Atmosphere, Clouds, and Climate (Princeton Primers in Climate)

Atmosphere, Clouds, and Climate (Princeton Primers in Climate)

by David Randall

ISBN: 9780691143750

Publisher Princeton University Press

Published in Calendars/Nature

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Sample Chapter

Chapter One



Robert Heinlein wrote that "[c]limate is what we expect, weather is what we get." What we expect is typical weather, but the weather at a given place, on a given day, can be very atypical.

A dictionary definition of climate is "the average course or condition of the weather at a place usually over a period of years as exhibited by temperature, wind velocity, and precipitation" (Merriam-Webster online, http:// Here "average" refers to a time average. In many reference works, climatological averages are defined to be taken over 30 years, a definition that probably has to do more with the human life span than with any physical time scale.

Simple 30-year averages are not enough because they hide important variability, such as differences between summer and winter. Because of the great importance of the seasonal cycle, climatological averages are often specified for particular months of the year; we might discuss the climatological average precipitation rate for new york city, averaged over 30 Julys, or 30 Januarys.

climate varies geographically, most obviously between the tropics and the poles. There are also important climate variations with longitude, at a given latitude. For example, the Sahara Desert and the jungles of southeast Asia have very different climates, even though they are at the same latitude. Climate also varies strongly with surface elevation; near the surface, the temperature and water vapor concentration of the air generally decrease upward, and the wind speed often increases upward.

The climate of the earth as a whole changes with time, for example when ice ages come and go. In fact, the climate of the earth as a whole is changing right now due to rapid, anthropogenically produced changes in the composition of the atmosphere.

The climate parameters of greatest importance to people are precipitation and temperature. The next few items on the list would include wind speed and direction, and cloudiness. Scientists are interested in a much longer list of parameters, of course.

The "average course or condition of the weather," mentioned in the dictionary definition of climate, includes not only simple averages, such as the climatological January mean surface air temperature, but also, importantly, statistics that characterize the fluctuations and variations of the climate system. Variability is of great and even primary interest. Predictions are all about change. examples of important variations that are aspects of climate include the following:

The seasonal variations of surface air temperature (and many other things)

Systematic day-night temperature differences

The tendency of thunderstorms to occur in late afternoon in many places

The frequency of snow storms

The occurrence, every few years, of "El Niño" conditions, which include unusually warm sea surface temperatures in the eastern tropical Pacific ocean

The list could easily be extended. Variations like these are important aspects of the climate state. All of them can be described by suitably concocted statistics; for example, we can discuss the average daily minimum and maximum near-surface air temperatures.

It is important to distinguish between "forced" and "free" variations. Forced variations include the day-night and seasonal changes mentioned above, which are externally driven by local changes of solar radiation that are associated with the earth's rotation on its axis and its orbital motion around the Sun, respectively. Volcanic eruptions can also force climate fluctuations that sometimes last for years. On the other hand, storms and El Niños are examples of unforced or "free" variations that arise naturally through the internal dynamics of the climate system.

For the reasons outlined above, I would modify the dictionary definition to something like this: "climate is the (in principle, infinite) collection of statistics based on the evolving, geographically distributed state of the atmosphere, including not only simple averages but also measures of variability on a range of time scales from hours to decades."

Since "weather" refers to the state of the atmosphere, the definitions given above make climate appear to be a property of the atmosphere alone. Climate scientists don't think of it that way, though, because any attempt to understand what actually determines the state of the climate, and what causes the climate to change over time, has to take into account the crucial roles played by the ocean (including marine biology), the land surface (including terrestrial biology), and the continental ice sheets. These, together with the atmosphere, make up the four primary components of what is often called the "climate system."

The ocean is about 400 times more massive than the atmosphere and has a heat capacity more than a thousand times larger. When the ocean says "Jump," the atmosphere asks "How high?" Nevertheless, the thin, gaseous atmosphere exerts a powerful influence on the climate. How can the relatively puny atmosphere play such a major role in the much larger climate system?

The explanation has two parts. First, the atmosphere serves as an outer skin, standing between the other components of the climate system and space. As a result, the atmosphere is in a position (so to speak) to regulate the all-important exchanges of energy between the earth and space, which take the forms of solar radiation coming in and infrared radiation going out.

