Convective motions in a free atmosphere

Table of contents :
PREFACE . vii
INTRODUCTION . 1

Chapter I. A METHOD FOR STUDYING CONVECTIVE MOTIONS IN
A FREE ATMOSPHERE. .
1. The physical foundations of the method.
2. Airplane thermometric equipment 12
3. Measurement errors 22
4. Verification of the method . 25
5. The technique of the flight and the primary processing
of the measurements 30
6. Measurements in clouds 32
7. A method for studying descending currents around
developing cumulus clouds 38

Chapter II. STATISTICAL INTERPRETATION OF THE MEASUREMENT
RESULTS . 45
1. Formulation of the problem . . 45
2 Distribution of convective currents according to their real
dimensions and concentrations of convective currents . 46
3. The relative area and relative volume of ascending
currents . . . 50
4. Case of wind varying with height 53
5. Distribution of convective currents according to their dimen-
sions and temperatures at their centers 54
6. Generalization of the solutions to the case of n
independent variables . 57
7. Average temperatures at the centers of convective
currents . 58
8. Equilibrium cases 60
9. The method and accuracy of the calculations 61

Chapter III. CONVECTIVE MOTIONS IN A FREE ATMOSPHERE 67
1. Atmospheric conditions during the measurements 67
2. Temperature profile of convective currents . 70
3. Preparation of the experimental data for calculations 71
4. General regularities of convective motions 73
5. Vertical variation of the convection parameters. 80
6. The daily variation of convective motions 92
7. The dependence of convection parameters on the degree of
atmospheric instability . 102
8. Dependence of the convection parameters on the nature of
the underlying surface 108
9, The clearing-up mechanism of instability in a free
atmosphere . 121
10. Temperature and velocity of ascending currents. 126
11, A hydrodynamical model of convective motions in an
unstable atmospheric layer. 129
12. The form of ascending currents in the atmosphere 133

Chapter IV. CONVECTIVE MOTIONS IN CUMULUS CLOUDS 136
1. Conditions of measurements and character of flights 136
2. The temperature profile of convective currents in clouds 140
3. General regularities of convective motions in thick
cumulus clouds . 141
4. Vertical variation of the convection parameters in clouds . 145
3. Dimensions, temperature and velocity of ascending
currents in thick cumulus clouds 153
6. Descending currents caused by developing cumulus clouds . 155
7. The relation between convective motions in the atmosphere
and the formation and development of cumulus clouds . 161

APPENDIX . . 172
A. The humidity of ascending convective currents . 172
B. Nonuniformities in the atmospheric refractive index in the
range of radiofrequencies due to convective motions 174

TABLES . 179
BIBLIOGRAPHY 182

Citation preview

N.L VUL'FSON

CONVECTIVE MOTIONS IN A FREE ATMOSPHERE (Issledovanie konvektivnykh

dvizhenii v svobodnoi

Izdatel'stvo, Akademii Nauk SSSR Moskva 1961

Translated from Russian

Israel Program for Scientific Translation Jerusalem 1964

atmosfere)

Copyright © 1964 Israel Program

for Scientific Translations Ltd.

IPST Cat. No. Translated

1032

and Edited by IPST Staff

Printed in Jerusalem by S. Binding:

VIII/6/3.5

K.

Wiener

Monson

CONTENTS PREFACE

.

vii

INTRODUCTION Chapter I. 1. 2. 3. 4. 5. 6. 7. Chapter II. 1. 2 3.

.

A METHOD FOR STUDYING A FREE ATMOSPHERE.

CONVECTIVE .

MOTIONS

IN

The physical foundations of the method. Airplane thermometric equipment Measurement errors Verification of the method . e The technique of the flight and the primary processing of the measurements Measurements in clouds A method for studying descending developing cumulus clouds STATISTICAL INTERPRETATION RESULTS .o Formulation of the problem

12 22 25 30 32

currents around 38 OF THE

MEASUREMENT 45

e

e

e

45

Distribution of convective currents according to their real dimensions and concentrations of convective currents . The relative area and relative volume of ascending

46

currents

50

.

.

-

4. 5.

Case of wind varying with he1ght Distribution of convective currents according to their dimen-

53

sions and temperatures at their centers Generalization of the solutions to the case of n independent variables .

54

6. 7.

Average temperatures currents

8. 9.

57

at the centers of convective

.

Equilibrium cases The method and accuracy of the calculations

Chapter III. CONVECTIVE MOTIONS IN A FREE ATMOSPHERE 1. Atmospheric conditions during the measurements 2. Temperature profile of convective currents .

iii

58 60 61 67 67 70

3. 4. 5. 6. 7.

71

Preparation of the experimental data for calculations General regularities of convective motions Vertical variation of the convection parameters. The daily variation of convective motions The dependence of convection parameters on the degree of atmospheric instability . Dependence of the convection parameters on the nature of

8.

73 80 92 102 108

10. 11,

the underlying surface The clearing-up mechanism of instability in a free atmosphere . Temperature and velocity of ascending currents. A hydrodynamical model of convective motions in an unstable atmospheric layer. The form of ascending currents in the atmosphere

129

12.

9,

Chapter IV. CONVECTIVE MOTIONS

IN CUMULUS

Conditions of measurements and character of flights The temperature profile of convective currents in clouds General regularities of convective motions in thick

4. 3.

Vertical variation of the convection parameters in clouds Dimensions, temperature and velocity of ascending

6.

currents in thick cumulus clouds Descending currents caused by developing cumulus clouds

A. B.

136 136 140

.

141 145

.

153 155

The relation between convective motions in the atmosphere and the formation and development of cumulus clouds .

161

cumulus clouds

APPENDIX

133

CLOUDS

1. 2. 3.

7.

121 126

.

.

. The humidity of ascending convective currents . Nonuniformities in the atmospheric refractive index in the range of radiofrequencies due to convective motions

TABLES . BIBLIOGRAPHY

172 172 174 179 182

iv

ANNOTATION This book describes the methods and results of investigations of convective motions in a free atmosphere and in clouds, and the equipment necessary for their measurement. The theory of the statistical interpretation of the observed results is given, since the interpretation of these data permits the establishment of the basic parameters of convection in the atmosphere, and shows the dependence of these parameters on various physicogeographical conditions. These factors, in turn, clarify the way in which convective motions develop in the atmosphere, and the relation between convective motions outside and inside clouds. In addition, the results may be used as quantitative descriptions of certain phenomena caused by convection or related to it. The book may be of interest to scientists in the field of atmospheric physics and in other fields (e.g., aviation, propagation of various radiations, air pollution) in which these data are used. The book may also be useful to students at meteorological institutes and university physics faculties.

I. A. KIBEL' Associate Member

of the Academy

of Sciences of the USSR

Responsible Editor

PREFACE As the title implies, this book sets out to describe my investigations of convective motions in a free atmosphere. It is not a general or systematic exposition of various theoretical and experimental studies of the phenomenon of convection. Thus, accounts of other work are included only insofar as they may assist in understanding the problems involved in the investigation, or in interpreting the results. Consequently, a number of original works are given considerably less attention than they deserve. Furthermore, it is very likely that some papers dealing with the problems discussed in the book have remained unknown to me; however, those which I encountered after the manuscript went to press are cited as much as possible in footnotes. I have tried to be as objective as possible in interpreting the results of experiments. However, the data do not always permit a single interpretation. In such cases, and in a number of others, my personal opinions are reflected

to a certain

sions

drawn

are

on the

extent

in the

basis

book.

Nevertheless,

of sufficiently

detailed

since

all

experimental

concludata,

I

am confident that the reader will not be prevented from forming his own opinions on the nature of convection in the atmosphere, even if they should differ from my own. Certain problems touched upon in the book require further studies, and I hope to conduct some of them in the near future together with a group of collaborators, The investigation of convective motions in natural conditions requires fairly comprehensive preparation, including the development of special equipment, appropriate equipping of airplanes, organization of expeditions, various theoretical investigations and the like. It was possible to carry out all this mainly because of the help and encouragement of E.K. Fedorov, Member of the Academy of Sciences. His useful advice and comments were of considerable

assistance

to me

in the

various

stages

of the

work,

and

I am

sincerely grateful to him. My collaborators took part in the investigations of convective motions in the atmosphere. The original instruments and equipment which were used to make the basic measurements and to check the method of investigation were developed by V. V. Shchelokov, V.I. Skatskii and A.M. Gromov. In assembling the equipment and in the measurements during flights N. V, Davydkin and 1. S. Pavlova participated. The laborious processing of the oscillograms and a considerable part of further calculations were carried out by L. M. Bartosh and M. G. Firsova.

vii

A

series

of special

flights

(in thick

to the surface) were successfully crew commanders A.l. Korzhov, Kolesov.

clouds,

My discussions with V. M. Bovsheverov

faced

in stages

helpful.

A

of basic

number

importance

of critical

over

mountains

and

close

carried out owing to the efficiency of the V.N. Shlyakov, P.N. Radkevich and N.S.

and L. M. Levin on problems

to the work,

comments,

which

and their

I took

outcome,

almost

wholly

were into

consideration, were made by I. A. Kibel' and A. M. Obukhov, Associate Members of the Academy of Sciences of the U.S.S.R., Professor A, Kh, Khrgian and N. Z. Pinus, Doctor of Physicomathematical Sciences. Errors in presentation were largely eliminated by S. V., Pshenai-Severin, who assisted in editing certain sections of the book. To all these I express sincere thanks.

N.I.

viii

Vul'fson

INTRODUCTION A whole series of atmospheric processes is associated with the phenomenon of convection. Convective motions contribute to the most intensive air mixing in the lower troposphere. Therefore, particles or vapor, particularly evaporated moisture, are rapidly carried to higher layers after entering the atmosphere from the surface of the earth*; the concentration of particles suspended in the air /144, 97, 38/, and especially the

amount

of water

vapor

/73,

20/,

seems

to bemore

or less

constant

throughout the whole convection layer. Convective currents are directly connected with the formation and development of clouds. They not only transport the amount of moisture necessary for the development of clouds

to higher layers,

but through the cooling of the ascending air /12/ also

create

for

conditions

currents

the

condensation

create the initial conditions

of this

moisture.”

necessary

and feed them during their development

/14/.

Thus,

convective

for the formation

of clouds

The powerful ascending

currents inside cumulus clouds are also convective; their rapid ascent is due to the release of latent condensation heat /12/. In addition, it would seem that convective currents in clouds are directly connected with processes of precipitation formation /62/. Convective motions are one of the main sources of turbulence in the atmosphere /44, 31, 58, 91, 98, 116/. They cause the roughest air conditions for airplanes /48-50, 88/%*%*, and influence a number of other processes, including that of the propagation in the

atmosphere

of various

and UHF waves

[80/%%%,

kinds

of radiations,

especially

acoustical

179/

Convective motions are thus one of the determining factors in a whole series of atmospheric processes and their study becomes more important as the knowledge of these processes, particularly those of cloud and precipitation-formation increases. Similarly, the importance of this study is enhanced as the influence of convection on certain parameters of the atmosphere, in which airplanes fly and various radiations propagate, is being

discovered.

atmosphere * st

Convective

has

Therefore,

grown

the

noticeably,

interest

in convection

particularly

currents also cause the most intensive transport of heat,

A large number

of measurements,

taken under various conditions,

overloads over a plain are usually due to convective motions, #4%

The

processes

in recent momentum have

in the

years. and so on.

shown that the largest airplane

particularly inside clouds.

influence of convection on the propagation of UHF waves is indirectly shown by studies published

in a special number

of the journal Proceedings IRE (Vol,

gation of UHF waves in the atmosphere, (J. Met,, of UHF

Vol.

waves

17,

No, 2,

43,

No, 10,

and also by studies of Klinker

1960) mentions that special

in convection conditions were

1955), /90/

concerned with the propaand others /21/.

Atlas

studies of certain features of the propagation

carried out by Plank,

Cellular, or ordered convection has been studied most extensively. Since approximately 1900, a large amount of experimental (laboratory) and theoretical work has been done, for example /65, 66, 113, 86, 87, 103, 130, 22/, in which a fairly detailed investigation was made of the conditions in which cellular convection appeared, its character, and its variation under the influence of various factors. However, it is unusual for this type of convection to appear in atmospheric conditions. The cellular structures of certain forms of cirrocumulus, altocumulus and

stratocumulus

clouds

offer

an

indirect

proof

of cellular

convection

in

a free atmosphere, as do cloud strips and arcs of dark cloud usually oriented windwise. It is assumed that these cloud forms are a result of convective motions inside cloud layers /94, 136, 82, 68, 67/* or of the presence in these layers of convective motions and a wind velocity gradient simultaneously /84, 94, 22/, The development of cellular convection in cloud layers may be due to the heating of the lower boundary of the layer by terrestrial radiation, the cooling of the upper boundary through radiation, and some other proces ses which lead to instability inside the cloud layers or the layers directly bordering on them /94, 68, 59, 22/. However, it is difficult to expect intensive vertical motions in such thin layers, particularly since the liquid-water content of these clouds is relatively low. Besides, these layers are encountered relatively rarely and at high levels, In addition convective motions in the atmosphere, giving rise to such processes as transport of contamination, intensive turbulence, development of thick clouds and so on, are the result of strong heating of tt ground surfaceby the sun (all the above-listed processes have aclearly pronounced diurnal course) or the result of the liberation, ina shorttime, oflarge amounts of condensation heat, which takes place only in vertically develope clouds. However, no single thick cumulus cloud, nor an aggregate of such clouds can develop as a result of cellular convection, since any of the clouc parameters to be measured have an irregular horizontal distribution /12, 139, 137, 128, 129, 30, 80, 89/, and neighboring clouds differ from each other greatly, even in size. Near

the

ground

surface,

cellular

convective

motions

cannot

exist,

if

only because of the consistent lack of uniformity in the relief, vegetation and heat capacity of the underlying surface, and also because of the turbulence of the air currents. Even under laboratory conditions, where the distribution of the temperature is irregular or the thickness of the unstable layer

/94/.

varies,

the

Cellular

terrain®**.,

This

form

and

positions

convectionis,

is indirectly

of the

apparently,

confirmed

convective

cells

also impossible

by the following

are

nonuniform

over a uniform

considerations.

