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Introduction to Weather and Climate Science [1 ed.]
 1609273311, 9781609273316

Table of contents :
Table of Contents
Chapter 1: The Science of the Atmosphere
Chapter 2: Radiative Transfer in the Atmosphere
Chapter 3: Water in the Atmosphere
Chapter 4: The Dynamic Atmosphere
Chapter 5: Tropical Cyclones

Citation preview

Introduction to Weather and Climate Science

By Jonathan E. Martin University of Wisconsin–Madison

Bassim Hamadeh, CEO and Publisher Christopher Foster, General Vice President Michael Simpson, Vice President of Acquisitions Jessica Knott, Managing Editor Kevin Fahey, Marketing Manager Jess Busch, Senior Graphic Designer Jamie Giganti, Senior Project Editor Brian Fahey, Licensing Associate Copyright © 2013 by Cognella, Inc. All rights reserved. No part of this publication may be reprinted, reproduced, transmitted, or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information retrieval system without the written permission of Cognella, Inc. First published in the United States of America in 2013 by Cognella, Inc. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe.

Figure 1.1a: Source: commons.wikimedia.org/wiki/File:Green_Grass_With_Dew.jpg. Cleared via Creative Commons Attribution-Share Alike 3.0 Unported license. Figure 1.1b: Source: photolib.noaa.gov/htmls/wea02087.htm. Copyright in the Public Domain. Figure 1.1c: Source: commons.wikimedia.org/wiki/File:DSCI0179.JPG. Cleared via Creative Commons Attribution-Share Alike 3.0 Unported license. Figure 1.1d: Copyright © 1998 by EUMETSAT. Figure 1.1e: Source: visibleearth.nasa.gov/view.php?id=68479. Photo by Jacques Descloitres, MODIS Rapid Response Team, NASA/GSFC. Copyright in the Public Domain. Figure 5.1: Provided courtesy of University of Wisconsin-Madison Space Science and Engineering Center.

Printed in the United States of America ISBN: 978-1-60927-331-6 (pbk) / 978-1-60927-332-3 (br)

Contents Chapter 1

1

The Science of the Atmosphere: Introduction and Fundamental Physical Principles What is the Atmosphere?

3

What are Some Properties of the Atmosphere?

4

The Chemical Composition of Earth’s Atmosphere: Present Mixture and Past History

5

Some Basic Physical Axioms

10

The Physical Meaning of Temperature

11

The Ideal Gas Law

12

The Vertical Structure of the Atmosphere

15

Energy

20

Energy, Temperature, and Heat

21

Heat Transfer in the Atmosphere

27

Chapter 2

33

Radiative Transfer in the Atmosphere Radiation and Temperature

36

The Effect of an Atmosphere on Surface Temperature

40

Why the Earth has Seasons

45

The Seasonal Temperature Lag

48

The Global Distribution of Radiative Energy

50

The Daily Temperature Cycle

51

Controls of Temperature

52

Scattering of Radiation

53

Rainbows and Refraction of Light

56

Chapter 3

61

Water in the Atmosphere: Humidity, Clouds, and Precipitation The Hydrologic Cycle

63

Saturation

63

The Influence of Temperature on Condensation

65

Measures of Humidity

65

Condensation

69

Cloud Formation

70

Bouyancy

71

Stability

73

Precipitation Formation

78

Droplet Growth into Precipitation-Sized Particles

81

Precipitation Type

82

Chapter 4

87

The Dynamic Atmosphere: The Winds and Weather of the Mid-Latitude Cyclone The Forcing of the Horizontal Wind

89

Force Balance and Balanced Flow

96

Winds Near Cyclones and Anticyclones

101

The Continuity of Mass

105

Cyclones and Anticyclones as Wavelike Disturbances

107

The Structure of Mid-Latitude Cyclones

113

Vertical Structure of Cyclones

118

Vertical Shear of the Geostrophic Wind

121

Thunderstorms

124

Chapter 5

131

Tropical Cyclones: The Most Powerful Storms on Earth The Tropical Setting

133

Tropical Cyclone Structure

135

Where do Tropical Cyclones Form?

139

Tropical Cyclone Formation

141

Hazards Associated with Tropical Cyclones

147

Differences Between Tropical and Mid-Latitude Cyclones

150

Tropical Cyclones in the Earth’s Energy Budget

151

Tropical Cyclones in a Warmer Climate

152

Chapter 1 The Science of the Atmosphere: Introduction and Fundamental Physical Principles

The Science of the Atmosphere

3

What is the Atmosphere? he atmosphere of Earth is a thin, gaseous mixture of chemicals that surrounds the solid Earth. Within this thin layer of gases many powerful, intricate, and spectacular phenomena occur. On the smallest scales, sometimes just millionths of a meter across, microscopic liquid water droplets and tiny shards of ice make up the clouds in our atmosphere. Millions of such cloud droplets constitute a single raindrop. Such raindrops number in the billions in a single thunderstorm. Billions of suspended raindrops, a curtain of rain, serve as the prism through which a beautiful rainbow can be formed. Hundreds of thunderstorms, alternately generated and extinguished over a period of days or weeks can organize into a ferocious hurricane in which winds can approach 100 m s-1 (200 miles per hour). In the middle latitudes, cyclones such as the one appearing on the front cover of this book can occupy millions of square kilometers of area, last nearly a week, and affect Havana, Cuba, and Montréal, Québec, Canada, simultaneously. It is these types of storms that are responsible for bringing much of the “weather” with which most of us are familiar. A number of these phenomena are presented in Fig. 1.1.

T

(a)

(c)

(b)

(d)

(e)

Figure 1.1. Several examples of the types of phenomena produced in our atmosphere. (a) Dew drops on blades of grass, (b) a selection of snowflakes, (c) a waterspout over the ocean, (d) an extratropical cyclone over the British Isles and the Low Countries of western Europe, (e) Hurricane Isabel over the Carribean in 2003.

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Amazingly, most of the atmosphere within which this great variety of beautiful and powerful phenomena are generated resides within about 50 km (~30 miles) from the surface of the Earth. This fact is particularly remarkable when one considers that the solid Earth has a radius (distance from its center to the surface) of 6370 km. Thus, the Earth’s atmosphere is only 1/132nd the thickness of the planet. When you cut an apple in half, the thickness of the skin is about 1/75th or so the thickness of the fruit in that cross-section. So, the atmosphere is even thinner relative to the solid Earth than the skin of an apple is to the fruit inside it. Despite that thinness, all of the phenomena listed above occur in that thin skin. Today you are breathing essentially the same atmosphere that all of your ancestors breathed. It is the same atmosphere in which Jurassic thunderstorms poured down upon the dinosaurs and in which lightning strikes the Earth 1000 times each second. The atmosphere is an amazing object that has inspired art, poetry, mythology, and music for centuries while simultaneously presenting science with a most worthy subject for inquiry. I suspect that you will agree after this term that the beauty, power, and majesty of the atmosphere, far from being “de-romanticized” by scientific investigation of it, are instead amplified after it is formally studied and better understood. Despite what may sometimes appear to be the case, the behavior of the atmosphere is not arbitrary but rather is governed by strict physical laws that describe the nature of energy, mass, and momentum (all of which will be defined in this book). In short, study of the atmosphere is a branch of physics and chemistry that has, in the last 100 years or so, matured into a distinct science of its own with an ever-increasing public profile that reflects the centrality of weather and climate in human affairs. In this book we will pursue a formal study of some of the foundational aspects of the science of the atmosphere. Central to the power of the scientific perspective as a way of learning about the world is observation. Thus, our formal study of the atmosphere will begin by considering what characteristics of the atmosphere can be measured.

What are Some Properties of the Atmosphere? Though it may not always be apparent, and certainly was not to many ancient thinkers, the atmosphere has weight. In more precisely physical terms, the atmosphere has mass. Mass can be thought of as a measure of the substance of an object. An object’s weight is the product of its mass times the acceleration due to gravity. The Earth’s atmosphere weighs an astounding 5,825,000 billion tons—yes, almost 6 million billion tons. The atmosphere is a type of object known as a fluid. A fluid is any substance that conforms to the shape of its container. Clearly, not all substances fit this simple definition. For instance, wood is not a fluid. Neither are steel or stone. Water, toothpaste, and glass are all fluids, though it is perhaps easiest to keep water in mind as a prime example of a fluid. In fact, water is the fluid from that short list that is most similar to the fluid atmosphere. A number of properties of this atmospheric fluid can be quantified or measured.

The Science of the Atmosphere

5

A characteristic of the atmosphere that is readily apparent on a cold winter day is the temperature of the air. Colloquially, temperature is considered a measure of how hot or cold it is. We will find that a more physically appealing definition for temperature, to be discussed later, is also more useful in our study of the atmosphere. Thermometers are instruments that can be used to measure the temperature. On a hot July day you might notice that your skin is covered with sweat. This is often a response to the fact that the air surrounding your body is rather full of invisible, gaseous water vapor. We will broadly refer to a measure of this water vapor content as the humidity of the air. A hygrometer is an instrument that can measure the humidity of the air. Interestingly, the very best hygrometers use human hair, as it is remarkably sensitive to the level of humidity. The fluid atmosphere is also in motion, as can be felt on a windy day. The wind has both a speed and a direction, and both must be measured in order to create an accurate description of the wind. Later in the course we will discuss the physical circumstances that control the wind. Finally, perhaps least obvious to most of us, is that the pressure that is exerted by the air above us can be measured as well. One way to consider pressure is that pressure is formally equal to Pressure = Weight / Area so that when one refers to the atmospheric pressure one is only indirectly referring to the weight of the atmosphere above. The weight of the air column that extends from this page to the very top of the atmosphere is 1176 lbs. Given that this page has a surface area of 80 in2 (8” x 10 ”), the atmosphere exerts 14.7 lbs/in2 of pressure near sea level. Pressure can be measured using a barometer. The atmospheric pressure varies from place-to-place and, at any single location, from day-to-day and is often reported in units of millibars, abbreviated as mb. Observed extremes in sea-level pressure (the pressure measured at the height of the ocean surface) range from 1083 mb (recorded in Siberia in 1993) to 860 mb at the center of Typhoon Tip near Luzon, Philippines, in 1979. It turns out that these measurable variables can be related to one another in a couple of important physical relationships. Before we talk about these relationships we will consider what constituent gases compose our atmosphere and how that mixture has evolved over the history of the Earth.

The Chemical Composition of Earth’s Atmosphere: Present Mixture and Past History The story of the chemical evolution of the Earth’s atmosphere begins with the origin of the universe itself. Current thinking suggests that the universe formed as a result of a massive

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Introduction to Weather and Climate Science

explosion known as the Big Bang that occurred some 13.7 billion years ago.1 The lightest elements composed the vast majority of the debris from the Big Bang, and that remains the case today. In fact, nearly 98% of the universe is still composed of hydrogen (H) and helium (He), the simplest atoms. Gradually, organized by gravitational forces, swirling masses of hydrogen began to congeal into large masses of hydrogen as time passed. As these balls of gas grew larger and larger, they got more massive and the pressures inside them grew larger and larger as well. As a result, in some of the larger such bodies, hydrogen was turned into helium by nuclear fusion: H + H → He + energy a reaction that is still occurring in our Sun today. Smaller balls of matter did not grow large enough to force fusion at their cores and so they became non-stars, like our planet Earth. As these planet-sized balls of gas cooled over millions of years, some of the material solidified into a solid crust while other portions remained gaseous, forming the Earth’s first atmosphere. So, it is very likely that Earth’s original atmosphere was composed mostly of H and He and other light gases such as methane (CH4) and ammonia (NH3). Such gases still compose the atmospheres of the so-called “gas giants” like Jupiter and Saturn in our own Solar System. Clearly, the atmosphere does not have the same composition today as it likely had billions of years ago. What has happened in the meantime to afford the change? First, the Earth’s gravity was not sufficient to retain all of the original H and He since those elements are the least massive ones. The closeness of the Earth to the Sun also contributed to these gases being burned off from our atmosphere. Second, hot gases trapped inside the Earth were out gassed through volcanoes and steam vents as the planet began to cool. These gases included water vapor (H2O), carbon dioxide (CO2), and some molecular nitrogen (N2). Given these two major changes, the revised atmospheric composition of Earth may well have been that given in Table 1.1 (in order of amount by volume). Table 1.1 CH4 NH3 N2 CO2 Ar H20

Methane Ammonia Nitrogen Carbon Dioxide Argon Water Vapor

1 To give you an idea of what 13.7 billion means, there are 13.7 billion seconds in 434.1 years.

The Science of the Atmosphere

7

Earth gradually cooled over a long time, and though the continual out gassing had supplied a considerable amount of H2O vapor, it is unlikely that all of the water on Earth entered the atmosphere in this way. Instead, it is now believed that much, if not most, of the water on Earth was imported from outer space via impacting comets that contained ice. There may even have been impacting proto-planets, roughly the size of the smallest icy moons of Jupiter and Saturn, which delivered large amounts of water to Earth in its early history. As the water vapor content of the atmosphere increased and the planet cooled, clouds formed and it began to rain on Earth for the first time. Over many millions of years this rain created oceans, lakes and rivers on the early Earth. These reservoirs of liquid water soaked up an enormous amount of CO2 and, consequently, the atmosphere gradually became rich in molecular nitrogen (N2). N2 is an inert gas, which means it is not chemically active. Then, some 2 to 3 billion years ago a major change occurred on Earth that eventually completely transformed the chemical composition of its atmosphere. For reasons that are still not well understood, primitive life forms (single-celled plants) developed in the oceans. It is likely that life tried many experiments (and even some on land), but the first experiments in life were successful only in the oceans because there, life was safe from lethal ultraviolet radiation from the Sun, which is damaging to DNA. These plants, like all life forms, require some kind of food for survival. Plants manufacture their own food by combining CO2 and H2O in the presence of sunlight in a remarkable process known as photosynthesis. The photosynthesis reaction can be written out as Sunlight + 6CO2 + 6H2O → 6O2 + C6H12O6 where C6H12O6 is glucose, the plant’s food. For 2.5 billion years, life on Earth remained fairly primitive and entirely in the oceans. During this time huge amounts of O2 (molecular oxygen) were produced. In fact, the only source of O2 in our atmosphere’s history comes from photosynthesis, so life itself played an enormous role in the chemical evolution of the Earth’s atmosphere. By about 400 million years ago, there was so much O2 in the atmosphere that some of it began to be involved in another chemical reaction of great significance for the future of life on Earth. This reaction involved the destruction of an O2 molecule and the production of a new chemical, ozone (O3). This ozone cycle involves two chemical reactions: O3 + UV energy → O2 + O

(1)

O 2 + O → O3

(2)

Reaction (1) uses the energy of ultraviolet (UV) light from the Sun to rip an existing ozone molecule (O3) apart, producing an oxygen molecule (O2) and a free oxygen atom (O). Reaction (2) describes the fact that O and O2 react rapidly to form a new ozone molecule. This

8

Introduction to Weather and Climate

new ozone molecule is then available to absorb more UV radiation, split into O2 and O, and thus provide the raw materials to form yet another ozone molecule. In this cyclical manner, enormous amounts of lethal UV radiation are absorbed by a very little bit of ozone in Earth’s atmosphere. The consequences of the presence of ozone in our atmosphere were immediate and profound. Suddenly life was not required to remain in the oceans as its only means of avoiding UV radiation. Thus, life immediately colonized the dry land. Given the small amount of O3 necessary to perform this important job in our atmosphere, it is perhaps not surprising that the ozone cycle is very sensitive to outside influences. A class of industrial chemicals known as chloroflourocarbons (CFCs) has long been used in commercial refrigeration. These chemicals, one of which is trichloroflouromethane (CCl3F), or freon-11, possess chlorine atoms that are dissociated by UV radiation. The resulting free chlorine atoms can combine with the free oxygen (O) atoms liberated in the ozone cycle. This process effectively removes those oxygen atoms from the ozone cycle, resulting in a gradual reduction in the O3 content of the atmosphere. This O3 reduction was most famously manifest in the ozone hole, which first garnered international attention in the 1980s. As a result of the work of a number of atmospheric chemists, this human-induced problem was addressed by an international agreement, adopted in 1987, to phase out the use of CFCs. This agreement, known as the Montréal Protocol, represents an inspiring example of both the power of science to inform important public policy and international cooperation on a global problem.2 The newfound abundance of O2 in the atmosphere was not good news for all Earthlings, however. A large fraction of the earliest life forms found this O2 toxic and succumbed to the growing O2 concentration in what is known as the “oxygen catastrophe.” Only those life forms whose physiology allowed them to avoid this fate were able to reproduce. Some of these evolved the ability to use O2 to greatly increase their metabolism. O2 is a very potent and efficient fuel, so such animals were able to become large and complex. Human beings are among the many animals that respire molecular oxygen, so in a very real sense we would not be here today had it not been for the billions of years of photosynthesis accomplished by simple plants in the oceans of the primordial Earth. The changes wrought by life on the chemical composition of the atmosphere have led us to the current recipe listed in Table 1.2. 2

Former United Nations Secretary General Kofi Annan has said “... perhaps the single most successful interna-

tional agreement to date has been the Montréal Protocol.”

The Science of the Atmosphere

9

Table 1.2: Permanent and Variable Gases Permanent Gases Symbol

Name

Percent by Volume

N2 O2 Ar Ne He H Xe

Nitrogen Oxygen Argon Neon Helium Hydrogen Xenon

78.1% 20.9% 0.9% 0.002% 0.0005% 0.00006% 0.000009%

Variable Gases H2O CO2 CH4 NO2 O3

Water Vapor Carbon Dioxide Methane Nitrous Oxide Ozone

0–0.04% 0.037% 0.00017% 0.0003% 0.000004%

Notice that a number of very important chemicals (O3, H2O, and CO2), exist only in small quantities. The fact that they, nonetheless, have an enormous impact on the behavior of the atmosphere and its ability to sustain life on Earth testifies dramatically to the delicate balances at work in the Earth’s atmosphere. Most important meteorologically is the variable constituent, water vapor (H2O). Water is the only substance on Earth that exists in all three of its phases (solid, liquid, and gas) at characteristic Earth temperatures. We will find later that water’s change of phase from vapor to liquid or solid is an extremely important driver of the atmospheric circulation that eventually distributes the Sun’s energy over the globe. Now that we have some recipe for the gaseous mixture that constitutes the Earth’s atmosphere, we want to describe the behavior of that gaseous mixture under the variety of conditions that might be observed on Earth. In order to do so most effectively, we need to discuss some basic physical ideas that we will use as axioms in our construction of more elaborate theories.

10

Introduction to Weather and Climate

Some Basic Physical Axioms The basic ideas that we will employ in this next discussion are: 1. 2. 3. 4.

Area Volume Force Kinetic Energy.

Area is most simply thought of as the product of the length times the width of an object, and we will consider the surface area of various objects. Of course, even three-dimensional objects can have surface area, though it is sometimes more difficult to measure. Certain geometric objects have formulas for their surface areas that may be familiar to the reader. For instance, the surface area of a sphere, like the Earth, is given by the formula Area = 4πR2 where R is the radius of the sphere. Area is always measured in the units of meters squared (m2). Volume is most often thought of as the space occupied by an object. If that object is a cube, the volume can be easily calculated as the product of the length, width, and height of the object. Every three-dimensional object has a volume, though not all can be calculated using a simple formula. However, the volume of an irregularly shaped object such as a dinner fork can be discerned, for instance, by carefully measuring how much water is displaced in a beaker when the fork is fully submerged in it. The unit of volume is the cubic meter (m3). Force can be thought of in a couple of complimentary ways. We have already said that force is equivalent to weight. A force might also be thought of as a measure of the push given to an object. For instance, one can impose varying degrees of a force on a Styrofoam cup. Small forces might only deform the cup, whereas larger forces can crush it. Kinetic energy (KE) is just one particular type of energy. Energy, in general, is a measure of an object’s ability to do work. The word “kinetic” comes from a Greek word meaning “motion.” Thus, kinetic energy is an object’s ability to do work based upon its motion. The formula for calculating an object’s kinetic energy makes reference to the object’s mass and the square of its velocity: KE = (1/2) x Mass x Velocity2. Automobile manufacturers are required to crash some of their cars into walls and examine how the car responds to the impact. The car is moving when it hits the wall, and since the car has mass, the considerable amount of kinetic energy it has at impact is precisely what does the “work” of destroying the car on impact. Note that since the KE depends upon the square of

The Science of the Atmosphere

11

the velocity, the degree of destruction in such a crash test is predominantly a function of the speed of the car. Now that we have defined these important physical quantities, we will proceed in using them to describe some important relationships between some of the measurable characteristics of the atmospheric gas. We’ll begin by considering a more formal definition of temperature.

The Physical Meaning of Temperature We often think of temperature as a measure of how hot or cold some object is. As it turns out, this colloquial definition is not the best physical definition. In fact, the best definition arises from what is known as the Kinetic Theory of Gases and has to do with the speed of the molecules making up the substance. For instance, the room in which you are reading right now has air molecules in it that are moving at nearly 1000 mph. Were you in a freezer, the air molecules would be moving considerably more slowly. What we would feel as a difference in air temperature between the library and a freezer is really a manifestation of the different speeds with which the air molecules in those two locations are moving. For reasons that are more deeply explained in a course in physical chemistry, the following definition of temperature will be used throughout the rest of this book: The temperature of a substance is a measure of the average kinetic energy of the molecules that compose that substance. In all calculations that you might need to perform during this course you will need to use a temperature scale that defines as its zero point the temperature at which molecules stop moving. This temperature is known as absolute zero, and the scale that uses it is the Kelvin scale (K). The conversion from the more commonly used Celsius scale to the Kelvin scale is easy: °K = °C + 273.18. The Kinetic Theory of Gases also allows us to reconsider the concept of pressure more formally. Recall that pressure is defined as P = Force / Area. Previously we have thought about this only as WEIGHT divided by AREA. But, recall that we also talked about FORCE as a push. By doing so again, we can relate temperature and pressure in a solidly physical manner.

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Introduction to Weather and Climate

Imagine a small box full of rubber balls that are forever bouncing around and impacting the six walls of the box. Each time a ball strikes a wall it exerts a force or a push on that wall. If we add up all the forces of impact made by every ball that strikes a wall over a short period of time, we get the total force exerted on that wall in that time interval. It is far simpler to measure the area of that wall. Knowing those two measurements, we can calculate the pressure exerted on that wall by the rubber balls in the box as Pressure = Total Force / Area. The physical connection between temperature and pressure might now be emerging from the discussion. If we consider the molecules of air in a similar box to be analogous to the rubber balls, then the force each molecule imparts on the wall is proportional to the speed at which it is moving—that is, to the temperature of the gas. So there is a clear physical relationship between pressure and temperature. Before we investigate this relationship further, we consider one other variable that will figure into the discussion. The density (symbolized using the Greek letter rho, ρ) is defined as Density = Mass / Volume so that the mass of a sample of air is a function only of the number and type of molecules in the sample. If we were to measure the mass of the air in a lecture hall and divide that number by the volume of the lecture hall, then we would have a measure of the density of the air in the lecture hall—simple. If we were to put more molecules in the lecture hall, the density would increase, and vice versa. Now, we are ready to investigate the physical relationship between the three variables: Pressure, Temperature, and Density.

The Ideal Gas Law Science often advances by carefully choosing simplifications to reality that provide conceptual footholds to new insights about nature. One such simplification is the concept of an ideal gas—a gas in which the individual molecules do not interact with each other at all, even to the point of not colliding with one another. This is clearly not the case in reality and yet by making this seemingly ridiculous assumption, we will shortly arrive at the universal rule that quite accurately governs the relationship between pressure, temperature, and density in real gases. The following three examples will illustrate the various combinations of circumstances needed to derive this so-called Ideal Gas Law.

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13

Case I: Density held constant Imagine a steel tank within which a constant number of molecules reside. The tank has a constant volume, and, since there are a constant number of air molecules in it, it also has a constant mass. Therefore, the air in this case has a constant density. Now, let’s imagine what happens if the temperature of the air inside the tank is increased. By definition, the temperature of the air can only increase if the average KE (kinetic energy) of the molecules increases. If the average KE of the molecules increases then each impact a molecule of air makes on the side of the tank imparts a greater force than it did before. The sum of all of these forces is therefore greater than it was before the temperature increase. Since the volume of the tank has remained constant, then the surface area inside the tank has also remained constant. Therefore, since Pressure = Force / Area and Force has increased while Area has remained constant, the pressure exerted by the air inside the tank increases. Summarizing the results, when density (ρ) is constant, then an increase in temperature (T) forces an increase in pressure (P).

Case II: Pressure held constant For this thought experiment we will consider a perfectly elastic balloon (i.e. a balloon in which no work is involved in stretching the skin of the balloon when it expands or contracts). Why? Any balloon stays inflated only if the pressure exerted by the air inside the balloon (pushing outward) is equal to the pressure exerted by the air outside of it (pushing inward) as illustrated in Fig. 1.2. Thus, we can keep the pressure constant in this thought experiment by performing it in a balloon. Now, imagine we increase the temperature of the air inside the balloon. As this happens, the average KE of the air molecules inside the balloon increases by definition. Assume also that we are not adding or subtracting any molecules of air to or from the balloon. Upon experiencing the temperature increase, the air molecules inside the balloon will move faster than they did before and will exert a greater total force as a result. But, since the pressure is constant in the face of an increase in the total force, the balloon must expand in order to increase its surface area. This expansion accomplishes an increase in the volume of the balloon. Since the newly expanded balloon contains the original number of air molecules (i.e. the same mass), the ratio of mass to volume has decreased. Thus, the result of this experiment is that the density decreases. Summarizing, for constant Pressure (P) (and constant mass), an increase in Temperature (T) leads to a decrease in Density (ρ).

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Introduction to Weather and Climate Science

Figure 1.2. Illustration of a balloon as a constant pressure container. The air inside the ballon pushes outward (black arrows) with the exact same force as the air outside pushes inward (gray arrows).

Case III: Temperature held constant In this thought experiment we return to our rigid steel tank and hold the temperature constant. If we now add some new molecules to the tank, which still has a constant volume, we have increased the density of air inside the tank. This means that there are more molecules than before and they are moving at a speed that is directly proportional to the temperature, T. So, after the addition of the extra gas, more objects are hitting the sides of the tank than before but each is imparting the same amount of force per impact as before. The result is that a larger total force is exerted by the gas in the tank after the addition of the new molecules. Since the surface area of the tank is unchanged, this means that the pressure has increased. Summarizing, at a constant Temperature (T), as the Density (ρ) increases, the Pressure (P) also increases. So we have found in our three thought experiments 1. With constant ρ, T increases lead to P increases 2. With constant P, T increases lead to ρ decreases 3. With constant T, ρ increases lead to P increases

Of all the possible multiplicative relationships between P, T, and ρ the only one that satisfies all three of our thought experiments is that Pressure is proportional to the product of Temperature and Density.

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In mathematical terms P ∝ ρT This statement can be transformed into an equality by introducing a constant of proportionality, R, known as the gas constant for dry air3. Our relationship is then more precisely P = ρRT. This relationship is known as the Ideal Gas Law, and it describes in precise mathematical terms the physical relationship between the measurable quantities Pressure, Temperature, and Density of the atmospheric gas.

The Vertical Structure of the Atmosphere The distributions of Temperature, Density, and Pressure in the atmosphere are highly variable in space and time. In fact, the manner in which they vary plays a central role in creating the weather. For this reason, it is instructive to consider these variations. We’ve already stated that the atmosphere is only about 50 km thick, so we will begin our study of the variations of P, T, and ρ by discussing how they vary in the VERTICAL direction.

The Variation of Pressure with Altitude Pressure is the force divided by area. Consider two beakers filled with different amounts of fluid as depicted in Fig. 1.3.

Beaker A

Beaker B

Figure 1.3. Two beakers, A and B, filled with different amounts of fluid. 3

The value of R is 287 Joules per kilogram per Kelvin (J kg-1 K-1).

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Introduction to Weather and Climate Science

They both have the same surface area at the bottom. Which beaker has a greater pressure at the bottom? Obviously the answer is B because there is more fluid in B and it weighs more. The atmosphere is also a column of fluid, so we can consider the analogous example illustrated in Fig. 1.4. By analogy, the atmospheric pressure will be lower at the top of the hill in Fig. 1.4 than on the plain. This suggestion motivated Evangelista Torricelli4, who invented the barometer in Pisa, Italy, in 1643, to test his invention by climbing a hill on the outskirts of town. This physical fact also motivates the pressurization of the cabins of airliners since the pressure outside of an airplane at flight level is much lower than the pressure we are all used to on the ground. Based upon a physical consideration of pressure and the foregoing examples, we conclude that Pressure ALWAYS decreases with increasing altitude.

Shallow Column

Deep Column

This means, of course, that your 4th floor apartment has an air pressure that is lower than the pressure on the street-level.

Figure 1.4. Illustration of the fact that the depth of the atmospheric column depends on the surface topography of the Earth.

4 Torricelli succeeded Galileo as Professor of Mathematics at the University of Pisa. In June 1633, when the Vatican condemned Galileo, Torricelli bravely declared his adherence to the Copernican view of the solar system. He had a lifelong interest in meteorology and once wrote, “We live submerged at the bottom of an ocean of air.”

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The Variation of Density with Altitude Consideration of the variation of density with height is facilitated by a simple thought experiment. Imagine a container filled with pebbles and a container filled with water. Nearly everyone would be able to unequivocally assert that the beaker of pebbles weighs more than the beaker of water. If one were to drop a single pebble into the water, the pebble would sink to the bottom. As it turns out, the reason the pebble sinks is that it is more dense than water. Conversely, a dry piece of wood would float on the water because it is less dense than the water. Now, it is a generally observed fact that the air at any level above the ground in the atmosphere does not spontaneously sink toward the ground. This fact might lead us to suspect that the air density must decrease with increasing altitude since only less dense air could sit atop air with greater density without sinking to the ground. This suspicion turns out to be true; the density of air does decrease with altitude. By definition, a decrease in density with altitude means that the number of molecules in a given volume of air is smaller at upper levels in the atmosphere than near the surface. Hikers and mountain climbers refer to the air being “thinner” at high elevations. What this really means is that since one’s lung capacity (i.e. the volume of air needed to fill one’s lungs) is essentially unchanged by elevation differences, a deep breath of air at the seashore contains substantially more air molecules than a deep breath at an altitude of 3000 m (10,000 ft). Very occasionally, as a result of the vigorous mixing that occurs in violent thunderstorms, the density can be made to increase with height momentarily and only in limited areas in the near vicinity of the storm itself. Thus, it is nearly always the case that density decreases with altitude, but there are rare exceptions.

