“In this crystal-clear little book, Geoffrey Vallis masterfully explains the basics of physical oceanography and the role of the oceans in the climate system. He writes for those conversant with some university-level mathematics and physics, but whose knowledge of the oceans and climate is limited. The book moves smoothly from fundamental principles to topics of current research interest, including natural climate variability, such as El Niño, and the daunting challenge of man-made climate change, or global warming.”–Richard Somerville, Scripps Institution of Oceanography

“Readers interested in understanding how the ocean influences climate have had to choose between journalistic, grossly oversimplified accounts and the very technical professional literature. Geoffrey Vallis has now successfully filled that gap with a clear explanation of the ways in which the ocean is both influenced by and influences global climate.”–Carl Wunsch, Massachusetts Institute of Technology

“Climate and the Oceans is an accessible, effectively organized, and very well-written introduction to the subject.”–Peter R. Gent, National Center for Atmospheric Research

Geoffrey K. Vallis is professor and senior scientist in the Atmospheric and Oceanic Sciences Program and the Geophysical Fluid Dynamics Laboratory, Princeton University. He is the author of the standard graduate text “Atmospheric and Oceanic Fluid Dynamics”.

CLIMATE AND THE OCEANS

By Geoffrey K. Vallis

PRINCETON UNIVERSITY PRESS

Copyright © 2012 Princeton University Press
All right reserved.
ISBN: 978-0-691-15028-4

Contents

Preface……………………………………………….vii1 Basics of Blimate…………………………………….12 The Oceans: A Descriptive Overview……………………..223 A Brief Introduction to Dynamics……………………….414 The Ocean Circulation…………………………………755 The Ocean’s Overall Role in Climate…………………….1056 Climate Variability from Weeks to Years…………………1287 Global Warming and the Ocean…………………………..156Notes…………………………………………………205Further Reading………………………………………..211Glossary………………………………………………215References…………………………………………….223Index…………………………………………………229

Chapter One

BASICS OF CLIMATE

The climate’s delicate, the air most sweet. —William Shakespeare, A Winter’s Tale

To appreciate the role of the ocean in climate, we need to have a basic understanding of how the climate system itself works, and that is the purpose of this chapter. Our emphasis here is the role of the atmosphere—we don’t pay too much attention to the oceans as we’ll get more of that (lots more) in later chapters—and we assume for now that the climate is unchanging. So without further ado, let’s begin.

THE PLANET EARTH

Earth is a planet with a radius of about 6,000 km, moving around the sun once a year in an orbit that is almost circular, although not precisely so. Its farthest distance from the sun, or aphelion, is about 152 million km, and its closest distance, perihelion, is about 147 million km. This ellipticity, or eccentricity, is small, and for most of the rest of the book we will ignore it. (The eccentricity is not in fact constant and varies on timescales of about 100,000 years because of the influence of other planets on earth’s orbit; these variations may play a role in the ebb and flow of ice ages, but that is a story for another day.) Earth itself rotates around its own axis about once per day, although earth’s rotation axis is not parallel to the axis of rotation of earth around the sun. Rather, it is at an angle of about 23°, and this is called the obliquity of earth’s axis of rotation. (Rather like the eccentricity, the obliquity also varies on long timescales because of the influence of the other planets, although the timescale for obliquity variations is a relatively short 41,000 years.) Unlike the ellipticity, the obliquity is important for today’s climate because it is responsible for the seasons, as we will see later in this chapter.

Earth is a little more than two-thirds covered by ocean and a little less than one-third land, with the oceans on average about 4 km deep. Above earth’s surface lies, of course, the atmosphere. Unlike water, which has an almost constant density, the density of the air diminishes steadily with height so that there is no clearly defined top to the atmosphere. About half the mass of the atmosphere is in its lowest 5 km, and about 95% is in its lowest 20 km. However, relative to the ocean, the mass of the atmosphere is tiny: about one-third of one percent of that of the ocean. It is the weight of the atmosphere that produces the atmospheric pressure at the surface, which is about 1,000 hPa (hectopascals), and so 10⁵Pa (pascals), corresponding to a weight of 10 metric tons per square meter, or about 15 lb per square inch. In contrast, the pressure at the bottom of the ocean is on average about 4 x 10⁷Pa, corresponding to 4,000 metric tons per square meter or 6,000 lb per square inch!