The experiments of Chandra /72/ and the data of Dassanayake, given by Sutton /131/, show that in thin gas layers convection starts under tempera-

ture *

gradients

considerably

smaller

by the Rayleigh-

According to some theoretical and laboratory investigations it seems possible that cellular structures in clouds may be due to internal waves

**k

than that required

Woodcock

and Wyman

propagation of smoke

/143,

145/

/83/,

and also to the fall of droplets /41/,

consider that their observations of the soaring of sea

over the sea testify to the presence

data given.in Chapters I and III show that, inprinciple, way differ from convection over land.

there of cellular convection.,

gulls and the However,

the

convective motions over water surfaces in no

Jeffreys' theory /87/. The convective currents which appear are not cellular, but consist of irregularly distributed and ascending air columns, having no fixed position. In contrast to the cellular, this type of convec-

tion was called by Chandra ''columnar'.

If the heating of the lower sur-

face of the studied gas layer is considerably intensified, columnar convection is transformed into cellular convection and this is precisely what happens under the conditions of the Rayleigh-Jeffreys' criterion*. The atmospheric convection layer is quite thin as compared with the dimensions of the ground sections over which convective motions are observed. Analogously, therefore, it may be expected that the currents developing in this layer will also be disordered** and will appear in conditions of temperature gradients smaller than those required for the development

of cellular

ground

only

convection.

for Rayleigh

Indeed,

cellular

convection

can

arise

_L,

® % __ > 1100

(1)

V

where lapse

g is the gravity acceleration, rate

in a fluid

layer

at the

numbers

0 the potential

of thickness

h,

#

and

temperature,

v the

coefficients

g

the

of mo-

lecular thermal conductivity and kinematic viscosity. If we replace the coefficients of molecular thermal conductivity and viscosity by turbulent coefficients and assume that these coefficients

(averaged over the layer) are approximately

I_(Hzl.fmzak*h‘g—:‘—

where

u

is the

wind

terion

is transformed

smaller than unity,

velocity,

then,

%k is Karman's

(2)

constant,

as shown by Priestley

into Richardson's

criterion

/107/,

and

a

is

a constant

Rayleigh's

g%

6 oz = —Ri > 28a.

cri-

(3)

(%) 0z

From (3) it follows that in the presence of a wind gradient (always existing during the day at the ground surface) cellular convection cannot exist as long as -Ri does not reach a value of the order of 1-10, In a former work [/ 106/ Priestley showed that free convection arises at the earth surface under - Ri=0.02-0.03%%*%, According to the above, this convection cannot be cellular. *

Sutton proposed a theoretical explanation of this phenomenon convection is due to heat conduction whole

fluid layer.

tures at the upper

The

and arises in some

criterion for the appearance

and lower boundaries of the layer.

/131/.

sub-layer,

According to his theory,

of the convection

is the ratio between the tempera-

Within the thin layers of the fluid this ratio is

considerably lower than that required by Rayleigh's theory (both criteria coincide, starting from #k

critical layer thickness}. The absence of an upper solid wall apparently has no importance, over heated slabs takes plade mainly

*%k

These

data were

in the form of colummar

also confirmed by Taylor /134/.

columnar

independent of the thickness of the

in principle,

convection

/34,

a certain

since the motion of air 52,

112/,

The growth

development of convective motions considerably inhibits further in the surface layer, even under continued intensive heating of the

earth's surface by the sun.

Cellular convection,

therefore,

does not appear

at all*., The majority of atmospheric processes are thus caused by or connected with disordered convective currents. Disordered convective motions have been studied considerably less than ordered motions. Most of the laboratory investigations of individual ascending currents over isolated, mainly axially-symmetric heat sources /24, 46, 47, 127, 78/, as well as of unstable columnar convective cur-

rents over heated slabs

/34,

nomenon

since

52,

112,

35,

135/ were carried out under

conditions different from the atmospheric conditions during the convection. It has not yet been adequately shown that it is possible to simulate the pheof convection,

the

reproduction

of all the

natural

conditions

has not been achieved /40/. This is particularly so with respect to convection caused by the liberation of latent condensation heat by the ascent or descent in a fluid of separate masses of another fluid with a respectively lower or higher density /125, 127-124, 147/, Some of the phenomena observed in laboratory conditions are indeed encountered under natural conditions**, These include the appearance of vertical narrowing jet /112/ or the formation of bubbles quite resembling in form a thick cumulus cloud /126, 124/, Nevertheless, the range of applicability of laboratory data to the conditions of a real atmosphere is not clear, Considerably

motions

under

more

important,

naturally,

natural conditions.

are

Convective

the

studies

motions

surface have been closely studied by A. A, Skvortsov

of convective

near

the earth's

/52-54 /%%,

formulated the hypothesis of the so-called 'level" convection.

to this hypothesis, whose

thickness

convective

increases

motions

with

height,

occur and

inside

the

some

layers

interaction

who

According (levels),

between

which

takes place by their periodical destruction and restoration. To these layers correspond characteristic dimensions of the ascending currents, also in-

creasing with height,

theoretical

views

The "level exchange' scheme is in agreement with

on the

system

of purely

thermal

turbulence

/31/,

with

the

only difference that according to the latter the scale spectrum of the turbulent elements is assumed continuous; this also follows from the results of experimental investigations /11/ and particularly from the data given in Chapter IIL Existing experimental data on the nature of convective motions in a free atmosphere are inadequate®*** These data were obtained mainly from *

The

appearance

of cellular convection

inunstable

number for a layer with two free surfaces /113/,

cloud layers is due apparently to the smaller Rayleigh particularly if they are non-heat

and also to the considerably weaker turbulence within the cloud layer as compared

conducting

/133/,

with the surface

layer, It is also possible that the cellular structure of clouds, as already indicated, is caused by internal waves /83/, by the fall of droplets /41/ orby some other reasons not connected with processesof cellular convection /64/, #% %%k

Vertical narrowing jets were observed at the earth's surface by A, A, Skvortsov /52/ and Bryson /70/. The relation between convective motions and the nature of the underlying surface and certain meteorological

fokdok

elements was also studied by Albrecht .

This is explained by the inaccuracy of existing theories on the phenomenon in particular the original hypothesis made

by Scorer and Ludlam

/125,

of atmospheric

124/,

convection,

of constant-level

observations

/69,

glider flights of the

dimensions

148,

and

140,

pilot

93,

/63,

balloons

8/

the

currents,

of convective

velocities

7,

81,

or

during

146/ and give only rough estimates

102,

heights

of

to which

they rise, their temperature and humidity increase with respect to the surrounding air or a qualitative description of certain features of the structure Some information on ascending currents, also of convective currents. mainly descriptive, was obtained from observations of the spread of smoke /2, 53, 54, 145/, and the flight of dragonflies, birds /143, 120/ and locusts /111/. It should be noted that the method of studying convective motions in a free atmosphere with the aid of balloons and gliders has a number of basic In addition to the fact that the balloon method is apparently inapfaults.

plicable above

300-400m /7/,

balloons cannot be used to determine the di-

In glider flights these measurements can mensions of convective currents. usually be made, but they are only approximate since gliders usually circle in ascending currents chosen at random, and are roughly guided with reAt best, they intersect spect to the center and boundaries of the currents. the currents indiscriminately (from this point of view, the results of measurements made on a glider of any other parameters of convective currents In addition, glider flights are made in zones are random quantities also). with the strongest ascending currents {which sustain the flight of the glider Glider pilots avoid regions with relatively weak or for a fairly long time). Therefore, their data cannot reflect the whole /102/. currents narrow Results range of convective motions which are observed in the atmosphere. of other

investigations

/11,

80,

12,

48,

88/

show

that

convective

currents

of various dimensions, in a range beyond the scope of balloons and gliders, Furthermore, almost all atmooccur simultaneously in the atmosphere. spheric phenomena which have to do with convection depend primarily on These phethe dimensions and concentration of the convective currents, nomena include rough airplane flights, the propagation of all kinds of radiations, the transport of contamination, the processes of cloud-and precipitaTherefore, the first problem of the present ' tion-formation and others. work was to develop a method for the study of convective motions in a free which would include a means of tracing convective curatmosphere, It was also necessary to formulate rents in a wide range of dimensions. a theory whereby random measurements could be used to determine the dimensions

true

of convective

currents,

their

concentration,

and,

conse-

guently, the relative areas or volumes which they occupied /13, 17/. Theoretical investigations are quite effective for the study of disordered while

convection,

no

theory

of convective

motions

due

to an

infinite

heated

plane exists* (it seems impossible to approach this problem fully at present Nevertheless, the relatively small number of theoretical studies of /64]). individual convection elements (in the form of isolated air masses or jet streams) has played an essential part not only in determining the nature of the

motion

general %

of the

laws

elements

of convective

under

consideration,

but

also

in understanding

processes.

a system of equations, which can be used for the solution of the problem of turbulence arising in system small Iayer over a non-uniformly heated horizontal plane, and the approximate solution of this were obtained by L A. Kibel' /32, 33/,

The

the

The nature of the motion and the temperature of the isolated buoyant air parcel, rising through a stationary atmosphere of varying stratification in the presence of friction or turbulent mixing, was investigated by A.F.

Dyubyuk

/28/ and Priestley

/104/.

Batchelor

/64/ established the laws

governing the variation with height of the temperature, velocity and dimensions of a mass of air (cloud) which is put into turbulent motion in a neutral atmosphere by an instantaneous point heat source. The case of the motion of a cloud in a stable atmosphere was considered by Morton, Taylor and Turner /99/; they carried out laboratory experiments whose resulis agreed with the obtained theory. In 1937, Ya.B. Zel'dovich /29/ considered for the first time the motion of convective jets rising freely from a point or line heat source in a neutral atmosphere. Using the methods of the theory of similitude he discovered the laws of variation with height of the temperature, velocity and dimensions of laminar and turbulent convective streams. Similar results were

obtained by equations

Humphreys

for

I1..N. Gutman laminar

/114/,

/25/ who solved the corresponding

flow,

and

by

W.

Schmidt

for turbulent streams.

/118 /

and

system

Rouse,

Yih

of

and

Verification of these laws under

laboratory conditions /118, 114, 110/ gave satisfactory results. However, according to the data of Railston /110/, the decrease of temperature with height obeys a law which is intermediary between those obtained for laminar and turbulent streams’. A more complete investigation of the nature of the motion of turbulent thermals (over a maintained circular heat source), allowing for atmospheric

stratification, was performed by Priestley and Ball /109/, 1. V. Vasil'chenko /3/%*% and Morton, Taylor and Turner /99/ (the latter considered only the

case of a stable atmosphere but confirmed the theory experimentally). These theories explained a number of aspects of convective motions in the atmosphere, particularly the fact that for a stable stratification the streams decay at heights, where the temperature excess in them always has a

negative value***, streams

However,

is particularly

vective motions

the theory of the so-called "spontaneous"

relevant

to the processes

in the atmosphere.

Batchelor

of development

/64/ and Priestley

of con-

/108/

investigated the possibility of the appearance of such streams in an unstable atmosphere. The potential temperature profile in conditions of free convection in the atmosphere, discovered by A.S. Monnin, A.M. Obukhov /42/ and Priestley /105/, made it possible to establish the law of variation with height of the temperature and velocity of these convective currents formed in the absence of heat sources. These theories describe quite well the behaviour and features of convective motion in various conditions. However, the possibility of applying them to the phenomenon of atmospheric convection has not been verified experimentally. Since each of these theories has its own laws of variation with height of the temperature and velocity of the ascending currents, such a verification, as well as estimating the extent to which this or that theory *

Railston considers that the results of his measurements based on empirical

%% #¥k

agree better with Sutton's theory /132,

55/,

data.

1.V, Vasil'chenko /4/ proposed an approximate theory of cloud stream also. This result, as well as its essential effect, the cooling of air layers near the upper part of a convective layer,

was frequently observed by the author /12,

14/,

could be applied and determining the numerical values of the constants involved in the laws, would establish (by comparison) the conditions for the development of convective motions in the atmosphere. This, however, is not easily accomplished under laboratory conditions because it is difficult to reproduce atmospheric instability; under natural conditions such a verification seems at first sight even more difficult to achieve. In order to carry

out

such

verification,

then,

the

second

problem

of this

work

was

the

development of statistical methods which would make it possible to obtain the values of the temperature at the center of convective currents from data or random measurements of the temperature of these currents in the atmosphere. If these methods are applied to a large number of measurements made at various heights it is possible to obtain the law of variation with height of the temperature of convective currents, particularly (assuming the convective currents to be in the form of jets) along the axes of the jets. Thus the experimental results may be compared with the theories /18/. It is obvious that the method for obtaining the temperature at the centers of nscending currents from data of measurements in sections chosen at random can be applied to other parameters of convective currents. It is thus a general method for determining the actural parameters of convective cur-

rents from observed

data

/17/.