The Variation of Temperature with Altitude The average vertical temperature structure of the atmosphere is much more complicated than that of P or ρ. Thus, we must start this discussion by defining a new term; lapse rate. The lapse rate is defined as The rate of change of air temperature in the vertical direction and is measured in units of °C km-1. This lapse rate is different in different layers of the atmosphere. Let’s begin by considering the lowest layer of the atmosphere, the one in which we live, known as the troposphere.

a. Troposphere The lowest 10 km or so of the Earth’s atmosphere is called the troposphere. This word comes from the Greek tropien which means “to turn or change.” This portion of the atmosphere is highly changeable and, in fact, it is where all of the actual weather occurs. The temperature

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Introduction to Weather and Climate Science

generally decreases in the troposphere at a rate of about 6.5°C km-1, though at any given location and time it can be larger or smaller than this average value. The surface is usually warmest because sunlight is absorbed quite well by the surface of the Earth and not so well by the air above the surface (as we shall discuss in more detail later). Above about 10 km (6.12 miles) the temperature stops decreasing with increasing height and a layer of constant temperature (an isothermal layer) called the tropopause is found. This tropopause caps the troposphere and its height is highly variable. The tropopause tends to be high in summer and low in winter and, on a given day, the tropopause can be low over Canada and high over the Gulf of Mexico. The height and slope of the tropopause are intimately related to the position of the jet stream and to weather systems, connections we will explore later in the text.

b. Stratosphere The next layer of the atmosphere is called the stratosphere and it stretches from roughly 10–15 km to ~50 km. In this layer, the air temperature actually increases with height. Any such increase in temperature with height is known as a temperature inversion. The inversion present in the stratosphere is almost entirely a consequence of the presence of ozone, which, when dissociated by ultraviolet radiation in the stratosphere, results in a warming of the air there. Similar dissociation of molecular oxygen (O2) in the upper stratosphere also contributes to warming. Because of this strong temperature inversion, there is not much weather in the stratosphere. The stratosphere is capped by an isothermal layer known as the stratopause.

c. Mesosphere Above the stratopause is the mesosphere, a layer of the atmosphere that extends from 50 km to roughly 85 km. The mesosphere contains very little of the atmosphere’s mass as indicated by the very low pressures in this layer that range from 1 mb to 0.01 mb (or 0.001% to 0.1% of sea-level pressure). In the mesosphere, temperature decreases with height up to 85 km. This decrease is a consequence of the fact that there are so few air molecules that cooling by emission of radiation exceeds heating by absorption of sunlight. At the top of the mesosphere sits an isothermal layer known as the mesopause that is the coldest spot in the Earth’s atmosphere, with temperatures hovering near -100°C (-148°F).

d. Thermosphere At heights above 85 km, molecular oxygen (O2) is the primary absorber of sunlight (specifically, the UV radiation) and warms the air. This warming is manifest in the temperature inversion that characterizes the thermosphere. It must be pointed out that at the level of the

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thermosphere so few molecules are present that the concept of temperature as the average KE of the molecules is troublesome. Nonetheless, in this layer the effect of solar eruptions and solar flares is very significant. A schematic summarizing the vertical temperature structure we have just discussed is shown in Fig. 1.5. Another rather separate but very important point concerning the vertical structure of the atmosphere must now be made. Amazingly, if one were to fill a number of bags with air from a variety of levels at or below about 80 km in the atmosphere, one would find that, despite the fact that the total number of molecules in each bag would be different by virtue of the continual decrease in density with increasing altitude, the ratio of molecules of each chemical constituent (N2 to O2 to CO2 to Ar etc.) would be identical at all levels. This 80 km deep layer where the atmosphere is well mixed is known as the homosphere. So little gas exists above about 80 km that the molecules tend to settle based upon their molecular weights, with the heaviest molecules settling to the bottom. This stratified layer of the atmosphere is known as the heterosphere (shaded gray in Fig. 1.5).

100

80

T

100

Mesopause

80 60 40

Thermosphere

60

Homosphere

Altitude, km

120

20

Mesosphere

Stratosphere Tropopause Troposphere

0

40

Stratopause

-100 -50 0 50 o Air temperature, C

Figure 1.5. Vertical temperature structure of Earth's atmosphere.

20

0

Altitude, mi

140

Heterosphere

160

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Introduction to Weather and Climate Science

Energy Now that we know something about mass, we must consider another fundamental physical quantity that has great relevance in any study of the atmosphere. That quantity is energy. Most of us have a reasonably sophisticated sense of what energy is. For instance, when entering a dark room and turning on the light, we are aware that energy is required to light the room. Before we embark upon a physical activity we know to eat well, thus providing our bodies with energy. An industrious person is one who might be known to have boundless energy. In all of these everyday applications of the word energy, we find ourselves at the threshold of a reasonable physical definition of the term. We will hereafter refer to energy as: Energy is the ability to do work on some form of matter. Work is done when a force is applied to an object in order that it be pushed, pulled, or lifted over some distance. There are many kinds of energy: nuclear energy, chemical potential energy, kinetic energy, and potential energy, to name a few. Of those four examples, only kinetic and potential energies are of great relevance to our study of the atmosphere. But there is another form of energy that is even more relevant. It is the type of energy that might warm your face on a sunny winter day. This type of warming is accomplished directly by solar radiation encountering your face. Thus, radiant energy, energy in the form of radiation, is extremely important. In fact, almost all of the energy that fuels the atmosphere/ocean system comes from the Sun. This radiant energy is so important that it will constitute an entirely separate segment of this text. A major question in the physical sciences is: If all these types of energy exist, how are they all related to one another? The basis of such a relationship can be summed up in a statement known as the First Law of Thermodynamics, which states: The sum of energies in the Universe is constant. This means that the total energy content of the Universe does not change with the passage of time. Energy may change from one kind to another (i.e. nuclear to kinetic) but the sum of all the energy in the Universe cannot change. This may seem like an innocuous statement, but it is remarkable and very useful. A simple example illustrates the utility of such a universal law. Consider a book being dropped from a table onto a Styrofoam cup on the floor beneath. When the book is on the table it has considerable potential energy (PE) but no KE. That is, it has only potential to do work on the cup. If the book is pushed off the side of the table and begins to fall toward the ground it acquires KE at a rate equal to its rate of loss of PE. By the time the book hits the floor, all of the original PE has been converted into KE and the fast moving book is able to do considerable work on the cup—in fact, it crushes the cup. A conversion

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from PE to KE, not an overall change in the total energy, characterizes this simple experiment. Amazingly, the First Law states that this result can be extended to the entire Universe. Recall the warm feeling you get when turning your face toward the Sun on a cold winter day. One might colloquially say that the Sun is “heating” one’s face. That very feeling suggests that there is some physical relationship between energy, temperature, and heat. We will explore this relationship next.

Energy, Temperature, and Heat In order to understand the relationship between energy, temperature, and heat we will define a quantity known as the internal energy (IE). The internal energy is the total energy (PE plus KE) of all the molecules in a substance. Recall that temperature is defined differently; it is the average KE of the molecules in a substance. Imagine we have three equally-sized cups of water, each with the same temperature. In such a case, all three have the same IE. If cups 1 and 2 are then added together in a bigger container, we find that the IE of the bigger container is larger than the IE of cup 3. This is because the large container has twice as many molecules as cup 3. Now let’s consider a different example. Imagine you are on a rowboat in Lake Michigan and you are drinking hot tea. It is a rather simple matter to determine that your teacup has a higher temperature than the water in the lake. But, since Lake Michigan has a much larger number of water molecules in it than does your teacup, the lake has a much larger IE. Upon sticking your teacup into the lake you are not likely to be surprised that the teacup cools rapidly. The teacup temperature decreases as it cools, and therefore the average KE of the water molecules in the teacup decreases. The First Law demands that we account for that lost energy—where does it go? The energy goes into Lake Michigan. In fact, the energy that was transferred from the hot tea to the cool water of Lake Michigan, a consequence of the temperature difference between the two objects, is called Heat. Thus, we might reasonably state that; Heat is energy in the process of being transferred from one object to another because of the temperature difference between them. This transfer occurs, so far as we know, in only one direction—from hot to cold. Think about it: on a camping trip with friends, you would never decide to sit around a block of ice on a cold night and expect that the assembled bodies would warm while the block of ice got colder. You know you can only get warmer by sitting around a fire whose temperature is warmer than your body. This peculiar one-way nature of heat transfer is formalized in what is known as the Second Law of Thermodynamics, which asserts:

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Introduction to Weather and Climate Science

Heat is always transferred from warm to cold objects so as to warm the originally cooler object and cool the originally warmer object. Unlike the First Law of Thermodynamics, the Second Law cannot be proved—it is only an assertion. The great physicist James Clerk Maxwell spent a great deal of his career thinking about the Second Law and developed a conceptual sketch of why it is unprovable. Maxwell imagined two containers of gas connected to each other by a valve as shown in Fig. 1.6.

Chamber A

Chamber B

Figure 1.6. Experimental device imagined by Maxwell in his consideration of the Second Law of Thermodynamics. Circles represent gas molecules in both Chambers. The temperature of the gas in Chamber A is 0.1K higher than the gas in Chamber B and gas is sent from Chamber B to Chamber A. The dark circles in Chamber B represent those molecules of gas with KE higher than the average of the entire mixture in both B and A. See text for explanation.

Imagine that the gas in Chamber A has a temperature 0.1K warmer than the gas in Chamber B and that some gas is allowed to flow into Chamber A from Chamber B. Since temperature is the average KE of the molecules of gas in each container, some of the molecules in Chamber B have greater KE than some of those in Chamber A. If only those molecules were allowed to pass from Chamber B to Chamber A, the average KE of the gas in A would be increased while the average KE of the gas in B would be decreased. Again, appealing to the definition of temperature, this would mean that the gas in Chamber A would have warmed while the gas in Chamber B would have cooled, and some heat would have been transferred from the originally colder B to A. Maxwell concluded that it is thus possible for heat to be transferred from a cold to a warm object but that it is exceedingly unlikely since it would require the unnatural

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preferential transfer of only the most energetic molecules from B to A. Thus, what we call the Second Law is only an assertion of the unlikeliness of this event. The Second Law of Thermodynamics, as stated above, applies only to the spontaneous (i.e. unforced) transfer of heat. In the refrigerator in your home, heat can be made to flow from cold to warm, but only when work is done on the environment inside the refrigerator by the external compressor. Informative as it may be, it is not enough to know simply that heat is transferred from warm to cold. It turns out that a number of heat and energy transfer mechanisms exist in nature, and quite a number of them have relevance for a study of the atmosphere. We now investigate several of these heat transfer mechanisms after introducing some central concepts. If you have ever been charged with the task of heating a pot of water on the stove, you may have noticed that it takes a considerable amount of time to render the water warm enough for a cup of tea. This is because it takes a relatively large amount of heat to bring about a small change in the temperature of the water. The ratio of the heat required to the amount of resulting temperature change is known as the Heat Capacity. In symbols: Amount of heat absorbed Heat Capacity = Change in Temperature Though the heat capacity is a very important physical quantity, it does have its limitations. For instance, the heat capacity of a glass of water is considerably smaller than the heat capacity of Lake Michigan. One might erroneously conclude that this difference reflects a profound physical difference between the glass of water and Lake Michigan. Of course, this is not the case since both contain liquid water. The heat capacity of the glass is smaller simply because Lake Michigan has so much more water in it. Therefore, it is often more convenient to consider the heat capacities of different substances when comparing a common amount (mass) of each substance. To do this, we define a quantity known as the Specific Heat as: Specific Heat =

Heat absorbed by 1 g Change in Temperature

It follows that an object with a high specific heat is an object that requires a large amount of heat energy in order to change its temperature. Of course, the opposite is true for objects with low specific heats. Table 1. 3 lists some common objects along with their specific heats. Water has a specific heat of 1, which means that 1 calorie of heat is required to raise the temperature of 1 gram of water by 1°C. With a specific heat of 0.19, only 0.19 calories of heat are required to raise the temperature of 1 gram of sand by 1°C. Thus, it takes roughly five times more energy to raise the temperature of water than it takes to raise the temperature of sand. You may have encountered the unfortunate consequences of this fact upon coming out of the water at the beach and having to walk barefoot across the sand.

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Introduction to Weather and Climate Science

Table 1.3: Specific Heat of Various Substances Substance Pure water Wet mud Ice (0°C) Sandy clay Dry air Beach sand Granite

Specific Heat (cal g-1 °C-1) 1.00 0.60 0.50 0.33 0.24 0.19 0.19

Not only does an object with a high specific heat warm slowly, but it also cools slowly. As a result, large bodies of water have a modifying effect on local climate, as they tend to keep adjacent locations warmer or cooler than they might otherwise be. An example with which some of you may be familiar is the fact that Milwaukee, by virtue of its proximity to Lake Michigan, tends to be slightly warmer than Madison in the winter and slightly cooler than Madison during the summer. Since Lake Michigan is full of a fluid with a high specific heat (i.e. water), it warms only slowly during the summer and keeps Milwaukee slightly cooler. In the winter, Lake Michigan cools only slowly so it tends to be warmer than the air most of the time. Thus, Milwaukee stays slightly warmer than Madison in the winter. Such an effect will, of course, similarly influence the annual temperature cycle of any city adjacent to an ocean or large lake.

Latent Heats Another everyday experience will illustrate another vitally important concept. On a hot summer day you might be interested in a refreshing glass of ice water. Ice is, of course, the solid phase of the water substance. The recipe for refreshment is simple: place ice cubes into a glass of liquid water and wait. As you wait, the ice cubes begin to melt into the liquid water. As the melting occurs, the temperature of the liquid water in the glass falls. By definition, this means that the average KE of the liquid water molecules has been reduced. The central physical question, then, is where did the energy go? It can’t have just disappeared, as this would be in direct violation of the First Law of Thermodynamics. Instead, the energy went to changing the phase of the ice from solid to liquid. The implication of this familiar sequence of events is profound; energy is required to change the phase of a substance. We have a special name for this type of energy—latent heat energy, or latent heat. The word “latent” is chosen here because it connotes something “already present but hidden” within the substance. Latent heat can be defined as:

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The heat energy required to change a substance from one phase to another. As water is the only substance that exists naturally in all three of its phases in the Earth’s atmosphere, we are only going to be concerned with the latent heats that describe the phase changes of water. In order to change 1 gram of solid water (ice) at 0°C to 1 gram of liquid water at 0°C, 80 calories of energy must be supplied to the ice. Not surprisingly, if 1 gram of liquid water at 0°C transfers 80 calories of heat to its environment (which would have to be colder in accord with the Second Law of Thermodynamics), that water freezes into 1 gram of ice at 0°C. The 80 calories of heat goes by two names, depending upon the source of the heat. When the ice melts into liquid water and the requisite heat is supplied by the environment (i.e. the liquid water), it is known as the Latent Heat of Melting. When, in your freezer, the liquid water is transformed into ice and heat is removed from the liquid water and deposited into the environment (i.e. the air in the freezer), it is known as the Latent Heat of Fusion. The heat added to the air in this case has to be removed by the action of the external compressor in order to keep the freezer cold in the face of the release of this Latent Heat of Fusion. Notice that the Latent Heat of Fusion/Melting does not change the temperature of the water substance, only its phase. Water can also change from liquid to gaseous vapor. In order to convert 1 gram of liquid water at 20°C to 1 gram of water vapor at 20°C, ~600 calories of energy are required5. The flip side is that if 1 gram of water vapor at 20°C transfers 600 calories of energy to its environment, 1 gram of liquid water at 20°C will result. When the energy is required of the environment, this is known as the Latent Heat of Vaporization. When the energy is transferred to the environment, it is known as the Latent Heat of Condensation. This is a huge amount of energy, and you have likely felt its effect more than once in your life. Upon stepping out of the shower, a swimming pool, a lake, or the ocean, you might feel a chill. This is because the liquid water on your skin, being cooler than your skin in most cases, receives energy from your body through your skin and evaporates. A loss of energy from your skin lowers the temperature of your skin and you feel a chill. This same physical principle underlies the tremendously useful physiological ability to perspire. On hot days your body secretes liquid water onto your skin from your sweat glands. This water is not cooler than your body; in fact, it has precisely the same temperature as your body does. Provided the air surrounding you is not saturated with respect to liquid water (a concept we will discuss in detail later), the liquid water is evaporated away into the air. The requisite latent heat of evaporation comes from your body and lowers your body temperature—thus shielding you from overheating. 5

The actual value is 586 calories. It is important to note that liquid water can evaporate into gaseous water

vapor at any temperature and that within the range of meteorologically important temperatures (-40°C to 40°C), the amount of energy required varies by less than 8%. For simplicity, we will use the value of 600 calories as if it applied to this entire range.

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Introduction to Weather and Climate Science

It is also possible for the water substance to transform directly from the solid phase to the gaseous phase and vice versa. When a water molecule in the ice phase is given sufficient energy, it will break away from the ice phase and move directly to the gas phase. In order that 1 gram of ice at 0°C becomes 1 gram of water vapor at 0°C, ~680 calories of energy are required. Conversely, if 1 gram of water vapor deposits itself onto a pre-existing piece of ice, 680 calories of heat are released to the environment. This amount of heat is known as the Latent Heat of Sublimation (when the transfer is from solid to gas) and the Latent Heat of Deposition in the other case. On a planet where phase changes of a substance are routine (as with water on Earth)6, latent heats are a crucially important mechanism for transferring heat in the atmosphere. Heat is transferred to the atmosphere (which will consequently warm) anytime water is changed from a high energy to a lower energy phase. Such transformations include gas to solid (deposition), gas to liquid (condensation), and liquid to solid (fusion). Heat is required of the atmosphere (which will consequently cool) anytime water is changed from a low energy to a higher energy phase. Such transformations include solid to vapor (sublimation), solid to liquid (melting), and liquid to vapor (evaporation). Finally, it is useful to acquire some concrete sense of what these amounts of energy really mean. We can do so by asking a simple question motivated by a common winter phenomena in southern Wisconsin: How much latent heat energy is released into the atmosphere in the formation of snow sufficient to cover Dane County, WI with 5”? A reasonable assumption is that 10” of snow corresponds to 1” of melted liquid water. Thus, the 5” in this problem corresponds to 0.5” of liquid equivalent, or 1.27 cm. So a 5” snowfall is equivalent to a depth of 0.0127 m of water over Dane County. Dane County covers 3.174 x 109 m2 (square meters) in area. Therefore, 3.174 x 109 m2 x 0.0127 m of water means that we are dealing with 4.03 x 107 m3 of water (volume). Since water has a density of 1000 kg per m3, we are dealing with 4.03 x 1010 kg of water. This amount of water had to go from the vapor phase to the solid (snow) phase during the snowstorm. Thus, the latent heat of deposition (2.845 x 106 J kg-1)7 must be multiplied by this mass of water. The result is that 1.146 x 1017 Joules of energy are released to the atmosphere during the production of this much snow. There are 3.6 x 106 Joules per Kilowatt-hour (KWh). A typical January day in the Madison metro area uses 7.9 x 106 KWh of energy. Thus, the energy released to the atmosphere in producing this modest snowfall could power the Madison metro area for 402 days. Clearly, we are dealing with phenomenal amounts of energy when we are considering latent heats. Interesting as this fact is, we still need 6 Titan, a moon of the planet Saturn and the largest moon in our Solar System, has large amounts of methane (CH4) in the form of oceans, icebergs, and atmospheric vapor. Thus, CH4 plays the same role on Titan that water (H2O) plays on Earth. 7 We convert the Latent Heat of Deposition to the appropriate units in the following way: LDEP = 680

J cal 1000 g 4.184 J x x = 2.845 x 10 6 kg g kg cal

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to discuss the mechanisms by which this heat is transferred in the atmosphere. Amazingly, the story gets even more interesting.

Heat Transfer in the Atmosphere In this section we will discuss three distinct mechanisms of heat transfer in the atmosphere: Conduction, Convection, and Advection. We will begin with a discussion of Conduction.

Conduction If you were holding a metal rod at one end and stuck the other end into a fire, you would not immediately be penalized for your folly. It takes time for the heat of the fire to be transferred through the length of the rod and finally to your fingers. This is a consequence of the fact that only a certain portion of the rod is subjected to a heat source in this example. Thus, only the molecules directly in contact with the fire will react to its energy immediately. The reaction is an increase in temperature, which, by definition, will result in increased KE of the molecules. When the molecules near the end of the rod start to increase their KE, they bump into adjacent molecules and transfer some of their KE to those adjacent molecules. So long as the heat source remains applied to one end of the rod, the transfer of energy, molecule by molecule, will continue along the length of the rod, and you will eventually burn your hand. This transfer of energy molecule by molecule through a substance is known as conduction. In accord with the Second Law of Thermodynamics, the transfer of heat is from the hot end of the rod toward the cooler end. The rate of transfer is dependent on the temperature difference between the ends as well as the unique heat conducting properties of the metal being used in the experiment. Some substances can transfer heat from one molecule to another very well and are thus considered good heat conductors. The efficiency of heat conduction in a substance depends upon how the molecules are arranged in that substance. Metals or other solids are usually very good conductors of heat. Table 1.4 shows the heat conductivity of a number of common substances. Since metals are very good conductors of heat, it is often difficult to judge the temperature of metal objects by touch. In fact, a metal file cabinet at room temperature will feel very cold to the touch because it conducts the heat of your hand away from the point of contact very efficiently.

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Introduction to Weather and Climate Science

Table 1.4: Heat Conductivity of Some Substances Substance Still air Wood Water Snow Ice Wet soil Dry soil Sandstone Granite Iron Silver

Conductivity (W m-1 °C-1) 0.023 (at 20°C) 0.08 0.60 (at 20°C) 0.63 2.1 2.1 0.25 2.6 2.7 80.0 427.0

Air, on the other hand, is a very poor conductor of heat. Poor conductors of heat are known as insulators. The hair on our bodies tends to stand erect when we are cold. This allows a thin layer of air to be trapped near our skin, thus insulating us against heat loss since air is such a poor conductor of heat. In cold climates, homes with double-paned windows enjoy lower heating bills during winter as a layer of still air is trapped between the two panes of glass, thus insulating against heat loss from the interior of the home. At this point in our discussion you might be wondering: If air is such a poor conductor of heat, how does the air temperature increase after the sun rises on a summer day? The answer to this question lies in the fact that there is a much more efficient way for heat to be transferred in a fluid.

Convection If you have ever prepared a bath for yourself or someone else and found that the water is too hot, you have a couple of options to ameliorate the situation. You could turn on the cold water and let the tub cool by internal mixing. Or, if you are in a hurry, you might turn on the cold water and start mixing it around the tub with your hand. Clearly, the second option accomplishes the exchange of heat a lot faster than the first. In the second case you have relied upon heat transfer by the mixing of masses of fluids. Such a heat transfer process is known as convection; specifically, it is mechanical convection in which forced mixing is accomplished by means of an outside agent. In order to construct an explanation of the way in which the air temperature increases after sunrise on a summer day, we will have to appeal to spontaneous mixing—a process known as free convection. First, air near the Earth’s surface is unevenly heated by conduction. The unevenness is a result of the fact that the surface is covered by different objects such as water, blacktop, trees, etc. All of these different objects have different heat capacities and heat conductivities. Air

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molecules in contact with the hot spots are warmed by conduction. The heated air expands, becomes less dense than its surroundings, and rises in a bubble. This bubble exchanges heat with its cooler surroundings as it rises and cooler air rushes in to replace the air that has risen away from the surface. This cooler replacement air is then warmed by conduction and the process continues. The net result of this process is that large amounts of warm air are mixed with large amounts of cool air and the entire airmass is thus made warmer. Note that the mixing we have just described is not forced by a stirring agent but rather occurs spontaneously in response to heating of the surface and the thin layer of air in direct contact with the surface. The resulting convective mixing is much more efficient at transferring heat than the much slower and more local process of conduction. Extreme examples of convection are observed in atmospheric thunderstorms in which enormous amounts of warm air, warmed even more by the release of Latent Heat of Condensation, are able to rise to great heights in a cooler environment. You can witness convection in a pot of boiling water if you decide to cook spaghetti in it. The strands of spaghetti act as tracers in the water and can illustrate the circulation that develops as a result of the convection. Convection ovens create a circulation of hot air in which objects are cooked more thoroughly in a closed container.

Advection Finally, if you stand outside in a northwesterly wind on a winter day, you might feel the temperature drop as the day goes on. This temperature drop, measured with a thermometer, is not a result of conduction or convection. It is a consequence of the horizontal movement of colder air, carried by the winds, toward your location. This transfer of air properties by the horizontal movement of the air itself is known as advection. Advection is a rather unique heat transfer property of fluids. Transport of colder air toward City A would be termed cold air advection, as illustrated in Fig. 1.7a. If the winds were directed from the southeast, with the same background temperatures, as illustrated in Fig. 1.7b, then City A would be experiencing an importation of warmer air. In that case, we would say that City A is experiencing warm air advection.

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Introduction to Weather and Climate Science

City A N W

(a)

E S

City A N W

E

(b)

S

Figure 1.7. (a) Schematic of cold air advection at City A. Dashed lines are isotherms every 5°C. Arrows represent the direction from which the wind is coming. (b) As for Fig. 1.7a but illustrating warm air advection at City A.

Any property of the air can be advected. So it is completely proper to consider moisture advection (the advection of water vapor content), smoke or pollution advection, even locust advection! The concept of advection plays a central role in many of the arguments we will make in subsequent sections of the course, so you should make yourself comfortable with the idea.

Chapter 2 Radiative Transfer in the Atmosphere

Radiative Transfer in the Atmosphere

35

s we’ve already mentioned, upon turning your face toward the Sun on a crisp winter day your face can be warmed by the sun while the air itself is not warmed. The energy transferred from the Sun to your face is called radiant energy. Since most of the energy involved in the atmosphere/ocean system originates in the Sun, we need to discuss the properties of radiation and the radiative transfer of energy. This radiant energy travels in the form of waves that release energy when they are absorbed by an object. The waves are called electro-magnetic waves because they share properties of electricity and magnetism. One of the most important facts concerning these waves is that they do not need molecules in order to propagate from one location to another. Since most of the universe is empty space—that is, space without molecules—this is the only option available for energy transfer throughout most of the universe. Another important fact concerning electromagnetic waves is that, in a vacuum, they travel at 3 x 108 m s-1 (186,000 miles per second). This speed is known as the speed of light, and nothing can travel faster. It is sometimes hard to understand the enormity of these types of numbers. When I was a boy, I recall figuring out how long it took a flashlight beam launched from my backyard to hit the surface of the moon. I was astounded to discover, upon calculation, that it only takes 1.36 seconds. The extraordinary speed of light is, in fact, used as a means of measuring the almost unimaginable distances that characterize interstellar space. A “light year” is the distance light will travel in one

A

year. Since a year has, 365.25

days hours sec sec seconds seconds × 24 × 3600 = 31, 557, 600 that distance year day hour year

is 31,557,600 s × 3x10 8 m = 94,672,800 x 10 8 m , which converts to 5.793 trillion miles. year

s

year

These electro-magnetic waves come in a large variety of types. A convenient way to divide the whole collection is by the wavelength of each type. The wavelength (which we will signify by the Greek letter lambda, λ), is just the distance between two successive crests in the wave (Fig. 2.1). This distance is measured in micrometers, millionths of a meter (10-6 m). We will refer to such a unit of measure with the symbol μm, and will sometimes refer to the unit as a micron. One micron is about 1/100th the width of a human hair.

Wavelength (λ)

Wavecrest

Wavecrest

Figure 2.1. Schematic of an electromagnetic wave illustrating the concept of wavelength. Wavelength is measured in millionths of a meter, or microns (μm).

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Now, since all of these varieties of electro-magnetic waves travel at the same speed, the number of wave crests that pass a fixed point in space in 1 second will vary with wavelength. Consider two extremes to illustrate this point. Since the speed of light is 3x10 8 m s-1, or 300,000 km s-1, then a single wave crest of any type of electro-magnetic radiation will travel 300,000 km in one second. For radiation with a wavelength of 1 km, that means 300,000 individual wave crests will pass a fixed point in space in that 1 second. For radiation with a wavelength of 300,000 km, only 1 wavecrest will pass in that 1 second. The number of wave crests passing a fixed point in 1 second is known as the frequency of the wave. We will denote frequency with the Greek letter nu, ν. Thus, another interesting property of electro-magnetic waves presents itself; the product of the wavelength times the frequency yields the constant speed of light. In symbols: C = λυ Since we are interested in energy transfer in the current discussion, we want to know what energetic characteristics these different wavelengths of electro-magnetic radiation possess. It turns out that long wavelength radiation carries low energy and short wavelength radiation carries high energy. By extension and with reference to the above equation, high frequency radiation carries high energy and low frequency radiation carries low energy. Now that we know something about the energetic characteristics of radiation, we will explore the relationship between radiation and temperature.

Radiation and Temperature All objects with a temperature above absolute zero (0°K) emit radiation. The energy originates from the vibration of electrons that make up the object in question. It turns out that the particular wavelengths of electro-magnetic radiation that an object emits depend primarily upon the object’s temperature. This makes physical sense if we consider that the higher the object’s temperature, the faster are the vibrations of the electrons and, therefore, the higher the energy (shorter the wavelength) of emitted radiation. In fact, objects with a very high temperature emit energy at a greater intensity than objects at a lower temperature. This fact can be expressed mathematically in the Stefan-Boltzmann Law as: E = σT 4 where E is the maximum rate of emission of radiation (per square meter of surface area), σ is a constant of proportionality1 and T is the object’s temperature in K. This relationship describes 1

The constant σ is known as the Stefan-Boltzmann constant and has a value of 5.67 x 10-8 W m-2 K-4.

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a profound physical fact: a small increase in the temperature of an object can lead to a huge increase in its emitted radiation. For instance, a 33% increase in the amount of emitted radiation occurs when an object’s temperature is increased modestly from 273°K to 293°K. Alternatively, we can consider the enormous difference in emitted energy between the Sun (whose average surface temperature is 6000°K) and the Earth (whose average surface temperature is 288°K). The Stefan-Boltzmann Law reveals that the Sun emits an astounding 188,380 times more energy over each square meter of its surface than does the Earth. Though the Stefan-Boltzmann Law tells us an important quantity—how much energy is emitted by an object based upon its temperature—we might also want to know what type (wavelength) of radiation constitutes the bulk of the emission from a given object. Amazingly, there is a means to do exactly this and it is based upon the fact that an object having a temperature, T, will generally emit radiation at all wavelengths. The amount of radiation emitted at wavelength, λ, however, is strictly determined by T. The physical development of this relationship is beyond the scope of our course, but Wein’s Displacement Law states that the wavelength of maximum emission of an object is related to the object’s temperature as

λmax =

2897 3000 ≈ μm T T

where λmax represents the wavelength of electro-magnetic radiation at which the largest fraction of the object’s total radiative energy is emitted. In the light of Wein’s Law, consider the λmax for the Sun and the Earth. For the Sun, λmax = 3000 / 6000 = 0.5 μm. This means that the Sun emits most of its energy at wavelengths near 0.5 μm. For the Earth, λmax = 3000 / 288 ≈ 10 μm, which means that Earth emits most of its energy near 10 μm. For this reason the Earth’s radiation is often referred to as longwave radiation. Analogously, the Sun’s radiation is often referred to as shortwave radiation. It is important to note that although Wein’s Law tells us the wavelength of maximum emission for an object, all objects with a T > 0K emit radiation over a spectrum of wavelengths. This important point is illustrated by considering the emission spectra of both the Earth and Sun, shown in Fig. 2.2. Our eyes are sensitive to wavelengths ranging from 0.4 to 0.7 μm, what is known as visible light. The Sun emits 44% of its radiation at these wavelengths. The shortest visible wavelengths (0.4 μm) are violet light. Thus, electro-magnetic waves with wavelengths shorter than 0.4 μm are known as ultra-violet light. The longest visible wavelengths (0.7 μm) are red light. Electro-magnetic waves with wavelengths longer than 0.7 μm are known as infra-red light. Clearly, Earth emits almost all of its energy at infra-red wavelengths. Later we will see that the difference in wavelength between solar and terrestrial radiation has important implications for how the Earth is heated and cooled by radiation.