The atmosphere is composed of nitrogen, oxygen, carbon dioxide, water vapor, and a number of other minor constituents, as shown in table 1.1. Most of the constituents are well mixed, meaning that their proportion is virtually constant throughout the atmosphere. The exception is water vapor, as we know from our daily experience: Some days and some regions are much more humid than others, and when the amount of water vapor reaches a critical value, dependent on temperature, the water vapor condenses, clouds form, and rain may fall.

Earth’s temperature is, overall, maintained by a balance between incoming radiation from the sun and the radiation emitted by earth itself, and, slight though it may be compared to the ocean, the atmosphere has a substantial effect on this balance. This effect occurs because water vapor and carbon dioxide (as well as some other minor constituents) are greenhouse gases, which means that they absorb the infrared (or longwave) radiation emitted by earth’s surface and act rather like a blanket over the planet, keeping its surface temperature much higher than it would be otherwise and keeping our planet habitable. However, we are getting a little ahead of ourselves—let’s slow down and consider in a little more detail earth’s radiation budget.

RADIATIVE BALANCE

Solar radiation received

Above earth’s atmosphere, the amount of radiation, S, passing through a plane normal to the direction of the sun (e.g., the plane in the lower panel of figure 1.1) is about 1,366 W/m². (A watt is a joule per second, so this is a rate at which energy is arriving.) However, at any given time, half of earth is pointed away from the sun, so that on average earth receives much less radiation than this. How much less? Let us first calculate how much radiation earth receives in total every second. The total amount is S multiplied by the area of a disk that has the same radius as earth (figure 1.1). if earth’s radius is a, then the area of the disk is A = πa², so that the rate of total radiation received is Sπa². Over a 24-hour period, this radiation is spread out over the entire surface of earth, although not, of course, uniformly. Now, earth is almost a sphere of radius a, and the area of a sphere is 4πa². Thus, the average amount of radiation that earth receives per unit area may be calculated as follows:

total radiation received = Sπa². (1.1)

Area of earth = 4πa². (1.2)

Average radiation received = Sπa²/4πa² = S/4. (1.3)

That is, the average rate at which radiation is received at the top of earth’s atmosphere is 1,366/4 [approximately equals] 342 W/m², and we denote this S₀; that is, S₀ = S/4 [approximately equals] 342 W/m².

Distribution of incoming solar radiation

The distribution of solar radiation is obviously not uniform over the globe, as figure 1.1 illustrates. Plainly, low latitudes receive, on average, much more solar radiation than high latitudes, which is the reason why temperatures, on average, decrease with latitude.

The situation is made more complex by the nonzero obliquity of earth’s axis of rotation; that is, the rotation axis of earth is not perpendicular to its orbital plane, as illustrated in figure 1.2. The axis of earth’s rotation is fixed in space and does not vary as earth rotates around the sun; that is, relative to the distant galaxies, the line from the South Pole to the north Pole always has the same orientation. But because earth rotates around the sun, the orientation varies relative to the sun. One day a year, the north Pole is most inclined toward the sun, and this day is known as the northern Hemisphere’s summer solstice. These days, it usually occurs on June 20 or 21. The northern Hemisphere receives much more radiation than the Southern Hemisphere at this time of year, so this corresponds to the northern Hemisphere’s summer and the Southern Hemisphere’s winter. In fact, not only is the sun higher in the sky during summer, but the day is also much longer, and at latitudes above the Arctic circle, the sun does not set for about two weeks on either side of the summer solstice.