It has been mentioned that a theory of convective motions from an infinite heated plane does not exist. Nevertheless, the total effects of convective motions over the earth's surface can be obtained by combining the effects of a large number of separate convective jets. However, there are no data on the concentration and dimensions of convective currents, nor on the

dependence

surface,

the

of these

weather

values

on

conditions,

time, etc.

height, Thus,

the

the

nature

third

of the

problem

underlying of the

pre-

sent work was the investigation of the dependence of these parameters of ascending currents on various physicogeographical conditions. Finally, it should be noted that convective motions inside clouds have hardly been studied*. Existing data on the order of magnitudes of the velocities

of vertical

in clouds

/95,

96,

motions, 97,

88,

current 102,

60,

dimensions, 62/

are

few,

and

temperature

and

usually

excesses

unsystematic,

since they are frequently individual random measurements. Owing to inertia of the equipment, it is difficult to relate these data to specific rents, especially as the majority of researchers did not consider this lem. Therefore, until recently only the most general ideas existed on nature of convective processes in clouds. Since the developed method studying convective motions in a free atmosphere is also applicable to measurements

convective convective

*

in clouds,

the

fourth

problem

of the

currents inside thick cumulus clouds motions inside and outside clouds.

The danger of flights in clouds is partially associated with this,

work

was

the

study

the curprobthe for of

and the relation between

Chapter A METHOD

1.

I

FOR STUDYING CONVECTIVE IN A FREE ATMOSPHERE

MOTIONS

The physical foundations of the method

The method for studying convective motions in a free atmsophere, including those in clouds /11-13/, is based on tracing ascending convective currents by means of their temperature, which is always different from the temperature of the surrounding air. Convective currents consist of rising masses of air which are less dense than the surrounding medium, since they are relatively warm. Therefore, ascending currents crossed by an airplane flying horizontally are recorded by a fast response sensitive thermometer as zones with a higher temperature than that of the surround-

ing air. The heating of the convective currents may take place through the contact of the air with relatively warm sections of the earth's surface, or during an ascent through a surface layer with a superadiabatic lapse rate or, in higher layers through the liberation of latent condensation heat. If currents, heated by any of the above-indicated ways, continue to rise ina medium with lapse rates close to the adiabatic, then the temperature excess arising in them will be maintained to a considerable extent during the whole subsequent ascent. Such conditions exist almost throughout the whole layer in which convective motions are observed. In such a layer the temperature

of the

ascending

air

mass,

as

well

as

of the

surrounding

medium,

decreases, with increasing height, roughly according to the same (adiabatic) law (the higher part of the layer is excepted from this). Therefore, the initial

temperature

excess

in the

ascending

mass

decreases,

albeit

very

slowly, mainly due to mixing with the surrounding, colder air. Compensatory descending currents in a convective layer, on the other hand, are usually very weakly pronounced in the temperature field. The temperature of the descending currents differs from the temperature of the surrounding air only when a temperature gradient v, different from the adiabatic gradient y, is observed in the latter. If yy. they will be colder. The smaller the difference between the temperature of the descending currents and the temperature of the surrounding air, the smaller is the difference between the temperature gradient in the convection layer and the adiabatic gradient.

FIGURE a) 50m

1.

(upper curve);

Patterns of oscillograms recording b} 300m;

c) 500m;

d) 1,000m.

air temperatures

The temperature

at various heights

rises for a decreasing

ordinate.

The

vertical lines are 0.5 sec time-marks

In flights at heights of 50m or more in convection conditions, the observed temperature gradients are close to the adiabatic gradient. Therefore, ascending currents are well marked in the temperature field, whereas the temperature of the compensatory descending currents is only slightly different from the temperature of the surrounding air*. Similar conditions are observed inside cumulus clouds, where the decrease of temperature with increasing height is close to the moist-adiabatic lapse rate. Thus, the temperature of descending currents in clouds also differs little from the temperature of the surrounding cloud air and in any case this difference is small compared with the temperature excess in the ascending currents. *

Convective quite

currents are apparently formed

probable

the jets break down., may

be of the same

stationary jets) but of small vertical further

limits

in the form of jets.

However,

of wind,

and other factors,

As a result of this the vertical dimensions of the order as the horizontal

will be located near the ascending This

near the earth's surface

that during their further ascent due to the influence

the

masses

In this case,

and will thus appear

extension,

difference between

ture of the surrounding medium.

dimensions. flowing

ascending

masses

the compensatory

as currents not of large

around the

the temperature

turbulence

of the

ascending

masses

descending

it is

of the hotter air descending

currents

(as in the case of

{(bubbles) of warm

currents

air.

and the tempera-

FIGURE

2,

Recording

a) 6 to 10m;

of air temperatures

b) 50m;

c) 300m;

ordinate.

In Figures flights

are

at various heights

d) 500m;

e) 1000m.

The

Temperature

rises for a decreasing

The vertical lines are 0.5 sec time marks

1 to 3 typical temperature

shown*.

(with an increased oscillograph chart feed)

ascending,

recordings

warmer

made

currents

during horizontal

quite

clearly

appear

on the oscillograms, whereas the descending motions are either not parent or are extremely weakly pronounced in the temperature field central part of the oscillogram in Figure 2, a). The steepness of the perature pulses, particularly near the earth's surface and inside

*

Almost immediately Convective marized,

Motions

James'

following

paper /85/

appeared.

during flights at heights from ing motions were

the publications

in a Free Atmosphere"

in the temperature

in 1953,

/11/,

This gave

150 to 900m.

10

recordings,

as Murgatroyd

in England

obtained.

" A Method

for Studying

the basic features of these motions were

air temperature

Later on,

field was conducted

of the author's work

in which

ap(the temclouds,

mentions

and some

similar to Figure /100/,

1,

summade

a study of ascend-

of the results published

in /11/

rojewiplo

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ays

11

shows the absence of a distinct boundary currents and the surrounding medium?*. Thus,

the

conditions

for

vertical

layer

motions

between

during

the ascending

convection

make

warm it pos-

sible to isolate in the temperature field ascending currents which determine the transport of various contaminations in the atmosphere and constitute regions in which a series of phenomena related to convection, in particular, processes of cloud and precipitation-formation, aremost sharply pronounced.

2.

Airplane

thermowmetvic equipment

Airplane-borne thermometric equipment for the study of convective motions in a free atmosphere includes sensitive fast-response thermometers, potentiometric velocity-sensing elements, a flight height statoscope, a chronometer with contact time marker and a loop oscillograph for recording the readings of the instruments. In flights over mountains or over very rugged ground the oscillograph also records the readings of a radioaltimeter. In addition, one of the galvanometers of the oscillograph is adapted for marking on the chart normal events, for example entry and exit from clouds, variation of the nature of the underlying surface, etc.

Airplane

thermometer

The thermometers used in the equipment were developed by V. V. Shchelokov /61/ and are of the electric resistance thermometer type, used with an unbalanced-bridge system. Two thermometers are usually

= Sensing element I H Bridge

IH

Amplifier | J

.

.

Visual

To the oscillograph

Rectifier II

Rectifier III B

Sensing element

II HBridge

IIH

FIGURE 4.

Block diagram

indicator

Visual

indicator

.

Amplifier IIJ

To the oscillograph

of a two-channel

thermometer

used in the equipment, the sensing elements of one of them providing two temperature measurements simultaneously. The block diagram of this instrument is shown in Figure 4. Each channel of the thermometer %

The

recordings (Figures 1~3)

agree

also with some

theoretical representations.

tained for a constant mass flow with height in a neutral atmosphere in jets.

According

It therefore of the jet, ture field),

to these profiles appreciable

follows that the temperature even in a neutral i.e.,

atmosphere

descending

currents may

profiles of the ascending (where

almost throughout the whole

descending

Schmidt

/117/

ob-

exist at the boundary of the jet.

currents should be sharp on the borders

currents are not pronounced

convection layer .

12

F.

profiles of the vertical velocrty

in the tempera-

consists of a wire temperature sensing element, constituting an arm of the resistance bridge, an amplifier, two phase rectifiers, a recording galvanometer and an indicator. A generator supplies the bridges and rectifiers. The variations in the sensing element's resistance, proportional to the temperature fluctuations, give rise to corresponding variations in the voltage of the bridge's unbalance, which, after amplification and rectifiare

recorded

by

a loop

oscillograph

and

a control

middle

instrument.

s A\ D

Ay

\

L

22

{1

ol

s

o v

o o ob

cation,

FIGURE

5.

Circuit diagram

of a two-channel thermometer

The scheme of the two-channel thermometer is shown in Figure 5%, Each channel consists of a bridge with a resistance temperafure—sensing, and an electronic system providing the necessary sensitivity of the instrument.

In order

to attain

a sensitivity

of the

order

of

0.01

to 0.02°,

and

also to ensure recording of the temperature fluctuations without appreciable amplitude distortions, the whole measurement interval of the thermometer (~100°) is divided into 50 approximately equal ranges, divided into two groups. This division is made by step balancing of the bridge by *

The

diagram

of Figure 5 is an improvement

on that given in /61/.

airplane's electricity system for supplying the instrument. meter over a longer period without

additional adjustments,

13

A developed feature

is the use of the

This ensures uniform operation of the thermo-

connecting

resistances

which

shunt

one of the arms

of the bridge

(see

Figure 5). The current through the element does not cause a perceptible heating of the sensing element (1073 a)*. The required voltage for the galvanometers

is provided

feedback).

FIGURE

6.

by a stable four-stage

amplifier

(with negative

General view of the two-channel thermometer

The frequency response of the instrument (determined mainly by the inertia of the sensing elements) is linear up to approximately 30 cps and the amplitude response reaches 3 to 4°. Thus, the thermometer provides undistorted measurements of high frequency temperature fluctuations (see Figure 2, a). The general view of the two-channel thermometer is shown in Figure 6. A more detailed design and electronic diagram of the instrument is given

in /61/. The

meter

temperature-sensing

of

50

microns,

or

elements

a tungsten

consist

wire

with

of a copper

wire

a diameter

of

21.3

with a diamicrons,

having a resistance of 40+ 0.2 ohm at a temperature of + 20°**, For a resistance of 40 ohm, one range of the thermometer is inthe case of copper, 2.5°, and in the case of tungsten 3.12°. The ranges overlap by approxi-

mately *

20 %o***,

Under such a current a tungsten wire with a diameter of 20 microns

is heated,

even when

it is not sub-

jected to an appreciable airflow around it (which always occurs in flight) and its temperature increases by approximately 0.01° /37/. **

Sensing

elements with a high resistance possess certain advantages.

elements were used at first, their

resistance

elements #¥%

was

limited to 40 ohm

is about 5 m,

decreases by a factor of ten.

since copper sensing

(even with that resistance the length of a copper wire for the

whereas that of a tungsten wire

When recording temperature

However,

and the preparation of elements with high resistances was quite intricate, is approximately

pulses with amplitudes of more than 2-3°

However,

25 cm). the sensitivity of the indicator

the scale of the temperature recording on the oscillograph

chart is not changed by this.

14

FIGURE

7.

Temperature-sensing

a) of copper

FIGURE 8.

wire;

b)

elements

of tungsten

wire.

Temperature-sensing elements in shields fixed on a projecting arm

1) made of tungsten wire; 2) made of copper wire; 3) in a drip~proof shield; 4) a copper wire slow-response element for measuring the average air temperature during flight .

15

The copper wire is wound inside and outside a plexiglass cylinder at a distance of 4 to 5 mm from the walls (Figure 7a), and the tungsten wire is wound inside a rectangular frame of elliptical cross section

(Figure ).

both sensing frames are are attached of the IL 12 tance of 2.3

The angle between the wire direction and flow direction in

elements is approximately 2°. The plexiglass cylinders and suspended on spiral springs inside nickel plated shields, which to a projecting arm (Figure 8) mounted below the nose section plane, together with the cantilever of the Pitot tube, at a dism in front of the propellers.

....................

FIGURE (the time

9.

Intertia of a sensing element

of copper wire

of establishment of a given temperature

flight velocity of 11 m/sec).

The

for a

points are 0.02 sec

time marks,

The sensitivity of tungsten elements is approximately 25% lower than that of copper wires. However, in recording temperatures on an oscillograph it is easy to establish an approximately equal recording sensitivity, its scale being adjusted within very wide limits (up to 0.01° per 1 mm of the chart's ordinate). Usually the scale of temperature recording is approximately 25 mm per 1°. The inertia of a sensing element made of a copper wire was determined by recording on the oscillograph the rate of temperature decrease of the

heated

element by the method

described by S.1.

Krechmer

/37/.,

When

the element was subjected to an airflow with a velocity of 11 m /sec its time constant was found to be 0.075 sec (Figure 9). For velocities from 3.9 to 11 m/sec the well-known reciprocal relation between the inertia of the sensing element and the square root of the flow velocity was verified. If this relation is extrapolated up to the flight velocities, i.e., to 70 m/sec, the time constant of a sensing element of copper wire should be somewhat less than 0.03 sec. An even smaller value (approximately 0.01 sec) is obtained by calculating the inertia by the more exact formula proposed by

S.I1. Krechmer For

a time

/37/.

constant

of the

sensing

element

of

~0.03

sec,

the

tempera-

ture excess even in rarely intersected narrow streams of 7 to 8 m size will be determined with an error not exceeding 5%. This is confirmed by

16

the identical temperature recordings in flights (Figure 10) by a copperwire sensing element and by a tungsten-wire sensing element, which has

a considerably lower inertia (0.0015 sec according to /57/); speed

of the oscillographic

detects

the

finer

thermal

chart

(Figure

structure

element

convective

although

of the

the width and amplitude of the corresponding pulses, convective currents as a whole, are the same*.

FIGURE

10,

Simultaneous

temperature

sensing elements.