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Ultraviolet

Infrared

V isible

Blackbody radiation for the Sun

300 200

Actual radiation for the Sun

Radiation Intensity (W m-2 μm-1)

100 50 30

20

Blackbody radiation for the Earth

5 3

Estimated emission from the Earth

2

Absorption by CO2,H20, CH4 and other gases

1 0.5 0.3 0.2 0.1 0.1

0.2

0.5

1.0

2.0

5

10

20

50

100

Wavelength (μm)

Figure 2.2. Emission spectra of the Sun and Earth. Shaded regions indicate portions of the EM spectrum in which the atmosphere does very little absorbing of radiation.

Radiation and temperature change At this point in our discussion it might be reasonable to ask why doesn’t everything just get progressively colder with the passage of time given that Earth and everything on it are continuously radiating energy? The answer is rather simple. Objects not only radiate energy away, they can also absorb energy. In fact, only if an object radiates more energy away than it absorbs will it get colder. If, on the other hand, an object absorbs more energy than it radiates away, it will get warmer. If the amount of absorbed energy is exactly equal to the amount of emitted energy, a condition known as radiative equilibrium, an object’s temperature will not change. How well an object absorbs radiation depends on the nature of its surface characteristics, its color, or its texture, among other attributes. For instance, if you have ever traveled to the southern United States, you may have noticed that roads are not paved with blacktop as they are in many of the northern states. This is because a blacktop road (by virtue of its color) would suffer from excess absorption of the more intense solar radiation in Florida. One final radiation law will arm us for other coming discussions. Kirchoff’s Law states that an object’s efficiency of absorption of a certain wavelength of energy is exactly equal to its emission efficiency at that same wavelength. Thus, if an object is a good absorber at a certain

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wavelength, it will also be a good emitter at that wavelength (provided its temperature allows it to emit a substantial amount of energy at that wavelength). A perfect absorber is an object that absorbs all of the radiation that strikes it with 100% efficiency. Such an object must also be, by Kirchoff’s Law, a perfect emitter (that is, an object that, for its given temperature, emits the maximum possible radiation). Any object that is a perfect absorber and a perfect emitter is called a black body. The Earth’s surface and the Sun absorb and emit with nearly 100% efficiency for their temperatures and so are both considered black bodies. Physically, this means that the Earth’s surface absorbs all of the shortwave solar radiation that strikes it. Upon absorbing this radiation, the temperature of the Earth’s surface increases. At its new temperature, it is able to emit an amount of longwave radiation specified by the Stefan-Boltzmann Law, at a preferred wavelength determined by Wein’s Displacement Law. If we imagine Earth as a bald rock in space being subjected to absorption of solar radiation over half of its surface and emitting infra-red over its entire surface, as depicted in Fig. 2.3, we can imagine a state of radiative equilibrium becoming established over time. In such a case, the amount of shortwave solar radiation absorbed at the surface is exactly equal to the amount of infra-red radiation emitted from the surface. The temperature of the surface at which this equilibrium is reached is known as the radiative equilibrium temperature. The radiative equilibrium temperature of the Earth is 255°K, or 0°F. This might strike you as colder than you would have guessed. There is a good reason for that surprise; the actual observed average temperature of the surface is 288°K, or 59°F.

EARTH

Figure 2.3. Schematic of Earth illustrating the fact that the Earth absorbs shortwave solar radiation (light arrows) over only half of its surface at any time whereas it emits longwave IR radiation over its whole surface all the time.

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What accounts for this astounding and significant difference? Our atmosphere, the thin layer of gas that surrounds the bald rock of the Earth and accounts for the subject of this course, is an object with a temperature above 0°K. Therefore, the atmosphere also emits and absorbs radiation. Unlike the surface of the Earth, however, the atmosphere does not behave like a black body. In fact, it absorbs some wavelengths of electro-magnetic radiation and is totally transparent to others. Any object that absorbs and emits only some wavelengths of electro-magnetic radiation is known as a selective absorber. The Earth’s atmosphere is composed of a number of selectively absorbing gases. This means that there are wavelength regions in the electro-magnetic spectrum in which our atmosphere is transparent—in other words, regions in the spectrum in which none of the constituent gases absorb radiation. Such wavelength regions are known as atmospheric windows. The regions of low emittance shown in Fig. 2.2 reflect the presence of gases such as H2O, CO2, and others that absorb outgoing infra-red radiation. Notice that there is very little absorption of radiation in the wavelengths from 0.3 to 0.7 μm. This wavelength band corresponds to the visible spectrum. Thus, we conclude that the atmosphere is almost entirely transparent to visible light, which, recalling the discussion of Wein’s Displacement Law, is precisely the wavelength band in which the Sun emits most of its radiation. Longwave infra-red radiation in the wavelength band from 8 to 11 μm is similarly only weakly absorbed by the atmospheric gases. This wavelength band is approximately the one in which most of the Earth’s longwave radiation is emitted. However, the atmosphere is transparent to only some infra-red radiation, as some of the gases in the atmosphere, notably water vapor (H2O), carbon dioxide (CO2), and methane (CH4), are good absorbers of certain wavelengths of infra-red radiation. By Kirchoff’s Law, these same gases must also be good emitters of those wavelengths. We will next investigate the consequences of the presence of selectively absorbing gases in an atmosphere.

The Effect of an Atmosphere on Surface Temperature In order to understand the effect that an atmosphere composed of selectively absorbing gases has on the average surface temperature of a planet, we consider two scenarios. First, imagine a hypothetical planet without an atmosphere whose surface behaves as a blackbody (Fig. 2.4a). We might refer to this planet as a cue-ball planet since it can be thought of as a bald rock. Let the amount of incoming solar radiation on this planet be denoted by S. The amount of outgoing infra-red radiation emitted by the surface, Ec, has a direct correspondence to the surface temperature via the Stefan-Boltzmann Law. Radiative equilibrium on such a planet occurs when the incoming solar radiation equals the outgoing infra-red radiation. In symbols this can be expressed as S = Ec.

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41

From the Stefan-Boltzmann Law, the surface temperature of this cue-ball planet is related to Ec by Ec = σTc4 so that Tc ∝ Εc where Tc is the surface temperature of the cue-ball planet.

S Ec

(a)

Surface of Planet

S

A

0.2 Ea

Atmosphere

S

A Surface of Planet

Ea

(b)

Figure 2.4. (a) Radiation balance on the cue-ball planet. (b) Radiation balance on the planet with a selectively absorbing atmosphere. See text for complete explanation.

Now, let us imagine that this same planet has an atmosphere that is 1) transparent to solar radiation, and 2) translucent to infra-red radiation (Fig. 2.4b). Since the planet is the same distance from the source of solar radiation as the cue-ball planet, the amount of incoming solar radiation at the top of the atmosphere is S. Since the atmosphere is transparent to solar radiation, the amount of incident solar radiation at the surface of the planet is also S. The amount of infra-red radiation emitted by the surface we will designate as Ea. And since the hypothetical atmosphere in this problem absorbs some infra-red, only a fraction (20% in this example) of the emission from the surface will make its way through the atmosphere to space.

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The remaining fraction of Ea is absorbed by the atmosphere, which will also emit an amount of radiation, A, both upward and downward. Since the atmosphere is an object just like the surface of the planet, we must consider radiative equilibrium expressions both at the top of the atmosphere and at the surface (the top of the solid planet). At the surface, there is incident solar radiation, S, as well as infra-red radiation from the overlying atmosphere, A. This amount is balanced by the outgoing infra-red radiation from the surface, Ea. In symbols this is expressed as S + A = Ea. At the top of the atmosphere, there is incident solar radiation, S. This is balanced by the outgoing infra-red radiation from the atmosphere, A, as well as a fraction of the outgoing infra-red emitted at the surface, 0.2 Ea. (We have assumed that 80% of the outgoing infra-red emitted at the surface has been absorbed as by the atmosphere.) In symbols this is expressed as S = 0.2 Ea + A which, for convenience, can be rearranged into S – A = 0.2 Ea. Now, we can solve this system of two equations rather simply for a relationship between S and Ea.

S + A = Ea S − A = 0.2 E a 2S

=1.2 E a

Thus, we find that S = 0.6 Ea. Now, remember that for the cue-ball planet we found that S = Ec. Therefore, it must be true that 0.6 Ea = Ec. Consequently, Ea has to be greater than Ec. If Ea is greater than Ec, then by the Stefan-Boltzmann Law, Ta, the surface temperature of the planet with an atmosphere, has to be greater than Tc, the cue-ball temperature. Thus, the surface temperature of a planet with an atmosphere composed of selective absorbers is greater than the surface temperature it would have if it had no atmosphere. This retention of infra-red radiation by the atmosphere is colloquially known as the greenhouse effect. It accounts for the whopping 33°K difference between the Earth’s radiative equilibrium temperature (the Earth’s cue-ball temperature) and the actual observed average surface temperature of the Earth. If our average surface temperature were not above 273°K, a value which itself is 18°K above the radiative equilibrium temperature of Earth, water might not be abundantly available in the liquid form and life on Earth would perhaps never have evolved. As you can see, this thin little blanket we call the atmosphere is remarkably important to our very existence.

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43

To be perfectly accurate, the atmosphere’s retention of infra-red radiation should be called the atmospheric greenhouse effect. Actual greenhouses remain warm because the greenhouse does not allow colder, outside air to mix with the warmer air inside the house. The extra warmth provided by our atmosphere is purely a consequence of the physics of radiative transfer and has nothing to do with a restriction on mixing. Despite this physical difference, the term greenhouse effect has a firm footing in modern discussions of this phenomenon and may be difficult to dislodge. Earth is not the only planet whose atmosphere exerts an atmospheric greenhouse effect. Our nearest planetary neighbor, Venus, also possesses a substantial atmosphere. In fact, the Venusian atmosphere is much more massive than our own (800 times as massive!). Venus is closer to the Sun and is shrouded in sulfuric acid clouds (H2SO4), which reflect nearly all of the incoming solar radiation. As a consequence, very little of the solar radiation that strikes the top of the Venusian atmosphere penetrates to the surface of the planet. The massive atmosphere of Venus is composed of enormous amounts of carbon dioxide (CO2)—in fact, 95% of the Venusian atmosphere is CO2. As we have seen, CO2 is a very good emitter and absorber of infra-red radiation. As the Venusian surface absorbs the meager solar radiation that penetrates through the sulfuric acid clouds, its temperature increases and it emits infra-red radiation. The 95% CO2 atmosphere above the surface absorbs nearly all of that infra-red radiation, prohibiting nearly all of it from ever leaving the atmosphere. As a consequence, radiative equilibrium is met at the Venusian surface only after the surface temperature rises to 750°K! The radiative equilibrium surface temperature (or cue-ball temperature) of Venus is, by contrast, only 320°K. The effect of a 95% CO2 atmosphere on Venus is that its average surface temperature is 430°K higher than its radiative equilibrium temperature. This extraordinary atmospheric greenhouse effect is perhaps the signature example of what is known as the runaway greenhouse effect. Dire consequences can arise from an increase in so-called greenhouse gases in an atmosphere. Our prior discussion has highlighted H2O, CO2, and CH4 as among the primary greenhouse gases in the Earth’s atmosphere. Much of the current debate concerning the specter of global warming centers around linking the rate of observed warming over the last 150 years to the increased presence of anthropogenic (i.e. human induced) CO2 in the atmosphere. Much of this increase in CO2 is suggested to have resulted from the energetic by-products of the industrial revolution. A continuous measurement of the CO2 content of the atmosphere has been made at Mauna Loa Observatory in Hawaii since 1958, under the supervision of Dr. Charles Keeling2. These observations have resulted in the famous “Keeling curve,” which is illustrated in Fig. 2.5. The measurements show a steady increase in average CO2 concentration from about 315 parts per million (ppm) (i.e. 315 molecules of gas out of every 1 million are CO2 molecules) in 1958 to 385 ppm in 2008. The observations also show an annual variation of about 5 ppm that corresponds to the seasonal cycle of CO2 uptake by the world’s vegetation—most of which is in the Northern Hemisphere. 2

Keeling died in 2005, and the measurements are now supervised by his son, Ralph.

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Introduction to Weather and Climate Science

CO2 Concentration (ppmv)

390 380 370 360 350 340 330 320 310 1960

1970

1980

1990

2000

2010

Figure 2.5. Time series of atmospheric concentration of CO2 measured at Mauna Loa, Hawaii, from 1958–2010—the so-called Keeling Curve. Thin black line is the time series while the superimposed bolder gray line is the annual average calculated from the time series. The annual cycle of CO2 in the Northern Hemisphere, corresponding to the growing season (minimum) and cold season (maximum) is clearly evident in the time series.

A reasonably reliable instrumental record of surface temperatures exists back to about 1850. The data from these measurements shows a surface temperature increase, averaged over the globe, of about 0.74°C (1.33°F) during the last 100 years. This increase has been referred to as “global warming.” The evidence for human influence on this most recent global warming is considerable and multi-dimensional. For instance, though the reservoir of O2 in our atmosphere is vast, as we’ve already seen, it is not unchanging. In fact, in the last 20 years, the O2 content has decreased roughly in proportion to the amount of fossil fuels that have been burned (precise measurements of which are available, since these fuels are the inventory of a global business enterprise). We run no risk of serious O2 depletion but this example illustrates how the trail of evidence clearly points to industrialization as a substantial factor in the recent CO2 increase and its physical influence on raising the global average temperature. Of course, the climate of the Earth is determined by a complicated, interconnected system of physical processes of which CO2 concentration and its radiative effects is only one. Many of the relevant physical processes are related to one another via feedbacks, which makes the problem even more complicated. An example is the so-called “water vapor feedback,” which is

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45

conceptualized as follows. As the CO2 concentration increases and leads to a warmer average temperature, the warmer atmosphere can increase the amount of water vapor it holds. Water vapor is a primary greenhouse gas, and so an increase in H2O vapor content exacerbates the warming instigated by the CO2 increase in what is known as a positive feedback. To the extent that more H2O vapor might also mean increased cloudiness, a cloudier planet might reflect more solar radiation away to space, which would act to cool the Earth—a negative feedback. This one example highlights how enormously complex is the problem of determining how the Earth/atmosphere system will respond to subtle changes in the chemical composition of the atmosphere. Over the last 50 years or so, scientists have spent considerable amounts of energy developing computer models that attempt to simulate such interactions mathematically in order to arrive at projections of the future behavior of the atmosphere. During this time, the precision of these numerical models has greatly increased, as has our confidence that they can inform us about the nature of the multifarious physical interactions that shape the Earth’s climate system. Based upon the output from these models, current best estimates for further warming are suggesting that between 2 and 5°C additional global average temperature increase is likely in the next 50–100 years if the present rate of input of greenhouse gases remains unaltered. The atmosphere is complex enough that even today’s state-of-the-art numerical forecast models cannot fully account for all of the physical feedbacks that may actually occur in nature. Despite their limitations, however, they are without a doubt the best tools we have for peering into the long-term future of the climate—a future in which continued increases in greenhouse gases will unequivocally alter the natural radiative balance of Earth in such a way as to promote a warming of the planet. In many locations on Earth, temperatures change dramatically within a single calendar year. Such changes are associated with the progression of the seasons. We next investigate the physical factors that underlie the seasonal cycle on Earth.

Why the Earth has Seasons In order to discuss this interesting issue, we must first define some terms that will be used in the discussion. First, the Earth’s axis is an imaginary stake that runs through the Earth from the North Pole to the South Pole. The Earth is said to rotate on its axis through one complete revolution every 24 hours. We commonly refer to this amount of time as a day. Second, the Earth is said to revolve around the Sun one revolution every 365.25 days, what we commonly refer to as a year. The Earth revolves around the Sun in an elliptical, not circular, orbit. As a result, the Earth finds itself slightly closer to the Sun in January than in July (see Fig. 2.6). If you live in the Northern Hemisphere, this might strike you as counter-intuitive based upon your own life experiences.

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147 M km

152 M km

Sun

January

July

Figure 2.6. Schematic of the Earth and its distance from the Sun at the two extremes in its orbit.

For instance, if you have ever sat near a fire, you can testify that the closer you are to the flames, the warmer you feel. This follows from the fact that the intensity of radiation you feel from the fire varies as the inverse of the square of the distance you are from the fire. Since the Earth is closer to the Sun in January, a reasonable question might be: Why is it hotter in July than in January? Clearly, there are other factors involved in shaping the July and January temperatures than just the Earth’s distance from the Sun. It turns out that the seasons are regulated by the amount of solar radiation that is received at the Earth’s surface. This amount, in turn, is regulated by two somewhat interrelated factors: the angle of incidence and the length of the day. Angle of incidence is defined as the angle at which the Sun’s radiation strikes the surface. A simple experiment can prove that the greater the angle at which radiation strikes the surface (see Fig. 2.7), the more the intensity is reduced by virtue of the fact that the energy from the radiation is spread over a larger area. On a perfectly sunny day, the Sun is more intense at noontime, when the angle of incidence is high (i.e. the solar zenith angle, the angle between the local vertical and the incident radiation, is low), than it is near sunset when the angle of incidence is low. This fact is in line with our colloquial sense that the Sun is more intense at noontime. wall

(a)

wall

(b)

Figure 2.7. Depiction of the effect of angle of incidence on intensity of radiation. Flashlight is the same distance from the wall in (a) and (b) but the area over which the radiation is spread in (b) is larger because of the low angle of incidence.

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Regardless of the intensity of radiation a specific location might receive at noontime, the total amount of radiation absorbed at the location during one day will depend on how long the Sun is up during that day. Thus, the length of the day is a crucial factor in determining the amount of radiation that a given location receives. These two factors are not independent of one another because the Earth is tilted on its axis at a 23.5° angle to the plane in which it revolves around the Sun (Fig. 2.8), the so-called plane of the ecliptic. On or about June 22 (the Summer Solstice) of each year, the Northern Hemisphere is pointed maximally toward the Sun. As a consequence, the longest day of the year occurs then at latitudes north of 23.5°N and the noontime angle of incidence is as high at such locations as it will ever be during the year. Six months later, on or about December 22 (the Winter Solstice), the Southern Hemisphere points maximally toward the Sun. As a consequence, the shortest day of the year occurs then at latitudes north of 23.5°N, and the noontime angle of incidence is as low at such locations as it will be all year.

Sept. 21 Autumnal Equinox Dec. 22 Winter Solstice

SUN June 22 Summer Solstice March 21 Vernal Equinox

Figure 2.8. Path of the Earth around the Sun with dates of the Solstices and Equinoxes indicated. Thick dashed line through the Poles is the Earth's axis. Thin dashed line is the Equator. Shading indicates region of Earth on which no sunlight falls.

High latitudes in the Northern Hemisphere experience long days during the summer. In fact, north of 66.5°N, the sun does not set at all on the day of the summer solstice. Fairbanks, Alaska, is famous for its all-night softball tournament on July 4 every year. Many of those games are played without artificial lighting in this “Land of the Midnight Sun.” One might be led to believe that since the day is so long near the summer solstice at these high latitudes, the amount of absorbed solar radiation must be a maximum at these latitudes as well. In fact, within a week or two of the summer solstice, it is true that the maximum absorbed solar radiation occurs at the pole even though the angle of incidence is quite low throughout the entire day.

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Northern winter is characterized by just the opposite situation. On the day of the solstice, the Sun does not rise north of 66.5°N (the Arctic Circle). At lower latitudes the angle of incidence is low and much of the ground is covered with snow, which reflects large amounts of the incident solar radiation3. The combination of long nights, reflection by snow, and low Sun angle during the day leads to the formation of frigid arctic air masses in northern Canada, Siberia, and Alaska. The progression of the Sun throughout the year is summarized in Fig. 2.9. On (or about) June 21, the Sun is directly overhead at noontime at 23.5°N (the Tropic of Cancer). It moves southward on every successive day over the next six months, reaching the Equator, where it is directly overhead at noontime, on (or about) September 21. The dates on which the Sun is directly overhead at the Equator are known as equinoxes, as the length of day is identical everywhere on Earth on those days. The autumnal equinox takes place at the end of Northern Hemisphere summer. On (or about) December 21, the Sun is directly overhead at noontime at 23.5°S (the Tropic of Capricorn). This is as far south as the Sun will progress, and it moves northward each day for the next 6 months, arriving directly overhead again over the Equator on (or about) March 21. This last event is known as the Vernal Equinox.

The Seasonal Temperature Lag If we use the 50 United States as a proxy for the meteorological behavior of the rest of the middle latitudes on Earth, a very interesting fact arises from inspection of temperature records. When one considers the all-time high temperatures in each of the 50 states and the calendar date on which each was set, the record shows that 35 out of the 50 states recorded their all-time high temperature at least 3 weeks after the Summer Solstice. Remember that the Summer Solstice is the day on which the highest angle of incidence and longest day of the year occur. This combination of circumstances makes the Summer Solstice the date of maximum absorption of solar radiation for every location in the Northern Hemisphere middle-latitudes. Why do 70% of locations experience a lag between the date of maximum absorption of radiation and the warmest day? This so-called seasonal temperature lag has a solid physical explanation.

3

Throughout the foregoing discussion we have been referring to the amount of radiation incident at the top of

the atmosphere. Of course, clouds, snow, and various other surface characteristics will also determine how much of this maximum possible amount might be reflected away from the surface.

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June 21

Sept. 21

March 21

Equator

December 21

Figure 2.9. The dates and latitudes at which the Sun is directly overhead at noontime in a calendar year.

The amount of outgoing infra-red radiation is completely controlled by the surface temperature of the planet. Even though the incoming solar radiation is maximized on or about June 21, the temperature of the Northern Hemisphere is controlled, to a large extent, by how ocean temperatures respond to the incoming solar radiation. Since water has a high specific heat and most of the hemisphere is covered by oceans, the response time is rather slow—i.e. it takes time to warm the hemisphere because of all the water. Thus, the incoming radiation exceeds the outgoing radiation for weeks after the solstice. So long as the incoming solar radiation exceeds the outgoing infra-red radiation, more energy is put into the system than is radiated away. Naturally, the average temperature at a location can continue to rise each day until finally the incoming radiation (now diminished some weeks after the solstice) is equaled by the outgoing infra-red (increased as the summer warms up). A similar seasonal temperature lag occurs in the winter as evidenced by the same kind of data. Record low temperatures have been set more than three weeks after the winter solstice in 39 of the 50 United States. A similar argument underlies this observation. The shortest day and lowest angle of incidence occurs on (or about) December 21. As a result, the minimum incoming shortwave radiation at every location in the northern Hemisphere midlatitudes occurs on that date. Since it takes time for the Hemisphere to cool off (again, thanks to the abundant liquid water covering the majority of the surface), the outgoing infra-red exceeds the incoming solar radiation for sometime after the solstice. So long as this remains the case, more energy is radiated away than is replenished by sunshine. Thus, the temperature will continue to fall until the ever-shrinking outgoing infra-red radiation finally becomes as small as the incoming

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Introduction to Weather and Climate Science

solar radiation (which grows each day after the solstice). We will see that similar energy budget arguments will be made to explain the daily temperature cycle.

The Global Distribution of Radiative Energy Figure 2.10 shows the distribution of annual-average radiative energy in latitude bins from pole to pole. The thick black line represents the yearly-average incoming solar radiation while the dashed line represents the annual-average outgoing radiation. Intersection of the two lines indicates that the amounts of incoming and outgoing radiation are balanced. These balance points occur near 30° in each hemisphere. The high latitudes (i.e. locations poleward of 30°) in each hemisphere, by virtue of the fact that more energy is radiated away than is absorbed there in the course of a year, run an annual deficit of radiative energy, while the tropical regions in each hemisphere run a surplus of radiative energy. Now, in the face of the observation that the tropics do not systematically get warmer with each year and the high latitudes do not systematically get cooler with each passing year, there must be some mechanism(s) to transfer the surplus energy of the tropical regions to the deficit regions at high latitudes. How is this energy transfer accomplished? Nature has several tricks up its sleeve.

Radiant Energy in One year

Solar IR

NP

SURPLUS DE

T

ICI

F DE

EQ

FIC

IT

SP

Latitude

Figure 2.10. Amount of incoming solar radiation absorbed (solid line) and outgoing IR radiation emitted (dashed line) over the course of one year at each latitude on Earth. Dark shading represents radiative surplus regions while lighter shading represents the radiative deficit regions. Thirty percent of the necessary transfer is accomplished in a particularly ingenious manner: by latent heat. We have already seen that energy is required to change the phase of the water substance. Some of the surplus energy in the tropics is used to evaporate water (a job that requires energy). The newly created water vapor is then transported, by the winds, to higher latitudes where it may condense back into the liquid phase. When vapor condenses, the latent heat of

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condensation is released into the environment. Thus, the energy that was expended in the tropics to evaporate the water is released in the middle-latitudes through the condensation process. Forty percent of the surplus energy is transported to the high latitudes in the circulations associated with midlatitude cyclones. These storms are organized circulation systems, covering millions of square kilometers, which transport warm air poleward and polar air equatorward. In so doing, the tropics are made cooler and the higher latitudes are made warmer in a transfer of so-called sensible heat, the kind you can sense directly. The nature of these midlatitude cyclones will be a topic of inquiry for us in Chapter 4. Finally, the vast oceans that cover our planet contribute 30% of the necessary transfer through ocean currents. In the Northern Hemisphere the warm Kuroshio and Gulf Stream currents usher huge amounts of warm water northward. Since water has a high specific heat, it only slowly loses heat along its slow journey northward. The California current along the west coast of North America is an example of a cold current that transports cooler water toward the Equator. The net result of such currents is, as in the case of the mid-latitude cyclones, to cool the tropics and warm the high latitudes.

The Daily Temperature Cycle I had a morning paper route as a boy, and so I kept my eye on the morning temperatures. Often waking at 5:30 a.m. to get the papers done by 7 a.m., I would leave my house before the sun was up and arrive home just about the time it was coming up. On many days I noticed that the minimum temperature would actually occur only after I got back home, by which time the sun had just recently risen over the horizon. How could the temperature continue to drop after the Sun had peaked over the horizon? I wondered. Years later, this perplexing observation finally made physical sense. As we have already seen, any object will experience a temperature decrease if it emits more radiation than it absorbs. At night, the Earth’s surface emits infra-red radiation, but since the Sun is not shining, it absorbs very little radiation (in fact, it only absorbs the infra-red that is emitted by the atmosphere downward toward the surface). Thus, the Earth’s surface cools all night long. When the sun finally peaks over the horizon, the Earth is still emitting a good amount of infra-red radiation. In fact, it is still emitting more than it absorbs from the first faint rays of sunshine at dawn. Not until the incoming solar radiation grows larger, some time after sunrise, does the incoming radiation finally equal the outgoing infra-red radiation. At that precise moment, the temperature will have reached its minimum value, for in the next minute, the incoming solar radiation will be larger than the outgoing infra-red, and so absorption will exceed emission and the temperature will rise as a consequence. A similar argument can be made to explain the reason why the maximum daily temperature is often recorded some hours after noontime. The early afternoon maximum might seem equally counterintuitive given that the maximum incoming solar radiation for any given day will occur

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at noontime. This is when the sun is at its highest angle of incidence. Despite the fact that the maximum in incoming solar radiation occurs at noontime, the incoming radiation usually still exceeds the outgoing for a few hours. Remember that the outgoing radiation is a function of the surface temperature, which responds to the incoming solar radiation only over some amount of time. The maximum temperature will occur when the surface has heated sufficiently that the outgoing infra-red radiation finally equals the incoming solar radiation. Since by this time the incoming radiation is getting smaller with each passing moment, in the next second the incoming will be exceeded by the outgoing and the temperature will begin to fall. This often occurs between about 2 and 5 p.m. local time on a sunny, breezy, summer day. A number of physical factors have not been accounted for in the foregoing argument, and their inclusion would surely change the results. For instance, if clouds develop during the early part of the day, the maximum temperature will be reached earlier. The same result often occurs in locations adjacent to large bodies of water, where afternoon sea breezes develop and tend to lower afternoon temperatures. Temperature advection associated with organized storms can overwhelm the local radiation and lead to a maximum temperature for the day at just about any hour. Surface wetness can lead to a later high, as some of the energy absorbed earlier in the day must be used to evaporate water rather than increase the surface temperature. Finally, humidity and haze tend to retard the amount of direct solar radiation absorbed at the surface at a specific location. An interesting consequence of this fact is that the record high temperature in Miami, Florida, consistently humid and hazy during summer, is lower than the record high for Madison, Wisconsin. On very still, clear nights during winter when the night is long, the ground (which behaves like a blackbody) can cool much faster than the air above it. As a consequence, the temperature is lowest near the ground at dawn on such days. The resulting temperature inversion is specifically known as a radiation inversion, as it forms as a direct result of the more efficient radiation of energy by the solid ground. This effect is exacerbated by the presence of snow on the ground in the winter, as snow is an excellent absorber and emitter of infra-red radiation.

Controls of Temperature The characteristic average temperature for a given location on Earth depends on a number of physical factors. Chief among these is the latitude of the location, as that determines both the angle of incidence of solar radiation and the length of day, as we have already seen. There are a number of non-radiative factors as well. The proximity to water makes a huge difference in the thermal characteristics of a location. For instance, Portland, Maine, and Minneapolis, Minnesota, are both at the same latitude, but the winter is much colder in Minneapolis. This is because the Atlantic Ocean, near Portland, is an enormous heat reservoir during the winter. Ocean currents are another major factor that influences the average temperature of a given location. Edinburgh, Scotland, is at the same latitude as Moscow, Russia (~ 55.8°N), but

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Edinburgh is at the eastern end of the warm Gulf Stream current and so enjoys winters that are much milder than one might expect at such a high latitude. Finally, elevation above sea-level is also a factor in determining the average temperature. Mauna Loa (4168.7 m) and Honolulu (5.5 m) in Hawaii are both at the same latitude and are near the ocean. Nonetheless, Mauna Loa is much cooler year round than Honolulu because of the significant differences in elevation between the two locations.

Scattering of Radiation We have already seen that solar radiation can be absorbed by, reflected by, and transmitted through objects. As it turns out, radiation can also be scattered by contact with an object. We have all used a mirror at one time or another and so are likely quite familiar with the concept of reflection of radiation. In formal terms, reflection occurs when a wave of electromagnetic radiation, incident upon an object at some angle of incidence, bounces off that object at the same angle (Fig. 2.11a). It is, however, quite possible that an incident wave of electro-magnetic radiation will bounce off the object at an angle different from the angle of incidence (Fig. 2.11b). When light bounces off an object at any angle that process is known as scattering. Based upon these two definitions, then, reflection is a particular type of scattering.

