Solar Energy And The Upper Atmosphere

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Power from the Sun

In comparison with some of the far larger stars to be seen on a clear, dark night, our sun is often airily dismissed as a second-rate star. All the same, its energy output is impressive; it produces 3.8 x 1026 J (joules) per second, without interruption.

The rate at which a source yields energy is its power. Power is measured in watts (W), and one watt is one joule per second. Writing this as an equation, 1 W = 1 J s-1. The sun's power therefore is 3.8 x 1026 watts, a quantity known as the solar constant.1

The sun radiates in all directions, and only a tiny fraction of its output is intercepted by the earth, 150 million kilometers away. On average, the solar power received by the earth is 340 watts per square meter of surface2 or, more concisely, 340 W m-2. It is important to be aware of what the averaging entails. First, the averaging is over the whole surface of the earth: it allows for the difference between the polar regions where the sun never rises high in the sky and the tropics where the midday sun is not far from the zenith on every day of the year. Second, the 340 W

m-2 is averaged over time: over day and night, and also over all the days of the year. Averaging over the year has nothing to do with the weather (the incoming radiation is measured above the atmosphere) or the seasons (averaging over the whole of the earth's surface takes care of that). Rather, it allows for the earth's elliptical orbit, which brings it nearest to the sun in January and takes it farthest away in July; this causes the energy received by the whole earth to be above average in January and below average in July.

The Solar Energy Budget

Now consider the fate of this incoming energy. The first point to notice is that solar energy does not accumulate appreciably. The earth's net gain of solar energy over the year is close to zero, and were it not for global warming it would remain at zero, on average. If we take the long-term view, disregarding slight temporary climatic wanderings caused by atmospheric changes, it is safe to say that all the energy that comes in must go out. Over the past several hundred million years a certain amount of solar energy has, admittedly, become stored as fossil fuels. The amount is negligible, however; it has been estimated that the heat content of all known fossil fuel reserves represents no more than the solar energy intercepted by the earth in ten days.3

The way the incoming and outgoing energies balance each other is shown in figure 4.1. The incoming sunlight, shown in the left panel, is chiefly short wave radiation in the visible and near ultraviolet parts of the spectrum. On average, 30 percent of it is reflected back to space by clouds and does not contribute any heat to the earth. Of the remaining 70 percent (about 240 W m-2), 19 percent is absorbed by the atmosphere, chiefly by the water vapor in it, and the remaining 51 percent by land and ocean combined.4 The right panel shows what subsequently becomes of this 70 percent; it is radiated back into space again, as infrared radiation for the most part; some is reflected back as light.5 Of the 51 percent absorbed and then reradiated by land and sea, 45 percent is absorbed again on the outward journey, this time by the atmosphere, where it is held temporarily, adding itself to the 19 percent of solar energy absorbed on the incoming journey. The atmospheric ingredients responsible for the absorption are the "greenhouse gases," primarily water vapor, carbon dioxide, and methane. The total energy reradiated by the atmosphere therefore becomes 64 percent of the original input. The remaining 6 percent still "owing" radiates as infrared rays, directly from the ground to outer space.

Figure 4.1. The partitioning of incoming solar radiation (on the left) and outgoing radiation from the earth (on the right). The latter adds up to the 70 percent of incoming radiation that was not reflected back to space.

Greenhouse gases are always naturally present in the atmosphere; if they were not, a much smaller fraction of incoming solar energy would be trapped to warm the earth, and a much larger fraction would be reflected directly back to space. If there were no atmosphere the earth's average surface temperature would be -18°C, that is, 33°C lower than the actual average of 15°C.6

Greenhouse gases in what humanity now thinks of as "natural" quantities—the quantities present before the Industrial Revolution—are an undoubted blessing; they are indispensable to our comfort, indeed, to our very survival. The global warming currently in progress is probably (not certainly) being brought about by the recent "unnatural" increases in greenhouse gases caused by pollution of the air with vehicular exhausts and effluent gases from a wide range of industries.

South Latitude North

Figure 4.2. How incoming radiation (solid line) and outgoing radiation (dashed line) change with latitude. Between latitudes 37° N and 37° S, incoming radiation exceeds outgoing radiation. Poleward of these latitudes, incoming radiation falls short of outgoing.