The second reason is that the atmosphere can transport energy, momentum, and other things from place to place much faster than any other component of the climate system. Typical wind speeds are hundreds or even thousands of times faster than the speeds of ocean currents, which are in turn much faster than the ponderous motions of the continents. The atmosphere (and ocean) can also transport energy through the pressure forces exerted by rapidly propagating fluid-dynamical waves of various kinds.

The climate system is of course governed by the laws of physics. Its behavior can be measured in terms of its physical properties, analyzed in terms of its physical processes, and predicted using physical models. It is influenced by a variety of "external" parameters that are (almost) unaffected by processes at work inside the climate system. These external parameters include the size, composition, and rotation rate of the earth; the geographical arrangement of oceans, continents, mountain ranges, and so on; the geometry of the earth's orbit around the Sun; and the amount and spectral distribution of the electromagnetic radiation emitted by the Sun.

Over the past few decades, the possibility of ongoing and future anthropogenic climate change has been widely recognized as a major scientific and societal issue, with huge economic ramifications. As a result, the physical state of the climate system is now being intensely monitored, like the health of a patient with worrisome symptoms. Ongoing changes are being diagnosed. The future evolution of the system is being predicted, using rapidly improving physically based models that run on the fastest computers in the world.


The atmosphere is big. Its total mass is about 5 × 1021 g.

The most abundant atmospheric constituents are nitrogen and oxygen. They are very well mixed throughout almost the entire atmosphere, so that their relative concentrations are essentially constant in space and time.

Ozone and water vapor are "minor" but very important atmospheric constituents that are not well mixed, because they have strong sources and sinks inside the atmosphere. Ozone makes up less than one millionth of the atmosphere's mass, but that is enough to protect the earth's life from deadly solar ultraviolet (UV) radiation. Water vapor is only about a quarter of 1% of the atmosphere's mass, but its importance for the earth's climate, and for the biosphere, would be hard to exaggerate, and it will be discussed at length throughout this book.

The term "dry air" refers to the mixture of atmospheric gases other than water vapor. As shown in Table 1.1, dry air is a mixture of gases. Each gas approximately obeys the ideal gas law, which can be written for a particular gas, denoted by subscript i, as

piV = NikT (1.1)

Here pi is the partial pressure of the gas, V is the volume under consideration, Ni is the number of particles, k is Boltzman's constant, and T is the temperature. If the gas is in thermal equilibrium, then the temperature will be the same for all gases in the mixture. This is an excellent assumption for dry air, valid up to at least 100 km above the surface. We can write Nik = niR*, where ni is the number of moles and R* is the universal gas constant.

The total mass of the gas, Mi, satisfies ni = Mi/mi, where mi is the molecular mass. Substituting, we find that

pi = ρ [R*/mi]T, (1.2)

where ρ [equivalent to] Mi/Mi is the density.

The temperature is a measure of the kinetic energy of the random molecular motions. It normally decreases with height in the lower atmosphere, although, as discussed later, it actually increases upward at greater heights. The range of temperatures encountered throughout most of the atmosphere is roughly 200 K to 300 K.

The pressure of a gas is, by definition, the normal component of the force (per unit area) exerted by the moving molecules. In an ideal fluid, the pressure at a point is the same in all directions.

you have probably experienced the increased pressure that the water exerts on your ears (and the rest of your body) at the bottom of a swimming pool. What you are feeling is the weight (per unit horizontal area) of the water above you. At greater depths, there is more water above, it pushes down on you more heavily, and the water pressure increases as a direct result. The density of the water, ρwater, is very nearly constant, so the pressure at a given depth, D, is given by p = ρwater gD, where g is the acceleration of gravity, which is about 9.8 m s-2 near the earth's surface.

Similarly, the air pressure at a given height is very nearly equal to the weight (per unit horizontal area) of the air above. In a "high-pressure" weather system, you are buried under a thicker (more massive) layer of air. With a low-pressure system, the layer of air is thinner. This "hydrostatic" relationship applies to each gas separately because the weights of the gases simply add. For a particular gas, denoted by subscript i, the hydrostatic relationship can be expressed in differential form by

[partial derivative]pi/[partial derivative]z = -ρig, (1.3)

where z is height. The minus sign appears in equation (1.3) because the pressure increases downward while height increases upward. We use a partial derivative of p with respect to z in (1.3) because the pressure also depends on horizontal position and time. The hydrostatic equation, (1.3), expresses a balance between two forces, namely the downward weight of the air and the upward pressure force that arises from the upward decrease of pressure. The balance is not exact. It is an approximation, which is another way of saying that it has an error because something has been neglected. That something is the actual acceleration of the air in the vertical direction. Further discussion is given in chapter 3.