α

α

Reflection

(a)

Scattering

(b)

Figure 2.11. (a) Schematic of reflection in which the incident radiation leaves the obstacle at the same angle, α, at which it strikes the obstacle. (b) Schematic of scattering in which the incident beam of radiation bounces off the obstacle at any angle. The particular angle that meets the definition of reflection is indicated in light gray. In both pictures the incident beam of radiation is the bold dashed line.

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When radiation is scattered by an object, the object absorbs none of the radiation—it simply sends it off in another direction after contact. In the atmosphere, scattering is caused by, among other things, air molecules, dust particles, water vapor molecules, liquid water droplets, a variety of ice crystals, and pollutants. It turns out that cloud droplets with a radius of 20 μm can scatter all wavelengths of visible light equally (i.e. without preference for any particular wavelength). As a consequence of this fact, clouds (which are largely composed of such tiny liquid water droplets) appear white. This results from the fact that the incident visible light that enters the top of the cloud (i.e. the sunlight) is made up of an infinity of discrete wavelengths, each of which corresponds to a different “color” in the visible spectrum. Since the cloud droplets constituting the cloud scatter each of these myriad wavelengths equally, your eye receives equal amounts of each color upon looking at the cloud. With no particular color predominating in such a view, your brain “sees” white. In fact, as a cloud grows thicker, its bottom appears gray and then black. This is because in a deep cloud the radiation incident at the top of the cloud is scattered out of the sides of the cloud before it can reach the bottom. The absence of visible radiation reaching the bottom renders that part of the cloud dark. Just as molecules of gas in the atmosphere are selective absorbers of radiation, they are also selective scatterers. In fact, the molecules in the Earth’s atmosphere (predominantly N2 and O2, as we have seen) scatter short wavelengths of visible light best. The amount of radiation that is scattered depends upon both the size of the particles doing the scattering and the size of the wavelengths of radiation that are being scattered. A baseball analogy may help make this important interaction more conceptually clear. The primary responsibility of the infielders on a baseball team is to catch ground balls and throw base runners out. The difficulty of catching a ground ball depends both on the type of ground ball and the condition of the field. In my experience as a baseball player, there were two broad categories of ground balls: 1) the high bouncing ball and 2) the low bouncing ball. The high bouncing ball makes contact with the ground only a few times as it approaches the infielder, while the low bouncing ball makes considerably more frequent contact with the ground over the same distance. These two varieties of bounce are illustrated schematically in Fig. 2.12. By analogy, one might be tempted to call the high bouncing ball a “long wavelength” bounce and the low bouncing ball a “short wavelength” bounce. In order to catch the ball, the infielder has to predict its path accurately and position her glove at the end of that predicted path. Given that the ground is populated by pebbles and other such objects, the difficulty of this task varies according to the type of bounce and the size of the pebbles. The high bouncing ball is not as likely to bounce off (i.e. be “scattered off”) the path predicted by the infielder as is the low bouncing ball because it has fewer interactions with the pebbles on the ground. If the size of the pebbles is decreased to zero, there is likely to be zero “scattering” of ground balls of either type. On the other hand, if the size of the pebbles is substantially increased, the paths of both types of ground balls would become unpredictable and fielding would be impossible. In a similar way, the interaction of wavelength with particle size determines the characteristics

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(a)

(b) Figure 2.12. (a) A high bouncing ball on a pebble-strewn infield makes infrequent contact with the obstacles and is less likely to be scattered off of its original path. (b) A low bouncing ball hit over the same set of obstacles makes frequent contact with the obstacles and is more likely to be scattered off of its intended path. The discussion in the text ties this analogy to the relationship between wavelength and particle size in determining scattering of radiation by the atmospheric gas.

of scattering of visible light in the atmosphere. It turns out that our atmosphere scatters short wavelengths (violets, blues, and greens) best. At the same time, our eyes are more sensitive to blue light. Therefore, since the N2 and O2 molecules are preferentially scattering short wavelengths of radiation in all directions as those wavelengths make contact with the molecules, the sky appears blue. On humid summer days you might have noticed that the sky can turn a milky white color. This is also a consequence of scattering, but scattering of light by different particles. On humid days, haze particles form. Haze particles are tiny liquid water drops whose size depends upon the amount of water vapor in the air (i.e. the humidity). On particularly humid days, these haze particles can grow to nearly the size of cloud droplets (20 μm in diameter). Hence, they scatter all wavelengths of visible light equally, and the sky, filled with these haze particles, appears white. Another optical phenomena we all experience is the reddish sky at sunrise or sunset of a clear day. This is also a consequence of scattering in the atmosphere. At midday, when the sun is as high in the sky as it will be all day, the angle of incidence is high, and so the column of atmosphere through which the solar radiation must pass is as short as it will be all day (Fig. 2.13). At sunrise or sunset, the angle of incidence is as low as it will be all day, and so the column of atmosphere through which the solar radiation has to pass is as long as it will be all day. Since the short wavelengths are being scattered by the presence of N2 and O2 in the atmosphere at all times of the day, it stands to reason that if the path-length through which

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the solar radiation must pass is long, then a larger fraction of the short wavelength radiation (violets, blues, and greens) will be scattered out of the path before the beam of light makes contact with the ground. If the short wavelengths are scattered out, then only the long wavelengths (yellows, oranges, and reds) remain. Hence the reddish glow to sunrises and sunsets. Pollutants and smoke and ash particles such as those that occur in association with volcanic eruptions can exacerbate these naturally occurring colors. For instance, in September 1982 (my first month at college in St. Louis), El Chichón erupted in Mexico. It was a big eruption and spread an enormous ash cloud over the Northern Hemisphere. I distinctly recall that the sunsets were much redder in color that year than any other year I can remember. Being from Boston, I just assumed this striking difference in the sunsets was a Midwest phenomenon.

Noon Sunrise

Sunset

Atmosphere

EARTH Figure 2.13. Schematic illustrating the difference in path length through the atmosphere for solar radiation emitted at noontime versus at sunrise and sunset. The heavy solid lines indicated the path length at each indicated time of day.

However, it turns out that the ash particles from the eruption assisted in the scattering of the short wavelength radiation and left the sky redder than usual as a result.

Rainbows and Refraction of Light Our last stop in the radiation section of the course will offer a succinct explanation of rainbows, a phenomena that has captured humankind’s imagination for millennia. In order to understand rainbows, we must remind ourselves that electromagnetic radiation propagates as a wave and so is subject to a property of wave phenomena known as refraction. When an electro-magnetic wave passes from one media to another of greater density, the transmitted light slows down. In fact, the speed of light (3 x 108 m s-1) is actually only the speed of light

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when that light travels in a vacuum. If the light is coming through our atmosphere, it travels at a slightly slower speed. If a light wave passes from a less dense to a more dense medium at an angle, the slow down causes the wave to bend. The resulting wave bending is known as refraction. Our common experience offers some simple examples of refraction. Who has not wondered why the spoon in a glass of water looks bent at the interface of the water and the air above it? The answer is that the light reflected off the spoon under water is bent upon exiting the water and heading toward your eye. It is even possible to understand refraction by considering a different kind of wave—a wave at the beach. The waves that roll in at the beach have a higher speed out in the open ocean than they do near shore. This is mostly a result of the effect of friction near the shore, which tends to slow down the waves. This slower speed near shore is analogous to the slower speed that light waves have in a dense media (like water vs. air). At the beach, the consequence of this slowdown of the waves is that they break. If the waves at the beach approach the shoreline at an angle, then one side of each approaching crest slows down as it makes contact with the shore. Since the end of the wave that remains at sea is not slowed, the wave crest bends (Fig. 2.14). Such a bent wave at the beach has been refracted through contact with the shoreline. Light passing through a water droplet is refracted, since the water is more dense than air. The amount of refraction depends upon the wavelength of light, with the short wavelengths being refracted (bent) the most. Tracing just the violet and red portions of the refracted beam, note that they propagate through the droplet and may exit the back side of the droplet. They may, however, be internally reflected on the back side of the droplet as shown in Fig. 2.15. The wavecrest

Shoreline

(a)

Sh

ore li n e

wavecrest

(b)

Figure 2.14. Schematic illustrating the slowing down of waves as they approach the beach as a result of friction with the ocean bottom. (a) Wave crests are parallel to shore as they approach. (b) Wave crests hit the shore at an angle and refract (bend) as they do so.

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reflected violet beam will then head out of the droplet into the air and will be refracted again upon doing so. The path of that violet beam may strike the eye of the person next to you but not your own. You may see the red beam from the same original beam of white light. Were the incident droplet the only droplet into which the sun was shining, you and the person next to you would see different colors. Thus, in order to see the full spectrum of visible light in a rainbow, it is necessary that countless raindrops showering down from the sky be struck by countless beams of visible light. As a result of this interaction, each raindrop within which internal reflection occurs sends every color in the visible spectrum, at different angles, back toward the observer whose back is to the Sun. So your perception of the rainbow results from your brain integrating millions of separate signals, sent by a discrete set of distant raindrops. This means, of course, that the rainbow you see is, physically speaking, not the same one seen by the person standing next to you, since the signals gathered by that person’s eyes are coming from different raindrops and have processed different visible beams. Therefore, the rainbow is a profoundly personal phenomenon. Had the ancients known about the physics of rainbows, they would have undoubtedly ascribed even more meaning to them. The primary rainbow (the common, single rainbow) is thus the product of two refractions and one reflection. If the raindrops through which the sunlight is refracted are large enough, there may be two, three, or four internal reflections of the incident beam on the back side of the raindrop. In the case of two reflections, a double rainbow will be formed. In the case

Beam o f White Light Red Vio let

Observer A

Raindrop

Observer B

Figure 2.15. Illustration of the refraction of violet and red light through a raindrop from an incident beam of white light. Violet is refracted the most. Notice that the beam is refracted both upon entering the droplet and upon exiting the droplet. Both wavelengths are reflected off the back side of the droplet. Note that different people see different colors from the beam refracted through a single raindrop.

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of three reflections inside the raindrop, a tercerary rainbow will form. Each bow after the primary bow will be less bright than the last as less light is available. Of course, the rainbow itself is an impossibility without raindrops. Next, we will investigate the nature and measure of water vapor in the atmosphere—a discussion of humidity and its sensible weather consequences.

Chapter 3 Water in the Atmosphere: Humidity, Clouds, and Precipitation

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n this section of the course we will discuss how we measure the moisture content of the air; the nature of condensation in the atmosphere; fog, cloud, and precipitation formation; why rising air cools; how to assess the stability of the stratification; and something about precipitation type. We will begin this extremely interesting story with two important ideas that set the stage for the more comprehensive discussion to follow.

I

The Hydrologic Cycle At any instant in time, the Earth’s atmosphere contains 3.75 x 1016 gallons (1.42 x 1017 liters) of water in the vapor phase. This is a staggering amount of water. In fact, it is enough to cover the entire surface of the Earth with 1” (2.54 cm) of rain. Now, if that weren’t amazing enough, this very amount of water is recycled through the Earth’s atmosphere 40 TIMES in one calendar year. That means that a water vapor molecule has an average residence time (length of time it remains in the gaseous state each cycle) in the atmosphere of only ~9 days. Now, consider that this enormous amount of water vapor has to condense into liquid or transform into ice by fusion or deposition every 9 days. We already know that such phase changes release energy, since vapor is the highest energy state of the water substance. Knowing how much water is involved, it is possible to calculate the amount of energy involved. It turns out that in one cycle of this hydrologic cycle, enough latent heat energy is released through these phase changes to power the United States, the largest consumer of energy in the world, for 3,441 years. And, of course, the same amount of energy released in the phase change to liquid water and ice in this one cycle is provided by the Sun to power the global evaporation required to maintain the vast water vapor capacity of our atmosphere. This is a truly astounding amount of energy.

Saturation We all have a colloquial sense of what this term means. How many times, perhaps while studying for an exam, have you felt as if not a single additional fact could be stuffed into your head before the exam? You might even say to a friend who is interested in your well-being that your brain is “saturated”—filled to the brim! But notice that even in this example, saturation is not an absolute term—it can only be employed with reference to some other variable. This concept can be brought to bear on the actual physical reality of saturation that we will use. If a beaker of liquid water is left uncovered in your bedroom (Fig. 3.1a), the situation is far

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from unchanging. In fact, it is likely that quite a large number of liquid water molecules will evaporate into the air. It is also likely that some of the vapor molecules in the air will condense back into liquid water. In fact, the situation in most homes would dictate that more liquid molecules will evaporate than vapor molecules will condense. In such a case we could say that the air in the room is unsaturated with respect to liquid water. This means that liquid water will evaporate into such air spontaneously.

(b)

(a)

3 evaporate 1 condenses

1 evaporates 1 condenses

Air above liquid water is unsaturated

Air above liquid water is saturated

Figure 3.1. The nature of saturation with respect to liquid water. (a) Without a cover liquid water evaporates away into unsaturated air. (b) With a cover the evaporated water soon saturates the air above the liquid surface.

If you decide to place a cover on the beaker of water and let it sit for a while you will notice that after some time the inside wall of the beaker will get wet (Fig. 3.1b). This is because by that time the number of molecules evaporated from the liquid surface in one second is equaled by the number of vapor molecules that have condensed back into liquid. When such a condition is reached in a sample of air, we can say that the air in contact with the liquid water is saturated with respect to that surface of liquid water. This means that there is no more “room” in the air for an additional water vapor molecule, and every time another one is added by spontaneous evaporation from the liquid phase, a vapor molecule is forced to condense into the liquid phase. Clearly, saturation is a relative term—something can only be declared saturated with respect to something else.

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The Influence of Temperature on Condensation If we consider a closed container filled with water vapor molecules we can examine the influence of temperature on condensation in a series of thought experiments. Recall that temperature is defined as the average kinetic energy of the molecules composing a substance. If the air in the hypothetical container is heated to a high temperature, the water vapor molecules inside will move faster than they would at a low temperature. For a variety of reasons best explained in detail in a physical chemistry class, the fast moving molecules (in the high temperature case) are statistically less likely to condense and can more easily remain in the vapor phase than can the rather sluggish molecules in the low temperature case. Even though it is not physically accurate, you can imagine, if you’d like, that it is more difficult for the fast moving molecules to “stick together” upon bumping into each other than it is for the slower moving molecules. The important result of this thought experiment is that the number of water vapor molecules needed to reach saturation in a given sample of air is greater in warm air than in cold air. Saturation can be thought of as the limiting value of humidity. Based partly upon the results of the preceding analysis, a given sample of air can approach this limit in two ways: 1) water vapor can be added to the air, or 2) the air can be cooled. In either case, the sample of air will be closer to its maximum possible vapor content than it was before the change.

Measures of Humidity There are several measures of humidity that find use in meteorology. Some of them are fairly well known while others are not so well known. In our subsequent examination of some of them we will consider each with respect to the fundamental goal of such a measure—to unambiguously testify to the amount of water vapor present in the air.

Absolute Humidity Absolute humidity measures the mass of water vapor in a given volume of air. It has units of grams per cubic meter (g m-3) and can be expressed as the ratio AH =

Mass of water vapor . Volumeof sample

Absolute humidity is not a commonly used measure of humidity because it is dependent on the volume of the air sample that contains the water vapor. As we have already seen in our development of the Ideal Gas Law, volume can change as a result of temperature or pressure

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changes. Thus, the absolute humidity can change even when there is no change in the actual water vapor content of the air. This property makes it undesirable as a measure of humidity.

Specific Humidity and Mixing Ratio We can avoid this problem by considering the ratio of the mass of water vapor in a sample of air to the mass of the air sample itself. This ratio is known as the specific humidity and is measured in grams of water vapor per kilogram of air (g kg-1). A limitation of the specific humidity as an unambiguous measure of the moisture content can be exposed in the following thought experiment. Suppose you have a 1 kg sample of air that is determined to contain 10 g of water vapor. In such a case, the specific humidity would be 10g kg-1. If this sample of air were cooled until some of the vapor within it were condensed, say 2 g of vapor, then the mass of the remaining vapor would be 8 g and the mass of the air sample would drop to 998 g (0.998 kg). Thus, the specific humidity would become 8g / 0.998 kg or 8.016 g kg-1, and this change does not uniquely reflect the change in the water vapor content of the sample (because it also incorporates the change in the mass of the sample itself ). This limitation of the specific humidity can be avoided by considering a related measure known as the mixing ratio. The mixing ratio is defined as MR =

Mass of water vapor Massof dry air containingit

where the denominator (the “mass of dry air”) represents the mass of all the molecules except the water vapor molecules in a given sample of air. The distinct advantage of the mixing ratio is that it does not change unless water vapor is added to or removed from the air parcel. For this reason, the mixing ratio is considered the best measure of actual vapor content in the atmosphere. If a parcel of air is known to be saturated with respect to liquid water, then the mixing ratio of a sample of that saturated air is known as the saturation mixing ratio, and is defined as SMR =

Mass of water vapor . Massof dry air in saturated sample

Another way to think of the saturation mixing ratio is that it is the limiting value of mixing ratio that a parcel can have at a given temperature and pressure.

Vapor Pressure Even though the atmosphere is composed of a variety of gases, each one of those gases exerts its own partial pressure. The sum of all these partial pressures exactly equals the total pressure exerted by the entire atmospheric mixture. Since water vapor is a gaseous constituent of the

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atmosphere, it also exerts its own partial pressure. A special name is given to the partial pressure exerted by water vapor in a sample of air; it is known as the vapor pressure. As you might suppose, the vapor pressure depends upon both the number of water vapor molecules in the air and the temperature of the air. It is the former characteristic, the number of water vapor molecules, that we are most interested in when we desire a measure of humidity. Thus, vapor pressure is another reasonable way to measure humidity. If a parcel of air is known to be saturated with respect to liquid water, that means that the number of liquid water molecules evaporating from the liquid surface is equal to the number condensing back into the liquid. Since the evaporating molecules need a certain amount of kinetic energy to enable their transformation to the higher energy gaseous state, the number that evaporate is directly related to their temperature. Knowledge of the temperature is also enough to know how much pressure is exerted by that number of water vapor molecules. These molecules will exert a saturation vapor pressure that is, therefore, dependent only upon the temperature of the air parcel.

Relative Humidity Perhaps the most well-known measure of humidity is the relative humidity (RH). The relative humidity (usually expressed as a percentage) is a ratio of the actual amount of water vapor in the air to the maximum amount of vapor that is possible at the given pressure and temperature. This ratio can be defined in terms of the variables just discussed as RH =

Mixing Ratio x100% , Saturation Mixing Ratio

and RH =

Vapor Pressure x100% . SaturationVapor Pressure

It is important to note that the relative humidity does not indicate the actual amount of water vapor that is in the air—it only tells us how much vapor the air contains relative to what it could contain at the given temperature and pressure. The second of these two expressions for the RH leads us to a particularly important conclusion that we will use in subsequent discussions. Recall that the vapor pressure measures the amount of water vapor in the air and that the saturation vapor pressure is a function of temperature only. That being the case, it is clear from the above expression that the RH can be changed either by altering the numerator or the denominator of the ratio that defines it. That is, the RH can only be changed in one of two ways:

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1. Adding water vapor to, or subtracting water vapor from, the air, and 2. Changing the temperature of the air.

Dewpoint Temperature Another indirect measure of the water vapor content that is becoming increasingly common in the broadcast media is the dewpoint temperature. We will conduct a thought experiment to elucidate the physical meaning of the dewpoint temperature before actually giving the definition. Imagine you begin the experiment with a parcel of air saturated with respect to liquid water at a temperature of 10°C. Imagine that the air parcel is then warmed up to 20°C, keeping the pressure and mixing ratio constant (i.e. no addition or subtraction of water vapor occurs). Since the air at 20°C has a higher saturation vapor pressure (on account of its higher temperature) but has the same number of vapor molecules it had at 10°C, the relative humidity of the parcel is lower at 20°C. Now, to what temperature must the parcel be cooled (at constant pressure) before it becomes saturated again? Without much confusion one can conclude that the parcel must be cooled back to its original 10°C in order to become saturated. Thus, a definition of the dewpoint temperature presents itself as: The temperature to which air must be cooled at constant pressure in order to reach saturation. Based upon this definition, it follows that a high dewpoint temperature (abbreviated as Td) corresponds to a high water vapor content and a low Td corresponds to a low water vapor content. The dewpoint temperature can never exceed the air temperature because when they are equal, the air is saturated. Thus, when the air is unsaturated there is some difference between T and Td. The precise difference can be measured and is known as the dewpoint depression (Tdd). It is defined as Tdd = T – Td When Tdd is large, the relative humidity has to be low, and when Tdd is small, the relative humidity is high.

Wetbulb Temperature Another thought experiment will now be used to lead us to the definition of yet another indirect measure of the humidity known as the wetbulb temperature (Tw). Imagine we begin with the same parcel of air as in the prior example but at its unsaturated state at temperature 20°C. This time we will endeavor to make that parcel saturated by evaporating small amounts

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of liquid water into it. The energy required to evaporate the liquid water into the air parcel comes from the air parcel itself. As some of that latent heat of evaporation is used, the average KE of the air molecules in the parcel is reduced. This is synonymous with a drop in the air parcel’s temperature. As the air parcel cools, its RH increases, and with continued evaporation and cooling the saturation point will be reached at Tw. Thus, the following definition of the wetbulb temperature presents itself: The temperature to which air is cooled at constant pressure by evaporating water into it until it is saturated. Because the wetbulb temperature is reached through a combination of addition of water vapor and cooling of the air, the wetbulb temperature will always lie between the air temperature and the dewpoint temperature. When the air is saturated, of course, T=Td=Tw. Importantly for later discussion, the air that immediately surrounds a precipitation particle is always at the wetbulb temperature. It is also noteworthy that when your body cools by perspiration, the air above your skin cools to the wetbulb temperature, so Tw is a fairly good measure of human comfort.

Condensation All of this discussion of water vapor in the atmosphere is designed to prepare us for a discussion of cloud and precipitation development. In order to go from the vapor stage to the liquid or ice stage, the water vapor must change phase. In the atmosphere, water vapor condenses at expected temperatures because it condenses onto some other object such as a tiny dust particle, a salt particle, or a smoke particle, to name but a few. Any tiny object that is hygroscopic (water friendly) can serve as one of these important cloud condensation nuclei (CCN). As amazing as it might sound, these condensation nuclei are vitally necessary in order for condensation to occur in the atmosphere. As you might suspect, the smaller the particle, the easier it is for water vapor to condense upon it because less liquid is required to cover its surface. The smallest liquid water droplets in the atmosphere are known as haze droplets or simply haze. Some haze droplets are small enough that they can survive in unsaturated air but they may not be able to grow unless the RH increases. Haze particles that do grow large enough to be small (~20 μm diameter) cloud liquid water droplets are called fog droplets. As you might guess, fog formation depends on increasing the relative humidity. Therefore, there are only two physical mechanisms by which fogs can form. Fogs can form if the air is cooled. On a clear night the ground cools rapidly via radiation. If the air above the ground has a fairly high water vapor content, then the cooling of the ground can eventually lead to the formation of radiation fog, so named because of its association with radiative cooling. When moisture-laden air is advected over a cooler surface like a snowfield or a cold body of water, the air is cooled by contact with that surface and advection fog may form.

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Yet another fog formed by cooling of the air is upslope fog, in which the cooling occurs as the air is lifted to higher elevation. Another mechanism by which fogs might form involves adding water vapor to the air. A prime example of this type of fog is so-called steam fog that forms as cold, dry air moves over warm water. In such a case, water vapor is added to the air through evaporation off of the liquid water’s surface. The fog that forms in your bathroom when you take a shower is a result of the addition of water vapor to the air in the bathroom. Another type of fog, frontal fog, is formed when warm rain falls through cold, dry air or when rain falls onto a snow-covered ground. In either case, the fog is formed as a consequence of addition of water vapor to the air.

Cloud Formation The formation of clouds represents one of the most important meteorological phenomena on Earth. In order to investigate the manner by which clouds form we must examine a number of related issues. First, we will investigate why rising air cools. We will then have to consider how much the air cools when it rises. This discussion will lead us to a discussion of the concepts of buoyancy and stability. Clouds form as the RH reaches 100%. There are only two ways to increase the RH: 1) cool the air, or 2) add water vapor to the air. Most clouds form as a result of mechanism (1), which begs the question—how does this cooling take place? In nearly every cloud formation event, it takes place when air moves upward away from the ground. But exactly why does rising air cool? We can construct a logical argument to explain this physical fact. Recall that, without exception, pressure decreases with height in the atmosphere. Therefore, as a parcel of air rises to higher elevation, the environment surrounding the parcel exerts less pressure on it. Thus, the rising parcel expands into this lower pressure environment quite naturally. The expansion of the parcel implies that the parcel “walls” are pushed out. This “pushing out” requires work, and work requires energy. The energy required to do this work comes from the molecules of air within the air parcel. Since these molecules have mass and are moving, they have kinetic energy (KE) and they spend some of it to do the expansion work. After expansion, the collection of molecules constituting the air parcel has less KE, and so the average KE of the collection of molecules is also smaller after expansion. By the definition of temperature, this means that the temperature of the air parcel is lower after expansion. Thus, we conclude that rising air must cool. The rate of cooling is not arbitrary—in fact, there are only two possible rates of cooling available to rising air parcels. If the rising parcel of air is unsaturated (i.e. has an RH < 100%), the parcel will cool at what is known as the dry adiabatic lapse rate, which is equal to 10°C

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km-1.1 The word “adiabatic” means that the parcel of air neither gains heat from nor loses heat to its surrounding environment. For saturated parcels (RH ≥ 100%), the rising parcel will cool at the moist adiabatic lapse rate, which, though variable, is equal to approximately 6°C km-1 for most applications at midlatitudes. A parcel of air that begins its ascent as an unsaturated parcel will begin to cool at the dry rate. If the cooling it experiences is sufficient to increase its RH to 100% (i.e. to render it saturated), then its rate of cooling upon additional ascent will be reduced to the moist rate value. Why is the moist rate smaller than the dry rate? Well, during saturated ascent, each little bit of additional cooling results in condensation of water vapor in the parcel. This condensation releases latent heat into the air parcel and counteracts some of the cooling due to expansion. So long as there is available water vapor in a saturated air parcel, it will cool at a rate smaller than the dry rate as it ascends. However, once all the water vapor in a parcel has been condensed, if the parcel continues to ascend, it will cool further at the dry adiabatic rate.

Bouyancy We all have a sense of what is meant by buoyancy. Buoyancy can be thought of as “the ability to float.” We say that an object is positively buoyant if it floats and negatively buoyant if it sinks. Of course, the sinking or floating depends upon the environment into which the object is placed, so buoyancy is also a relative term. Consider the following thought experiment. You have a beaker full of water and you place a dry log into it as shown schematically in Fig. 3.2. If you push the log down into the water so that its entire volume is submerged, then you can see that a certain volume of water is displaced to make room for the volume of the log. In fact, the volume of displaced water is exactly equal to the volume of the log so long as you keep the log submerged. This displaced water has a certain mass, as does the log that has displaced it. If the mass of the log is less than the mass of the water it displaces, then the log floats in water. This is Archimedes’ principle. We can go one step further by dividing the mass of the log and the mass of the displaced water by the volume of the displaced water (which, recall, is equal also to the volume of the log). Performing this division will leave us with the density of the log (ρlog ) and the density of the water (ρwater). So, Archimedes’ principle can be expressed another way by comparing densities of substances: If ρlog < ρwater, then the log floats in water. This is a specific example of a general physical law, so the same type of relationship also holds true in the atmosphere. In the context of the atmosphere, it is particularly relevant to compare 1

The actual value for the dry adiabatic rate of cooling is 9.81°C km-1. We use 10°C km-1 because it simplifies

subsequent, edifying calculations.

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L og

Initial Condition

Condition after log is submerged

Figure 3.2. Result of submerging a log in a beaker of water. Hatching represents the original depth of the water in both cases. Gray shading represents the depth of water displaced by the log.

an individual air parcel’s density to that of its surrounding environment. We just discussed how the temperature of a parcel of air changes as it is lifted to higher elevation. Therefore, comparison of a lifted parcel’s density with that of its new environment must determine if that parcel is positively or negatively buoyant in that new environment. In fact, we can construct a simple set of rules for determining parcel buoyancy: If, ρparcel < ρenv – the parcel is positively buoyant in its environment ρparcel > ρenv – the parcel is negatively buoyant in its environment ρparcel = ρenv – the parcel is neutrally buoyant in its environment. Of course, as we encountered earlier, comparing densities is not so amenable to measurement, but we can invoke the Ideal Gas Law to solve this dilemma. Recall that the Gas Law tells us that P = ρRT and if we compare the parcel to its environment at the same pressure level, then Pparcel = Penv or

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ρ parcel RTparcel = ρ env RTenv which, since R is a constant, reduces to

ρ parcel Tparcel = ρ env Tenv . Now, if ρparcel < ρenv, then it must be true that Tparcel > Tenv. Similarly, if ρparcel > ρenv, then Tparcel < Tenv. So we can describe the buoyancy of air parcels in terms of comparing temperatures in the following way: If, Τparcel > Τenv – the parcel is positively buoyant in its environment Τparcel < Τenv – the parcel is negatively buoyant in its environment Τparcel = Τenv – the parcel is neutrally buoyant in its environment.

Stability Now that we have found a way to determine if a lifted parcel of air will be positively, negatively or neutrally buoyant, we need to consider the ramifications of these conditions on motions in the atmosphere. We will do so by considering the concept of stability. Stability is a characteristic of a physical system that describes the likelihood that that system will remain unchanged after it has been perturbed. A simple set of examples can amply illustrate this important concept. Consider the situation depicted in Fig. 3.3a in which a marble is placed at the bottom of a bowl. Imagine that the marble is given a modest impulse that moves it partway up one side of the bowl. When that impulse is stopped, the marble will slosh up and down the sides of the bowl for some time before finally coming to rest at its original location. In this case, the physical system of the marble and the bowl is left unaltered after the perturbation. Such a physical system is said to be stable to that perturbation. On the other hand, if the bowl is placed upside down and the marble is placed atop the overturned bowl, a slight perturbation to the marble will cause it to accelerate away from its original position (Fig. 3.3b). The acceleration of the marble away from its original position renders the physical system of the bowl and marble considerably altered after the perturbation. Such a physical system is said to be unstable to that perturbation. Finally, if the marble is placed on a flat table and then given a slight push to the right (Fig. 3.3c), it will move to the right without accelerating and come to rest in a new location. Because there is no acceleration away from its original position and because the marble comes to rest in a setting similar to the original one, such a situation depicts neutral stability.

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STABLE

(a) UNSTABLE

(b) NEUTRAL

(c)

Figure 3.3. (a) Marble in a bowl. (b) Marble on top of the bowl. (c) Marble on a flat table. In each case, the gray arrow indicates direction of push (perturbation) given to the marble.

In most meteorological examples, we imagine hypothetically moving an air parcel upward to higher elevation in order to assess the stability of the stratification (layering) of the atmosphere on a given day at a given location. Based upon available observations, we must then assess the likelihood that a parcel of air will: 1. accelerate away from its original location upon being lifted and then released, 2. sink back to its original position upon being lifted and then released, or 3. remain happily at its new location upon being lifted and then released.