Progressing from June on, as earth moves around the sun, the distribution of solar radiation becomes more equal between the hemispheres, and the length of day evens out. Then we enter autumn in the northern Hemisphere and spring in the Southern Hemisphere. At the equinoxes (about March 20 and September 22), the hemispheres receive equal amounts of radiation from the sun, which is directly above the equator. The northern Hemisphere’s winter solstice occurs on December 21 or 22, when the South Pole is most inclined toward the sun. It might seem from this description that in the northern Hemisphere the coldest day should be on December 21 and the warmest day on or about June 21. In fact, the coldest and warmest times of year occur a few weeks after these dates; the main reason is thermal inertia in the oceans, which delays the onset of the warmest and coldest days. We’ll discuss this effect more in chapter 5. Finally, we note that because of the eccentricity of earth’s orbit, earth’s distance from the sun varies throughout the year. However, this variation is a minor factor in seasonality, and for most intents and purposes we can regard earth’s orbit as circular.

A simple radiation model

Let us put aside the spatial variation of solar radiation for a while and try to obtain an estimate of the average surface temperature on earth, given the average solar radiation coming in at the top of the atmosphere. Solar radiation causes earth’s surface to warm and emit its own radiation back to space, and the balance between incoming and outgoing radiation determines the average temperature of earth’s surface and of the atmosphere. To calculate the temperature, we need to know a few pieces of physics; in particular, we need to know how much radiation a body emits as a function of its temperature and the wavelength of the radiation.

A blackbody is a body that absorbs and emits electromagnetic radiation with perfect efficiency. Thus, all the radiation—and therefore all the visible light—that falls upon it is absorbed. So, unless the body is emitting its own visible radiation, the body will appear black. Now, unless it has a temperature of absolute zero (0 K), the blackbody emits radiation and, as we might expect, the amount of this radiation increases with temperature, although not linearly. The amount, in fact, increases at the fourth power of the absolute temperature; that is, the flux of radiation emitted by the body per unit area varies as

F = σT⁴, (1.4)

where σ = 5.67 x 10^-8 Wm^-2 K^-4 is the Stefan–Boltzmann constant. The presence of a fourth power means that the radiation increases very rapidly with temperature. As a concrete illustration, let us suppose that earth is a blackbody with a temperature of -18°C, or 255 K (which is a temperature representative of places high in the atmosphere). The energy flux per unit area is F = σ x 255⁴ = 240 Wm². The sun, by contrast, has a surface temperature of about 6,000 K, and so the radiation it emits is F_sun = σ x 6,000⁴ = 7.3 x 10⁷ Wm². Thus, although the sun’s surface is only about 24 times hotter than earth, it emits about 300,000 times as much radiation per unit area. It is, of course, the sun’s radiation that makes life on earth possible.

A blackbody emits radiation over a range of wave numbers, but the peak intensity occurs at a wavelength that is inversely proportional to the temperature; this is known as Wien’s law. That is,

λ_peak = b/T, (1.5)

where λ_peak is the wavelength at peak intensity, b is a constant, and T is the temperature. For T in Kelvin and λ_peak in meters, b = 2.898 x 10^-3 mK. From equation 1.5, it is evident that not only does the sun emit more radiation than earth, it also emits it at a shorter wavelength. With T = 6,000 K, as for the sun, we find λ_peak = 0.483 x 10^-6m or about 0.5 µm. Electromagnetic radiation at this wavelength is visible; that is (no surprise), the peak of the sun’s radiation is in the form of visible light. (This fact is no surprise because eyes have evolved to become sensitive to the wavelength of the radiation that comes from the sun.) on the other hand, the radiation that earth emits (at 255 K) occurs at λ_peak = 1.1 x 10^-5m, which is infrared radiation, also called longwave radiation. The importance of this difference lies in the fact that the molecules in earth’s atmosphere are able to absorb infrared radiation quite efficiently but they are fairly transparent to solar radiation; this difference gives us the greenhouse effect, which we will come to soon.

