vc). This distribution has been measured extensively for atmospheric noise (see the bibliography by Spaulding et al., 1975, which deals with man-made noise but also contains an extensive section on atmospheric noise). The first model for the noise envelope was the Rayleigh distribution; P(V > V0) = e - v«J This simply assumes that the interference is Gaussian and was quickly recognized to be quite inappropriate, because the envelope distribution of atmospheric and man-made noise exhibits large impulsive tails (e.g.. Figure 14.3.5). Modeling of the non-Gaussian atmospheric noise processes began in the early 1950s. Spaulding and Middleton (1975) and Spaulding (1977) have given a complete historical summary of the various proposed models. Almost all of the early empirical models concentrated on the envelope of the received noise process. Such models, while useful in determining the performance of idealized digital systems using matched filter or correlation receivers (i.e., those optimum for white Gaussian noise), give no insight into the physical processes that cause the interference. Neither can they be used to determine performance of real systems that employ various kinds of nonlinear processing nor can they be used in optimum system detection problems. Various in­ vestigators have developed models for the entire interference process. The most significant of these models are those developed by Furutsu and Ishida (1960), Beckman (1962, 1964), Hall (1966), Omura (1969), Giordano (1970, 1972), and Middleton (1977, 1979). These models also have been summarized by Spaulding (1977). Currently, only the Hall and Middleton models are those in general use. While obtained quite differently, the Hall model is a special case of the Middleton model and is much simpler mathematically. Hall (1966) applied work on the applicability of a class of “self similar" random processes as a model for certain intermittent phenomena to signal detection problems considering low frequency (LF) atmospheric noise. The concept introduced is that of a random process that is controlled by one regime for the duration of observation, while this regime is itself a random process. The model that Hall proposed for received impulsive noise is one that takes the received noise to be a narrowband Gaussian process multiplied by a weighting factor that varies with time. Thus, the received atmospheric noise x(t) is assumed to have the form: x(t) = a(t) n(t)

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where n(t) is a zero-mean narrowband Gaussian process with covariance function R „( t ), and a(t), the regime process, is a stationary random process, independent of n(t), whose statistics are to be chosen so that x(t) is an accurate description of the received atmospheric noise. For a(t), Hall chose the two-sided chi distribution, X2(m,a), for the reciprocal of a(t), resulting in: (m/2r Q

. ' ^

1

^ ( 1 1 1 /2 ) |a |m+l CXP

m T ifr j2

and

Using the two equations above. Hall found the pdf of the noise to be given by:

n

poo =

'( I) T* ~ 1 __________ r ^e -

1

J h [xz + y T 2

where y — ml/W 1. For the special case a , = a, p(x) is Student’s t distribution. Hall terms the above the generalized t distribution with parameters 0 and y. Hall shows that 0 in the range 2 < 0 ^ 4 is appropriate to fit measured data of atmospheric noise and that 0 ** 3 is appropriate to fit a large body of data at very low frequency (VLF) and LF. (Unfortunately, for 0 in the range 2 < 0 s 3, x(t) has infinite variance and therefore cannot be a model for physical noise, although it fits the data very closely.) Hall then considers the envelope and phase of the received noise, i.e.: x(t) = V(t) cosfaiot +