These three conditions correspond to a lifted parcel being positively buoyant, negatively buoyant, or neutrally buoyant, respectively, upon being lifted. As we have just seen, buoyancy can only be assessed with respect to the environment into which the parcel is being lifted. Such an assessment requires that we have observations of the temperatures at a variety of vertical levels in the atmosphere. Thus, we require vertical temperature soundings. Such information is gathered twice daily at a limited number of stations around the globe using radiosondes. Radiosondes are balloons that carry an instrument package consisting of a thermometer, a barometer, and a hygrometer as well as a transmitter. As the balloon ascends, it records the temperature, pressure, and humidity at a number of vertical levels and then transmits the

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information back to the launching site. In this way, observations of the three-dimensional structure of the atmosphere at such locations are obtained regularly. From these actual observations, we can determine the measured lapse rate of the atmosphere (i.e. the way in which the observed temperature changes with increasing height) on a given day at a given location. In order to determine the stability of the stratification we must compare the temperature of a hypothetical lifted parcel (Tp) to the temperature of the environment at the same level (Te) (i.e. the observations).

Dr yR ate

ate tR ois M

Height

2 km

1 km

5oC

10oC

15oC

20oC

25oC

Temperature

Figure 3.4. Measured lapse rate (thick solid line) of 4 oC km-1. Dashed black (gray) line is the dry (moist) adiabatic rate line. See text for explanation.

The thick solid line in Fig. 3.4 shows an example of the measured lapse rate over Madison, Wisconsin, on a summer day. The two axes of the chart are °C and height above sea-level, respectively. The situation depicts a measured temperature of 25°C at the surface, 21°C at 1 km, and 17°C at 2 km. Thus, the measured lapse rate in this example is 4°C km-1, and this describes how the environment’s temperature changes with increasing height—it describes the observations. Recall that any parcel of air lifted from the surface will cool at only one of two rates: the dry adiabatic rate (10°C km-1) or the moist adiabatic rate (~ 6°C km-1). The dry and moist rate lines are indicated by the black and gray dashed lines, respectively. By following the dry rate line upward from the surface to 1 km, we can determine the temperature a lifted surface parcel would have at 1 km were the parcel unsaturated. We find, not surprisingly, that it would be 15°C, since its surface temperature is 25°C and the dry rate is 10°C km-1. Since the environment’s temperature at 1 km is observed to be 21°C on this day, it is clear that unsaturated parcels of air, when lifted to higher elevations, will find themselves colder than the environment. As a consequence, such parcels will fall back to their original locations when

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left to their own devices. This means that the stratification on that day is stable to unsaturated ascent. If the air parcel that is being lifted is saturated at the ground, then as it rises it will cool at the smaller moist adiabatic rate. Note that following the moist rate line to 1 km lowers the saturated parcel’s temperature to 19°C. Even with slower cooling, however, any lifted, saturated parcel will find itself colder than its environment at subsequent heights and is thus going to be negatively buoyant. Such a parcel will fall back to its original location when left to its own devices. Once again, this means that the stratification is stable. Since both possibilities, unsaturated and saturated air parcels, are found to return to their original locations upon being left to their own devices, we declare an environment characterized by such a measured lapse rate to be absolutely stable. Notice that a measured lapse rate of 4°C km-1 is smaller than both the moist adiabatic lapse rate and the dry adiabatic lapse rate. Whenever the measured lapse rate is smaller than the moist adiabatic lapse rate, the environment will be absolutely stable. If, as in Fig. 3.5, the observed temperature at 1 km is 13°C and 1°C at 2 km then we have a measured lapse rate of 12°C km-1 (again, indicated by the solid black line). Note that the dry rate and moist rate lines are identical to those shown in Fig. 3.4. Only the measured lapse rate line changes. Now, when we compare the temperature of a lifted parcel of air, be it unsaturated or saturated, to the temperature of the environment at some new elevation, say 1 km, we find that the parcel temperature (15°C at 1 km for an unsaturated parcel and 19°C at 1 km for a saturated parcel) is warmer than the environment’s temperature. This means that any parcel that is lifted into this environment will be positively buoyant and will accelerate upward away from its original location. This defines an unstable motion, and thus the environment characterized by this measured lapse rate is said to be absolutely unstable.

Dr yR ate

ate tR ois M

Height

2 km

1 km

5oC

10oC

15oC

20oC

25oC

Temperature Figure 3.5. Measured lapse rate (thick solid line) of 12 oC km-1. Dashed black (gray) line is the dry (moist) adiabatic rate line. See text for explanation.

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An example of the only remaining possibility is illustrated in Fig. 3.6. In this case we find that the observed temperature at 1 km is 17°C, while it is 9°C at 2 km. Therefore, the measured lapse rate (the solid black line) is 8°C km-1. An unsaturated parcel of air lifted into this environment will be colder than the environment at any elevation and will thus sink back to its original position when left to its own devices. If a saturated parcel of air is lifted into this environment, however, it will find itself warmer than the environment at each new level and will accelerate upward as a consequence of its positive buoyancy. Therefore when the measured lapse rate falls between the dry adiabatic rate and the moist adiabatic rate, the moisture characteristics of the parcel determine whether the environment is stable (unsaturated parcel) or unstable (saturated parcel). Such an environment is referred to as conditionally unstable, as its instability is conditional upon whether the lifted parcel is saturated or unsaturated. The average measured lapse rate of the troposphere is 6.5°C km-1—larger than the moist adiabatic rate but smaller than the dry adiabatic rate. Thus, on average, the troposphere is conditionally unstable.

Dr yR ate

ate tR ois M

Height

2 km

1 km

5oC

10oC

15oC

20oC

25oC

Temperature

Figure 3.6. Measured lapse rate (thick solid line) of 8 oC km-1. Dashed black (gray) line is the dry (moist) adiabatic rate line. See text for explanation.

On any particular day, of course, any of the three possibilities just described is likely to occur. Since the stability of the stratification depends on the size of the measured lapse rate, a quantity that changes all the time, a reasonable question might be: How can the stratification be made more unstable? Recall that in our prior discussion, we found that the larger the measured lapse rate the more unstable was the stratification. Therefore, increasing the measured lapse rate will destabilize the atmosphere. The measured lapse rate can be increased in any of three ways. If

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the surface temperature rises through the day with no change occurring to the temperature of the air above the ground, then the difference in temperature between the surface and some level above the surface (Tsfc – T1 km) will increase. This increase will be reflected in a larger measured lapse rate and a decrease of stability. Thus, daytime heating of the ground often leads to the development of fair weather clouds in the afternoon because the surface heating makes the stratification less stable. If the temperature of the air at some level above the ground is cooled through the day while the surface temperature remains unchanged, then the difference in temperature between the surface and some level above the surface will increase. Once again, this difference will be reflected in a larger measured lapse rate and a decrease in stability. Finally, a combination of surface warming and cooling of the air at some level above the surface will also result in a larger measured lapse rate and a decrease in the stability of the stratification. We will use these ideas as part of our investigation of the processes by which clouds and precipitation form in the atmosphere.

Precipitation Formation If one were to keep track of the sky rather faithfully from day to day, one would surely notice that precipitation does not fall from every cloud. It is reasonable to ask why this should be the case given that the precipitation that does fall comes from clouds and that almost all clouds contain liquid water cloud droplets. One might conclude (correctly!) that the precipitation itself comes, somehow, from the very cloud droplets that compose the cloud. These cloud droplets have a radius of only 10 μm. An average raindrop has a radius of 1000 μm. Since volume is proportional to the cube of radius ( Volume=

4 3 πR ), this means that a typical raindrop is one 3

million times as voluminous as a typical cloud droplet. So, somehow, one million cloud droplets must congregate/consolidate/aggregate in order to produce a single raindrop. This strikes me as something of a miracle given the fact that billions of raindrops fall in a single minute of a heavy summer downpour! The question that will occupy us in this section of the text is HOW does this organization of cloud droplets occur? What tricks does Nature have up its sleeve to induce such “cooperation” among cloud droplets? To answer this question we will have to consider a number of new physical ideas, starting with the notion of a liquid water droplet at equilibrium.

Equilibrium Vapor Pressure Any liquid water droplet in the atmosphere is subject to continuous evaporation and condensation events. In order that the droplet remain at a steady size, the number of water molecules that evaporate from its surface each second must be precisely equaled by the number of

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molecules that condense onto its surface in that same second. In order that condensation onto the surface is even possible, the environment surrounding the droplet must contain a certain number of water vapor molecules. These environmental water vapor molecules exert a vapor pressure, just like any other gaseous constituent of the atmosphere. Since the vapor pressure they exert characterizes the condition necessary for the droplet to remain at a steady size, we shall refer to this vapor pressure as the equilibrium vapor pressure. It is important to note that the equilibrium vapor pressure, being the vapor pressure that is necessary for the droplet to survive, unchanged, in a given environment, is simply a threshold value against which the actual environmental vapor pressure must be compared to determine whether or not a droplet will grow in that environment. It follows from the notion of equilibrium that if the actual vapor pressure exceeds the equilibrium vapor pressure, then the droplet will grow. This is because, in that case, the number of vapor molecules in the environment of the droplet exceeds the number needed simply to maintain the droplet, and there will be excess condensation onto the droplet as a consequence. Conversely, if the actual vapor pressure is smaller than the equilibrium vapor pressure, the droplet will shrink. A logical next question, then, is what physical factors influence the value of the equilibrium vapor pressure. One important factor is the curvature of the droplet. Creating a surface of liquid water involves overcoming something called surface stress. It turns out that, all other characteristics being equal, it is easier for a liquid water molecule to evaporate from a curved surface of liquid water than from a flat surface of liquid water because the surface stress over the curved surface is much larger. As a consequence, in order for a curved droplet to remain unchanged in a given environment, a large number of water vapor molecules are required in the environment of the droplet. In fact, that number must be larger than the number that would be required to maintain equilibrium over a flat surface of water at the same temperature. This even applies to conditions of saturation—a larger number of vapor molecules are required to saturate the environment, at a given temperature, over a curved droplet than that over a flat surface of water. The implication is fascinating; namely, small pure water droplets (which have large curvature) can be in equilibrium only if the air is supersaturated with respect to a flat surface of liquid water. Because the curvature of a sphere increases with decreasing radius2, the smallest droplets require the largest equilibrium vapor pressures. This presents a potential major problem for precipitation production in the atmosphere: How do small droplets ever grow into precipitation-sized particles? Nature has a couple of ingenious tricks up its sleeve. One of them is that, as we have already stated, the initial condensation events almost always occur on the surface of cloud condensation nuclei (CCN). CCN with large radii have smaller curvature than very tiny CCN.

2 Consider the difference in curvature between the Earth and a baseball. Both are approximate spheres, but even at the ocean shore it is difficult to discern the slight curvature of the Earth’s surface. The much greater curvature of a baseball’s surface, however, is immediately apparent.

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Thus, condensation onto these large CCN creates droplets that get a significant head start in conquering the limits on growth imposed by the curvature effect. In addition, if these CCN can dissolve in water (like salt can, for instance) then another trick, known as the solute effect, can further accelerate droplet growth. Consider the crosssections of the two droplets shown in Fig. 3.7. One of the droplets is a solution droplet with dissolved salt in it. The other is a pure water droplet. In the solution droplet, some of the surface molecular sites are occupied by salt molecules (gray shading). In the pure water droplet, all of the surface molecular sites are occupied by liquid water molecules. As you might imagine, salt molecules cannot evaporate into salt vapor on Earth. Therefore, not every surface molecular site in the solution droplet is available to be evaporated. As a result, in order for the solution droplet to remain unchanged, the environment surrounding it need not contain as many water vapor molecules as does the environment surrounding the pure water droplet (on which all surface molecular sites are available for evaporation). Therefore, the equilibrium vapor pressure is lower, all other characteristics being equal, over the solution droplet than over the pure water droplet. This means that droplets with dissolved CCN can grow at lower relative humidities than pure water droplets. The source of such soluble CCN on Earth is multifarious. Three-fourths of our planet’s surface is covered by the salt water oceans, and a considerable amount of sea-salt is placed into the atmosphere by the action of waves on the ocean surface. Other naturally occurring, soluble CCN come from plants or chemical reactions in the free atmosphere. Thus far we have examined mechanisms by which Nature permits droplet growth by condensation of water vapor onto existing droplets. Even employing some of the tricks just discussed, the million-fold growth in volume required to render a cloud droplet into a precipitation-sized particle cannot be achieved by condensation alone—it is simply not fast enough to produce the precipitation-sized particles that fall from the sky. So, how do precipitation-sized particles form in clouds?

Pure Water Droplet

Solution Droplet

Figure 3.7. Cross-section of a pure water droplet and a solution droplet. The boxes represent molecular sites on the surface of each droplet. The gray (white) boxes represent the position of salt (liquid water) molecules.

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Droplet Growth into Precipitation-Sized Particles Clouds within which precipitation-sized particles form can be classified into two broad categories: warm clouds and cold clouds. Warm clouds are clouds wherein the temperature is everywhere above 0°C (32°F). Within such clouds there is no cloud ice whatsoever. These clouds have droplets that exhibit a variety of sizes resulting from their relative successes at competing for the available water vapor during the condensational growth stage. Thus, as depicted in Fig. 3.8, a warm cloud characteristically has some large droplets and some small droplets in it. As you might guess, the larger droplets have a larger fall speed than the smaller ones due to differences in the balance each strikes between air resistance and gravity. Thus, the larger droplets fall faster than the smaller ones and so tend to collide with the droplets in their path as they fall. Some of these collisions between droplets result in creation of a new, larger droplet that incorporates the water content of both of the original droplets. Such a melding of two original droplets is known as coalescence of droplets. Continued collision and coalescence leads rapidly to the growth of precipitation-sized water drops in these warm clouds. Since the number of collisions is larger if a given falling droplet is able to fall through a deeper cloud, it is more likely that precipitation will emerge from the base of a deep warm cloud than from a shallow warm cloud. Those of you who have ever been in the tropics (where many clouds are warm clouds) can attest to the enormous size of raindrops that emerge from these warm clouds in tropical downpours.

Land or Ocean Figure 3.8. Schematic of the droplet size distribution in a warm cloud. Notice that the three droplet sizes do not fall through the cloud at the same speed. Each has its own characteristic fall velocity.

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Cold clouds are clouds wherein the temperature is lower than 0°C (32°F) at some level. Most of the clouds that populate our stormy skies in the continental United States (at any time of year) are cold clouds. In such clouds, small droplets can remain in liquid form as supercooled droplets. The water in such supercooled droplets has a temperature less than 0°C. If the supercooled water droplets are struck by a piece of ice (or another such droplet) in the cloud, the water in the struck droplet begins to freeze by first forming an icy shell on its outer surface. As the freezing continues, a smaller and smaller amount of liquid water at the center remains unfrozen. When the last bit of liquid water finally freezes (and expands, as ice does), it can crack the outer shell and send shards of ice into the cloud, initiating additional droplet freezing events. In this way, the amount of ice in a supercooled water cloud can grow very rapidly—a process known as ice multiplication. Yet another amazing characteristic of the water substance is that the saturation vapor pressure with respect to a flat surface of ice is lower than the saturation vapor pressure with respect to a flat surface of liquid water. This implies that once ice forms in the clouds, deposition of water vapor onto the ice proceeds much faster than does condensation of vapor onto the liquid droplets. This essentially means that the ice, once formed, gobbles up the available water vapor better than the liquid droplets. As a consequence, the initial ice particles grow rapidly into precipitation-sized pieces. The growth of ice and precipitation-sized particles in cold clouds is known as the Bergeron process. You may have noticed that the foregoing story about precipitation generation in cold clouds did not make any reference to how ice originally arises in cold clouds. This omission is a result of our ignorance about this issue—currently there is no single, broadly accepted answer to the question of how the ice originally appears in the cloud. It is among the more profound mysteries of atmospheric science. Now that we have examined the factors that conspire to produce the precipitation that falls from the sky, we turn our attention to another important question: What determines the precipitation type that actually hits the surface?

Precipitation Type In many locations in the United States, such as in my home of Madison, Wisconsin, a large variety of precipitation types are often experienced in a given calendar year. Those of us who live in Madison have seen snow, sleet, freezing rain, and rain not to mention hail (which we will describe in another section of the book). In this short section we will examine the vertical temperature structure that is associated with each of these various types of precipitation. We will begin with rain.

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Rain Rain is simply liquid water when it hits the ground. Given this fact, it is probably clear that the temperature must be above 0°C at the surface when it is raining. But since most of the clouds that drop rain on us in the continental United States are cold clouds, there is a good chance that the liquid rain that falls on your head started out as an ice particle at a higher elevation. Thus, a rather deep layer of temperatures above 0°C—deep enough to allow enough time for the original frozen particle to melt as it falls to the ground—is required for rain to fall. The characteristic temperature sounding associated with rain might look like the one shown in Fig. 3.9.

Snow Snow is frozen water that, given its crystalline structure, has never been in the liquid form. Since snow might form at the top of any cold cloud in any season, in order for snow to remain snow all the way to the surface, the temperature surrounding the snowflake must be below 0°C throughout the entire atmospheric column. Though this often means that the temperature

H e ight

T

-10oC

0oC

10oC

Temperature

Figure 3.9. Vertical temperature sounding characteristic of rain. Shaded area represents the region of the atmosphere in which the temperature is above the freezing point (0 oC).

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itself is below 0°C, it is usually only necessary that the wetbulb temperature remain below 0°C for that entire descent3.

Sleet Sleet pellets are frozen raindrops. Again, since they generally fall from cold clouds, the sleet pellets often originate as snowflakes at some high elevation in the cloud. Since they end up being frozen raindrops, sleet pellets must encounter a layer of above-freezing temperatures at some level above the ground. In this layer, the original snowflake melts. In order that the resulting raindrop re-freezes before hitting the surface, the air below the melting layer must be below 0°C and sufficiently deep to allow enough time for the refreezing to occur. Thus, a sounding like that depicted in Fig. 3.10 characterizes sleet. Note, then, that sleet cannot fall at a location unless a temperature inversion exists there and the melting layer is located at a reasonably high elevation.

H e ight

T

-10oC

0oC

10oC

Temperature

Figure 3.10. Vertical temperature sounding characteristic of sleet. Shaded area represents the region of the atmosphere in which the temperature is above the freezing point (0 oC).

3 Strictly speaking, the ice-bulb temperature must remain at or below 0°C. The ice-bulb temperature is the temperature to which air is cooled at constant pressure by sublimating ice into it until it is saturated.

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H e ight

T

-10oC

0oC

10oC

Temperature

Figure 3.11.Vertical temperature sounding characteristic of freezing rain. Shaded area represents the region of the atmosphere in which the temperature is above the freezing point (0 oC).

Freezing Rain Freezing rain is rain that freezes upon contact with cold objects (objects whose temperatures are less than 0°C) at the surface. Since the raindrops that strike these cold surfaces at the ground begin as snowflakes at some higher elevation, there must be a layer above the ground in which the temperature is above 0°C. Since the raindrops do not refreeze while in the atmosphere, only a very shallow layer of sub-freezing air immediately adjacent to the ground must be colder than 0°C. Thus, again, a temperature inversion characterizes the sounding in which freezing rain will occur (Fig. 3.11). The distinction between the freezing rain sounding and the sleet sounding is evident through comparison of Figs. 3.10 and 3.11. In a freezing rain sounding the cold air beneath the temperature inversion is extremely shallow, sometimes not more than a few tens of meters deep. The shallowness of the cold air makes prediction of freezing rain events among the most difficult winter weather types to anticipate, only compounding the danger represented by this most treacherous of winter weather elements.

Chapter 4 The Dynamic Atmosphere: The Winds and Weather of the Mid-Latitude Cyclone

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fundamental element of our experience with the atmosphere is the fact that the fluid atmosphere moves. The movement of the atmosphere is known as wind. We could not conduct an introductory examination of the atmosphere without considering the following question: Why does the wind blow? Classical physics dictates that only forces can change the inertia of objects and thereby make them move. Thus, we can ask our question in another fashion: What forces the air to move? In this section of the course we will examine the nature of the wind, both at the surface and at levels above the surface. We will also consider the nature of cyclones and anticyclones, the predominant weather producing circulation systems in the middle latitudes of Earth. Finally, we will examine the nature of smaller scale circulation systems such as thunderstorms and tornadoes. We begin by considering the horizontal wind.

A

The Forcing of the Horizontal Wind The horizontal wind (wind in the north, south, east, or west direction) is a result of horizontal forces acting on air parcels to move them. Any force has two important, measurable characteristics: its magnitude (i.e. size or strength) and its direction. In our subsequent discussions and exercises, it will be necessary to schematically draw force diagrams in which the length of an arrow will indicate the magnitude of a given force and the orientation of the arrow will indicate the direction in which the force is acting. There are three horizontal forces that control the evolution of the horizontal winds on Earth. These forces are 1) the Pressure Gradient force, 2) the Coriolis force, and 3) Friction. We will investigate each of these forces one at a time beginning with the pressure gradient force.

Pressure Gradient Force In order to discuss the pressure gradient force, we must first consider what is meant by a gradient. The gradient of any physical quantity is a measure of the difference in the value of that quantity at two different locations divided by the distance between those two locations. For a hypothetical quantity, X (which could be air temperature, or moisture content of the air, etc.), the gradient of X is

Gradient X =

X 2 − X1 D

where X1 is the value of X at one location and X2 is the value of X at another location. The distance between the two locations is D. By extension, the pressure gradient between Madison and Chicago on a given day is equal to

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A

B

Figure 4.1. A fluid container with a divider between compartments A and B. Compartment B contains more fluid than A.

PG =

PresMadison − PresChicago . DMadison to Chicago

Consider the simple example illustrated in Fig. 4.1. Does a pressure gradient exist between columns A and B in that diagram? It is clear that the pressure is higher at the bottom of column B since the water is deeper there. Now, what happens if the divider in Fig. 4.1 is removed? Everyone knows that the water will flow immediately from column B to column A. The physical reason why it moves in that way is that the fluid is reacting to a pressure gradient force that is always directed from the region of high pressure to the region of low pressure. In the atmospheric fluid, the same rule applies: The pressure gradient force (PGF) compels fluid to move from regions of high pressure to regions of low pressure. Importantly, this force acts along the shortest possible path between the regions of high and low pressure. The distribution of atmospheric pressure is represented on a horizontal map by connecting locations of equal pressure observations by continuous lines known as isobars (literally, “same pressure”). Thus, when drawing the pressure gradient force arrow on such maps, one must draw it, from high to low pressure, perpendicular to the isobars.

Coriolis Force The Coriolis “force” is actually not a true force in the same sense as the forces of gravity, Friction, and the just discussed PGF. All three of these forces are able to produce accelerations in the

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direction of an object’s motion and can thereby increase or decrease the object’s speed. The Coriolis “force” is an effect that arises from the fact that the Earth rotates on its axis. Consider the room in which you are sitting. The floor, the walls, and the ceiling of this room serve as a convenient reference frame by which you might measure motions within the room. Because of the rotation of the Earth on its axis, despite all evidence to the contrary, both the room and your reference frame are accelerating. As a consequence, in order to accurately apply the laws of motion to objects on Earth or in its atmosphere, we must correct for this acceleration with the Coriolis force. A few terms must be defined before we can expeditiously proceed with our investigation of the Coriolis force. Most of those terms can be illustrated by consideration of the hypothetical amusement park ride depicted in Fig. 4.2. The ride consists of a horizontal arm, populated by a number of seats that extend from a central axis of rotation. If every seat on the ride costs the same amount, which one is the best deal for the thrill-seeker? Everyone probably has a sense that seat B is the best choice. A rigorous proof of that contention will arm us with the tools necessary to interrogate the Coriolis force.

Axis of Rotation

Seat B

Seat A

2 meters 5 meters

Figure 4.2. Carnival ride in which a rotating arm contains several seats. Seat A is 2 meters from the axis of rotation while Seat B is 5 meters from the axis of rotation. See text for explanation.

Imagine the horizontal arm makes one complete revolution each second. We can define its rotation rate as Rotation Rate =

Number of Rotations . One Second

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The radial velocity of each seat is simply the speed each seat travels around the circle swept out by the rotation. The general formula for radial velocity is

VRadial = Rotation Rate × Radius of Rotation where the radius of rotation is simply the distance between the axis of rotation and the object in question. Thus, the radial velocities of both seats A and B can be rigorously calculated assuming 1 revolution (equivalently 2π radians1) occurs each second. In such a case,

VRadialA =(2π/second) × (2m) = 12 m s−1 and

VRadialB =(2π/second) × (5m) = 31 m s−1 thus conclusively proving our suspicion that seat B is a better deal than seat A. The Earth also rotates at a constant rotation rate of one complete revolution per day. This translates to 7.292 x 10-5 rotations each second. As the cross-section of the Earth in Fig. 4.3 illustrates, the radius of rotation for objects on this rotating Earth is related to the latitude; it is largest at the Equator and shrinks to zero at the Poles. As a consequence, the radial velocity of an object at the Equator (latitude 0°) is substantially larger than the radial velocity of an object at New York City (latitude 40.8°N) or Fairbanks, Alaska (latitude 64.8°N).

Axis of Rotation

N. Pole Radius 1

Radius 2

Equator

Figure 4.3. Cross-section of Earth showing the relation of radius of rotation to latitude.

1 Radians are a measure of distance along a circle with radius 1. They are a convenient, non-dimensional means of discussing characteristics of radial (i.e. circular) motions. One full circle sweeps out 2π radians, a half circle sweeps out π radians, and a quarter circle sweeps out π /2 radians.

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Any object on the Earth, in its oceans, or in its atmosphere, is constrained to conserve a quantity called angular momentum so long as no real forces act upon it. For our purposes, examination of angular momentum conservation requires that we consider the motion of any object as the sum of its radial velocity and its velocity relative to the Earth. The radial velocity (VRadial Earth) is purely a function of latitude as we have just discussed. An object has a velocity relative to the Earth (VRelative to Earth) any time it moves from one location on Earth to another. We will further refine our description of this relative motion by measuring it in the direction of the rotation of the Earth. Thus, an eastward (westward) directed relative velocity will be considered positive (negative) and north or south motion will have zero relative velocity in the direction of the rotation of the Earth. With these specifications in mind, the conservation of angular momentum for an object can be expressed as

AM = (VRadial Earth + VRelative to Earth ) = Constant . Using this relationship we are able to consider the effect of rotation on terrestrial objects. We will begin by considering south-to-north motion in the Northern Hemisphere.

a. South-to-North Motion (N. Hemisphere) Imagine the scenario illustrated in Fig. 4.4 in which a ball is stationary at the Equator and is then given a kick directly northwards toward 20°N. At its initial position at the Equator, the ball has a radial velocity equal to the radial velocity of the Equator. Since it is stationary and is given an impulse to the north, it has no motion in the direction of the rotation of the Earth, so its VRelative to Earth is equal to zero. Imagine it makes its way to 15°N, without any real forces acting upon it, at which point we want to examine its velocities again. At this new latitude, it will have a radial velocity equal to the radial velocity at 15°N. We do not know its VRelative to Earth at this new latitude, and so we must invoke the Conservation of Angular Momentum to discover this velocity. Since no real forces have acted on it during its migration, we set the initial and final angular momemtums equal to each other:

VRADEQ + VREL EQ = VRAD o + VREL o . 15 N 15 N  Now, we want to solve for VREL  our original expression as

15oN

and we know that VREL is equal to zero. So we can rewrite EQ

VRADEQ = VRAD o + VREL o 15 N 15 N .  Next, though we don’t know exact numbers, we do know that VRAD  we can rearrange our expression into,

15 N

is less than VRAD . Thus EQ

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20oN Intended Path of the ball

Actual Path of the ball

Equator

South to North Motion Figure 4.4. Effect of the Coriolis force on south to north motion in the Northern Hemisphere. D eRAD mo - VRAD V EQ

15cN

= VREL REL

15 15ccN

from which we conclude that

VREL

15cN

2 0.

Thus, the relative velocity of the ball at 15°N is positive, which means that the ball has acquired a velocity in the direction the Earth’s rotation—eastward. Therefore, the rotation of the Earth, made manifest in the Coriolis force, has compelled the ball to turn to the right of its original path, as illustrated in Fig. 4.4. A similar argument can be made for north-to-south motion.

b. North-to-South Motion (N. Hemisphere) Imagine the opposite situation in which a ball is initially stationary at 15°N and is then pushed directly southward toward the Equator as shown in Fig. 4.5. Initially the radial velocity of the ball has the radial velocity of the Earth at 15°N and a relative velocity of zero. As the ball nears the Equator it has a radial velocity equal to the radial velocity of the Equator and an unknown relative velocity. We can express these statements in mathematical terms, upon invoking the conservation of angular momentum, as mo VD eRAD

15cN 15c

= VRAD + VREL RAD REL EQ EQ

EQ EQ

or, rearranging: mo VD eRAD

15cN 15c

- VRAD = VREL REL EQ

EQ EQ

.

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20oN

Actual Path of the ball

Intended Path of the ball

Equator

North to South Motion Figure 4.5. Effect of the Coriolis force on north to south motion in the Northern Hemisphere.

The radial velocity is largest at the Equator, so the difference on the left side of the above expression is negative. Therefore, we conclude that the ball has a negative relative velocity upon reaching the Equator. This means that the ball must have a velocity that is opposite to the direction of the rotation of the Earth, or westward. Therefore, the rotation of the Earth, made manifest in the Coriolis force, has compelled the ball to turn to the right of its original path, just as in the prior example. Similar arguments can be made for motions in the east-west direction on Earth, although in that case it is not conservation of angular momentum, but excess centrifugal force, that governs the physics. Nonetheless, the conclusion is the same: the Coriolis force deflects objects to the right of their intended paths in the Northern Hemisphere. It behaves oppositely in the Southern Hemisphere. Although it is not apparent from the argument we have made here, an important note concerning the Coriolis deflection is that it acts at right angles to the motion and therefore cannot change the speed of a moving object, only its direction. Thus we can conclude that; The Coriolis force acts to the right of motion (at right angles) in the Northern Hemisphere. Because the Coriolis force can not change the wind’s speed, only its direction, the Coriolis force is unable to initiate the wind.

Friction The last of the three horizontal forces we will investigate is Friction. Everyone has at least some rudimentary sense of how the Friction force behaves. If you have ever tried to generate some initiative at work or in your family that meets with opposition, you have experienced Friction.

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In such a situation you have probably felt as though the Friction was acting directly against your efforts. That is a precise analogy for how the Friction force acts in the atmospheric fluid. The Friction force always acts in the direction opposite to the motion. The operation of Friction in the movement of a book across a table is illustrated schematically in Fig. 4.6. Of the three forces we have thus far discussed, Friction is often the easiest to conceptualize. Given that the PGF, the Coriolis force, and the Friction force are somehow involved in the creation of the winds in the atmosphere, we might want to know what their relative contributions are to the mix. In fact, we will investigate winds that result from balances between a couple of combinations of these three forces, and so we must first examine the concept of force balance.

Motion

Friction Text book

Figure 4.6. Friction acting on a book pushed across a table.