A simple climate model

We are now in a position to make what is probably the simplest useful climate model of earth, a radiation-balance or energy-balance model (eBM), in which the net solar radiation coming in to earth is balanced by the infrared radiation emitted by earth. A fraction, α, known as the albedo, of the solar radiation is reflected back to space by clouds, ice, and so forth, so that

Net incoming solar radiation = S₀(1 – a) = 239 Wm², (1.6)

with α = 0.3 (we discuss the factors influencing the albedo more below).

This radiation is balanced by the outgoing infrared radiation. Now, of course, earth is not a blackbody at a uniform temperature, but we can get some idea of what the average temperature on earth should be by supposing that it is, and so

Outgoing infrared radiation = σT⁴. (1.7)

Equating equations 1.6 and 1.7, we have

σT⁴ = S₀(1 – α), (1.8)

and solving for T, we obtain T = 255 K or -18°C. For obvious reasons, this temperature is known as the average emitting temperature of earth, and it would be a decent approximation to the average temperature of earth’s surface if there were no atmosphere. However, it is in fact substantially lower than the average temperature of earth’s surface, which is about 288 K, because of the greenhouse effect of earth’s atmosphere, as we now discuss.

Greenhouse effect

Earth is covered with a blanket of gas made mainly of nitrogen, oxygen, carbon dioxide, and water vapor. This blanket is essential to life on earth, for (at least) two reasons:

1. We breathe the air, taking in the oxygen and breathing out carbon dioxide. Similarly, plants use sunlight together with the carbon dioxide in the atmosphere to photosynthesize and create organic compounds.

2. The atmosphere absorbs the infrared or longwave radiation emitted by Earth’s surface and re-emits it back to Earth, so warming the surface up to a habitable temperature.

Because this is a book on physical science, not biology, we will consider only this second effect, which is similar to the effect of glass in a greenhouse and for that reason is called the greenhouse effect.

Let us, then, consider the path of solar and infrared radiation through the atmosphere, as illustrated in figure 1.3. If the sky is clear, then most of the solar radiation incident at the top of the atmosphere goes through the atmosphere to the surface. If the sky is cloudy, then roughly half of the solar radiation is reflected back to space, with the rest either absorbed in the cloud or passing through to Earth’s surface. When the solar radiation reaches the surface, a fraction is reflected and returns to space, and the rest of the radiation is absorbed, warming the surface. All told, combining the effects of the reflection by clouds and at earth’s surface, the fraction of solar radiation reflected back to space—that is, the planetary albedo—is about 0.3. The albedo of clouds themselves is higher than this, typically about 0.5, but it can be as high as 0.9 for thick clouds; the albedo of the surface is on average about 0.1 but is much higher if the surface is covered with fresh snow or ice.

The surface is warmed by the solar radiation absorbed and so emits radiation upward, but because the surface temperature of Earth is so much less than that of the sun, the radiation emitted has a much longer wavelength—it is infrared radiation. Now, the atmosphere is not transparent to infrared radiation in the same way that it is to solar radiation; rather, it contains greenhouse gases—mainly carbon dioxide and water vapor—that absorb the infrared radiation as it passes through the atmosphere. Naturally enough, this absorption warms the atmosphere, which then re-emits infrared radiation, some of it downward, where it is absorbed at earth’s surface. Thus, and look again at figure 1.3, the total downward radiation at the surface is much larger than it would be if earth had no atmosphere. Consequently, the surface is much warmer than it would be were there no atmosphere, and this phenomenon is known as the greenhouse effect.

A simple mathematical model of the greenhouse effect

Let us now construct a simple mathematical model illustrating the greenhouse effect. Our purpose in doing so is to see somewhat quantitatively, if approximately, whether the atmosphere might warm the surface up to the observed temperature. Let us make the following assumptions:

1. The surface and the atmosphere are each characterized by a single temperature, T_s and T_a, respectively.

2. The atmosphere is completely transparent to solar radiation.

3. Earth’s surface is a blackbody.

(Continues…)

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