The

recording

for a high

10) the tungsten-wire currents,

characterizing

inflight by 1) copper-

vertical lines are 0.5 sec time

the

and 2) tungsten -wire marks

The thermometers are calibrated in a 10 liter alcohol bath with good transient thermal system. Checked mercury thermometers with a multiplying factor of 0.02 to 0.05° were used as standard references. Examples of calibration curves for copper and tungsten sensing elements are given in Figure 11. Some non-linearity in the calibration curves is due to the non-linearity of the electric characteristic of the bridge, as a result of which equal unbalanced voltages correspond to non-equal variations in the resistances of the

sensing

elements.

Because

of this

non-linearity,

the

extreme

ranges differ in sensitivity among themselves by approximately 10%, and the extreme points inside the ranges by approximately 0.5%. Investigation of the dependence of the thermometer's readings on the supply voltage /61/ has shown that when using accumulators and dry batteries, the variation in the instrument's readings does not exceed 0.01° during 20 minutes of operation. When these improved circuits were used such a stability was maintained quite well when the thermometer was supplied from the electrical system of the airplane,

*

A slight difference

in pulse amplitudes,

shown in Figure

17

10,

is due to different recording sensitivities,

’6‘

T

g 2 -3

2

T T

7

:;hmllll

Y o z04080831

2

FIGURE

11.

i

J

1

4

1

5

i

6

i

Patterns of calibration curves for 1) tungsten

7

1

8

i Ranges

g

1

0

|

and 2) copper sensing elements

Potentiometric sensing elements of the flight velocity and of the flight height statoscope Potentiometric sensing elements are assembled of standard parts and units. The sensing elements of the velocity and of the height statoscope are elastic diaphragmal corrugated boxes US-35 and VAR-10, whose distortions are transmitted to the moving arms of potentiometers included in the circuit of an unbalanced direct current bridge (Figure 12). The unbalance voltage, depending on the flight velocity or on the deviation from the prescribed height, is recorded by a loop oscillograph. The general view of the potentiometric sensing elements is shown in Figure 13. Each

of the

instruments

is

enclosed

in

a hermetic

jacket,

standard

for aviation instruments. In the height statoscope, both the diaphragmal unit and the housing of the instrument are connected to the static pressure receiver of the Pitot tube (Figure 12), as a result of which the instrument does not react to variations in the flight height if not engaged. The instrument is engaged by shutting off, with the aid of a special electromagnetic valve B, the conduit leading from the Pitot tube to the aneroid. In order

that the box should not react to the sum increase in air pressure, appearing at the moment of shutting off the conduit, a damping volume of about 500 em? is introduced between the valve and the aneroid. r=————="=—=

=

' '

1Lr°

|

J

=———co-=d

irStatoscope unit |

T

!

o1

< : 32!

3

(o

T

T

=

l

'

]

T

1

|

!

:

|

rg

! 1

—o

of

|

b0

—-]

1 ¢

|

:

Control desk

:!

{

|

'

1| | t |

I 1

o N

| |t

g

fb———= o

?

T

N

%o :

2

{

’ |

\

T T T T

5P

=

S|

T T

o

!

3

|

'

T

!

2

unit

}

T

oot

: Velocity

F

I

|

|

2!

b—o

4

6w

+

|

Pitot tube

FIGURE

12,

Principle of action and control of the potentiometric sensing elements of the flight

velocity and height statoscope

The potentiometric velocity and height statoscope sensing elements together with the electromagnetic valve and the additional volume (Figure 14) are mounted in the nose section of the airplane in front of the pilot cabin.

FIGURE 13.

1) Potentiometric flight velocity and 2) flight height statoscope sensing elements

This makes it possible to shorten the piping leading from the Pitot tube to the instruments to the minimum. The instruments are remote-controlled

from a special desk (Figure 15) mounted permits

complete

monitoring

of their

in the airplane's cabin,

operation.

19

which

The instruments are calibrated by creating in the pressure chambers an artificial pressure or vacuum, simultaneously recording their readings on the oscillograph. Inaddition, itis possibletomake a control calibration

FIGURE 14,

Potentiometric sensing elements of the flight velocity (1) and of the

flight height statoscope

(2) in hermetic housings,

damping volume

in the flight comparing

cator and altimeter.

tion from

a prescribed

FIGURE

(4),

the results

electromagnetic valve

(3) and

fixed on a special stand.

with a carefully checked

velocity

indi-

The scale of the recording of the velocity and deviaflight height

15.

can also be changed

Control desk of the potentiometric

within wide limits.

sensitive

elements of the flight velocity and height statoscope

Depending on the number of recorded elements, the scale of the velocity recording is from 5 to 15 mm of the chart's ordinate per 10 km /hour, and that of the height statoscope is from 6 to 12 mm per 10 mm of water. When converting the readings of the water column pressure into flight height variation the scale of the recording of the latter is variable, since its sensitivity slightly decreases with increasing height. Figure 16 shows examples of calibration curves for the velocity and height statoscope sensing elements and the variation of the calibration curves with the supply voltage and with the direction of operation of the pressure chamber.

20

g 160

g 140 =120

140 $120

@

s

g 40 2 20 Q

S0

100 ; 80

160180

5 60

S &

g 40 §20

200 220 240260 280300320

-0100-80 60 -40-20 0 2040 60 80 100

U, km/hour

P, mm

a

180

180

E 760

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e

8140

3 120

g 100

g 120

\

80

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80

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2

40

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b

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5100 8

X

of water

7/

; 60

20

& 20

%0/80200220240250230300.?20

-0700'80 -60-40-20

U, km/hour

p, mm

c

FIGURE

16.

0

20 40 60 80

of water

d

Calibration curves of the velocity and of the height statoscope for

various supply voltages of the potentiometric sensing elements

(2,

b) and for both

directions in which the pressure chamber is operated (c,

The

oscillograph

a continuous

18-loop oscillograph

fers*

4

£

g 60

For

5

o

=100 o ‘g 80

S

v

5

in a special

recording

(Figure

frame

and the rest

of the equipment

of the elements

17) is used,

mounted

d),

measured

suspended

in the airplane's

in flight a OMS

on flexible cord buf-

cabin.

The

recording

is made on a paper chart 20 cm wide by ""Geofizika'' type tensometric

galvanometers

with a sensitivity

of 10-%a/mm

frequency of the order of 250 cps**,

and

a proper

oscillation

Much use of the galvanometers has shown that they can last for long periods under conditions of vibrations and severe roughness, without changing their characteristics. The galvanometer sensitivity referred to is necessary for recording the temperature pulses only. The rest of the elements can be recorded with galvanometers of lower sensitivity (by 1 to 2

orders % #%

These

of magnitude).

instruments

and equipment are fixed on the plane with "Lord"

The frequency characteristic of the galvanometers much of temperature frequency, meter

fluctuations.

Therefore,

type buffers.

exceeds the frequency range

to avoid the smearing of the recording,

of the recording

caused by the carrier

a filter with a transmission band from O to 50 cps is introduced at the output of the thermo-

(before the galvanometers).

21

The time marks on the oscillograph chart are synchronized, by means of an electric contact, with the readings of a naval chronometer fixed on a gimbal in a special housing. This in turn is suspended on flexible-cord buffers. The time marks have the form of 0.5 sec vertical lines. In addition, the time marker of the oscillograph makes heavier lines each 1 sec, and

the

chronometer

1 sec and

makes

FIGURE

and

one

contact

each

1 minute also appear on the charts

17.

OMS

minute,

Thus,

(Figures

1,

marks

every

3b and others).

18-loop oscillograph

A RB-2 low altitude radioaltimeter is also included in the equipment its readings are recorded on the oscillograph chart. The radioalti-

meter

has

are used flight.

two

measurement

depending

ranges:

on the nature

3.

0 to

Measurement

The dimensions of cross sections of by an airplane as the product of the air the current. Errors are thus incurred in determining the time of crossing the

curve,

120

of the terrain

(a mean of those shown in Figure

m

and

0 to

1200

m,

and the conditions

which

of the

errors

convective currents are determined velocity and the time of crossing in measuring the flight velocity and jets. By using a velocity calibration

16),

as was done in the processing

of the measurement results, the error in the determination of the instrument velocity is 1%. Approximately such an error is incurred in determining the air velocity*. Thus, denoting the errors of measurement of the dimensions of convective currents, due to errors in the determination of the velocity, respectively by 8/ and &/; we obtain:

81, =~ 81, = 0.01Z, where ! is the dimension by an airplane. *

In flight conditions this accuracy at the surface and the temperature

(cross

section)

of a convective

(1) current

measured

is generally reached by calculating the air velocity from pressure at the flight level,

known (from the readings of a specially graduated used for greater accuracy.

altimeter or the data of a meteorograph)

22

data

although the pressure at the flight level is also and may be

The errors in the determination of the crossing time of convective The dimencurrents depend on the speed of the oscillograph chart, sions of small temperature pulses or the position of the beginning or end of relatively large pulses with respect to neighboring time marks can be determined with an accuracy up to 0.2 to 0.25 mm. For a chart speed of about 30 mm /sec, the maximum error in the determination of the crossconverted

of currents,

ing time

does

to length,

not

exceed

1 m.

However,

such a chart speed limits the time of recording, as a result of which it is difficult to obtain sufficient statistical material. Therefore, recordings are made, as a rule, at chart speeds from 4.0 to 2.4 mm/sec (depending on the type of the cassette of the oscillograph and of the supply voltage of In this case the impulse durationis determined withanaccuracy the board). from 0.05 to 0.1 sec or, when converted to distance, with an accuracy from approximately 3-4 to 6~8 m, this error being introduced twice in determining the duration of large temperature pulses (from the difference in the Thus, the maximum error introduced in times of their beginning and end). the determination of the dimensions of convective currents under most unfavorable

measurement

conditions,

is:

‘ L Blimax = { 2(51)3] * = fw=)

V2-10% + 100m.

(2)

In crossing relatively small convective currents whose extent is determined by a single reading, the maximum measurement error does not exceed 6-8 m. The temperature excess of convective currents with respect to the surThe amplirounding air can be determined with a high degree of accuracy. tudes of the temperature pulses are read off the oscillograph chart with an The measurement errors of the thermometer are accuracy up to 0.01°. caused mainly by the neglect of the non-linearity of the bridge's unbalance within each of the ranges (which for most intense currents outside clouds with

a temperature

supply

ponents

system

(0.01°)

excess

(0.01°)

/61/.

of

2° amounts

and the influence

to

0.01°),

the

of temperature

instability

of the

on the circuit's

com-

However, besides these errors, the amplitudes of the temperature pulses taken from the oscillograms may contain errors which are due to variation in the velocity or height of the flight while the airplane crosses convective This was one of the reasons for the inclusion of the velocity and currents*. of height stability sensing elements, whose data make the corresponding corrections possible. A variation in the flight velocity while crossing convective jets leads to variation AT in the heating of the temperature sensing element due to the change in the flow:

AT = k?,

(3)

where & is a coefficient, depending primarily on the form of the sensing The value of k is determined exelement and v.the plane's air velocity. perimentally by measuring the air temperatures at some level for various %

The variation in the flight height also generally distorts the dimensions error is negligible as compared with the ones mentioned.

23

of the jet.

However,

this

flight velocities*. For a sensing element of copper wire they were found to be 29.3.10-% degree -hour?/km?, and for a sensing element of tungsten

wire 25.8 . 10-% degree - hour? /km?,

The variations inthe heating of the sensing elements for a velocity decrease of 5 km /hour versus flight velocity are given in Figure 18. Since the variation in the velocity can be read from the oscillograph charts with an accuracy up to 0.5 km /hour, an error, not exceeding 0.01° when convertedtotemperature, is present in the correction for the variation in the flight velocity in crossing a jet. Distortions of the temperature excess in convective currents due to variation in the flight height while crossing the currents occur if the temperature varies with height at the flight level. During a developed convection, the temperature gradient is usually close to the adiabatic gradient. Therefore, a correction which takes into account the variation in the flight height ar’ is approximately 0.01° per 1 m of height

009

008

and involves an error of the order of 0.01°

1

0.07

since the variation

Z

006 0.05)

0.0#200

720

FIGURE 18.

240

260 280 ¥, km/hour

velocity and height-statoscope sensing elements (Figure 16). By using curves, (between those shown in Figures 16c and 16d), permissible errors do not exceed

Variation in the heating of

2 km /hour for the velocity and 2 mm

per and 2) tungsten wire, (for a velocity 8

of 5 km

is determined

Some friction exists in the transmission mechanisms of the potentiometric

temperature-sensing elements of 1) copchange

in height

with an accuracy up to 1 m.

/hour) versus flight velocity,

fhous)

&

.

water for the height statoscope. errors

are

also

.

carried

over

.

into

of

These the

cor-

rections for the variation in flight velocity and height in crossing convective currents. Converted to temperature, the error in the flight velocity determination does not exceed 0.03°, and the error in the height determination, 0,02%%, Clearly, the first six errors and any of the errors due to friction are independent of each other. At first sight, the errors due to friction may seem interrelated. An airplane in a strictly horizontal flight crossing an ascending current loses velocity and at the same time is lifted upward. Both effects lead to a decrease of the temperature recorded by the oscillograph. However, the pilot, feeling the shock on entering convective jets, usually counteracts by accelerating the airplane in ascending currents. Often,

the

errors

due

to friction

should

be

subtracted

and

not

added.

It is

therefore more logical to consider these errors also as independent of one another. Inthis case (assuming the inertia of the thermometer of the velocity and height statoscope sensing elements negligible) the maximum error in the measurement of the temperature excess of convective currents with

* *%

1032

These measurements perature gradient.

must be made

in two opposite

With airplane vibration always present in flight,

directions in order to eliminate the horizontal tem-

it is possible that the friction effect is smaller.

24

respect

to the surrounding

air is

8T max = [Z (57)3-]7 = 0.04°.