Force Balance and Balanced Flow We have already seen that when a force is exerted upon an object, the object can be made to move. Common examples might be pushing a door open, rolling a snowball across the yard, or dropping a book from a table. The simplest notion of force balance might be that portrayed in Fig. 4.7, in which two forces are acting on a block with equal strength but in opposite directions. The fact that the forces are equal in size but pulling in opposite directions means that they are balanced and the net force acting on the block is zero. In this case of force balance, the object (the block) does not move.

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If we imagine dropping a cannon ball off of the roof of a tall building, we could measure the forces acting on the ball upon being dropped. One force is surely the gravitational force that is equal to the product of the mass of the ball and the acceleration due to gravity. The gravity force would act downward toward the center of the Earth. Another force that would act on the ball would be Friction due to air resistance. This force would act upward, against the tendency of gravity. For the case of a cannon ball, the force of gravity would be much larger than the Friction force and the ball would accelerate toward the ground upon being dropped. If, on the other hand, a drop of water the size of a raindrop were released from the top of the same tall building, things might be different. It would still be true that the forces of gravity

F1

100 lb Stone

F2

Figure 4.7. Two forces, F1 and F2, tugging on a 100 lb stone. When F1 and F2 are equal, the net force on the stone is zero and the stone will not move.

and Friction would act on the drop in opposite directions. However, it is likely that in this case, given some time, the two forces would be exactly the same size so that their opposing directions would render an exact balance between them. In other words, the net force acting on the drop would be zero—a state of force balance. When such a state is met for a falling object, it continues to fall but it no longer accelerates downward. In fact, as the state of force balance is established, the drop would reach its terminal velocity. This example might serve to alert you to the fact that even when an object is in a state of force balance, it can still move. Objects in force balance are only prohibited from accelerating. Armed with this distinction, we can now examine winds that result from balances among the three horizontal forces we have discussed. Since Friction is one of those forces, we will have to consider a balance between the PGF, Coriolis, and Friction forces when we examine the winds near the surface of the Earth, as contact with trees, mountains, and buildings provides friction to the atmospheric flow. When we are talking about flow well away from the surface, however, these obstacles are not present, and so Friction can be neglected as unimportant. We will begin our examination by considering this simpler case of the winds aloft (at upper levels in the atmosphere).

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The Winds Aloft: Geostrophic Balance Well above the surface of the Earth (anything higher than 1 km or so above the ground will usually qualify), there if very little friction in the atmospheric fluid. As a consequence of this fact, the only two horizontal forces that act on the motion of that fluid are the PGF and the Coriolis force. If the isobars are configured in the horizontal as shown in Fig. 4.8a, then the PGF acting on the indicated air parcel (black square) must be directed from HIGH to LOW pressure along the shortest possible path from high to low. Thus, the PGF force arrow is drawn as indicated, perpendicular to the isobars. Now, since the Coriolis force is the only other force acting at this level, and we desire to describe a balanced flow, then the Coriolis force arrow must be drawn with the same size but in exactly the opposite direction as the PGF arrow. We describe this by saying that the Coriolis force has equal magnitude but opposite direction (Fig. 4.8b). If we assume we are in the Northern Hemisphere, then we know something about how the Coriolis force acts with respect to motions; namely, to the right of the motion and at right angles to it. Thus, we have no choice, given the Coriolis force arrow drawn in Fig. 4.8b, but to draw the resulting balanced wind as shown in Fig. 4.8c, exactly parallel to the isobars. The balance we have depicted between the PGF and the Coriolis force is known as the Geostrophic Balance, and the wind that results from the balance is known as the geostrophic wind. Several important properties of this geostrophic wind come right out of the nature of the geostrophic balance. First, the geostrophic wind is always parallel to the isobars. Second, the speed of the geostrophic wind is proportional to the horizontal spacing of the isobars. If the isobars were closer together than portrayed in Fig. 4.8, then the size of the PGF in Fig. 4.8a would have to be larger. Correspondingly, the Coriolis force arrow in Fig. 4.8b would have to be larger. The Coriolis force can only be larger (at a given latitude) if the speed of the moving object that gives rise to the Coriolis force (in this case, the air parcel) is larger; hence, a larger geostrophic wind speed corresponds to a larger PGF. Finally, in the middle latitudes, the observed winds aloft are often very nearly equal to the geostrophic wind because of the near equality of the PGF and Coriolis forces under mid-latitude conditions. The fact that the mid-latitude winds aloft on Earth are nearly geostrophic is very useful for diagnosis, as it allows us to get a very accurate sense of the wind distribution over the globe by simply knowing the pressure distribution. Of course, near the surface we need to incorporate friction into a three-way force balance.

The Winds Near the Surface: Friction and the Three-Way Balance The presence of a number of obstacles to the flow near the surface necessitates the inclusion of friction in any discussion of balanced flow near the ground. Imagine a set of sea-level isobars as shown in Fig. 4.9a. As in the prior discussion, the PGF acting on the indicated parcel can be represented by an arrow drawn from high to low pressure, perpendicular to the isobars. In order that we describe a balanced flow near the surface, this PGF must be balanced by the sum of the Coriolis and Friction forces, represented by the dashed arrow in Fig. 4.9b. Now, recall

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PGF P-ΔP

P+ΔP

(a)

y x

PGF P-ΔP

P+ΔP

COR

y

(b)

x

PGF P-ΔP

Vgeo P+ΔP

COR

y x

(c)

Figure 4.8. (a) Pressure gradient force arrow in a field of isobars. (b) Coriolis force arrow that exactly balances the PGF. This is the geostrophic balance. (c) In the Northern Hemisphere, the resulting geostrophic wind is parallel to the isobars with lower pressure to its left.

that there are rules regarding the way in which the Coriolis and Friction forces act on objects in motion. In the Northern Hemisphere, the Coriolis force acts to the right of motion at right angles to it. Friction, of course, acts exactly opposite to any motion. If we draw those two force directions relative to a hypothetical motion arrow, as in Fig. 4.9c, we find that the Coriolis and Friction forces act at right angles to one another as well. Thus, the sum of the Coriolis and Friction forces is the hypotenuse of the right triangle made by the two forces; that sum is represented by the dashed arrow in Fig. 4.9c. We can now overlay the dashed arrow from Fig. 4.9c (along with the three other arrows surrounding it) onto the dashed arrow in Fig. 4.9b. Upon doing so we find that the balanced wind that results from a three-way balance between the PGF, Coriolis, and Friction forces blows across the isobars at a slight angle from high to low pressure, as illustrated in Fig. 4.9d.

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PGF P-ΔP

P+ΔP

(a)

y x

PGF P-ΔP

P+ΔP

COR+FR

y

(b)

x

V

FR

Sum of FR and COR y

(c)

COR x

PGF v FR

P-ΔP

P+ΔP

COR COR+FR

y x

(d)

Figure 4.9. (a) Pressure gradient force arrow in a field of isobars. (b) With Friction involved, only the sum of Coriolis and Friction forces can balance the PGF. (c) The Coriolis and Friction forces have characteristic relationships to the wind arrow, V. (d) Final balanced wind from the three-way force balance.

The angle of across-isobar flow will be determined by the size of the Friction force. For instance, imagine that, for the sum of Coriolis and Friction shown in Fig. 4.9c, the Friction arrow were larger. Mentally overlaying a revised four-arrow diagram onto the dashed arrow in Fig. 4.9b would result in a much larger across-isobar angle for another possible balanced flow. Another way to convince yourself that the size of the Friction arrow will determine the angle at which the surface wind crosses the isobars is to recall that with zero Friction, the flow is in geostrophic balance and there is zero across isobar angle. Now that we have an understanding of the geostrophic flow above the ground and the three-way force balance at the ground, we can investigate the balanced circulations around the major weather producing systems in the middle latitudes: cyclones and anticyclones.

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Winds Near Cyclones and Anticyclones Cyclones are local regions of low pressure. Cyclones can occur at sea-level or at levels in the middle and upper troposphere; in any case they are characterized by a local minimum in pressure as measured on a surface of constant elevation. Anticyclones are local regions of high pressure and, similarly, can be identified at any level in the atmosphere. Let us consider the geostrophic winds associated with a cyclone first.

Figure 4.10. Diagram showing the nature of the geostrophic wind around a cyclone (region of low pressure). (a) Sea-level isobars. (b) PGF arrows at four stations around the low. (c) COR arrows added to balance the PGF arrows drawn in (b). (d) Geostrophic winds drawn for Northern Hemisphere conditions.

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Cyclones A pair of circular isobars along with four parcel locations are indicated in Fig. 4.10a. The capital “L” in the center of the diagram indicates that the pressure is lowest in the middle, thus describing a cyclone. In order to determine the direction of the winds around this cyclone we must first draw the PGF arrow at each of the four parcel locations. Recall that the PGF arrow must be drawn directed from high to low pressure, perpendicular to the isobars as indicated in Fig. 4.10b. The geostrophic balance involves a balance between the Coriolis and PGF forces so the Coriolis forces must be drawn opposite to the PGF at each of the four parcel locations. These arrows are shown in Fig. 4.10c, along with the PGF arrows from Fig. 4.10b. Finally, let us assume we are in the Northern Hemisphere. Given that assumption, the resulting geostrophic winds must be directed, at each parcel location, as indicated in Fig. 4.10d. Thus, we see that The flow around a cyclone in the Northern Hemisphere is counterclockwise. This fact is an inescapable result of the force balances just discussed.

Anticyclones Another pair of circular isobars along with four parcel locations are indicated in Fig. 4.11a. The capital “H” in the center of the diagram indicates that the pressure is highest in the middle,

Special Historical Note Science does not often progress in a linear fashion with theory and observations meshing perfectly and simultaneously to create new insight about Nature. For instance, the fact that the flow around mid-latitude cyclones is counterclockwise in the Northern Hemisphere was known long before it was physically understood. Benjamin Franklin (1706-1790) was the first great American scientist and was very interested in a number of meteorological phenomena. He undertook voluminous correspondence with this family in Boston while he was in Philadelphia. By comparing notes about the weather in these letters, Franklin came to recognize that stormy days with northeasterly winds in Philadelphia tended to occur just before such days in Boston. Further, he noted that when such northeasterly winds were occurring in Boston, the winds were often from the northwest or west in Philadelphia. From these observations, he concluded not only that the flow around such storms was counterclockwise but that the storms were moving entities.

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thus describing an anticyclone. As in the previous example, we first draw the PGF arrows at each of the four parcel locations. These arrows are indicated in Fig. 4.11b. A Coriolis force arrow of equal magnitude but opposite direction (Fig. 4.11c) is required at each of the four locations in order to describe a geostrophic balance. Finally, again assuming we are in the Northern Hemisphere, where the Coriolis force acts to the right of the wind at right angles, we are forced to draw the wind arrows as indicated in Fig. 4.11d. Thus, we see that The flow around an anticyclone in the Northern Hemisphere is clockwise.

P-ΔP P

H (a) PGF Arrows P-ΔP P

H (b) PGF Arrows P-ΔP P

H (c)

COR Arrows PGF Arrows

VGEO Arrows P-ΔP P

H COR Arrows

(d)

Figure 4.11. Diagram showing the nature of the geostrophic wind around an anticyclone (region of high pressure). (a) Sea-level isobars. (b) PGF arrows at four stations around the low. (c) COR arrows added to balance the PGF arrows drawn in (b). (d) Geostrophic winds drawn for Northern Hemisphere conditions.

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Of course, thus far we have only considered the geostrophic winds around regions of high and low pressure. We next consider the flow around such disturbances in the presence of friction.

Surface Winds Near Cyclones and Anticyclones The addition of Friction to the mix, to describe the surface flow around cyclones and anticyclones, is a straightforward extension of our previous discussion of the three-way force balance. For the Northern Hemisphere cyclone, the flow remains counterclockwise, but since the inclusion of Friction dictates that there will be an across-isobar angle from high to low pressure, the counterclockwise flow is directed slightly inward toward the center as shown with bold arrows in Fig. 4.12a. This inward directed flow means that a small component (or portion) of the surface wind, indicated by the gray arrows in Fig. 4.12a, is directed straight toward the lowest pressure. We could alternatively say that this component of the wind is convergent toward the center of the cyclone. The addition of Friction to the Northern Hemisphere anticyclone picture does not change the general clockwise rotation of the winds, but it does force the flow outward from the center of the anticyclone, as shown by the bold arrows in Fig. 4.12b. The outward directed, clockwise flow around the anticyclone means that a small component of the surface wind, indicated by the gray arrows in Fig. 4.12b, is directed away from the center of the anticyclone. We could alternatively say that this component of the wind is divergent from the center of the anticyclone.

P+ΔP P

L (a) P-ΔP P

H (b) Figure 4.12. (a) Schematic of wind around a surface cyclone. Black arrows are the full wind, gray arrows are the portion of the wind that is convergent into the center of the low. (b) Wind around a surface anticyclone. Black arrows are the full wind, gray arrows are the portion of the wind that is divergent from the center of the high.

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The ideas of convergence and divergence will next be related to the production of upward and downward motions in cyclones and anticyclones. In order to make this argument we must first investigate the notion of the continuity of the atmospheric fluid. This is most easily conveyed through comparing the atmospheric mixture to other substances.

The Continuity of Mass The atmospheric gas is different from a number of other substances with which we have frequent contact. For instance, consider something like mashed potatoes. It is quite possible to make a pile of mashed potatoes. For that matter, it is possible to make a pile of bricks, logs, socks, or many other substances. It is not, however, possible to make a reasonable pile of water. It is similarly impossible to make a pile of air. This may seem like a foolish list to compile but it serves an important purpose. Water and air are continuous rather than discrete substances. As a consequence, there will be a relationship between the horizontal convergence or divergence at certain locations in these fluids and upward or downward motions within them. For instance, imagine that, over your location on a certain day, the fluid atmosphere is diverging from some point at the surface. Since the atmospheric fluid cannot pile up, this horizontal divergence must be related to the sinking of a column of air at the point above which the air is diverging. This idea is portrayed schematically in Fig. 4.13a. The sinking air warms as it sinks (since the pressure rises toward the ground and the air is compressed). As it warms, the air experiences a decrease in its relative humidity, and any clouds that might have populated the sky will soon evaporate and clear skies will develop. Recall that surface high pressure regions (anticyclones) are associated with surface divergence of the winds. Thus, based on the continuous nature of the atmospheric fluid, we can unequivocally relate surface high pressure regions with clear skies and slowly sinking air.

Sinking

Rising

Surface Divergence

(a)

Surface Convergence

(b)

Figure 4.13. Schematics of the relationship between (a) surface divergence and sinking motion and (b) surface convergence and rising motion.

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Conversely, if the atmospheric fluid is converging toward a point at the surface, as it does in the case of surface cyclones, and it cannot pile up, the fluid must rise at the point of convergence. This is portrayed schematically in Fig. 4.13b. As this air goes upward, it cools as it expands, thereby increasing its relative humidity and increasing the likelihood that clouds and precipitation will develop. Thus, surface low pressure regions are unambiguously associated with cloudiness and precipitation. These are major insights we have just gained about the nature of the very weather systems that affect us on a daily basis. All of the insight comes from arguments that we have built a step at a time. The fact that rising (sinking) air cools (warms) and that that, in turn, leads to an increase (decrease) in the relative humidity of the air was all described in the prior section of the course, using ideas from the very earliest lectures. Science builds explanations by acquiring knowledge and insight on very specific pieces of nature, not always knowing what those pieces will end up telling us or how they will come together. Now, the fact that fluids don’t come in clumps (i.e. they are continuous) means that they behave a certain way when regions of divergence and convergence exist within them. Consider the case of surface convergence again. We already know that surface convergence must be associated with upward vertical motion starting at the ground. Once the air that is rising reaches the middle or upper troposphere, what happens to it? The answer is illustrated in Fig. 4.14a; the

Upper Divergence

Upper Convergence

RISING

SINKING

Surface Convergence

Surface Divergence

(a)

(b)

Figure 4.14. The relationships between (a) surface convergence, upper-level divergence and rising motion, and (b) surface divergence, upper-level convergence and sinking motion.

air must be divergent at upper levels. Thus, we can complete our understanding of this process by noting: Lower level convergence is associated with upper level divergence, and there is upward vertical motion in the column of air between the two levels. The corresponding picture for surface divergence is shown in Fig. 4.14b. We note that;

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Lower level divergence is associated with upper level convergence and there is downward vertical motion in the column of air between the two levels. The implications of this full expression of the continuity of mass are profound for our continued investigation of cyclones and anticyclones. It means that surface cyclones, the major weather producing entity in the middle latitudes, must be associated with regions of upper level divergence. Conversely, surface anticyclones must be associated with regions of upper level convergence. By what mechanism these upper level regions of convergence and divergence arise we still must investigate. We will do so in the context of viewing cyclones and anticyclones as wave phenomena.

Cyclones and Anticyclones as Wavelike Disturbances If one examines the distribution of surface or upper level cyclones and anticyclones, it becomes apparent that these disturbances occur in sequence—high, low, high, low—as illustrated in Fig. 4.15. Our fully three-dimensional picture of a cyclone consisted of a region of surface low pressure, into which the surface air converges, along with an upper level region of divergence of air and upward vertical motion in the intervening column. These elements are illustrated in Fig. 4.16. Since the air has mass, the surface convergence depicted in Fig. 4.16a represents a flux of mass into the center of the surface cyclone. Were this addition of mass the only change made to the mass of the column, then the column would weigh more and the surface pressure would increase. However, there is also divergence at upper levels, which exports mass from the top of the column. If this amount of mass is greater than the amount that is fluxed into the column at sea level, then the weight of the column will decrease with time and the surface pressure will correspondingly decrease. Thus, we can draw the physical conclusion: When the upper divergence is greater than (less than) the surface convergence, the mass of the column decreases (increases) and the surface pressure will decrease (increase).

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500 mb (a) L

L

SLP (b) Figure 4.15. Weather maps for a typical spring day over the continental United States illustrating the characteristic sequential distribution of mid-latitude weather systems. (a) 500 mb geopotential height (solid lines) with trough axes marked by bold dashed lines and ridge axes by bold solid lines. (b) Sea-level pressure (SLP) analysis with isobars of low SLP (SLP < 1012 mb) dashed and isobars of high SLP solid. Note that at both levels highs and lows appear in sequence across the continent.

DIV

CON

500 mb

500 mb

Surface

Surface

(a)

(b)

Figure 4.16. Three-dimensional view of (a) a cyclone and (b) an anticyclone. Note the relationship between surface convergence and rising motion in (a) and between surface divergence and sinking motion in (b).

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If the surface pressure at the center of a cyclone decreases (increases), the storm is said to be intensifying (weakening). A fully three-dimensional view of the surface anticyclone consisted of a region of surface high pressure, away from which surface air diverges, along with an upper level region of convergence of air and downward vertical motion in the intervening column. These elements are illustrated in Fig. 4.16b. The surface divergence depicted in Fig. 4.16b represents a flux of mass out of the center of the surface anticyclone. Directly above it, there is a region of upper level convergence that fluxes mass into the column. Using an argument similar to that used in the case of the surface cyclone, we conclude: When the upper convergence is greater than (less than) the surface divergence, then the mass of the column increases (decreases) and the surface pressure at the center of the anticyclone rises (falls). Whenever the central pressure of an anticyclone rises (falls), the anticyclone is said to be intensifying (weakening). The foregoing analysis, fundamental though it is, begs an even more fundamental question: What causes the regions of divergence and convergence at upper levels in the atmosphere? As a first step toward answering this question, the characteristic relationship between the positions of surface cyclones and anticyclones and regions of upper level cyclones and anticyclones is shown in Fig. 4.17. It turns out that changes in the local rate of spin of the air are directly related to the production of divergence and convergence at upper levels.

Ridge Axis

Ridge Axis

P-ΔP

P

H

L

P+ΔP

P

H P+ΔP

N E

Trough Axis

Figure 4.17. Solid lines are isobars at the 5.5 km level. "L" and "H" represent the low and high pressure regions at that level, respectively. Gray "L" and "H" represent locations of surface cyclone and anticyclone, respectively. Positions of ridge and trough axes at 5.5 km are indicated. A quantity called vorticity is a measure of the rate of spin of the air. Note that the word “vortex” is embedded with the word “vorticity.” It may seem strange, at first thought, that the

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air can spin, but a vast catalogue of atmospheric phenomena illustrate that the air can, indeed, spin. If you have ever seen a dust-devil or a swirling mass of dry leaves in the fall, you know that the air can spin. Sometimes, when really frigid air comes rushing over a large lake or the ocean in the early winter, one can observe steam devils: swirling masses of steam fog reacting to both the presence of the cold air over the warm water and the strong winds. Of course, almost everyone who has grown up in the central United States is aware of the existence of even larger swirling masses of air known as tornadoes. Still larger swirling masses of air, the mid-latitude and tropical cyclones you have undoubtedly seen in satellite movies either in class or in the broadcast media, are all compelling evidence that the air can spin. The cyclones and anticyclones that we have been discussing are among the largest examples of air spinning, and so measuring that spin with vorticity is very relevant for understanding the day-to-day weather. By convention (e.g. international agreement on terminology), positive vorticity describes the counterclockwise spin of an air parcel. Negative vorticity describes the clockwise spin of an air parcel. These two types of vorticity are illustrated in Fig. 4.18.

Positive Vorticity

Negative Vorticity

Figure 4.18. Illustration of positive and negative vorticity.

Vorticity in an atmospheric flow can be the result of horizontal differences in straight line wind speed (horizontal shear) or curvature in the flow itself. Horizontal shear vorticity, as illustrated in Fig. 4.19, arises as a result of straight line flow speed differences. The diagram shows flow in a river in which the flow speed is strongest in the middle of the river. On the north side of the river, a paddlewheel placed in the water will tend to rotate counterclockwise, since the speed of the flow is stronger on the south side of the paddlewheel. Meanwhile, a paddlewheel placed on the south side of the river would turn clockwise, since the speed of the flow increases toward the center of the river. Thus, we would observe positive vorticity in the water on the north side of the river and negative vorticity in the water on the south side. Flow around bends in the river are shown in Fig. 4.20. If one places a paddlewheel in the flow depicted in Fig. 4.20a, the bold spoke will cover more ground as the whole wheel rounds

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N

Figure 4.19. Shear vorticity in a river. Thick black arrows represent the flow speed in the river strongest in the center and weaker to the north and south. Paddlewheels on either side of fastest flow have opposite vorticities. the bend than its opposite spoke. Thus, we see that the wheel itself turns clockwise around the bend depicted in Fig. 4.20a. Notice that the flow of water (represented by the bold arrows) also traces out a clockwise turn through this bend. Therefore, we conclude that any clockwise

Negative Curvature Vorticity

(a)

Positive Curvature Vorticity

(b)

Figure 4.20. Illustration of curvature vorticity in a river. Heavy black arrows indicate flow direction. Bold spoke of the paddlewheel has to move further around the bend than its opposite spoke. (a) Clockwise flow around a bend in the river. Turning is clockwise, so the vorticity is negative. (b) Counterclockwise flow around a bend. Turning is counterclockwise, so vorticity is positive.

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curvature in the fluid flow is characterized by negative vorticity. Conversely, counterclockwise curvature in the flow (as depicted in Fig. 4.20b) is characterized by positive vorticity. Though we have imagined flow in a hypothetical river, the same rules apply to the flow of air in the atmosphere. If we now return to the atmospheric flow at 5.5 km above sea-level, previously illustrated in Fig. 4.17, we can identify the regions of positive and negative vorticity that arise there due to curvature in the flow. The largest values of negative vorticity occur in the ridge axes while the largest values of positive vorticity occur in the trough axes (Fig. 4.21). Recall that, as stated earlier, it is the local change in the spin (i.e. vorticity) that is related to the production of divergence and convergence. More precisely, when the vorticity is increased at a location, divergence is forced at the top of the fluid column at that location. Conversely, when the vorticity is decreased at a location, convergence is forced at the top of the fluid column at that location. Negative Vorticity

Negative Vorticity

P-ΔP

P

H

L

P+ΔP

P

H P+ΔP

N E

Positive Vorticity

Figure 4.21. Vorticity distribution in a trough/ridge wavetrain. Light shading represents negative vorticity center while darker shading represents positive vorticity center. Thin arrows are the geostrophic wind directions in the indicated locations. Regions of positive and negative vorticity advection are labeled PVA and NVA respectively. Solid lines are isobars at the 5.5 km level.

A simple way to change the local value of the vorticity at upper levels is through vorticity advection. This may seem like an impossibly obscure notion, but it is really quite the opposite. Recall that temperature, another measurable characteristic of the air, can be advected as well. When we refer to positive temperature advection (also known as warm air advection), we are describing a local increase in temperature resulting from the horizontal transport of higher temperature (warmer) air to a given location by the horizontal winds. By analogy, positive vorticity advection (PVA) describes a local increase in vorticity resulting from the horizontal transport of higher vorticity air to a given location by the horizontal winds. Negative vorticity advection (NVA) describes a local decrease in vorticity resulting from the horizontal transport of lower vorticity air to a given location by the horizontal winds.

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Now, returning to Fig. 4.21 and examining the geostrophic winds, we can easily determine where regions of positive and negative vorticity advection at that level will occur. As illustrated in the diagram, the region of negative vorticity advection (NVA) will occur to the east of the maximum negative vorticity feature, whereas the region of positive vorticity advection (PVA) will occur to the east of the maximum positive vorticity feature. Since the geostrophic flow is moving from west to east in the diagram, an equivalent statement is: PVA (NVA) occurs downstream of the upper trough (ridge) axis. Recall that surface cyclones are found downstream of upper level trough axes while surface anticyclones are found downstream of upper level ridge axes, as shown in Fig. 4.17. Now, we have a physical explanation of this fact. Downstream of the upper level trough axes, positive vorticity advection occurs at upper levels. This PVA is associated with upper level divergence, which evacuates mass from the column downstream of an upper level trough axis. The upper divergence is attended by surface convergence and upward vertical motion in the intervening column of air. As the air rises, it expands and cools, increasing the relative humidity. Clouds and precipitation form along with a surface cyclone. Downstream of the upper level ridge axes, negative vorticity advection occurs at upper levels. This NVA is associated with upper level convergence that stuffs the column full of mass downstream of the upper level ridge axis. The upper convergence is attended by surface divergence and downward vertical motion in the intervening column of air. As the air sinks, it is compressed and it warms up, decreasing its relative humidity. Clear skies and fair weather form along with a surface anticyclone. Our physical understanding of cyclones is clearly growing. Next we investigate the structure and evolution of middle latitude cyclones, as both have implications for the types of weather that are associated with them.

The Structure of Mid-Latitude Cyclones We must investigate both the horizontal and vertical structure of mid-latitude cyclones in order to most comprehensively understand the relationship these cyclones have to the sensible weather at middle latitudes. We begin with the horizontal structure.

Horizontal Structure Mid-latitude cyclones cover millions of square kilometers in area and have lifetimes, during which they intensify and die, of about one week. As we have seen, they are characterized by counterclockwise rotation of the winds (in the Northern Hemisphere) and are associated with a minimum in sea-level pressure. To this point, we have been drawing these disturbances as if

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they were perfectly circular disturbances in the sea-level pressure field. This is not accurate, as they have considerable smaller scale structure embedded within them. In actuality, the mid-latitude cyclone is rather elliptical as depicted in Fig. 4.22. Within the generally elliptical shape there are two pronounced pressure troughs: one that extends southward and one that extends eastward from the central pressure minimum. These pressure troughs are lines of enhanced surface convergence, which tend to separate air masses of distinctly different temperatures and humidities. These lines are known as fronts and were first referred to as such in 1922 in a famous scientific paper by J. Bjerknes and H. Solberg. The cold front occupies the southward extending pressure trough and represents the warm edge of a cold air mass advancing eastward or southeastward. The warm front occupies the eastward extending pressure trough and represents the warm edge of a warm air mass advancing northward or northwestward. The fronts tend to separate the cyclone into sectors, as shown in Fig. 4.22. The air poleward of the warm front and westward of the cold front tends to be of polar origin, while the air between the cold and warm fronts is homogeneously warm. This region is known as the warm sector.

COLD

L C

OL

P+ΔP

Warm front

DP AR W

M

Cold front

Surface Cyclone Analysis Figure 4.22. Sea-level isobars (thin solid lines) and surface fronts in a typical sea-level pressure analysis of a mid-latitude cyclone. This model of the instantaneous structure of the mid-latitude cyclone is known as the Norwegian Cyclone Model, since it was introduced by Bjerknes and Solberg (two Norwegians). It was developed just after World War I, which likely accounts for its incorporation of the word “front” into the model to describe the boundaries between different airmasses. The Norwegian Cyclone Model was not the first to describe the instantaneous structure of the cyclone. Indeed, quite a number of excellent ideas concerning this subject had been devised in the 19th century. The genius of the Norwegian Cyclone Model (NCM) was that this instantaneous structure was, for the first time, placed into the context of an identifiable life cycle.

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According to the NCM, cyclones developed as perturbations on a globe-girdling, knife-like polar front that separated cold polar air from warm tropical air (Fig. 4.23a). The circulation around this perturbation acted to locally distort the polar front into the warm and cold fronts of the developing cyclone (Fig. 4.23b). After a day or two, the cyclone reaches its maximum intensity, or mature stage (Fig. 4.23c), at which time the fronts are fully developed. In its post-mature phase, the cyclone is said to occlude and it begins to weaken. During occlusion the sea-level pressure minimum becomes divorced from the peak of the warm sector and a new surface boundary, known as the occluded front, forms (Fig. 4.23d). Subsequently, the occluded cyclone eventually decays away to nothing and disappears from the face of the Earth. Polar Front

L Perturbation Stage

(a) Warm Front

L Cold Front

Incipient Stage

L

(b) Warm Front

Cold Front

Mature Stage

(c)

Occluded Front

L Warm Front Cold Front

Occluded Stage

(d)

Figure 4.23. Evolution of a mid-latitude cyclone according to the Norwegian Cyclone Model. See text for explanation.

Vertical Structure of Fronts in a Cyclone Recall that all fronts, including the occluded front, are lines of enhanced surface convergence. Therefore, it is probably not surprising that the frontal regions are among the most important weather-producing portions of the storm. By examining the vertical structure of the fronts in the cyclone, deeper understanding of their role as weather producers is obtained.