South Latitude North

Figure 4.2. How incoming radiation (solid line) and outgoing radiation (dashed line) change with latitude. Between latitudes 37° N and 37° S, incoming radiation exceeds outgoing radiation. Poleward of these latitudes, incoming radiation falls short of outgoing.

Latitudinal Temperature Differences and the Winds

Solar radiation is what energizes the wind and controls the weather. The two most important factors governing the atmospheric circulation are the way air temperature varies from the equator to the poles and the way the earth's rotation on its axis affects wind direction. We'll consider these factors in turn.

The way the solar radiation reaching the earth's surface decreases as you go from the equator to the poles is shown by the solid line in figure 4.2. The incoming power ranges from a high of about 350 W m-2 at the equator to a low of about 100 W m-2 at the poles, for an average over all latitudes close to 240 W m-2. The power decreases as the latitude increases because the angle of incidence of the sun's rays changes; in the tropics, the rays strike the ground almost perpendicularly much of the time, whereas at high latitudes they are always oblique.7

The dashed line on the figure shows how the absorbed energy is radiated back to space; it shows that absorption exceeds reradiation at latitudes between 37° N and 37° S and falls short of reradiation everywhere poleward of these latitudes. It follows that if it were not for redistribution of the sun's heat

Degrees Latitude North Map

Figure 4.3. Idealized model of the winds at the top of the troposphere as they would blow if the earth did not rotate. The air would move poleward at high elevation (solid lines) and back toward the equator near sea level (dashed lines), circulating independently in the Northern and Southern Hemispheres.

Figure 4.3. Idealized model of the winds at the top of the troposphere as they would blow if the earth did not rotate. The air would move poleward at high elevation (solid lines) and back toward the equator near sea level (dashed lines), circulating independently in the Northern and Southern Hemispheres.

by winds and ocean currents, the earth's climate would be entirely different: the tropics would be far hotter, and the polar regions far colder. In practice, however, air movements and ocean currents carry the sun's heat poleward from the tropics, reducing the climate contrast between high latitudes and low.

The general circulation of the atmosphere is controlled by the latitudinal temperature gradient, that is, by the way the temperature drops as you travel from low, tropical latitudes to high, polar latitudes. Here we consider the winds high in the atmosphere, far above the influence of friction with the surface (strictly speaking drag, but it is usually called friction). Air pressure depends on air temperature, being high where the temperature is high and low where the temperature is low.8 Therefore the atmosphere develops a pressure gradient more or less matching the temperature gradient, with high pressures in the tropics and low pressures in the polar regions. Moreover, the greater the height above the earth's surface, the stronger the pressure gradient. The wind blows down a pressure gradient, from high pressures toward low. Consequently, if it were not for the rotation of the earth on its axis, high-level winds would tend to blow always from the equator toward the poles (see fig. 4.3); at the same time, to prevent the atmosphere from piling up over the poles, winds at the surface would blow from the poles to the equator, returning the air to its starting point. In other words, huge convection cells would develop, one over each hemisphere.

The worldwide pattern of circulation just described, and shown in the figure, represents what would happen, in theory, if the earth did not rotate on its axis once every twenty-four hours. But of course it does rotate, and the effect of this rotation is what we consider next.

The Effect of the Earth's Rotation

Because of the earth's rotation any wind is deflected from its course unless it happens to be blowing parallel with the equator and directly above it. In the Northern Hemisphere the wind is always deflected to the right (as you stand with your back to it), and in the Southern Hemisphere, always to the left. This rule applies whatever the wind's direction. The deflection is known as the Coriolis effect.9 The magnitude of the effect depends on the latitude: it is greatest at the poles and decreases to zero at the equator.

It is easy to see why the earth's rotation should cause a wind blowing over one of the poles, say the North Pole, to be deflected. Imagine yourself in a stationary satellite looking directly down on the North Pole; you would see the earth and everything fixed to its surface rotating counterclockwise beneath you. Suppose a weather balloon, floating high above the ground, was carried past on the wind directly below. The balloon is not attached to the earth and therefore does not move with it; instead, it is left behind by the continents and oceans carried along on the earth's surface so that, relative to them, it appears to drift westward, that is, to the right. The balloon would be seen to be going in a straight line if the earth below it were invisible; the rightward deflection is entirely a relative matter, relative to the earth and to an observer on the earth.