(4)

To simplify the processing, it is possible to disregard the non-linearity of the calibration curve of the thermometer (see Figure 11), according to which, for a measurement interval of 20°, the extreme ranges differ by approximately 3%, and also to use the height of unit decrease of pressure of a standard

atmosphere,

which

may

lead

to an

error

in the

determination

of the flight height variations according to the statoscope of no more than 10%. In this case the maximum error in the measurements of the relative temperature of convective currents is of the order of 0.05 to 0.06°. It should be noted that under certain flight conditions, particularly severe roughness, the oscillograph vibrates considerably in spite of the damping. This results in small, short period deviations appearing on the recording and it is thus impossible to take readings from the charts of the oscillograph with an error less than 0.03 to 0.05°. In certain cases (in

clouds) this error reaches

4.

0.1 to 0.2°,

Vevification of the method

Figure 19a shows an oscillogram typical of flights inside a convective layer over the dunes of Kyzyl Kum. The oscillogram shows recordings of the air temperature and of the velocity and variations of the height of the flight. Positive temperature pulses (directed downward) indicate the crossing of warm convective currents. These are not due to variations in the velocity or height of the flight. The oscillograms show that in crossing certain currents the airplane is thrown upward or the flight velocity is reduced. Both of these effects should cause a temperature decrease (negative pulses are directed upward) and not an increase. Variations in the velocity and height mainly affect the general variation of the temperature, which almost exactly follows them (Figures 19b and 19¢). However, the temperature pulses indicating warmer ascending currents quite clearly stand out from this background. The temperature pulses are not a result of dynamic turbulence (which, generally, may cause vertical currents with a temperature differing from that of the surrounding air). To confirm this, special flights over mountains were made. Thesehave shownthatat slopes andover ridges considerable temperature pulses are observed only under sufficient solar heating (Figure

20a).

In

overcast

weather,

or

at

sunrise,

the

temperature

pulses,

despite wind and rugged terrain, arerelativelyweak, or absent (Figure 20b), It should also be noted that if the thermometer could record dynamical turbulence, positive and negative temperature pulses would be equally likely. It is seen from all the given oscillograms that in the majority of cases the temperature in the currents crossed is higher than in the surrounding air. Nor are the temperature pulses recorded on the oscillograms the result of the tensometric effect of the sensing element's wire. Simultaneous recording of temperature by copper and nickel wire sensing elements in a

gusty wind of 15-20 m/sec

on the ground

25

(Figure

20c),

and in flight

s

FIGURE a) recording during

100 m flight

19.

over

Oscillogram patterns Ky:zyl

Kum

from prescribed height and 3) flight velocity; 3) flight velocity,

The temperature

dunes of 1) temperature;

2) deviation

b, c) variations of 1) temperature;

2) flights;

and velocity increase for decreasing ordinates.

26

FIGURE

20.

Oscillogram

patterns

a, b) during flight over the slopes of the Kakhetiya ridge in the day and at sunrise respectively; ¢, d) simultaneous temperature recordings by 1) copper~and 2) nickeline-wire sensing elements, on the ground

and in flight respectively;

over coast respectively

(100 m);

e, f) nocturnal flight over central part of I1'men'

g) flight in the day over a forest area (containing

the horizontal line on the figure)_

27

Lake and

a small

lake,

(Figure

20d),

shows that a nickel wire sensing element

(whose resistance

hardly varies for a temperature variation) does not record any pulses, whereas the copper wire sensing element records quite sharp temperature fluctuations. Temperature pulses indicate convective motions. In order to prove this, special flights were carried out along routes passing over land and water surface. In flights over the Astrakhan region it was found that by day the rather sharp and large amplitude pulses over land were replaced by relatively weak pulses over the shallows of the marshy Caspian coast and completely disappeared farther out to sea with the disappearance of the convective motions. At night the opposite picture is observed. Temperature pulses are recorded only over the sea, where nocturnal convection develops over the relatively warm water surface; over land the temperature pulses disappear. Nocturnal convection is pronounced also over lakes (Figure

20e),

being completely absent over shores

(Figure

20f).

By day,

even at

the time of the strongest convection development, temperature pulses indicating convective motions disappear almost entirely over quite small water

reservoirs

(Figure

20g).

Finally,

it has to be noted that the amplitudes

of

pulses and the thickness of the layer where they are observed have a diurnal course over land approximately following the solar altitude. Convective currents, recorded by positive temperature pulses, are characterized by ascending motions. A simultaneous recording is shown in Figure 21 of a low-inertia thermometer and a sensitive electromechanical

= FIGURE

21.

Simultaneous

4) accelerometer. velocity.

The

recording

2) is deviation

temperature

are directed upward.

LR

of the readings of 1) a thermometer

from the

prescribed height

rises with decreasing The

vertical

28

ordinate,

and

and 3) is flight

positive

lines are 0.5 sec time

overloads

marks.

accelerometer

Skatskii

with piezocrystal

element,

especially

developed

/51/ to enable such a comparison to be made*.

by V. 1.

As seen from

the oscillograms, to almost each positive temperature pulse there corresponds an upward airplane overload, As mentioned, in conditions of developed turbulence the pilot corrects the airplane. This correction is also recorded by the accelerometer as the jolts of the airplane due to the dynamic turbulence. On the other hand, newly formed or already decaying warm currents do not possess sufficient kinetic energy to cause noticeable airplane overload. Therefore, there should not be complete agreement between the recordings of the thermometer and the accelerometer. Comparison of recordings of these instruments at heights of 50 to 1000 m shows that in roughly 90% of the cases upward airplane overloads correspond to positive temperature pulses

(Table

1).

TABRLE Correlation

between positive temperature

Flight height,

m

1 impulses

and upward

No.of cases

50 100 300 500 700 1000 Average

airplane overloads

Coincidence,

350 382 317 312 243 259

92 94 91 89 86 82

1863

89

%

Thus, in crossing warm convective currents, upward jolts of the airplane are almost always observed. This confirms the ascending character of the motions. When the airplane crossed columns of smoke rising over burning straw stacks, positive temperature pulses and upward airplane overloads were observed**, quite similartoneighboring pulses which indicate natural convective currents. This also indirectly confirms the ascending nature of convective

current

motions.

However,

it does

not

follow

from

this

that

convective currents rise only over relatively heated ground sections. Oscillograms obtained in flights at night over water surfaces (Figure 20e), and the data given in Chapter III show that convective motions may arise over a uniform underlying surface. The above experiment illustrates only the fact that warm convective currents are ascending currents.

*

This accelerometer

has some

important advantages over the mechanical

the most important of which are low inertia, absence of hysteresis, ing element. *%

Besides,

Similar pulses were buildings,

etc.,

aftereffects,

accelerometers usually used,

stability of the readings under temperature

fluctuations,

influence of the airplane's vibrations and the need to damp

the sens-

the electronic system of the instrument provides a considerably higher sensitivity.

recorded in low flights over asphalt roads,

or at greater heights,

fields or forests,

over snow-free mountain tops.

29

iron roofs of individual

5.

The technique of the flight and the primary processing of the measurements

The measurements were taken during horizontal flights heights. Usually, the measurements started at a height of and sometimes at a height of 5 to 10 m over fields, or at a over forests and continued up to the upper boundary of the layer,

for

example,

up

to

3000

to

4000

m

in Central

at various 50 to 100 m height of 30 m convective

Asia.

The

time

of the

horizontal journey was usually 5 to 10 minutes. Taking the measurements during equal time intervals over the same sectionoftheterrainat increasing levels, and then at decreasing heights, it was possible to obtain data which were characteristic of approximately the same time by averaging the measurement results. Carrying out successively several such series of observations, it was simple to obtain the variation of the measured quantities with time. In contrast to measurements which are made with the aid of an accelerometer, during which the pilot must not alter the steering of the airplane, investigations of convective motions with the aid of a thermometer permit such

alteration;

the

differences

in the

measurement

results

between

a

strictly horizontal flight and an uncontrolled flight, when the airplane goes additional vertical displacements due to the convective motions, inconsequential.

Furthermore,

investigations

of convective

motions

underare from

measurements of the temperature field can be accomplished, apparently, on any type of airplane, although the flight tests of the method and all the measurements given in the present work were carried out only by an I1.-12 airplane. During the measurements the captain of the flight was always in the pilot

cabin,

from

where

the

terrain,

cloudiness,

flight

conditions

etc.,

could be viewed most easily and effectively. From there all the operators in the airplane's cabin were instructed to vary the conditions of their work and the like, by telephone or by switching the instruments and the oscillograph on and off. For control, a special small board with signal lamps, lighted when an instrument or the oscillograph were in operation, was fitted in the pilot cabin. On the board there were toggle switches and pushbuttons, which

enabled

the

captain

to switch

on

and

off some

of the

instruments,

and

also to record on the oscillograph charts by means of one of the galvanometers any variation in the conditions or character of the flight. All three thermometers were used in the measurements. A manganin resistarice was used as the second sensing element of the two-channel thermometer, and a slow-response sensing element (the lower right one

in Figure

8) as the third (in a single channel thermometer).

With the aid

of the latter the average air temperature in flight was measured. The manganin resistance, fed by the same generator as the working sensing element, serve as a control for the electronic part of the two-channel thermometer. In the absence of variations in the conditions of operation of the thermometer a straight line was recorded. An example of an oscillogram with all the recordable elements is given in Figure 22. The recordings of the instruments, as a rule, do not interfere with one another and readings can be easily taken.

30

The primary processing of the measurement results consists of determining the dimensions and amplitudes of the temperature pulses on the

oscillograms.

one temperature

It should be noted that along with ""'simple' pulses having maximum,

complex

pulses

are

also met.

These

appar-

ently consist of several "simple' pulses (1 and 18 on Figure la).

e

FIGURE

.

22.

e

.

i

An oscillogram

recording of 1) a low-inertia and

height statoscope, 4) radicaltimeter, the recording

Before

5) accelerometer

of the readings of the manganin resistance

a statistical

investigation

3) slow-response

temperature

elements,

and 6) flight velocity; the horizontal line above controlling the

of the

2) is

operation of the thermometers.

measurement

results

is made,

it is not possible to determine whether complex pulses indicate ascending convective currents with several nuclei of warm air or whether they are a result of interflow of separate convective currents with one nucleus. Nor can

it be

determined

whether

this

complex

should

be

considered,

even

in the

case of interflow, as an independent large convective current or as a series of small currents. Therefore, when examining complex pulses, the separation of independent simple pulses was considered possible only when both edges of the latter approached the curve characterizing the general temperature variation (for example, pulses 4 and 5, 15 and 16 and others on Figure la). Such a division is arbitrary. However, a uniform application of this criterion made it possible to compare results of various flights and obtain

statistical

regularities.

In addition,

31

as

will

be

shown

in the

second

chapter,

the

relative

area

or

relative

volume

of convective

currents

is

determined by the sum of the dimensions of the cross sections of the currents crossed by the airplane. Thus, the determination of one of the most important convection parameters does not depend on whether or not complex pulses subdivide into simple pulses. The dimensions of pulses (the dimensions of the sections of convective currents crossed by airplanes) are determined as the product of the flight air velocity and the time of crossing the currents. The temperatures of the currents (the amplitudes of the pulses) are defined as the difference between the maximum temperature in the current and the temperature of the surrounding air, the latter being taken as the arithmetic mean of the temperatures on entering and leaving the convective current. If necessary, corrections for the variation in flight velocity and height during the crossing of the current can be introduced in the values of the temperatures of convective currents taken from the oscillograms. These corrections are usually small compared with the temperatures determined from the pulse amplitudes.

6.

Measurements

in clouds

The method of determining convective currents from the temperature field is applicable to the study of ascending motions in clouds. The thermometer's sensing element records convective currents according to their temperature, in spite of the fact that it gets wet and does not show the true temperature of the cloud air, since evaporation takes place from its surface due to the heating caused by decreased flow*. The dimensions of current sections crossed by the airplane are fixed in this method quite accurately; current temperature determinations may generally involve small errors due to losses of various amounts of heat by evaporation from the surface of the sensing element's wire when the flight velocity changes in the current, and also when the humidity of individual currents differs from the humidity of the surrounding cloud medium. The possibility of measurement in clouds with the aid of the described temperature-sensing elements is limited by the fact that in massive-droplet sections of the cloud (particularly in the presence of sleet or hail) the copper wire is usually broken, and the tungsten wire (due to its short length) is sensitive to the temperature of individual droplets falling on it). Therefore, measurements in clouds are best made by a sensing element with a drip-proof shield. This was used only with a sensing element of copper wire. A streamlined hood with holes or slots in the cylindrical section is mounted on the front part of the protecting cylinder of the sensing element, and a funnel on the back (Figure 8). With a sensing element thus shielded it is possible to perform measurements in strongly agitated clouds of any structure. Patterns of simultaneous recording of the readings of an exposed sensing element and a shielded one are shown in Figure 23. As seen from the %

This explains the sharp drop a cloud,

and the temperature

in temperature,

seen on some

increase on leaving

it.

32

of the oscillograms shown below,

on entering

FIGURE

23,

Patterns of temperature element

a) outside

clouds;

b,

recording

and 2) a shielded sensing

by 1) an exposed

c) in clouds; 3) is the airplane's time

33

sensing

element. in the cloud.

oscillograms, the dimensions approximately smaller pulse due to the fact This leads to

the structure of the temperature pulses, and in particular of current sections recorded by both sensing elements are the same, particularly outside clouds. The considerably amplitudes recorded by the shielded sensing element are that only a part of the wire is in contact with the air*. a decrease in the pulse amplitudes while preserving their convective

in crossing

since

structure,

a part

currents

wire,

of the

around

which air does not flow, maintains the lower temperature of the surrounting air, and the remaining part is sufficiently immersed in the siream so as The correcnot to increase noticeably the inertia of the sensing element. tion to the readings of a shielded sensing element is determined from simulThe same correctaneous measurements of both elements outside clouds. tion is introduced in the readings of the elements inside clouds.