By combining the ideal gas law with the hydrostatic equation, we find that


As you probably know, g decreases upward in proportion to the square of the distance from the center of the earth. The earth's atmosphere is very thin, though, so the variations of g with height inside the atmosphere are negligible for most purposes, and we will neglect them here. Suppose that the temperature varies slowly with height. treating it as a constant, we can integrate both sides of (1.4) to obtain


where the surface height is taken to be zero, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the surface partial pressure of gas i, and

Hi [equivalent to] [R*T]/[mig] (1.6)

is called the "scale height" of the gas. Equation (1.5) says that the partial pressure decreases upward exponentially away from the surface, at a rate that depends on the molecular mass of the gas and also on the temperature, which, again, is the same for all of the gases in the mixture. By putting in some numbers, you will find that a typical value of the scale height of nitrogen in the earth's atmosphere is about 8,000 m. According to equation (1.5), the partial pressure of nitrogen decreases upward by a factor of e in 8,000 m.

How heavy is a column of air? The total pressure (due to the weight of all atmospheric constituents) is typically about 100,000 Pa near sea level, where a Pa (pascal) is defined to be a newton (Nt) per square meter. For comparison, the weight of a typical car is about 20,000 Nt, so the weight of an air column per square meter is roughly equivalent to the weight of five cars piled on top of each other, over one square meter of a junk yard. That's pretty heavy. The total pressure at an altitude of 12 km is about 20,000 Pa, roughly 5 times less than the surface pressure.

By pushing the ideas presented above just a bit further, you should be able to show that the partial density of a gas also decreases upward exponentially, following a formula very similar to (1.4). The total density of the air near sea level is typically about 1.2 kg m-3. The total density at an altitude of 12 km is about 5 times less. As an example, the density of atmospheric oxygen decreases exponentially upward, which is why hiking is more challenging at higher altitudes.

As shown in table 1.1, the various atmospheric gases have different molecular masses, and as a result they have different scale heights. This suggests that the relative concentrations of the various gases should vary with height, so that the heaviest species would be more concentrated near the ground and the lighter species more concentrated higher in the atmospheric column. The process that could lead to such a result is called "diffusive separation" because it depends on the microscopic shaking due to molecular motions, in the presence of gravity. Diffusive separation is a real process, but it is negligible in the lower atmosphere because the turbulent winds act like a powerful mixer that homogenizes the blend of gases. The result is that, except for ozone, the concentrations (not the densities) of the gases that make up dry air, for example, nitrogen, oxygen, argon, and carbon dioxide, are observed to be nearly homogeneous, both horizontally and vertically, up to an altitude of about 100 km. Above that level, diffusive separation does become noticeable.

As an example, Figure 1.1 shows the variations of density, pressure, and temperature with height, from the surface to an altitude of 50 km, based on the U.S. Standard Atmosphere ( atmos/us_standard.html).

Vertical profiles are called "soundings," a term borrowed from oceanography. The approximately exponential upward decreases of density and pressure are obvious. The temperature decreases upward for the first 10 km or so, remains almost constant for the next 10 km, and then begins to increase upward. This vertical distribution of temperature will be explained later.

Water vapor is an important exception to the rule that the atmosphere is well mixed. There are two main reasons for this. First, water vapor enters the atmosphere mostly by evaporation from the ocean, so it has a tendency to be concentrated near the surface. More importantly, water vapor can condense to form liquid or ice, which then falls out of the atmosphere as rain or snow. Condensation happens when the actual concentration of vapor exceeds a saturation value, which depends on temperature. in effect, the water vapor concentration is limited to be less than or equal to the saturation value. At the colder temperatures above the surface, saturation occurs more easily, and the water concentration decreases accordingly. The fact that water can change its phase in our atmosphere is critically important for the earth's climate. Much additional discussion is given in later chapters.


Excerpted from "Atmosphere, Clouds, and Climate (Princeton Primers in Climate)" by David Randall. Copyright © 0 by David Randall. Excerpted by permission. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher. Excerpts are provided solely for the personal use of visitors to this web site.
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