In this particular case, of an object moving southward from the North Pole, it is obvious how the Coriolis effect works. But it is not intuitively obvious how the effect can cause a free-floating object borne on the wind—and the wind itself—to be deflected to the right everywhere north of the equator, whatever the wind's direction and wherever the object may be.

A full explanation requires some fairly advanced mathematics, but figure 4.4 gives an idea of what is going on. It shows the globe rotating, once each day, around its axis (the line through its center joining the North and South

Steiner M7xi Absehen

Figure 4.4. The Coriolis effect (see text). The earth is shown with three axes of rotation (solid arrows), the "true" axis and two "private" axes (see text). The perspective circles, with arrows, show the earth's spin at the three locations. The spin is wholly horizontal at the poles and wholly vertical at the equator. At intermediate latitudes it can be analyzed into horizontal and vertical components, as shown by the dashed arrows and circles at the midlatitude location. Inset: Horizontal (H-H) and vertical directions (V) at three representative points on the earth's surface.

Figure 4.4. The Coriolis effect (see text). The earth is shown with three axes of rotation (solid arrows), the "true" axis and two "private" axes (see text). The perspective circles, with arrows, show the earth's spin at the three locations. The spin is wholly horizontal at the poles and wholly vertical at the equator. At intermediate latitudes it can be analyzed into horizontal and vertical components, as shown by the dashed arrows and circles at the midlatitude location. Inset: Horizontal (H-H) and vertical directions (V) at three representative points on the earth's surface.

Poles). If you were to stand at either of the poles for twenty-four hours in summer (when the sun never sets), the sun would appear to move in a complete circle around you, with the center of the circle directly overhead. Likewise, observed from any other point on the globe, the sun is seen to move in a complete circle in twenty-four hours, but the circle's center is not directly overhead. Admittedly, the sun is out of sight at night for an observer in non-Arctic latitudes, but visualizing where it would appear if the globe were transparent isn't difficult. It follows that every point on the globe can be thought of

as rotating about a "private" axis of its own, parallel with the earth's axis. The figure shows two of these private axes, one at 40° N latitude and one on the equator, as well the true axis protruding from the North Pole. The three axes are parallel; they are shown by the straight, solid north-pointing arrows.

Before continuing, note the meanings of horizontal and vertical in what follows, and see the inset in figure 4.4. A plane tangent to the earth's surface at any point is the horizontal surface at that point. Except at the poles, it is not parallel with the top and bottom edges of the page. A line through the point at right angles to the tangent plane is the vertical through the point. Except at the poles, it is not parallel with the left and right margins of the page. Keep this in mind as you read on.

Only at the pole itself, where the axis is vertical, is the rotating circular movement completely parallel with the ground, or horizontal. This movement is shown by the "twirls" (circles seen in perspective) above each axis.

At any site at an intermediate latitude (for instance, at 40° N as in the figure), the private axis emerges obliquely from the ground. It may be regarded as the resultant of two subaxes, shown in the figure as dashed arrows; one of the subaxes is the projection of the true axis onto the vertical at the site; the other subaxis is its projection onto the horizontal at the site. As the figure shows, the subaxes are shorter than the true axis, and the speed of rotation around each of them is less than around the true axis, as shown by the smaller twirls over the dashed arrows. These two circular movements at right angles to each other combine to give the true, oblique movement.

The private axis of an observer on the equator is horizontal. The circular motion around it is therefore confined to the vertical plane; its horizontal component is zero.