I, m

S

S

&5

5

S

r

RN

S

S

S

®m

S

3R

T

S

SSaS8S8sesS & T T NN S N ¥ S a5s 83585845

STIST o o TS T

e

&

N3I& 8 3N S ST g < QANF

a

b

l,m

0

SYTLIRNSVFTFY

DD

/D

R

DL

D

OIS

D

DS

(a,

NI

24.

Distribution of covective

c) and according to the temperature clouds (a,

1) results of measurements

T

g DY

D

SIS

D

SR

IS

IS

¢ FIGURE

I YYT

IS

N

FSS

S

SIS O

d

g

currents according to cross section dimensions excesses in these

b) and inside clouds (¢,

by the exposed

element;

cross-sections (b, d) outside d).

2) results

of measurements

with

the shielded element,

Figure 24 shows the distribution of convective currents (according to section dimensions and temperature excesses) outside clouds and in clouds from measurement results of both sensing elements, obtained during the %

is confirmed by traces of droplets on the filter~paper, wrapped round coated with manganese-oxide powder. These traces were observed mainly and, particularly, close to the funnel. This shows that the wire is moved Besides, the fact that the which are formed behind the sensing element. surface of the wire of shielded sensing element is indirectly confirmed by This

stagnation of the element (k£ =13.5- 10-6 degree - hourz/kmz), which errors due to variation in the flight velocity in individual currents.

34

the sensing

element

and

lower part of the cylinder around, apparently, by vortices air does not blow at the whole inthe

the decrease by half in the in its turn reduces the measurement

flight of 21 July 1953 /12/, The distributions of the currents outside the clouds (Figures 24a and 24b) hardly differ. Due to the lower sensitivity of the shielded sensing element a smaller number of narrow and weakly heated currents

is

recorded.

In clouds,

the

distributions

show

greater

difference,

particularly in temperature measurements (Figures 24c and 24d). The larger number of relatively warm convective currents recorded by the

shielded sensing element

(compared with the data outside the clouds) testi-

fies to the fact that the difference in the measurement results in clouds is This eledue mainly to less wetting of the wire of the shielded element. ment generally registers the temperature in the cloud more accurately However, the wetting of the wire of the shielded than the exposed one. element probably depends on the distribution of droplet sizes in the cloud. Measurements have shown that these differ in different clouds and also in They differ in adjacent convective various sections of the same cloud. Therefore, currents and in the cloud conditions surrounding the currents., ) it is difficult to say which data are preferable, Processing simultaneous temperature recordings made by the exposed and shielded elements showed that some of the detected regularities of convective motions in cumulus clouds /12/ are evident from the data of any of the elements. The warm currents recorded by the thermometer are ascending currents. TABLE Correlation between

positive temperature

Flight height,

over the earth's

airplane

overloads

in clouds

m

over the cloud

surface

2

pulses and upward

No. of cases

Coincidence,

94 68 46 53 70 21

81 81 87 85 90 100

352

85

%

base

2000 2500 3000 3500 4000 4500

200 700 1200 1700 2200 2700

Average

—

As in currents under clouds, for almost each temperature pulse within clouds, there corresponds an upward airplane overload (Figure 3). As already mentioned, a complete correspondence between convective currents and overloads cannot exist. This is particularly so in highly turbulent cumulus clouds. However, even here positive temperature pulses correspond to upward airplane overloads in 85% of the cases (Table 2). It should

this *

be

noted

correspondence

that

in contrast

somewhat

to the

decreases

space

for

This difference in the wetting of the wire of the shielded element relatively uniform wetting of the exposed element) of small temperature

is,

apparently,

outside

cloud,

where

(Table

1),

in different sections of the cloud (for the reason for the different patterns

pulses recorded by the shielded and exposed elements

35

the

increasing height

(Figure

23¢).

inside clouds the number of cases of correspondence between positive temperature pulses and upward airplane overloads increases with height. This apparently is due to the fact that under clouds the intensity of ascending motions generally weakens for increasing height, whereas inside clouds it is intensified due to the liberation of latent condensation heat in the currents. In crossing relatively large convective currents the accelerometer records at least two distinct overload changes: one directed upward on entering the current and one directed downward on leaving it (Figure 3a). Therefore, the accelerometer data on the sizes of ascending currents in the atmosphere (determined from the time when the sign of the ¢ is maintained) may differ considerably from the real dimensions, which are quite accurately registered by the thermometer. The origination of cumulus clouds and condensation in individual convective currents are easily detected with the aid of the thermometer even when the condensation products are invisible or hardly distinguishable. These phenomena are usually revealed by negative and not positive temperature pulses (Figure 25). Negative temperature pulses are usually larger in width and amplitude than positive impulses. The latter characterize at similar heights convective currents without condensation. Negative pulses are registered as a result of the wetting of the sensing element's wire*, and not because the currents crossed are colder than the surrounding air¥*, That these negative pulses characterize condensation in convective currents or developing cumulus clouds is confirmed by the large number of coincidences of the passage moments of patches of veil like fog with these pulses (Figure 25c¢), and also by the recording of the condensation hygrometer 23/ **%, showing that high humidity corresponds to these

pulses

(Figures

25b and 25c¢).

There is still another form of negative pulses, having the same dimensions as the positive pulses. These characterize convective currents without condensation, but are distinguished by a relatively small amplitude

(Figure

reaching However,

25c,

left).

a maximum their

The number near

number

of these pulses

increases with height,

compared

that

the level

is small

of the lower with

base

of the cumulus

of the

positive

and in cumulus clouds and at levels near the ground-surface they appear. These negative pulses characterize convective currents which inertia above the level at which their temperature becomes equal temperature of the surrounding air. The velocity of these jets is *

The temperature the method

in flights along the upper, Random

temperature

observed here. It is possible that in certain cases developing air due to droplet evaporation, when the air temperature

#%k

hardly rise by to the small.

variation due to wetting by very small droplets even of the protected element makes

hardly effective

above the convective layer. #%

clouds.

pulses,

usually uneven

fluctuations,

boundary of a thick smoke

not associated with turbulence,

cumulus clouds may become

colder than the surrounding

particularly in the period of development of the convective

rises within almost the whole

tion level increases rapidly. The airplane hygrometer developed

by A. M.

Gromov

an accuracy of about 0.5° and lag of approximately

/23/ records the temperature 0.5 sec,

of the dew point with

The relative variations in the temperature

duration not less than 0.5 sec,

36

motions,

convection layer and the height of the condensa-

of the dew point (humidity fluctuations) are detected by the hygrometer, the order of 0.3° for a disturbance

plume are often

starting from

an amplitude

of

tpeopranc auedire (¢

oy,

ay3) samesadway (7

“A1ooraa B jutod map

(g

(P

ammjeradwre)

“ySrey 39S 9yl urody UOIIBIAID

€2 TUNOLL

{(e1Eurpio Surszalosp yirm sesu

spnoyo Surdolassp Jo onisttaloereyd sas(nd samyersduwta],

sastr amperadwa)

*8o3 3y 811 Jo Burssord Jo swrry oyl St awi [ejuwoziioy {(s3eurpio Burseasour yim

ayi) smeseduray

e

(]

37

Developing cumulus clouds, on the contrary, are usually characterized by active ascending motion. Recordings of the accelerometer show that negative pulses, indicating condensation in convective currents, are usually associated

with

positive

overloads

(Figure

25).

Thus,

the

method

of indi-

cating ascending currents from their temperature is applicable to the study of convective motions in cumulus clouds, at all stages of the cloud's development.

7. In

section

1

A method for studying descending curvents avound developing cumulus clouds it

was

mentioned

that

descending

currents,

caused

by

ascending convective currents, are very weakly pronounced in the temperature field since they do not have an initial temperature different from that of the surrounding medium and cannot acquire any considerable temperature difference during the descent (Figure 26). With the exception of

K

Convection layer outsidem——a{ the clouds

Height of the upper boundary of the clouds

Height_of— the lower boundary of the clouds

2

f Layerwith superadiabatic temperature gradients -

t

i FIGURE 1} at summer

Vertical

atmospheric

noon in the presence

rising air mass; or bubbles;

26.

3) indescending

4) in descending

temperature variation

of developing

clouds;

2) in a freely

currents, flowing

around

ascending jets

currents,

generated by developing

(the processes are assumed

clouds

adiabatic),

the surface layer, the temperature of the descending air varies almost identically as that of the surrounding medium. Only in the upper section of the convective layer could the descending air be warmer than the surrounding medium. However, here the convective motions already damp out and cannot cause descending currents of sufficient extension. The situation is different with descending currents caused by developing cumulus clouds. Due to the continuous liberation of latent condensation heat, ascending currents in clouds are considerably more intensive than

38

i

FIGURE 1) air temperature; prescribed height;

27.

Crossing thick cumulus

2) airplane's overloads;

clouds near the summits

3) flight velocity;

5) horizontal strips above

39

ffi'hm’hou:‘ ‘ |

indicate

4) deviation from the

staying time

in the clouds.

convective motions under clouds /12/. Therefore, developing clouds may give rise to compensating currents of considerable extension, although their summits usually build up in stable layers (with a slight temperature lapse, isothermal conditions and even temperature inversion). Because of this stability, the compensating currents acquire in their descent a temperature considerably higher than the temperature of the surrounding air (Figure 26), and therefore are also slightly recorded with the aid of the airplane-borne thermometer /15, 16/. This is illustrated by oscillograms with recordings of air temperature, airplane overload, flight velocity and deviation from the prescribed height along horizontal routes, partially passing through cumulus clouds (Figures 27 and 28). From the examination of the temperature variation it is seen that relatively narrow warm currents* quite differing from the surrounding medium, having a temperature considerably higher than that where cloud air atthe flightlevel is absent, appear clearly directly alongside the clouds and particularly between them. Currents of this kind are also sometimes observed when the airplane passes near developing cumulus clouds without crossing them (Figure 29). Thus, these warm currents may be interpreted as descending motions, generated by developing clouds**,

FIGURE

28.

Crossing the middle weather.

*

clouds of good

It was noted in the previous section that the sharp drop in temperature observed on entering the cloud and the rise on leaving it are due to evaporation of droplets from the temperature-sensing element which is always warmer

**%

section of flat cumulus

The notation is as in Figure 27,

than the cloud air.

According to data published recently by V. A, Zaitsev and A, A. Ledokhovich

(Instruments and Technique

of Cloud Investigation from an Airplane. Gidrometeoizdat, 1960), compensating descending currents may also be detected with the aid of equipment less sensitive than that described above, However, the dimensions and thermal

structure of the descending

40

currents are,

naturally,

distorted in this case.

Near isolated clouds, the sharp boundary between the compensating currents and the cloudless air is absent, and in the zone between a well pronounced descending current and the still air, considerable temperature

fluctuations are frequently observed

(see Figure

27a left of the cloud).

This shows that descending currents damp out horizontally in a certain layer, and also that smaller ascending and descending compensating currents, which may be regarded as turbulence formed around the main current, may exist in this layer.

FIGURE

29.

Passage

1) air temperature 2)

dew

point

3)

airplane's

5)

flight

near cumulus

(the temperature

temperature overloads;

velocity.

The

clouds (without entering)

rises with decreasing

(temperature

4)

deviation

dotted

line

in the cloud,

41

rises

from is the

with

the

the

ordinate); ordinate);

prescribed

time of the

height; airplane

According to readings of the accelerometer, considerable overloads are not observed during the crossing of descending currents. However, considerable overloads frequently arise at the moment when the airplane leaves these currents (see Figures 27b and 28). This indicates the sharp variation in the intensity of direction of the vertical motions in passing from the current to the surrounding air. The sign of the overloads (usually positive) and their sharpness confirm that the compensating currents are descending and that usually a considerably boundary layer between the descending currents and the surrounding medium is absent.

FIGURE

30.

Simultaneous

indication

of descending

currents by a thermometer

and a

condensation hygrometer 1) air temperature (temperature height;

(temperature rises for decreasing ordinate);

rises with ordinate);

5) flight velocity;

3) airplane'soverload;

6) cloud liquid-water time of the airplane

content,

2) dew point temperature

4) deviationfrom The

the prescribed

horizontal lines are the

in the cloud.

The measurement data of an airplane-borne condensation hygrometer also confirm that the compensating currents descend (Figure 30). The oscillograms show a sharp drop in the dew point temperature in compensating currents. The relative dryness of compensating currents with respect to the surrounding medium shows indirectly that these are descending currents, since they originate in higher and drier layers. They only start to intermix with the relatively moist layers lying below specifically as a result of the development of cumulus clouds and the compensating currents generated by them.

42

The relative dryness of the higher layers is well demonstrated by the right-hand side of the oscillogram in Figure 30. This shows that an increase in the flight height is immediately accompanied by a drop in the dew point.

FIGURE

31.

Descending

currents under clouds

1) air temperature; a) detected by the thermometer; b) by the airplane's trajectory in uncontrolled flight; 4) deviation from the prescribed height; the dotted line is the time of the airplane under the clouds (2 3, on Figure 312 and 2, 3, 5 on Figure 31b are the same as the corresponding recordings on Figures 27 and 30),

43

Descending currents are usually observed near the upper section of developing clouds. Only near weakly vertically developed clouds are they observed along the whole thickness of the cloud and even under them. In this case, descending currents under clouds are almost as well pronounced in the temperature field as near the upper sections of clouds (Figure 31a). Besides, they are easily discovered from the recording of the readings of the height statoscope in uncontrolled flight, i.e., when the pilot does not control the airplane after having set it in horizontal flight (Figure 31b). As is seen from the latter oscillogram, when the airplane approaches a cloud it loses height, gains height under the cloud, loses it again when the cloud ends. These data confirm once more that descending currents exist near developing cumulus clouds. Thus, with the aid of an airplane-borne low-inertia sensitive thermometer it is possible to record not only ascending convective currents under clouds and inside cumulus clouds, but also descending currents generated by these clouds.