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A vertical cross-section of the cold front is illustrated in Fig. 4.24. The cold front is a steeply sloped dome of cold air that barrels its way into the warm air to its east. The convergence that results from the cold air and warm air being forced together at the cold front leads to a horizontally narrow and intense updraft of air indicated by the spotted arrow in Fig. 4.24. By virtue of the narrow and intense nature of the updraft often associated with a surface cold front, severe weather, in the form of thunderstorms or squall lines, is not uncommon along the cold front. L A A`

Cold Air

Warm Air

A

A`

Figure 4.24. Vertical cross-section through a cold front. Dotted arrow represents the updraft of air into the cumulus cloud, from which precipitation falls. Location of line A-A' indicated in the inset at upper right. B

L B`

Cold Air

B

Warm Air

B`

Figure 4.25. Vertical cross-section through a warm front. Dotted arrow represents the sloping updraft of air along the warm front . Widespread, gentle rains often fall in association with the warm frontal ascent. Location of line B-B' indicated in the inset at upper right. A vertical cross-section through the warm front is illustrated in Fig. 4.25. The warm front is a shallow sloping ramp that lies atop a wedge of cold air to its north. The warm air in the warm sector to the south is forced to ascend over this ramp by the circulation of the cyclone. The

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resulting ascent is often less intense and of a wider horizontal extent than the ascent associated with the cold front. As a result, more widespread and stratiform (non-severe) precipitation is often associated with the warm front. Knowing these characteristic structures, we can say how this frontal structure relates to the weather. The cover of this book depicts a satellite image of a fully developed mid-latitude cyclone. It exhibits the characteristic comma-shape in its cloud shield. The comma shape is composed of a narrow, southward extending cloud tail and a broader cloud mass extending eastward from near the sea-level pressure minimum. These cloud elements are associated with the cold and warm fronts of the cyclone, respectively.

Occluded Fronts The Norwegian Cyclone Model suggests that occluded fronts form when one frontal zone encroaches upon and subsequently ascends the other frontal zone. In theory, two types of occlusions are possible: the cold occlusion and the warm occlusion. The cold occlusion was thought to occur when the warm front was forced to rise upon meeting up with the cold front. To date, there has been little or no observational evidence that this type of process occurs in Nature. In fact, it is widely believed that only the warm occlusion actually takes place. The warm occlusion forms when the cold front encroaches upon the warm front and subsequently ascends it. This sequence of events, and the resulting vertical frontal structure, is shown in Fig. 4.26. There has been a nearly century-long argument about whether or not the

Cold air

Warm air

Cold air

Warm air Cold air

Cold air

Figure 4.26. Development of a warm occluded frontal structure. Cold and warm fronts are separate in the pre-occlusion cross-section. Cold front ascends the warm front in the occluded cross-section. Gray frontal analysis represents the warm occluded front.

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warm occluded structure depicted here can actually form by this frontal catch-up mechanism. Recent research has demonstrated that it can, in fact, occur this way. Still, among the various frontal structures associated with mid-latitude cyclones, the occluded front remains the most controversial.

Vertical Structure of Cyclones We have thus far discussed the vertical structure of the frontal zones that are associated with mid-latitude cyclones. Now we shall examine the vertical structure of the entire cyclone environment. Part of this story stems from consideration of the simple geometric distance between any two isobaric levels in the atmosphere. Since pressure decreases with increasing height in the atmosphere, it is not surprising that there is a significant vertical distance between, say, the 500 and 1000 mb pressure levels on any given day. What may strike you as surprising, at first, is that the amount of mass per square meter between these two isobaric surfaces is identical everyday. Why? Recall that above the 500 mb surface there is enough atmosphere to exert 500 mb of pressure on a square meter. Similarly, above the 1000 mb surface there is enough mass to exert 1000 mb of pressure on the same square meter. Thus, in the 1000 to 500 mb layer, there must be enough mass to exert 500 mb of pressure on that square meter. Thus, the two columns illustrated in Fig. 4.27, despite their 500 mb

Height

T hickness

A

B

T hickness

500 mb

1000 mb

Figure 4.27. Two columns with different 1000-500 mb thicknesses. See text for explanation. different depths, must have the same mass contained within them since they are both bounded by 1000 mb at the bottom and 500 mb at the top. We shall refer to the geometric distance between these two isobaric levels as the “thickness” of the isobaric layer. Since column B in Fig. 4.27 has a greater volume than column A, and they both have the same mass, the air in column B is less dense than the air in column A. Since we are comparing air columns bound by the same pressure interval, we can conclude (based upon the Gas Law)

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500 mb

5 km

COLD

850 mb

1000 mb

L

Figure 4.28. Vertical cross-section through a cold core cyclone. "Warm" and "Cold" refer to the column average temperatures in the three columns. Solid lines are isobars, thin dashed line is 5 km elevation line. The PGF is much larger at the top black dot though both are in the same vertical column. Small "L" is the location of the lowest sea-level pressure. that the air in column B must be warmer than the air in column A. Thus, we find that the thickness between two isobaric surfaces is proportional to the column’s average temperature in that isobaric layer. This fact has profound implications for our understanding of mid-latitude weather systems. A typical mid-latitude cyclone has a cold core. This means that the coldest air in the cyclone, at all levels, is right in the center of the disturbance. Thus, as portrayed in Fig. 4.28, the thickness between successive isobaric levels is smallest at the center of the mid-latitude cyclone. As a consequence, the PGF (indicated schematically as the slope of the various isobaric surfaces in Fig. 4.28) increases with increasing height. Therefore, the intensity of the cyclone itself increases with increasing height. But let’s not forget that these mid-latitude cyclones also tilt to the west with height. If we tilt the cold column illustrated in Fig. 4.28 to the west, this also has profound implications for our understanding of how the cyclone works. Keeping in mind the relationship between upperlevel divergence and convergence and the position of the upper-level low, the tilt provides a setup for convergence and divergence couplets in the vertical that serve to produce strong upward vertical motions over the surface cyclone center (Fig. 4.29). In fact, one of the ways in which cyclones eventually weaken is that the westward tilt gradually decreases during the cyclone life cycle. As it does so, the convergence into the surface cyclone becomes vertically superposed with the upper-level convergence in the vicinity of the upper level cyclone, thus making it impossible to evacuate mass from the column. The result is often a pressure rise at sea level.

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500 mb

L

1000 mb

L

Figure 4.29. Vertical cross-section through a developing mid-latitude cyclone in which the cold core structure tilts westward with height. Dashed black line depicts the westward tilt of the low pressure center. C denotes horizontal convergence that occurs into both the surface and upper-level lows. D represents the horizontal divergence that straddles the convergence at both levels. Thick black arrows represent the upward and downward vertical motions of the storm that are tied to the vertical distribution of convergence/divergence set up by the structure. See text for further explanation.

300 mb

COL D

COL D

12 km

850 mb

1000 mb

L

Figure 4.30. Vertical cross-section through a warm core cyclone, such as a hurricane. "Warm" and "Cold" refer to the column average temperatures in the three columns. Solid lines are isobars, thin dashed line is 12 km elevation line. The PGF is large and inward directed at the bottom black dot. It is outward directed at the upper-level black dot though both are in the same vertical column. Small "L " is the location of the lowest sea-level pressure (which is well below 1000 mb!).

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Hurricanes are also cyclones, but they are tropical cyclones. As such, they have a characteristic warm core structure to them. In other words, the warmest air in the entire tropical cyclone occurs right in the center, a result of the tremendous latent heat release within the thunderstorms near the center of the storm. The consequences of this warm core structure are illustrated in Fig. 4.30. Recall that the central sea-level pressure in a hurricane is often quite low and the surface winds are extremely strong near the center, necessitating a large PGF near the surface. As a result of the warm core structure, the intensity of the tropical cyclone decreases with increasing height. In fact, it is not at all uncommon for a tropical cyclone environment to be characterized by very low pressure at the surface and a high pressure region directly above it at 12 km. Since the hurricane does not tilt with height as the mid-latitude cyclone does, this structure supports strong upward vertical motions which fuel the hurricane. We will visit the hurricane in more detail in Chapter 5.

Vertical Shear of the Geostrophic Wind There are other intriguing consequences to the fact that the thickness of a column depends on the column’s average temperature. Figure 4.31 shows a north to south cross section in the Northern Hemisphere. Given the location of the cross-section, the air column is colder to the north (nearer the North Pole) than it is to the south (nearer the Equator). If we assume that the surface pressure is everywhere equal to 1000 mb, then there is no PGF at the surface and, therefore, no geostrophic wind at that level. Because the air to the south is warmer, the b 500 m

PGF

Z=5.5 km

COL D

WAR M

COR

Zero wind

1000 mb

Z=0 km

Figure 4.31. Vertical cross-section across a region of horizontal temperature contrast. Solid black lines are isobars. Dashed gray lines are elevation contours. The lack of PGF at Z=0 km leads to "Zero wind" there. At 5.5 km in the same vertical column there is a large geostrophic wind into the page, signified by the "X" in the circle.

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1000–500 mb thickness is larger to the south than to the north. As a consequence, the 500 mb isobar has a considerable slope to it in the cross-section. The slope of the 500 mb surface means that at some middle tropospheric level such as 5.5 km, the pressure is higher to the south than it is to the north. Therefore, there is a northward directed PGF at 5.5 km above the surface as indicated. At such an elevation, we need not concern ourselves with Friction, so the only type of balanced flow we might expect is the geostrophic balance. In order for there to be geostrophic balance at this level, the Coriolis force at this level must be equal in size but opposite in direction to the PGF. The resulting geostrophic wind is large and directed INTO the page (i.e. directed from west-to-east). Thus, we have proven a fundamental fact about the mid-latitude atmosphere: The vertical change of the geostrophic wind is directly proportional to horizontal temperature gradients. The vertical change of geostrophic wind is often referred to as the geostrophic vertical shear. Since this geostrophic vertical shear is directly proportional to horizontal temperature contrasts, it is known more commonly as the thermal wind. The thermal wind represents a marriage of thermodynamics (it makes reference to temperature) and dynamics (the forces that compel the flow). As such, it is a relationship that is fundamental to a considerable body of more complex theory about the nature of cyclones.

500 mb

PGF Z=5.5 km

COL D

WAR M

COR

Zero wind

1000 mb

NORTH

Z=0 km

SOUTH

Figure 4.32. Vertical cross-section across a region of horizontal temperature contrast in the Southern Hemisphere. Solid black lines are isobars. Dashed gray lines are elevation contours. The lack of PGF at Z=0 km leads to "Zero wind" there. At 5.5 km in the same vertical column there is a large geostrophic wind into the page, signified by the "X" in the circle.

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Consider the well-known observational tendency for mid-latitude weather systems to move from west to east. Since mid-latitude cyclones (or other smaller-scale mid-latitude weather systems such as complexes of thunderstorms) are three-dimensional objects, the fact that they tend to move from west-to-east suggests that the winds in the middle troposphere that steer them are usually from the west. As we have just shown, at any time of year in the Northern Hemisphere the pole is colder than the equator, and so the 1000–500 mb thickness of the column of air above the pole is smaller than that above the equator. Consequently, as shown in Fig. 4.31, the thermal wind is westerly and carries mid-latitude disturbances with it. Figure 4.32 shows a vertical cross-section, from north-to-south, through the Southern Hemisphere. In this case, the latitudes toward the north are nearer the equator while those to the south are nearer the pole. Thus, given a flat 1000 mb isobar, the 500 mb isobar will slope upward to the north as shown. That implies that the PGF at 5.5 km is directed southward toward the pole, opposite to the case just discussed for the Northern Hemisphere. In order to achieve geostrophic balance at 5.5 km, the Coriolis force must be directed to the north as shown. Recalling that the Coriolis force is directed to the left of motions (at right angles) in the Southern Hemisphere, this results in an eastward directed wind at 5.5 km, just as in the Northern Hemisphere. Thus, we can conclude that the mid-latitudes of both hemispheres are characterized by a westerly vertical shear that is a consequence of the pole-to-equator temperature gradient. Another simple example of the ubiquity of the thermal wind as a structural element of the mid-latitude circulation arises from considering its relationship to a single mid-latitude cyclone. As the media becomes more sophisticated in its portrayal of weather systems both in print and in the broadcasting realm, the public has become aware of the presence of the so-called jet stream. The jet stream is a core of very high speed winds found at about 300 mb (9 km, about the flight level of a jet aircraft—hence the name). The position of the jet stream has a significant bearing on the type of weather a given location might expect. This expectation can be directly related to the thermal wind in the following way. If the jet stream happens to be directly over Madison, Wisconsin, on a given day, then the geostrophic vertical shear (i.e. thermal wind) would have to be large on that day at Madison. The only way the thermal wind can be large at a station is if that station finds itself in a region of large horizontal temperature contrast. The mid-latitude cyclone is always associated with significant temperature contrasts in its frontal zones. Thus, the jet stream position is intimately tied to the

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position of mid-latitude cyclones, as illustrated in Fig. 4.33. Now, the next time you happen to see a weather forecaster show viewers the forecasted position of the jet stream, you will know why she has gone to the trouble. We have concentrated much of our discussion in this section of the course on the large scale elements of the mid-latitude cyclone. Of course, the narrow precipitation region characteristic of cold fronts contains smaller scale weather elements, thunderstorms, which are among the most awesome phenomena in the atmosphere. Therefore, we turn our attention in this final portion of the current chapter to a brief examination of the thunderstorm.

L

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Relation of the Jet Stream to the Surface Cyclone Figure 4.33. Relation of the jet stream to the surface cyclone. 300 mb wind speeds of greater than 35 m s-1 are shaded light gray with speeds greater than 50 m s-1 shaded dark gray. The direction of the jet stream flow is indicated by the dark arrow.

Thunderstorms Thunderstorms, as the name suggests, are storms containing thunder and lightning. There are two broad categories of thunderstorms: the air mass thunderstorm and the severe thunderstorm. We will now examine some of the salient characteristics of each type.

Air Mass Thunderstorm If you have ever traveled to the southeastern United States in summertime you have most likely experienced an air mass thunderstorm. Air mass thunderstorms usually occur in mid to late afternoon and are associated with torrential rain, but they are over and done with in a relatively short time. The fact that they are most frequently a mid-afternoon phenomenon testifies to the importance of daytime heating as the primary destabilization mechanism that fuels their growth. Air mass thunderstorms usually develop in warm, humid airmasses, most often remote from any fronts or organized cyclone, and are not often associated with significant damage.

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These observational aspects of the air mass thunderstorm are a consequence of the 3-stage life cycle, illustrated in Fig. 4.34, that characterizes these storms. Stage One, also known as the cumulus stage, involves the growth of the cumulus cloud that will eventually house the air mass thunderstorm (Fig. 4.34a). In this stage, the entire cloud is characterized by rising warm air from which liquid water condenses. There is usually no precipitation falling out of the bottom of the growing cumulus at this stage. The rapid growth of the cumulus cloud during this stage offers the lucky viewer an awesome spectacle as the cloud will grow before one’s very eyes. A short time later, the air mass thunderstorm enters the second stage of its life cycle: the mature stage (Fig. 4.34b). During the mature stage the water droplets and ice particles that formed during the cumulus stage have grown large enough to begin falling out of the cloud. As these precipitation particles fall through the cloud they entrain (drag) dry air from just outside the cloud into the cloud itself. This dry air entrainment renders some of the in-cloud air negatively buoyant (through evaporative cooling of some precipitation particles). The negatively buoyant air helps to develop the significant downdraft that emerges in this stage of the life cycle. Lightning and thunder are also rather common during the mature phase. In most air mass thunderstorms, so much precipitation falls during this mature phase that the entire cloud quickly becomes overcome by the downdrafts, setting the stage for the final dissipating stage of the life cycle (Fig. 4.34c). In the dissipating stage the precipitation formation ceases as a consequence of the absence of updrafts. The entire cloud is characterized by

(a)

(b)

(c)

Figure 4.34. The three stages of the life cycle of the air mass thunderstorm. Dark arrows are updrafts and gray arrows are downdrafts. (a) Cumulus stage. (b) Mature stage. (c) Dissipating stage. See text for description.

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downdrafts in this stage and so evaporates rather quickly. The entire 3-stage life cycle of the air mass thunderstorm is often completely played out in about ONE hour.

Severe Thunderstorms Severe thunderstorms are “severe” because they are often associated not only with heavy rain and hail, but with damaging winds and tornadoes. Also, the severe thunderstorm can persist for many hours in contrast to the short-lived air mass thunderstorm. In fact, many of the damaging characteristics of the severe thunderstorm are a direct consequence of its extended lifetime. Therefore, in order to understand the nature of the severe thunderstorm, we need to understand what physical factors contribute to its long life. We saw that in the mature phase of the air mass thunderstorm, downdrafts developed. These downdrafts overlapped in space with the updrafts of warm, moist air that fuel the storm. As a consequence of this overlap, the downdrafts quickly act to extinguish the updrafts and the air mass thunderstorm soon dies. The long life of the severe thunderstorm is a result of tilting of the updraft. This tilting is accomplished by the vertical wind shear in the environment, as illustrated in Fig. 4.35. Several salient structural features of the severe thunderstorm are shown in Fig. 4.35. On the right side of the diagram, the environmental winds are seen to become more westerly with height, consistent with the westerly vertical shear that characterizes the mid-latitudes. Thus, the low level air that feeds into the storm is rushing westward, while the air at upper levels is moving much more slowly to the west. This has the effect of moving the precipitation generation region in the severe thunderstorm cloud back to the western half of the cloud. The downdrafts of air, forced by the falling precipitation in much the same way as they were in the air mass thunderstorm, are

Environmental Winds

Gust Front

Figure 4.35. Schematic of the severe thunderstorm and its environment. The heavy arrows at the right are the environmental winds, exhibiting westerly shear with height. The dark curved arrows are the updrafts and the gray curved arrows are the downdrafts. Dashed lines at the base of the cloud are the gust fronts of the thunderstorm. Rain and hail regions are indicated by the vertical lines and black dots, respectively.

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therefore restricted to the western portion of the storm. In this way, the tilted updraft keeps the precipitation from falling into the warm, moist inflow air that feeds the storm. The resulting separation of updrafts and downdrafts allows the severe thunderstorm to persist for many hours.

Tornadoes

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One of the most powerful phenomena associated with the severe thunderstorm is the tornado. Tornadoes are associated with severe thunderstorms because the severe thunderstorm often has a rotation to it. The rotation in the severe thunderstorm has its origin in the vertical wind shear that characterizes the severe storm environment. In the presence of the vertical shear displayed in Fig. 4.35, horizontal tubes of air can be made to rotate as shown in Fig. 4.36a. If the updraft that initiates the thunderstorm is added to the environment containing this rotating tube, a significant distortion of the tube results, as shown in Fig. 4.36b. With persistent rising motion in this environment, the rotating tube is further distorted (Fig. 4.36c) to the point that the portions

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(c)

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Figure 4.36. The production of rotation in severe thunderstorms. (a) Vertical shear of the wind (bold arrows) produces a horizontal vortex tube (light gray shading). (b) Updraft within the severe thunderstorms (darker shaded arrow) distorts the horizontal vortex tube. (c) Continued distortion of the vortex tube eventually creates vortex tubes with a nearly vertical orientation.

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of the tube on either side of the updraft are nearly vertically oriented. In this manner, the vertical wind shear (manifest in the original horizontally rotating tube) is turned into horizontal wind shear (manifest in the subsequent vertically oriented rotating tube). These vertically oriented rotating tubes are known as meso-cyclones, and they provide the rotation that characterizes the severe thunderstorm environment. The meso-cyclones are also very localized regions of low pressure. As air rushes into these meso-cyclones (as it must since the pressure is lowest there), the rotation rate of the column of air increases, sometimes to the point where a rapidly rotating funnel develops and a tornado is spawned. Tornadoes, though not unique to the United States, occur in our country with a frequency unmatched anywhere else in the world because of the unique meteorological and physiographical characteristics of the “Tornado Alley” region of the southcentral Plains. This part of the world is frequently characterized by a potent instability known as convective (or potential) instability. Convective instability is the most potent form of instability in the atmosphere. The basic ingredients for this instability are warm, dry air surmounting a lower level layer of warm, moist air. If the inversion layer that caps the moist air is lifted high enough, the entire layer becomes absolutely unstable and severe convection often results. The physical reasons why such a vertical superposition of dry and moist air conspires to form such a potent instability is material more suited for a course in thermodynamics. But the proximity of the southcentral United States to the Gulf of Mexico and the Mexican Plateau makes it easy to see why convective instability is so commonly observed in that part of the world (Fig. 4.37). Whenever an upper-level cyclone (say at 5.5 km) crosses the northern

P-ΔP

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Figure 4.37. Large-scale environment favorable for severe thunderstorms and tornadoes in the southcentral United States. Solid lines are isobars at 5.5 km, dashed lines are sea-level isobars. Dark shaded arrow represents low-level warm, moist flow off of the Gulf of Mexico. Lighter arrow represents the warm, dry air (at mid-levels) off of the Mexican Plateau. Such a flow creates convective instability just east of the surface low pressure system.

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states of Mexico as depicted in Fig. 4.37, a surface cyclone is often located over central Texas. Given that Friction acts near the surface, the surface flow around that surface cyclone comes right off of the Gulf of Mexico. Thus, a layer of warm, moist air is created at low levels over Tornado Alley. Meanwhile, at 5.5 km, the flow over the region is from the southwest. This southwesterly flow drags warm, dry air off the Mexican Plateau out over the Plains. This dry air sits atop the moist air from the Gulf of Mexico as depicted in Fig. 4.37. With the ingredients in place in the vertical, the fact that Tornado Alley is to the east of the upper wave shown in Fig. 4.37 means that the convectively unstable air column will be forced to rise. If the upward vertical motion is sufficiently strong, the convective instability will be released and severe thunderstorms, possibly including tornadoes, will develop. Though we understand the general conditions under which tornadoes are likely to develop, the exact details of tornado formation are still not well known. This makes the precise prediction of these storms a near impossibility. In order to protect the public as best it can in the face of this difficulty, the National Weather Service employs a network of trained Tornado Spotters along with Doppler Radar data to identify tornadoes as soon as they have developed. Though not a replacement for point specific forecasts of tornado occurrence, the combination of vigilance in the face of high likelihood and rapid public alert systems has saved many lives in the last 20 years. A notable example of the success of this vast effort is the amazingly small loss of life that occurred on May 3, 1999, when an F5 (extremely intense) tornado devastated urban areas of Oklahoma City, Oklahoma. The recent tragedy in Tuscaloosa, Alabama, in April 2011, however, points out that much still needs to be learned about these killer storms. Thunderstorms also occur with great frequency in the tropical regions of the Earth. Such tropical convection can come in a variety of organized structures and phenomena and it plays an enormously important role in the general circulation of the Earth’s atmosphere. One such form of organized tropical convection is the hurricane or tropical cyclone. In the last chapter of this book we will explore these powerful storms in some detail.

Chapter 5 Tropical Cyclones: The Most Powerful Storms on Earth

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The Tropical Setting alf of the surface area of the Earth lies between 30°S and 30°N, a range of latitude that is most definitely outside of the mid-latitudes. In fact, though the tropics on Earth technically span from 23.5°S to 23.5°N, the sub-tropics are generally regarded to extend poleward to 30° in both hemispheres. Thus, though we just discussed a number of important characteristics of the mid-latitude cyclone and some of the physical principles at play in creating them, these insights pertain to weather systems that occur over only one half of the Earth’s surface. In this chapter we will examine aspects of the nature of the cyclones that occur in the tropics, known as tropical cyclones. The most well-developed tropical cyclone is known in the Atlantic Ocean basin as a hurricane, in the Indian Ocean as a cyclone, and in the western North Pacific Ocean as a typhoon.1 We shall refer to them as tropical cyclones in our subsequent discussion of these storms. Before we examine tropical cyclones in detail, it is worthwhile to describe the nature of the tropics from which they originate. The weather in the tropics is different from that in the mid-latitudes in a number of ways. First, by virtue of the latitude, the Sun is at a high angle of incidence throughout the year, and so seasonal changes in weather are very minor compared to those in mid-latitudes. Also, daily variations in the weather are much more muted in the tropics since there are substantially fewer waves in the middle tropospheric flow (at 500 hPa, for instance) in the tropics than in the mid-latitudes. Consequently, there is no parade of surface cyclones and anticyclones in the tropics. The strong daytime heating of the surface, coupled with the high humidity of the lower troposphere, encourages the development of numerous cumulus clouds, which often develop into afternoon thunderstorms. Most often these thunderstorms are of the airmass variety, but occasionally they can become organized into what are known as tropical convective clusters or tropical squall lines. In most locations in the tropics, this convection has an annual cycle that roughly follows the highest Sun angle. In other words, convective activity near 20°N reaches an annual maximum around the summer solstice, while around 20°S it reaches its annual maximum around the winter solstice. In fact, as depicted on the satellite image in Fig. 5.1, there is a fairly continuous band of tropical convection girdling the globe on any given day. The latitude of this convective band depends on the time of year, but it is always located in the tropics. For this reason, this band is known as the InterTropical Convergence Zone (ITCZ). The convection that characterizes the ITCZ is the underlying physical process involved in the production of a planetary-scale tropical circulation known as the Hadley Cell.2

H

1

The word hurricane derives from the Taino language of Central America in which the word hurucan literally

means “god of evil.” The word typhoon comes from the Chinese word taifung, which means “big wind.” 2 George Hadley (1685–1768) was an English lawyer and amateur meteorologist who first proposed that the Earth’s rotation was a factor in the production and sustenance of the so-called Trade Winds that reliably blew from east-to-west at low latitudes across the Atlantic basin. Understanding these Trade Winds was crucially important for efficient navigation across the Atlantic.

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ITCZ

Figure 5.1. Visible satellite image of the Pacific Ocean basin showing the nearly continuous line of convection that marks the InterTropical Convergence Zone (ITCZ).

200 hPa

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H

1000 hPa

Figure 5.2. Schematic of the Hadley Cell. Thin arrows indicate the direction of movement of the air in the horizontal and vertical directions with the subsiding branches labeled "DRY" at 30 oN and 30 oS, where the subtropical high pressure regions develop (labeled as "H" in both hemispheres). ITCZ is located where the surface low pressure region ("L") and deep thunderstorm are depicted. The surface air that converges toward this convection is turned by the Coriolis force to produce the Trade Winds.

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The basic characteristics of the Hadley Cell are illustrated in Fig. 5.2. Convection at or near the equator is characterized by substantial rising motion, while the outflow of air at the top of these thunderstorms moves poleward, at 10–15 km elevation, to higher latitude. Convergence aloft at the poleward edge of this outflow (at roughly 30°), leads to gentle but persistent subsidence in the subtropics where, incidentally, most of the world’s deserts appear. To complete the circuit, the flow of air at the surface has an equatorward direction, but, since the Coriolis force is acting upon this moving air, it is turned to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. In both cases, this creates winds near the surface with an easterly (i.e. east-to-west) component—these are the so-called Trade Winds. These lower tropospheric easterlies account for another major difference between tropical and mid-latitude weather systems—namely that tropical systems tend to move from east to west. Within this tropical setting, a few times each warm season, tropical cyclones develop. Recall that mid-latitude cyclones are extremely frequent occurrences in the higher latitudes of Earth, with a new storm bearing down on a given location every 3 or 4 days during the peak season. Anyone who has paid attention to the hurricane season in the Atlantic basin (and this is a decent gauge of the other, more active basins) will recognize that hurricanes occur with considerably less regularity. In fact, perhaps only a dozen or so storms will develop in an average season in the Atlantic. Thus, this brief introduction prompts several intriguing questions regarding the nature of tropical cyclones—the most powerful storms on Earth. In the remainder of this chapter we will consider where the energy comes from for the development of these storms. An answer to why there are so few tropical cyclones each season will emerge from considering the environmental conditions necessary for their development. We will explore where on Earth, and at what time during the year, these storms develop. We will examine the structure of a mature tropical cyclone and consider how that structure facilitates the energy transfers that sustain the storm. We will dissect the life cycle of a tropical storm, considering its origins and its eventual decay. We will survey the several high profile hazards that accompany tropical cyclones and consider the most striking differences between the tropical cyclone and the mid-latitude cyclone. Finally, we will briefly consider the fate of tropical cyclones that migrate into the extratropics and undergo a process known as extratropical transition. We begin by describing the structure of a mature tropical cyclone.

Tropical Cyclone Structure Given the large number of names for such storms, all hurricane-like storms are known as tropical cyclones by international agreement. Figure 5.3 shows satellite pictures from four different tropical cyclones. The image instantly conveys a couple of the basic characteristics of a tropical cyclone. First, tropical cyclones are close to circularly symmetric in their general structure. Second, they possess a number of spiral arms extending radially outward from the center. Third, they possess

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(a)

(b)

(c)

(d)

Figure 5.3. Satellite images of four recent Atlantic hurricanes: (a) Erin in July 1995, (b) Mitch in October 1998, (c) Ivan in September 2004, and (d) Katrina in August 2005. a small, nearly cloudless “eye” at their center. Finally, though it cannot be discerned from the still images in Fig. 5.3, the storms rotate cyclonically about the center (i.e. counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere)3. We will examine all of these elements of the tropical cyclone structure in more detail momentarily. First, it is worth zooming in on the region around the eye. Immediately surrounding the eye of a fully developed tropical cyclone is a ring of very intense convection (thunderstorms), which comprise the eyewall. The tops of these convective clouds may reach to ~60,000 ft (18 km) above sea-level, the height of the tropopause in the tropics. Within the eyewall convection lie the heaviest rains in the entire storm along with the strongest winds, which occasionally reach 155 mph with gusts to near 200 mph. 3

One of the best websites for global coverage of tropical cyclones is that published by the Tropical Cyclone

Group at the Center for Meteorological Satellite Studies (CIMSS) at the University of Wisconsin-Madison. Their web address is http://tropic.ssec.wisc.edu.

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Figure 5.4. Schematic vertical cross-section through a mature tropical cyclone. The bold black lines with numerous arrowheads on them represent air parcel trajectories through the storm with cyclonic, low-level inflow toward the eyewall, abrupt ascent in the eyewell convection, and anticyclonic outflow at the top. Dashed arrows represent regions of subsidence between the spiral rainbands and in the eye (the dark shaded region). Solid arrows, within convective clouds, represent the updrafts of air in the sprial rainbands surrounding the eye. All of the spiral arms rotating around the eye are lines of thunderstorms4 as well. Consequently, the environment surrounding these spiral rainbands is also characterized by strong winds and heavy precipitation. At low-levels, these winds are directed toward the eyewall. As air is drawn toward the eyewall, it is made saturated through evaporation of water from the underlying warm ocean. By the time this air reaches the eyewall, it is saturated and very warm, contains an enormous amount of water vapor (saturation mixing ratio at 28°C is ~24 g kg-1), and is immediately ingested into the deep cumulus towers of the eyewall convection. In order to understand the clear skies that characterize the eye of the tropical cyclone, it is useful to consider a vertical slice through a fully developed storm as shown in Fig. 5.4. Recall that since the tropical cyclone is a warm core cyclone, it is not uncommon for an upper-level anticyclone to sit atop the low-level cyclone (Fig. 4.30). The eyewall convection processes the huge amount of air that converges toward the center of the storm as the central pressure of the tropical cyclone drops. Naturally, the rising air in the eyewall convection has to be exhausted out the top of the convective clouds. The largest fraction of this air is expelled from the center of the storm by the anticyclonic outflow that characterizes the upper troposphere near the storm. For reasons that are still being debated today, it is clear that some fraction of this exhaust turns inward toward the center of the tropical cyclone, converges at upper levels, and sinks. The sinking not only clears the sky of clouds but also leads to adiabatic warming of the eye. This warming forces a decrease in the sea-level pressure and further intensification of the storm. Additional warming in 4 Tropical convection has little lightning and, hence, not much thunder. This is believed to be a consequence of the small amounts of ice in such clouds. We use the word “thunderstorm” simply in order to remind the reader of their general convective nature.