Now consider a pendulum suspended at each of the sites; imagine that each pendulum is supplied with just enough power to overcome friction and keep it swinging regularly; also, that it is hung so it can swivel freely around the point of suspension, ensuring that the plane of its swing will not rotate with the rotating earth but will remain fixed relative to the distant stars while the earth rotates beneath it. When the pendulum is at the North Pole, each swing will shift far enough to the right of the previous one to complete a full circle in exactly twenty-four hours. When the pendulum is at a middle latitude (for example, at 40° N, as in the figure), it will tend to be deflected by exactly the same amount in a plane at right angles to the earth's axis of rotation, that is, in a plane tilted obliquely to the horizontal. But gravity is strong enough to prevent any deflection in a vertical plane; the only deflection possible is the horizontal component, and this is less than the total that the earth's rotation "ought" to cause. The pendulum will therefore take considerably longer than twenty-four hours to complete a rotation relative to the ground. When it is on the equator, the pendulum will not rotate at all relative to the horizontal; its tendency—unrealizable because of gravity—will be to rotate wholly in a vertical plane. Such a pendulum, known as Foucault's pendulum,10 was actually constructed in Paris in 1851, and its behavior gave incontrovertible evidence that the earth rotates on its axis; nowadays many museums have working replicas of it.

The argument shows how the earth's rotation sets up a "twist" affecting every point on earth except points exactly on the equator. The direction of the twist is the same everywhere and causes anything moving above the surface of the earth—the wind, a floating balloon, an airplane, a migrating goose, a swinging pendulum bob—to drift relative to the surface. To an observer on the earth, the drift appears rightward in the Northern Hemisphere and leftward in the Southern Hemisphere. Moreover, this drift, the Coriolis deflection, is greatest at the poles; at lower and lower latitudes, the horizontal component of the spin becomes less and less (the Coriolis deflection decreases); at the equator, the effect is zero and there is no deflection at all.11

How the Winds Respond

Now back to the upper atmosphere winds, above the level at which friction with the ground causes complications (we come to those in chapter 5). Friction becomes negligible about 1 km above the earth's surface, and above that the troposphere continues for a long way; the height of the tropopause (the boundary layer separating troposphere and stratosphere) is about 10 km at the poles and more than 15 km at the equator. In describing events in the troposphere beyond the influence of friction, we are therefore considering a very thick layer—roughly, between 9 and 14 km thick—and conditions are not the same all through the layer.

First, recall figure 4.3, which shows the wind pattern as it would be if the atmospheric pressure decreased steadily from the equator to the poles and if, also, the earth did not rotate. These two "ifs"—simplifications—will now be abandoned.

Conditions leading to a wind pattern like that in figure 4.3 are unlikely to occur except near the top of the troposphere, and only occasionally even there. At lower levels the highest air pressures are seldom directly above the equator: more often there are two ridges of high pressure, one on each side of the equator. High in the troposphere, the ridges tend to be close to the equator and to each other. At progressively lower elevations they become farther and farther apart, being between 15° and 20° north and south of the equator at a height of 1 km; near ground level, they are usually at about 30° north and south and are known as the "subtropical highs."

This shows that figure 4.3 is an oversimplification of the wind pattern above a nonrotating earth except, sometimes, at the very top of the troposphere. At a lower level in the atmosphere, say at 5 km above the surface, the wind pattern if the earth did not rotate would be as shown in figure 4.5a. The highest pressures are at some distance from the equator, on each side of it. This causes the winds between the subtropical highs to blow toward the equator; poleward of the subtropical highs, the winds blow toward the respective poles. To repeat, this is a highly simplified version of what the wind pattern might be like if the earth did not rotate.

Now let the earth rotate, so that the Coriolis effect comes into play. The result is shown in figure 4.5b. Wind directions have turned through a right angle. In the Northern Hemisphere, what were south winds have become west winds or "westerlies" and what were north winds have become east winds or "easterlies," and vice versa in the Southern Hemisphere. (Recall that the name of a wind relates to the direction it is coming from: for instance, a west wind blows from west to east.) These winds are known as geostrophic winds; the term combines the Greek geo-, earth, and strophe, a turning. The reason the winds blow at right angles to the pressure gradient is as follows.

Consider a south wind in the Northern Hemisphere: it blows northward down the pressure gradient leading from the northern subtropical high to the low pressure area over the North Pole: this wind is deflected to the right (east) by the Coriolis effect. Were it not for the pressure gradient, the rightward deflection would turn the wind back on itself. The pressure gradient prevents this, however; the tendency of the wind to blow "downhill"—down the pressure gradient—and its tendency to turn right because of the Coriolis effect come into balance with the wind blowing directly across the pressure gradient, due eastward in this case. In maps showing the isobars (contours of equal atmospheric pressure) as well as wind directions, it is easy to see that the winds are parallel or nearly parallel to the isobars; examples are given in the following section.