44

Chapter

II

STATISTICAL INTERPRETATION OF MEASUREMENT RESULTS

1.

THE

Formulation of the problem

The method for studying convective currents from their temperature characteristics gives experimental data on the dimensions of ascending currents and their temperature excess with respect to the surrounding air. By comparing corresponding distributions these of quantities, obtained in various flight or weather conditions, some characteristics of convective motions in the atmosphere can be discovered, and the interdependence between convective motions and cloud development can be determined /11, 12,

14/.

At

the

same

time,

it must

be

remembered

that

the

dimensions

of sections of convective currents and the temperature excess in these sections measured in flight are random quantities. This is both because the dimensions and temperatures of convective currents are themselves random quantities, and because the airplane crosses the convective currents indiscriminately at unknown distances from the center. The distributions of the quantities measured in flight characterize, to a certain extent, also the dimensions and temperature excess of the convective

currents.

However,

a knowledge

of the

distribution

of con-

vective currents according to the real dimensions and the temperatures at their centers, and the establishment of the statistical relationships between the dimensions and temperatures of convective currents may help to explain better the nature of convective processes. For example, knowing the laws of variation of the temperature with height in the centers of the currents makes it possible to say which of the existing jet theories fits the conditions

of the

atmosphere,

and

can

give

an

idea

of the

mechanism

of the

appearance of convective motions in it; these data make it easy to determine the values of the constants in the laws of variation of the temperature with height and velocity of ascending currents, i.e., to specify the form of these laws. The distribution of convective currents according tothe real dimensions and temperatures at their centers cannot be the same as their distribution according tothe dimensions of random sections and the temperature excess in these sections. The section of any current and the temperature excess in it are respectively smaller, usually, thanthe current diameter andthe temperature excess at its center. On the other hand, the probability of crossing large currents is higher than that of crossing small ones, and therefore recording

45

high temperature excesses is also more likely. These factors act in opposite directions and under certain conditions, as will be shown below, they may cancel each other. However, this rarely happens. Therefore, in order to find the distribution of convective currents according to the real dimensions and the temperatures at their centers, a suitable theory must be formulated. Such a theory can be applied both to the temperature and to a number of other parameters of convective currents (humidity, vertical velocity, concentration of any suspended particles, etc), and also to some of these parameters simultaneously. Other important convection parameters are the spatial concentration of the convective currents, their relative volume or relative cross-sectional area at a given level. However, it is very difficult to determine these parameters directly from measurement data. The statistical interpretation of data. of convective motions in the atmosphere is given in this chapter. It describes methods used in calculating the distributions of actual convection parameters (dimensions of convective currents,

their

concentration,

relative

volume,

relative

cross-sectional

area and the values of certain quantities at the centers of these currents). The calculations are made from observed distributions of the dimensions of random section and from the values of the quantities corresponding to

these sections

/17/.

The methods used are suitable not only for the study

of convective motions, but also for statistical investigations of other phenomena in geophysics, particularly prospecting. They are useful, too, in biology, astronomy, geology and industry, in the study of systems with inhomogeneous rotating bodies.

2.

Distribution of convective curvents according to theiv rveal dimensions and concentrations of convective curvents

At present /56/.

there

Available

is no single

experimental

opinion on the form data

(with

the

of convective

exception

of those

currents

taken

under

certain specific conditions) do not allow a single valued determination to whether convective motions are jets or rising isolated air masses

(bubbles).

Therefore,

In both cases,

rotating

around

as

both possibilities are considered below.

the form

a vertical

currents are distributed statistically uniform.

of the convective

axis.

at

In addition,

random

The

in

the

currents

is that of bodies

it is assumed

considered

that

space,

convective

but

are

jet case

For convective motions in the form of cylindrical jets*, the distribution of the dimensions and spatial concentration of the jets is the same as the distribution of circles according to the diameters and the concentration of circles on any horizontal plane intersecting these jets. Therefore, in the case of jets, the plane problem arises. This amounts to the determination of the distribution function of diameters of circles on a plane and of the *

According to data given in Chapter III,

the horizontal dimensions of convective

with height above 100-300 m,

46

currents hardly vary

concentration of these circles from a given distribution of the lengths of chords formed by the intersections of the circles with an arbitrary line

{the path of the light).

Denoting by N, the number of circle centers per unit area at the flight level*, and by F,(s) the density of the distribution of the probability of circle

diameters

with

the

diameters

s,

the

normalization

condition

oo

{Firas=1.

(1)

o

The number of circles with diameters from of a straight line intersecting these circles is

s to s+ds per

unit length

sNF, (s) ds, and the total number

of circles

is

(2)

(of all diameters)

is

(3)

{ sNiFi(s)ds = N,

o

where s is the first-order moment or the average circle diameter. The number of circles with diameter from s to s 4 ds intersected

straight line can also be

_

Nysuy (s)ds,

by the (4)

where u; (s) is the density of the probability distribution of the diameters of only those circles which are intersected by the straight line. Comparing (4) and (2), we obtain a functional relation between the distribution of circles lying over the whole plane and the distribution of those lying only along the airplane's route:

# (s) = -::F,(s).

The equal

probability w(l)dl of obtaining to the

product

of the

a chord

probability

u,(s)ds

(5)

with a length from of

intersecting

I to ! +dlis

a circle

with

a

diameter from s to s + ds and the conditional probability v, (x]s)dx of intersecting this circle at a distance from x to x+dx from the center, summed over all possible values of s:

w(t)dl = [ (s)ds-vy[x(l, 5)|s) %’.;ldt.

(8)

&

: since

x =3

1]

/

st—12,

In this problem an equal probability of flying at any distance from the centers of the currents (jets) is assumed. Therefore, the conditional probability is

v,(x]s)dx-——ul(xls)lg—;‘dl=

Substituting (7) and (5) in (6),

required

distribution

of circle

di sYss—I

(7)

we obtain an integral equation relating the

diameters

tained) distribution of chord lengths:

to the given

(experimentally

wl)= 2§ A6 g *

The chosen

area (volume)

units should be large enough

identically distributed in the diameters.

47

to contain equal numbers of convective

ob-

® currents

For

equation

a finite upper

limit (R) equation

(8) reduces

/149/* and its solution for R— oo _

is

-

o0

7

S‘JI[TJ

Iss ¢ d(w(l)

FI(S)-—‘

to the well-known

dl

(9 )

T

The concentration N, of jets, i.e., the number of circle centers unit area, is determined, according to (3), from the equation

n=LN,s, where

n is the number

of jets crossed

The

per

(10)

by the airplane

bubble

Abel

along a path L,

case

In representing convective currents in the form of bubbles, a spatial problem has to be solved independently of their forms. It seems most logical to assume that the bubbles have the shape of ellipsoids of revolution

along

the

vertical

axis.

In this

case,

the

tribution of the dimensions of the ellipsoids, space from distribution w(/) of chord lengths

in this case the intersections

It is easy to show

problem

is to find

the

dis-

and their concentration in considered above, their being

of the ellipsoids by a horizontal straight line.

that in an ellipsoid

of revolution with the axes a and

b,

the geometric location of the centers of horizontal chords of a given length ! is also an ellipsoid

of revolution with the axes**

b=t} Therefore,

if we

consider

ey

is a constant

similar

1—5. ellipsoids

CRy—

quantit

then the probability w(l)d! of a horizontal from

! to [ +dl

will

(11) the ratio of the axes

ellipsoid

section with a diameter

(13)

{

from

u,(a)da is the probability

a toa4da,

and

(12)

be

w()dl = | u,(a)da-v;1a, (1, @) |a) %‘fldl. Here

of which

v,la,(l, a)]a}

of intersecting

25t

an ellipsoid with an axis

dl = v,(a;| a)da, is the conditional

probability

of the secant being tangent to a concentric ellipsoid with an axis from q, to @, +da,. This conditional probability (when assuming equally probable flight at any distance from the center of the current) is equal to the ratio of the *

An equation similar to (8) was obtained by Wicksell

/141/ for the relation between the distribution of

spherical diameters in space and the distribution of circular diameters on an arbitrary plane these spheres.

Similar equations were also obtained by Zeipel /149/

astronomical problems. [(1):2?(4;(1)/1 *

We

and ®(s)

and Wicksell

intersecting

/141/ for certain

Abel's equation is easily obtained from (8} by introducing the new functions = Fy(s)/s and the variables A = R*—#

and y = R?* — 5%,

shall usually consider a and a, to be the horizontal axes of the meridional

48

sections of the ellipsoids.

a thickness da, t0 the

of an elliptic ring with the axes @, and aym and of an ellipse with the axes a and a/m

area area

g =2t

u(la)|5 =V a—1.

according to (11),

since,

(14)

If we denote by N, the number of ellipsoid centers per unit volume by F, (a) the density of ellipsoid distribution over the horizontal axes, which case

{F.(@yda =1,

0

then,

by

considerations

the number length is

of ellipsoids

similar

to those

made

when

by a horizontal

intersected

considering

straight

and in

(15)

circles,

line of unit

(16)

§;",§N,F, (a) da = Fhege,

where & is the second-order moment, ‘and a functional relation exists between the density F,(a) of the distribution of ellipsoids in the whole space and the density u,(a) of the distribution only of those ellipsoids which are

intersected by the straight line (airplane):

(1n

iy (@) = 5 Fa (0. we obtain an integral equation,

Substituting (17) 4nd (14) in (13),

the distributions

of ellipsoid

of random

and

axes

relating

chords

24¢ w (1) =§S F, (a)da.

(18)

I-

The

solution

equation

of this

is elementary,

giving

(19)

Ffi(a)z.—?’—"’i[_“i‘_“’]. a The

concentration

their centers equation

N,

of

ellipsoids,

in unit volume,

or,

more

is determined

exactly,

according

the

number

to (16) from

(20)

n=La,

where n, as in the case sected along a path L.

of circles,

of

the

is the total number

Equation (18) does not involve the quantity m,

of ellipsoids

and naturally,

inter-

is true also

Thus, the distribution of spheres over diafor the case of sphere (m=1)*. over the horizontal (or according to revolution meters and of ellipsoids of

(12) the vertical) axes are identical.

concentrations. %

According

to (20),

The difference occurs

the number

As was already found out after the publication of /17/, tained by Willis /142/.

However,

Willis and Lord /142,

of spheres (see (20)).

49

only in their

per unit volume

of ellipsoids

equation (18) for the case of spheres was ob-

92/ did not obtain the spatial concentration

along

the

vertical

axis

(m1), their number is larger than the number of spheres. For certain problems, the distributions of the dimensions only of those jets or bubbles intersected by the airplane (for example, causing a certain roughness) may be of interest. These distributions are obtained by the

solution of equations (6) and (13) taking into account only (7) or (14) reIn this case (6) and (13) become /11, 12/ spectively.

w0 =1§ w725

(21)

wil) =2 § u @)%

(22)

1

solutions

are respectively g (s) = — 2752305- ["_”_ifi_] |/lzd{_5:'

(23)

w@=—% 2[22].

(24)

Calculating the average

sides of equations infinity),

we

jet diameters

easily obtain a relation between

chords

(multiplying both

I,

the average

s* and the horizontal axes of the ellipsoid 4%,

this

is

relation

NI

the airplane;

lentghs I of random

(21) and (22) by ! and integrating over ! from zero to

3.

.mla

and their

5*

= -3.7.

values

of the

intersected by

(25)

The relative area and velative volume of ascending currents

Knowing F,(s)— the jet diameters distribution function — it is easy to calculate the relative area S, occupied by ascending currents. This area (at any level) is obviously determined v.), layers unstable inside place take heights at these reary zones between the ascending, relatively warm and the descending, observed be cannot they that sonarrow sometimes latively cold currents are

on the oscillograms** (see the middle part of the oscillogram

on Figure

2a).

The determinations of the dimensions of cross sections of convective becurrents in these parts were frequently overstated (as the distances dtween the points with the lowest temperatures, i,e., the points correspon to possible seem not does It *), ing to neighboring descending currents** TABLE with

Variation

of the

average

convective

urements

10

761

30 50

2480 7611

1 bubbles

5

Bubbles

Jets

km 306

31

42

8728

100

currents

jets

of meas~

m

of

(volumes)

areas

relative

and

concentration

dimensions,

Average dimensions of | Concentration of convective currents®* convective currents¥, m

Number

Flight height,

height

7

-

volume‘of

warmer

convective

[the

currents®** |

kmn

m

Relative | No.of ascending currents area or

0. 50kk%%

11200

49 55

37 43

217 138

6180 3180

0.50kk 0.50

61

46

87

1910

0.44

than

surrounding air, % 100

98 98 99

300 500 1000

4748 4007 2656

68 70 72

58 61 64

52 40 29

809 620 334

0.32 0.27 0.21

94 93 93

2000

1409

74

65

24

298

0.20

84

* %% #%k

#%k%

81

532

3000

203

20

74

85

0.19

the horizonta} axes of ellipsoids. dimensions of convective currents imply the diameters of jets or ellipsoids. the of axes vertical the to m is the ratio of the horizontal with the values of &£ obtained The values given for S, calculated by (2.26), coincide almost exactly experimentally; the maximum divergences do not exceed 5%.