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Eye

Tropopause

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Ocean Surface Figure 5.5. Schematic of the characteristic IN-UP-OUT circulation of a tropical cyclone. Nearsurface air rushes IN to the cyclone center (marked with an "L"), then ascends UP in the eyewall convection, and is pushed OUT at the tropopause. The sinking air characteristic of the eye is shown in the lighter arrows at the center.

the eye also intensifies the upper-level anticyclone, which consequently becomes more efficient at expelling air that has been processed by the eyewall convection. Thus, the storm structure (i.e. the warmth of the eye) and its intensity are so strongly interrelated that satellite measurements of the warmth of the eye supply extremely accurate estimates of the peak winds of tropical cyclones5. A schematic of the characteristic in-up-out circulation of a mature tropical cyclone is shown in Fig. 5.5 with the updraft portion of this schematic circulation restricted to the eyewall convection. Another interesting characteristic of tropical cyclones is that the air temperature is fairly uniform throughout the storm. This fact is surely not obvious since, as shown in the broadscale circulation depicted in Fig. 5.5, the air sinks and is warmed by compression on the periphery of the storm while near the eyewall, the air rises vigorously and cools by expansion. Even though some of that cooling is mitigated by the enormous amount of latent heat release that occurs in the eyewall convection, one might still reasonably expect the eyewall region to be cooler than the periphery of the storm. This is not the case because the low-level air that 5 A satellite-based technique for estimating the intensity of tropical cyclones based upon the thermal structure of the eye and other kinematic properties of the cloud field was developed in the early 1970s by Vernon Dvorak. The so-called Dvorak technique has been the gold standard for remote estimation of tropical cyclone intensity for nearly 40 years.

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is directed from the periphery of the storm into the center is greatly modified during that journey—making constant contact with a wildly windswept and very warm ocean surface. As a consequence of the warm sea-surface temperature (SST), the inflow air is both warmed and moistened as it flows toward the eyewall—evaporation from the ocean being enhanced by the strong winds and disturbed ocean surface. Such very warm, very moist air is the optimal fuel for the sustenance of a tropical cyclone, and its production derives directly from the structure of the storm as we have just seen. However, certain basic environmental conditions work in concert with this structure to create these powerful storms. These necessary conditions are relegated to certain locations on the globe and to certain times of year. Next, we investigate where, when, and under what conditions tropical cyclones develop.

Figure 5.6. Areas of the globe where tropical cyclones form in the warm season. The arrows indicate several common paths taken by storms that develop in the various regions but are not the only paths the storms can take. The bold dashed line represents the average position of the 26.5 oC sea-surface temperature isotherm. Note that not all such areas support the development of tropical cyclones.

Where do Tropical Cyclones Form? We have already seen that warm SST provides a mature tropical cyclone with a means to warm and moisten the air that flows toward the important eyewall convection. Thus, it is not surprising that tropical cyclones form where SSTs are very warm; in fact, tropical cyclones struggle to develop if the SST is not 26.5°C (79.7°F) or warmer. Tropical cyclones also thrive in environments where the vertical wind shear is small. This is a consequence of the fact that the

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Number of storms per 100 years

warm core structure of tropical cyclones (as depicted in Fig. 4.30) provides a vertical couplet of lower-level convergence (into the storm’s eyewall convection) surmounted by upper-level divergence (in the outflow anticyclone aloft). If a westerly vertical shear is imposed upon that structure, the upper divergence will be blown downstream of the lower-level convergence and the evacuation of mass from the tropical cyclone center, which is primarily responsible for intensifying the storm, will be extinguished. Certain vast stretches of the tropical ocean have SSTs above the threshold value of 26.5°C and thus qualify as locations where the development of tropical cyclones is favored (Fig. 5.6). However, within such areas it is only when the vertical shear from the surface to ~200 hPa is very low6 that tropical cyclones can form and grow to maturity. One might guess that the wind shear criteria is substantially less steady than the SST criteria—that is, that in a given location in the tropics, it is much more likely that the shear condition, not the SST, will vary from one day to the next. This is, indeed, correct, and there are a number of physical factors that can conspire to render the vertical shear too extreme to allow for tropical cyclone development. One such factor is the presence of the so-called subtropical jet stream, which is located between 20°–30° latitude (the poleward edge of the Hadley Cell) and ~200 hPa in both hemispheres. The subtropical jet stream is an ever-present feature of the general circulation of the tropics and has wind speeds routinely in excess of 65 m s-1. Such strong winds at 200 hPa are more than sufficient to provide a toxic amount of vertical shear to a nascent tropical cyclone.

May 10

June 1 June 20 Jul 10

Aug 1 Aug 20 Sep 10

Oct 1 Oct 20 Nov 10

Dec 1 Dec 20

Figure 5.7. Number of storms in the tropical Atlantic basin, by calendar day, over the last 100 years. Light (dark) shading represents the number of tropical storms (hurricanes).

6

A number of studies have concluded that vertical shears in excess of 10 m s-1 (extremely small) are often enough

to doom the nascent development of a tropical disturbance to failure.

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Also, since the boundary between the tropics and the extratropics is not rigid like a wall, it is possible for weather systems or jet streaks of extratropical origin to intrude upon the tropics (usually later in the tropical cyclone season) and add excessive vertical shear to the environment of a developing storm. In fact, though the basic ingredients for tropical cyclone formation— warm SST, high humidity—are plentiful in the tropics, the fact that so few tropical cyclones form each year testifies to both the hostility of the tropical atmosphere to their development and the degree of serendipity required for a tropical cyclone to emerge and grow to maturity in this generally hostile environment. Certain times of year are also preferred for the development of tropical cyclones. Consider the historical distribution of hurricanes in the Atlantic Ocean basin as depicted in Fig. 5.7. A dramatic peak in the number of hurricanes occurs from early August through mid-October (mimicked by the larger population of less intense tropical storms). By this time of year, the tropical North Atlantic has absorbed the abundant solar radiation of the Northern Hemisphere summer and the SST is as warm as it will be all year. In fact, the warmth of summer over the entire Northern Hemisphere also reduces the pole-to-equator temperature gradient, which results in a weakening and poleward retreat of the mid-latitude jet stream to its highest latitudes of the year by about August 1. This circumstance renders late summer/early fall as the time of year when the intrusion of extratropical weather systems into the tropical North Atlantic is least likely. Also, in response to the warmth of summer, the Hadley Cell expands poleward, placing the subtropical jet stream further north as well. All of these responses to summer’s intensified solar radiation conspire to best isolate the tropical North Atlantic from tropical cyclone-killing vertical shear at this time of year. After mid-October, a steep decline in the number of storms occurs, with tropical cyclones becoming extremely rare after November 1. By this time of year there is a much increased frequency of high shear events invading from the extratropics. Now that we have a clearer idea of the environments within which tropical cyclones are likely to develop, and have linked this to their seasonality in a physical way, we must consider the process(es) by which these organized circulation systems emerge from the nearly constant but isolated convective activity that characterizes the tropics.

Tropical Cyclone Formation The central problem of tropical cyclone development is a problem of organization. There are always a large number of thunderstorms occurring in the tropics, but a tropical cyclone will only develop if this convection is organized into a coherent weather system. There are a variety of means by which such organization might be encouraged. As is the case in the mid-latitudes, surface convergence of air is a major organizing factor, as convergence results in the development of a counterclockwise rotating eddy in the Northern Hemisphere under the influence of the Coriolis force. In fact, the rotation supplied by the Coriolis force is so critical to tropical cyclone

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Convective cluster Trough axis

Figure 5.8. Schematic of an African Easterly wave. Solid lines with arrowheads on them represent streamlines of the wave with the trough axis indicated. The convective cluster on the west side of the wave axis is also indicated. The bold, gray arrow indicates the direction of movement of the wave and its associated weather.

development that storms cannot form directly over the Equator because the Coriolis force is zero there (note the lack of tropical cyclone formation at the Equator in Fig. 5.6). What large scale mechanisms provide the necessary convergence? One viable candidate is the convergence supplied by the ITCZ. A number of large-scale tropical weather disturbances emerge from the ITCZ, occasionally even a tropical cyclone. Another feature that can serve to organize tropical convection is a structure known as an easterly wave. In the tropical Atlantic, the majority of such easterly waves originate over Africa, specifically at ~20°N, which is the boundary between the rainforest to the south and the vast Sahara to the north. Since the air is warmer over the Sahara than over the rainforest canopy, the thermal wind is directed to the west and the African Easterly Jet is formed in the lower to middle troposphere. This jet feature periodically spawns waves, like the waves we encountered in our study of the extratropical cyclone, which have characteristic distributions of surface convergence and divergence. A schematic of an African Easterly wave is shown in Fig. 5.8. For reasons we will not describe here, the surface convergence is on the leading (western) side of the wave, along with the thunderstorm activity, while the divergence is on the eastern side of the wave axis. Occasionally, the organized, unsettled weather located here will develop into a mature tropical cyclone. In fact, a large fraction of Atlantic hurricanes have their origins in these African Easterly waves. Another possible seat for tropical cyclogenesis can be the convergence of air along a preexisting surface front that has migrated from the extratropics into the tropics. This possibility is, of course, severely limited by the fact that such fronts are also quite often associated with

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fairly substantial vertical shears. Thus, only rarely does the surface convergence supplied by a stray, extratropical surface front lead to the sustained development required to produce a tropical cyclone.

Energy Transfers One need only consider the extreme winds associated with tropical cyclones to come to the conclusion that these storms are characterized by enormous amounts of kinetic energy (KE). In fact, it has been estimated that just the winds in a mature tropical cyclone of moderate intensity (i.e. with sustained winds of 90 mph) produce KE equivalent to 1.5 x 109 kW—enough to supply roughly half of the world’s electricity for each day of the storm’s existence. If we include all the latent heat energy released in such a storm as well, the estimated amount of total energy jumps to 1 x 1012 kW—equivalent to 70 times the daily world energy consumption by humans, 200 times the daily worldwide electrical energy usage, or exploding a 10 megaton nuclear bomb every 20 minutes! Given the First Law of Thermodynamics, we know that this energy has to come from somewhere. It turns out that it comes from the direct transfer of sensible and latent heat from the warm ocean surface. Such enormous energy is transferred only through the organization of a coherent circulation, and, as we have seen, the precise means by which a cluster of thunderstorms becomes organized into a large scale weather system is not yet settled science. One viable theory proposes the following sequence of events. Suppose a collection of thunderstorms begins to organize in association with the passage of an African Easterly wave. The air column on the western side of the wave axis has been thoroughly moistened by the persistent thunderstorm activity there, so a deep, nearly saturated, conditionally unstable environment exists there. Such an environment ensures that huge quantities of latent heat are released in the development of the thunderstorms. Given the isolated nature of the organized “clump” of thunderstorms associated with the easterly wave, this portion of the atmosphere is warmer (from release of latent heat) than the air at the same level but far afield from the thunderstorms. Recalling our prior discussion about thickness and its relationship to column average temperature, the thickness of the column near the clump of thunderstorms will be greater than that of the columns far afield. Consequently, a region of upper-level high pressure, and upper divergence, develops atop the clump of thunderstorms. The upper divergence is linked to surface convergence below which, by virtue of the Coriolis force, leads to a counterclockwise circulation at the surface. So long as the upper divergence exceeds the surface convergence, the pressure at sea-level drops. The pressure drop at the surface is also aided by the warming of the column via the enormous amount of latent heat release. Surface air from far afield begins to spiral in toward the developing low pressure center. As it does so, it enjoys a transfer of heat from the ocean surface—both sensible heat from contact with the warm surface (raising the temperature of the air) and latent heat from evaporation off the ocean (increasing its moisture content). The amount of heat transferred is proportional

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Eye

Tropopause

L

Ocean Surface S

3)

Latent heat released as 2) air expands adiabatically

1)

Heat removed as air cools radiatively

4)

Heat added as air warms adiabatically

Heat added as air expands isothermally

Figure 5.9. The tropical cyclone as a heat engine. One side of the IN-UP-OUT circulation is highlighted to illustrate the 4 steps in the heat engine model of the tropical cyclone. See text for explanation of the steps in the cycle.

to both the wind speed and the SST. Therefore, as the winds increase, the amount of energy transfer also increases in a positive feedback loop. So long as the eyewall convection persists, the energy gained by sensible and latent heat is converted efficiently into deep, powerful thunderstorms—the lifeblood of the tropical cyclone. It is possible to liken this sequence of events to the operation of a heat engine. A heat engine is a machine or a physical system that performs the conversion of heat energy into mechanical work. The mature tropical cyclone is a beautiful example of such a heat engine operating spontaneously in nature. Figure 5.9 illustrates the four basic steps characterizing the tropical cyclone heat engine. In step 1, heat is absorbed from the high temperature reservoir of the ocean surface and expands isothermally as an air parcel is warmed and moistened by its contact with the warm

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underlying ocean, expanding as the pressure lowers on its journey toward the cyclone center. In step 2, the air parcel expands adiabatically as it rises and releases latent heat. The expansion does work on the environment leading to the cooling that forces condensation and latent heat release. The latent heat release adds more heat to the air. Step 3 is the opposite of Step 1 and represents the removal of heat from the air parcel through radiational cooling at the tops of the tropical cyclone’s clouds. Finally, Step 4 is where the environment does work on the air through compressional warming as the air on the periphery of the tropical cyclone sinks back toward the surface. Once the air gets to the surface, it is warm and dry—but ready to be processed by the tropical cyclone “engine” again. The “engine” warms and moistens the air, removes that added heat, and converts the heat extracted into the mechanical work (i.e. the winds) of the tropical cyclone itself. Consideration of this relatively simple conceptual model of the tropical cyclone as a heat engine has led to the development of a theory of maximum potential intensity (MPI)7 that is a useful guideline for estimating the limit of development for a nascent tropical disturbance, given knowledge of some basic environmental parameters. Of course, the growth of a tropical cyclone from initial disturbance, to mature storm, and finally to its own decay represents a life cycle worthy of exploration. We now proceed to an examination of the tropical cyclone life cycle.

The Tropical Cyclone Lifecycle Although occasionally they can exist for weeks at a time8, most mature tropical cyclones have lifetimes of about one week. However, the complete lifecycle of tropical disturbances that mature into tropical cyclones is usually longer than this, and that lifecycle includes characteristic stages of development. Initially, a tropical disturbance appears as a clump of thunderstorms, as we have discussed previously. In such an early stage, there may not even be any discernible circulation to the system. When such a circulation does develop, and the associated winds increase to the range of 23 to 39 mph, the feature graduates to the tropical depression stage. If the depression continues to intensify and the winds associated with it increase to the 40 to 74 mph range, the storm graduates to the tropical storm stage. It is at this point that the storm first gets named. Continued intensification and wind speed increases to above 74 mph earn the storm the tropical cyclone (hurricane) designation. Tropical cyclones are then differentiated by the intensity of their maximum sustained winds into 5 categories of the Saffir-Simpson Hurricane Damage Potential Scale, known colloquially as the Saffir-Simpson scale (Table 5.1). 7

The MPI theory, developed by Dr. Kerry Emanuel in 1995, provides an upper limit to estimates of the

minimum pressure and maximum wind speeds of potential tropical cyclones by considering only the SST and temperature structure of the environment surrounding a potential development. 8 Hurricane Tina (1992) maintained hurricane-force winds for 24 days in the North Pacific Ocean—a remarkable record for longevity.

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Table 5.1 The Saffir-Simpson Hurricane Damage Potential Scale. Note that the scale is based solely on sustained wind speed and the damage the winds can cause. The values of SLP Minimum and Storm Surge that are listed here are reasonable estimates of those characteristics of the storms in each category. Category (Damage Potential) 1 2 3 4 5

(Minimal) (Moderate) (Extensive) (Extreme) (Catastrophic)

Maximum Sustained Winds 74–95 mph 96–110 mph 111–130 mph 131–155 mph > 155 mph

SLP Minimum

Storm Surge

> 980 mb 965–979 mb 945–964 mb 920–944 mb < 920 mb

4–5 ft 6–8 ft 9–12 ft 13–18 ft > 18 ft

Tropical cyclones are extremely sensitive to the temperature of the underlying ocean surface. If a tropical cyclone migrates over water even slightly cooler than the 26.5°C threshold mentioned earlier, it suffers a dramatic loss of intensity not unlike the sputtering of an engine whose carburetor is starved for more fuel9. The SST beneath a tropical cyclone can cool if the storm remains over a certain spot for too long. In such a case, if the depth of the warm water is not sufficient, prolonged evaporation from the sea surface will cool the surface water and the action of the wind and waves will mix cooler, subsurface water up to the surface, rendering the SST beneath the stationary storm sometimes too cool for maintenance or continued intensification. Tropical cyclones also decay rapidly when they move over large landmasses, as two major alterations to the storm occur in such a case. First, when a tropical cyclone moves over land it is removed from direct contact with its energy source, the warm tropical ocean surface. This has an immediate negative impact on the vitality of the storm. Second, though the surface winds are affected to a fair degree by friction while the storm is over the ocean (the huge waves that are created beneath the storm are substantial obstacles to the flow), the amount of Friction over land is very much larger. This Friction, as we discussed in Chapter 4, forces the air to be directed across the isobars from high to low pressure at some angle. This leads to an accumulation of mass at the surface that cannot be exhausted by the weaker thunderstorms of the landfalling tropical cyclone. Consequently, the central pressure of the storm begins to rise rapidly, causing the pressure gradient force to weaken, which, in turn, weakens the tropical cyclone.

9

This is actually a physically valid analogy since a cooler ocean surface results in less evaporation and water vapor

in the air is the energy source for the motive thunderstorms of the hurricane, just as gasoline (also in the vapor phase) is for the explosions that drive the pistons in an engine.

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100 mph

(100 - 60) mph

(100 + 60) mph =

= 40 mph

60 mph

160 mph

100 mph Figure 5.10. Illustration of the effect of forward motion of a tropical storm on the sustained winds in different quadrants of the storm. This hypothetical storm has sustained winds of 100 mph associated with it and is moving northward at 60 mph. Consequently, the winds on the eastern (western) side of the storm are 160 (40) mph.

Hazards Associated with Tropical Cyclones Tropical cyclones deliver a number of significant hazards to the regions of the globe that they frequent. Perhaps the most well-known hazard is the extremely strong winds that churn around these storms. Given that a mature tropical cyclone is nearly circularly symmetric about its eye, the devastating wind speeds measured at the surface will actually vary from one location to another in the storm’s path, depending on the forward motion of the storm, as suggested in Fig. 5.10. If a category 2 Atlantic hurricane with 100 mph winds in its eyewall is moving northward at 60 mph from Cape Hatteras, NC, toward New England, as is sometimes the case, the winds on the eastern side of the storm will be the sum of the storm-relative winds (100 mph) and the forward motion of the storm (60 mph)—so, 160 mph. On the western side of the eye, the storm relative winds are still 100 mph, but the storm moves in the direction opposite those winds so that the surface winds are only 40 mph on that side. Such a difference will obviously substantially impact the type of damage that the storm will deliver at landfall10. Though often of lesser renown, the greatest hazard to life and property associated with a tropical cyclone is flooding. In fact, the majority of fatalities associated with tropical cyclones during the last 100 years has been directly tied to this hazard. Additionally, the flooding hazard is not restricted to mature tropical cyclones—it can be delivered by tropical storms that never 10

Given that the kinetic energy of the winds depends on the square of the wind speed, 2.78 times more damage

potential (i.e. work) exists on the eastern side of this hypothetical storm.

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PVD

Narragansett Bay

115 mph

45 mph

70 mph

115 mph

185 mph

2 PM 21 September 1938

Figure 5.11. The Hurricane of 1938 bearing down on Narragansett Bay. The storm had maximum winds of 115 mph at the indicated time and a forward speed of 70 mph. The gray arrow indicates the storm surge direction and Narragansett Bay is outlined in thick black contours, Providence, R.I., is identified as PVD.

China

India

Myanmar

Bay of Bengal

Thailand

Path of Bhola Cyclone

Figure 5.12. Illustration of the path of the Bhola Cyclone through the center of the Bay of Bengal in November 1970. Bangladesh is shaded in gray and its south coast is the mouth of the Ganges River across which the storm passed.

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achieve tropical cyclone status. Tropical storms and tropical cyclones are both capable of dropping 2 to 3” of rain each hour over locations in their paths, with such heavy rain persisting for 12 to 24 hours (and sometimes longer). This is a huge amount of precipitation and, if delivered to hilly or mountainous terrain, can compound the hazard by initiating landslides or mudslides. Landfalling tropical cyclones pose two other substantial threats to life and property, one of which represents an additional flooding threat. That hazard is known as the storm surge, which is a local rise in the ocean level brought on by a combination of the low pressure at the center of the storm and the incessant winds around it acting to push the water ashore. By virtue of the extremely low sea-level pressure at the center of tropical cyclones, the ocean surface is elevated beneath them, though not by very much (perhaps as much as 1 meter). The persistent action of the winds around the storm, however, tends to substantially elevate the sea-level in preferred quadrants of the storm. On top of this, 30 to 50 ft waves (sometimes larger) are rolled up by the wind. When the storm makes landfall, all of this ocean water comes roaring ashore and inundates low-lying areas. As you might guess, if the storm surge is phased with the local high tide, the situation is rendered even more devastating. The impact of the storm surge is further intensified if the coastline is shaped in such a way as to concentrate the rush of the surging ocean. The famous Hurricane of 1938 in southern New England was particularly devastating to the state of Rhode Island, whose eastern half is dominated by the funnel-shaped Narragansset Bay (Fig. 5.11). As the storm surge associated with this northward moving storm approached Rhode Island (it was estimated to have a forward speed in excess of 60 mph), the surge was concentrated into Narragansset Bay and delivered a crippling flood to Providence. One of the most devastating natural disasters of modern times was the result of a similar set of circumstances but on an even larger scale. On November 12, 1970, the so-called Bhola cyclone, a category 3 tropical cyclone, made landfall in the northern apex of the Bay of Bengal (Fig. 5.12) in what was then East Pakistan but is today Bangladesh. The storm surge associated with the Bhola cyclone ravaged a large number of low lying islands in the Ganges Delta, killing an estimated 500,000 people. Many of these people were essentially washed off the face of the Earth without a trace. The Pakistani government was heavily criticized for its delayed and bungled relief efforts in the wake of the storm, sparking a series of events that would eventually lead to the creation of an independent Bangladesh, declared in March 1971 and secured in December of that year. This storm also inspired ex-Beatle George Harrison to organize, in 1971, the first-ever benefit concert, the Concert for Bangladesh, to raise money for the relief efforts. Still another hazard attendant with landfalling tropical cyclones is the development of tornadoes. Though these tornadoes are usually not of the F3 or stronger variety, they can be quite numerous, and they add to the destructive potential of an encounter with a tropical cyclone. The physical reasons underlying the development of tornadoes at landfall are not well understood, and this is a current topic of research in meteorology.

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Differences Between Tropical and Mid-Latitude Cyclones By now it is probably clear that tropical cyclones are very different from extratropical cyclones. For one thing, the typical tropical cyclone is a much smaller storm than the extratropical storm. Though there are a number of measures of size, one that has gained popularity is the radius of closed isobar (ROCI), the distance from the center of a tropical cyclone’s circulation to its outermost closed isobar. The ROCI can vary from less than 2° of latitude (222 km, very small) to over 8° of latitude (888 km, very large). This means that even the very largest tropical cyclone, by this most generous measure of size, is on the small end of the spectrum for extratropical storms, which, as we have seen, routinely cover millions of square km in area. The asymmetric cloud distribution of the extratropical storm—with clouds on its eastern side and clear skies on its west—is clearly very different from the axisymmetric structure of the tropical cyclone. In addition, the sub-synoptic structure of the extratropical storm is represented by fronts, along which a substantial portion of the cloud and precipitation of the storm is generated. By contrast, the sub-synoptic structure of the tropical cyclone consists of eyewall convection and the spiral rainbands—neither of which have any semblance of frontal structure. In addition, the eye of the tropical cyclone, its sea-level pressure minimum, is characterized by subsidence (that is what clears the sky there), whereas the center of an extratropical cyclone is characterized by ascent. Another structural element that contrasts between the two types of storms is their thermal structure. The tropical cyclone has a vertical, warm core structure that places an outflow anticyclone directly atop the surface SLP minimum. This structure leads to the characteristic that a tropical cyclone’s strongest winds are near the surface, and they weaken with increasing altitude. The extratropical storm, on the other hand, exhibits a tilted cold core structure, which mandates that the surface cyclone be located to the east of the stronger upper-level cyclone and that the intensity of the storm increase with increasing elevation. The energy source for development is also completely different for each type of storm. As we have seen, the tropical cyclone converts sensible and latent heat from the tropical ocean surface into the KE of the winds and the tremendous thermal energy of latent heat release in the storm’s convection. The extratropical cyclone, on the other hand, relies upon the conversion of the potential energy manifest as the horizontal density contrast between cold polar air and warmer subtropical air to generate the KE of its own winds and circulation. It is important to consider these differences between tropical and extratropical storms because, though tropical cyclones develop exclusively in the tropics, they almost as routinely migrate into the extratropics during the later stages of their life cycles. When this migration occurs, the tropical cyclone suddenly finds itself in an environment that is very different from that of its origin. For one thing, if the migrating tropical cyclone remains over water (as it often does), the SST at higher latitudes falls below the 26.5°C threshold for sustained tropical development. This factor conspires against preservation of the storm. The further poleward a

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tropical storm migrates, the more likely it is that the storm will encounter the strong vertical shear, characteristic of the mid-latitudes, from which it is sometimes preserved in the tropics. As we have already seen, this shear is yet another physical factor that conspires against the continued vigor of the storm. Connected with this shear in the lower mid-latitudes, however, is a substantial horizontal temperature gradient (via the thermal wind relationship). The combination of mid-latitude baroclinicity (i.e. horizontal temperature gradient) and the still intense circulation of the sputtering tropical cyclone can result in the incorporation of the baroclinicity into the storm as cold and warm fronts and its sometimes rapid conversion into a powerful extratropical cyclone. This process is known as extratropical transition, and it leads to the creation of some very strong extratropical storms, of tropical origin, that can devastate Maritime Canada and western Europe in the autumn. A particularly noteworthy example of such a storm was the Great October Storm of 1987 in the United Kingdom. This storm brought hurricane force winds to southern England, downing a number of 300-year-old oak trees and closing the London Stock Exchange—precipitating the Crash of 1987 in the New York Stock Exchange. Such extratropical transitions are common in the western North Pacific during autumn and can result not only in significant storms, but also a decrease in the accuracy of medium range (3–7 day) forecasts over much of the Northern Hemisphere. The nature of the physical interactions between the tropics and the extratropics, a fraction of which is manifest in such extratropical transition events, is currently a major topic of research inquiry in the atmospheric sciences.

Tropical Cyclones in the Earth’s Energy Budget Recall that we briefly examined the role of extratropical cyclones in the Earth’s energy balance, suggesting that the poleward advection of warm, moisture laden air and the equatorward advection of cold polar air helped to alleviate the radiative imbalance between the tropics and high latitudes—a fundamental requirement of the general circulation of the Earth’s atmosphere. Given the lack of thermal contrast in the tropics, one might reasonably wonder if a similarly important role in the general circulation is played by tropical cyclones. The net poleward transport of heat accomplished by extratropical cyclones is also accomplished by tropical cyclones, but in a different manner. Recall that tropical cyclones are fueled by sensible and latent heat taken from the tropical ocean surface. That heat is originally invested in the tropical ocean via the annual surplus of radiant energy that characterizes the tropical latitudes. Since tropical cyclones generally migrate poleward, they accomplish a poleward transport of this heat. In addition, as they churn poleward they disturb the sea surface, mixing cooler subsurface water up to the surface in a process known as upwelling. Once this colder water has been upwelled to the surface, it is available to be heated by solar radiation. The huge amount of evaporation that characterizes the tropical cyclone’s interaction with the ocean surface is yet another means of cooling the ocean. Thus, the tropical ocean is cooled by

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the development and propagation of tropical cyclones over it—yet another net transport of heat out of the tropics. One can correctly view tropical cyclones as the atmosphere’s primary contribution to ventilation of the tropical ocean. Thus, by substantially different means, tropical cyclones are also strongly involved in alleviating the radiative imbalance between the tropics and high latitudes and are, therefore, major elements of the general circulation.

Tropical Cyclones in a Warmer Climate It is an undeniable observational fact that the average surface temperature of the Earth has increased by about 0.8°C (1.5°F) over the last 150 years or so. This increase has prompted considerable scientific study over the past 50 years and, with the parallel development of high speed computers during that same period, has led to the development of increasingly sophisticated computer models of the climate system. At the dawn of the 21st century, these models are strongly suggesting that the immediate future will be characterized by additional warming, the degree of which is not certain, as there is some variability among the projections made by the different climate models. It appears beyond doubt, however, that the subtle changes to atmospheric composition that have resulted from the astounding success of the Industrial Revolution have had a substantial role in this warming trend. A warmer planet means that, even without an increase in relative humidity, the actual water vapor content of the atmosphere (for instance, the mixing ratio) will increase. A current high profile question regarding future climate concerns how such increased water vapor content might change the nature of the general circulation of the Earth’s atmosphere. Given the relatively unchanging input of solar radiation to Earth’s atmosphere and oceans during the Industrial era, the geometry of the Earth dictates that there will still be a radiative imbalance between the tropics and the higher latitudes that needs to be relieved by the combined circulations of the atmosphere and ocean. One projection is that the mid-latitude circulation, composed of the aggregate of all mid-latitude cyclones and associated jet streams, will become more sluggish, with fewer overall storms but perhaps a higher fraction of strong storms. It may be that, despite the possibly larger number of strong storms, the overall poleward heat transport accomplished by mid-latitude storms will decrease in the face of this projected sluggishness. If this were indeed the case, there would have to be an increase in the poleward heat transfer accomplished by ocean currents and/or tropical cyclones. Thus, a companion projection is that the heat transport accomplished by tropical cyclones will increase. This increase could be achieved either by 1) an increase in the total number of tropical cyclones relative to the present day but with no change in the proportion of strong storms, or 2) by an increase in the number of strong tropical cyclones. For reasons that are still being debated, the current consensus points to the latter—a larger fraction of all tropical cyclones are projected to be in the strong category in our warmer future. This is certainly consistent with the knowledge that a warmer planet will be characterized by a higher SST in the tropics and

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a greater amount of water vapor in the air, both of which are key ingredients to the tropical cyclone environment. In addition, the warmer planet is expected to be characterized by an expanded Hadley Cell, which, in combination with a mid-latitude jet stream that is displaced poleward as well, will widen the area in the tropics that is relatively free of the vertical shear that is so toxic to the development of tropical cyclones. With more favorable conditions in which to grow strong tropical cyclones and the possible requirement that they play a larger role in the global energy balance than at present, a larger population of strong tropical cyclones would respond to, and fit the needs of, the conditions on a warmer planet. Preliminary evidence, gathered through careful scrutiny of the last 50 years of tropical cyclone data, offers compelling support for this view and growing confidence in the validity of this prediction.