The

/ at the heights of 10 and The relative areas calculated from the automatically overstated values of 30 m,

are respectively 0.73 and 0.70.

determine

the

true

dimensions

of these

sections.

the

However,

average

the areas of dimensions I, of the sections can be determined assuming to be equal layer unstable the in the ascending and descending currents length relative the to equal are areas these (2.50) from Since /52, 108/. equality should following the , currents g ascendin by occupied course the of be satisfied inside the unstable layer:

(8)

ni, = 3L,

where * #%

n is the number

of currents

along route

L.

made only over forests and therefore are also As already indicated, flights ata beight of 30m were for the most part low-level flights. equal to the average temperature at the flight The air temperature in these boundary zones is not rate with height, the ascending currents are lapse Owing to the very rapid decrease of the level. level than the descending currents are cooled heated considerably more while rising to the (flight) while sinking to this level.

#%%

intersected

Some small error is introduced oscillograms.

in this connection also in the temperature

81

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w 206

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052

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82

Estimates made onthe basis of (8) have shown that the average dimensions 1

of the sections

taken from

the values 1, by 40 to 50%.

the oscillograms

exceed

flights may

in low-level

Tswf,*.

At a height of 50 m,

0 x

e et e s

sO

{

e

sz

NN

©

of Thus, the growth of convective currents with height up to the level 7. Table of data the from follows which that than 50 m is even faster The obtained vertical variation of the dimensions of convective currents agrees with results of measurements of the dimensions of nonuniformities in the atmospheric refractive index (in the range of radio frequencies) H, m during convection conditions**, gener300@— °p alized by Norton, Riceand Vogler /101/

These

on Figure 42).

(the crosses

data show that the average dimensions of the nonuniformities of the refractive index at all levels at which measure-~ ments were taken from the airplane

Figure

TG

==

e em

o

1500

O

1

T

2000t

o

(starting at a height of 750 m,

42), as well as the dimensions of convective currents, maintain approximately the same value and up to the level of 100 m they grow with height approximately according to the same The difference in the absolute law. values of the average section dimensions may be due to the different method of processing the recorded

]

10

0

FIGURE

20 42,

dimensions

40

60

on Figure

by figures

of "simple'" ones.

la) into a series

This is highly

probable since in simultaneous measurements of the fluctuations of the m

80 100 12054l

Vertical variation of the average 1) of convective currents (s are for

jets; a for bubbles, 1 for random intersections) and 2) of non-uniformities of the atmospheric

refractive index

of

refraction {similar to those marked

300

100

index

of the atmospheric

pulses

= O

500t

e.g., breaking ''complex"

pulses,

eO

P

e o

1000}

index of refraction and of

atmospheric

the air temperature

the obtained

forms are close to one another 75 [Hx%,

Table

dimensions,

lative

3

. 7

areas

gives,

the

besides

average

the concentration and re-

or

volumes

of convective

currents at various heights,

percentages

pulse

/74,

of the number

and the

of warm

over forests, the underlying surface being * Cases were observed in several flights at daytime hours mainly higher by approximately 20 to 25 m, where at a height of 50 m T exceeded T, by 10 to 20 %. This is confirmed by y above 50 m. However, the unstable layer does not seem to expand considerabl

the measurements of Webb /138/,

according to which the gradient of the potential temperature rapidly

vanishing at heights from decreases with increasing height during convection over a steppe, (July, August) i n the daytime. ** These measurements were performed in summer months

*k% The

nonuniformities

8 to 30 m.

in the atmospheric refractive index were measured mainly in the daytime.

This

25% of the measurements were per— difference, therefore, may be partially due to the fact that about were considerably formed in the morning and evenin, g bours when the dimensions of convective currents section). following the (see larger than during the day

83

convective currents in the total number of ascending currents (both warmer and cooler than the surrounding air); these percentages refer to the same extent to the concentration and volumes of convective currents, independently of the assumed form of the currents. The data show that the concentration of convective currents decreases relatively quickly with increasing height. As compared with the concentration at a height of 10 m, the concentration of jets decreases by an order of magnitude at the height of 1000 m (306 and 29 jets/km? respectively), and the concentration of bubbles, at a height less than 300 m (11,200 m and 809

m

bubbles/kma).

Such

a sharp

decrease

in the

concentration

of con-

vective currents with increasing height causes a situation where in spite of the growth in the dimensions of the currents their relative areas or volumes also decrease as they move away from the unstable surface layer. Starting from a height of 50 m, where the relative areas or volumes of ascending currents are approximately 1/2, they fall almost to 1/3 at a height of 300 m, and above 1000 m constitute only 1/5 of the corresponding areas or volumes of the convective layer,. The number of convective currents colder than the surrounding air is considerably smaller at all heights than the number of relatively warm currents. According to Table 7, the number of relatively cold currents constitutes at heights of 50 to 100 m 1-2%, at heights of 300 to 1000 m it does not ex-

ceed 7% and only at higher levels does it reach approximately

15% of the

total number of convective currents. If we average all normalized distributions of the dimensions of convective currents obtained for various heights (introducing corresponding measure-

ment

"weights",

see the preceding section),

the lengths of random chords

(intersections of the currents by the airplane), the diameters of jets and the lengths of the horizontal axes of ellipsoids averaged over the height in the 4500 m layer turn out to be approximately 100, 70 and 60 m respective ly, the average concentration of convective currents is 30 to 35 jets/km? or

approximately 500 m bubbles/km?,

and the relative area or volume

of the

convective currents, approximately 0.22. Thus, the results of this calculation give approximately the same value for the relative volume of convective currents as obtained in section 4, but with larger current dimensions and lower concentrations. The values given here are generally more characteristic of the averaged convection parameters in the 4500 m layer over a plain than those given in section 4. Inthe following sections, however, since the values of the convection parameters at various times of the day, under various weather conditions and over various underlying surfaces were calculated by the same method as those in section 4 (see footnote 2, page 75), it is better to use the values of the convection parameters given in the previous section when comparing these data with averaged parameters. The densities of the probability distributions of dimensions of convective currents and the temperatures at their centers for the jets and bubble cases at the heights of 10, 50, 300, 1000 and 3000 m are givenin Figure 43. These distributions also quite clearly reflect the above-mentioned growth of the dimensions of convective currents with height. For example, the number of currents with dimensions over 50 m, insignificant at a height of 10 m, continuously increases with height and at the level 1000 to 3000 m considerab ly exceeds the number in the 10 to 50 m layer.

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As

in the

case

able

currents

with

dimensions

of the

general

at all heights, of

0 to

50

distributions

with the m

and

exception

(Figure

a temperature

of the of 0 to

36),

10 m

the

0.1°;

most

level,

At a

prob-

are those height

of

10 m the most likely currents have the same dimensions but higher temperatures, in the order of 0.3° (Figure 43)*, The distributions shown in Figure 43 also show that the dimensions of relatively warm currents (To>0.5°) grow noticeably with height. At a height of 10 m, the most probable dimensions of these currents are smaller than 50 m, at a height of 50 m approximately 50 to 75 m, and from 300 m upwards, over 100 m. The number of relatively warm currents sharply falls with increasing height**. Thus, the largest number of relatively warm convective currents are observed near the ground surface, the dimensions of these currents being considerably smaller here than at greater heights. As indicated in the previous section, to this is due one of the peculiarities of convective motions in the atmosphere, which results in the warmest currents being mainly small ones (with dimensions of 0 to 50 m). The temperature distributions only of convective currents, numerically

calculated from

(7), are given in Figure

44 (the broken lines represent the

temperature distributions in random sections)***%. The represented distributions clearly reflect the vertical variation of the temperature of convective currents, and particularly of the increase, noted in Table 7, in the number of currents colder than the surrounding air. This number becomes considerable from a height of 1000 m. As indicated in Chapter I, ascending currents become colder than the surrounding air when they pass by inertia beyond the equilibrium level. This may occur only in the part of the atmosphere where the lapse rate becomes smaller than the adiabatic (yv..

It is

of the underlying

owing

the

to the

earth's

possible

that

all

simultaneously.

Dependence of the convection parameters natuve of the undevrlying surface

forms

varied

of bubbles,

take

surface,

state

and

surface,

the

particularly

properties

of the

relief,

nature

the

on the

of land,

soils, of the

the

are many minerals

vegetation

and

the like. Even a preliminary investigation of the characteristics of convective motions in all existing conditions is therefore unfeasible. We consider below the influence on the convection parameters only of the most characteristic underlying surfaces, namely water surfaces, fields and forests (in plain conditions) and mountains. These surfaces occupy the major part of the globe and include its most thickly populated areas. The investigation of the characteristics of convective motions over these surfaces is valuable. Convective currents over water surfaces transport the main mass of water vapor evaporating from the surface of the earth. Fields and forests occupy large areas of the territory of the Soviet Union., Most of the country's population, particularly those working in agriculture,

live

Convective lus clouds /1, quent damage able crops are In addition,

in these

parts.

motions in mountains lead to intensive development of cumu121, 14/ 6 which cause considerable precipitation and freby hail. Both are important factors in regions where valucultivated. as

indicated

above,

mountain

massifs

and

water

surfaces

create the extreme conditions for the development of convective motions in the atmosphere. In mountains the sharpest temperature contrasts of the underlying surface occur; over water surfaces, such contrasts are almost entirely absent. Finally, the investigation of the difference between the convection parameters over water, fields and forests may allow the calculation of local circulation effects caused by changes in zones suffering from drought. For greater clarity, the convection parameters over water surfaces and in mountain conditions are examined together with those over plain sections and over valleys below ridges. Thus, the convection parameters over land and water, fields and forests, and mountains and valleys are examined simultaneously.

Differences between the convection parameters over land and water surfaces It is impossible to obtain measurement data of convective currents over land and water surfaces during the same flights since convective motions

108

occur over land by day, and only at night over water. Therefore, the convection parameters given below were calculated from measurement data referring to different times of the day and averaged over the day or over the night respectively. The measurements over land and over water surfaces were taken on sections adjacent or close to each other. This eliminated the possibility of the measurement results being influenced by regional peculiarities in the climate, circulation, and so on. . Measurements were taken over the Caspian Sea and coastal land in the Astrakhan region along routes starting at the coast and ending 40 to 50 km out to sea or inland (22—23 September 1952) and over the II'men' Lake and the forests and fields of the Novgorod region (August 1954). The weather conditions in Astrakhan were not conducive to normal development of convective motions over the land, since dense cirrus clouds were observed during the day on 23 September. They were then transformed into altostratus and altocumulus clouds. The remaining measurements were made in conditions of well developed convection. 10-4m-1 140

120 100 80 60 40 20 i

100

50

0

I

a

250 m

200

150

10-4m-1 140 120 100 80 60 40 20

1 50

0(7 FIGURE

57.

! 100

1 150

b

200

Distributions of convective jets according

a) in the Astrakhan region;

b) in the Novgorod region;

109

250

300

m

to their diameters:

1) over land;

2) over water surfaces.

The measurements started in the Astrakhan region at heights from 100m and from 20 m over the Il'men' Lake (the average flight height over the adjoining land sections, if we consider the treetops as underlying surface)and

were confined

measurements

to heights of 1000 and 300 m respectively; at

greater

heights

is not

sufficient

the

number

in the Astrakhan

10-4 m-1 degree~1

600

500 400

-02

LTI

20

o)

04

7

05

°C

S S T KL Foo

TP LLLLL F

-02 —Va

a7

N

92

93

a

04

05

10~4 m=1 degree-1

800

700 -

600 500

02

03

04

M////}X/g?j/

L J w0yLA -02

-0r

00

01

= FIGURE

58,

02

03 b

0%

05

05

S

Distributions of convective jets according to diameters and temperatures a) over land;

at the centers of the jets: b) over lI'men'

110

Lake.

¢

of

region,

owing to the small number of flights, and owing to the fact that over Il'men' Lake at heights of 350 t0 400 m stratocumulus clouds usually formed. There were 685 measurements in the Astrakhan region including 371 over the sea, and 10,341 in the Novgorod region of which 2372 were over the lake. The small amount of data in the Astrakhan region permitted the calculation for the sea and land of the distributions of convective currents over the dimenFrom the measurement data in the Novgorod resions only (Figure 57a). gion, together with the distributions of convective currents according to

their dimensions

(Figure

57b),

distributions of convective

currents accord-

ing to the dimensions and temperatures at the centers of the currents (Figure 58) and according to the temperatures only at the centers of the currents (Figure 59) were also calculated separately for the lake and for As seen from the distributions represented in these figures they the land. It should be first noted that conconsiderably differ from one another. vective currents have larger dimensions over water surfaces than over land However, the current temperatures over water surfaces are (Figure 57). considerably lower than the current temperatures over land (Figure 59). degree'1

=0z 07 FIGURE

59,

00

0

7z

05

D04 1

05

08

077

Distributions of convective jets according to temperatures in their centers (1) over the I1'men'

Lake and

(2) over land.

These peculiarities are clearly seen also from examination of the distributions according to the two variables (Figure 58). Over the lake a larger number of relatively large (> 50 m) currents were observed, but their temperature seldom exceeded 0.4 to 0.5° particularly in the case of bubbles. Almost all the currents over the lake were confined to these temperature

limits.

A

(Figure

59).

negligible number

of relatively large currents (~ 100 m) had a

temperature above 0.5° (Figure 58b). Over the land relatively small currents, of the order of 50 m, had the maximum temperatures (Figure 58a), the number of such currents being considerably larger than over water Over water surfaces, convective currents extended to smaller heights than over land. The convective layer thickness over the lake never exceeded 500 m, whereas over the land it varied, depending on the atmospheric stratification, from 700 to 2000 m. The presence of a thinner convective layer should be manifested in a larger number of convective currents The formation of such currents, as frecolder than the surrounding air. quently mentioned above, is connected with their ascent by inertia above the

equilibrium level, which occurs at heights where y