The geostrophic winds are the dominant winds of the general atmospheric circulation, and it must be emphasized that they ultimately derive all their energy from the sun's heat, which produces atmospheric pressure gradients—

NH Equator

NH Equator SH

NH Equator

Poleward winds

Equatorward ^ winds

Poleward winds

Poleward winds

Equatorward ^ winds

Poleward winds

NH Equator SH

Figure 4.5. Idealized models of the winds at 5 km elevation, assuming (a) that the earth does not rotate and (b) that it does. NH and SH show the latitudes of the northern and southern subtropical highs.

Westerlies

Easterlies

Westerlies

Figure 4.5. Idealized models of the winds at 5 km elevation, assuming (a) that the earth does not rotate and (b) that it does. NH and SH show the latitudes of the northern and southern subtropical highs.

the immediate cause of the wind. The Coriolis effect, caused by the rotation of the earth, determines the winds' directions, but it does not "drive" the winds in the sense of contributing energy to them.

Jet Streams

The speed of the geostrophic wind at any point depends on the steepness of the pressure gradient and on the elevation. Consider elevation first. Low-level winds,

a b at less than 1,000 m above the surface, are slowed by friction; above the friction layer, wind speeds continue to increase at increasing heights because of the decreasing density of the air. The fastest winds are at the level of the tropopause.12

The speeds of these winds also depend on the steepness of the pressure gradient, which is not the same at all latitudes. In the Northern Hemisphere the gradient is steepest at two "steps," one at about 60° N, on average, the other between 25° and 30° N, on average. (Note the words "on average"; the steps swing north and south over a wide range of latitudes, as we shall see.)

The fastest winds in the Northern Hemisphere therefore tend to be at the level of the tropopause in two widely separated latitude belts. These winds are the jet streams. The northern one is known as the polar jet; it blows at about 10 km above the ground; the southern one is the subtropical jet, which blows at a greater height—about 13 km up—because the tropopause is higher in the tropics than near the poles. Both are westerlies; the subtropical jet forms in the zone of westerlies (see fig. 4.5b), on the poleward side of the subtropical high.13 A jet stream can be thought of as a current of air hurtling through the upper atmosphere at tremendous speed. In cross section it is shaped like a wide ribbon, hundreds of kilometers wide but only a few kilometers thick from top to bottom. The ribbon may be several thousand kilometers long.

The wind speed at the center of a jet stream is typically about 200 km/h, occasionally rising to over 450 km/h.14 The kinetic energy of a 200 km/h wind blowing 10 km above the ground is no greater than that of a 113 km/h wind blowing at the surface, because the density of the air is less at high elevations than at low.15 Even so, a jet stream is extremely powerful. When you see cirrus clouds ("mares' tails") drawn out into long, straight wisps far up in a blue sky, you are seeing clouds shaped by a jet stream. Even though the air may be calm at ground level, the evidence for a strong wind at great height is plain; the telltale clouds are seen most often in winter, when jet streams are strongest because the temperature contrast between the tropics and the polar regions is greatest.

Rossby Waves

The jet streams seldom blow "straight," in the sense of blowing steadily along a parallel of latitude; if they did, they would be little help in conveying the sun's heat from low latitudes to high. The polar jet usually follows a meandering course, blowing from the southwest and the northwest alternately. Figure 4.6 shows a typical path for it, snaking around the world in northern latitudes. The strongest winds follow this curving route in the same way that a

Figure 4.6 Representative map of the polar jet stream. The "waves" of its course are Rossby waves.

stream of water flows through a garden hose lying zigzag on the ground. The "waves" along its course are Rossby waves,16 sometimes called long waves. Four or five of them, with wavelengths averaging 4,000 to 5,000 km, encircle the earth. The whole pattern of waves usually drifts slowly downwind (eastward) at a rate of about 4° of longitude a day, but this does not always happen; the pattern sometimes remains stationary for days on end and occasionally drifts backward (westward) for a while.17

Rossby waves form because high-pressure and low-pressure regions (highs and lows for short, or anticyclones and cyclones) develop in the upper atmosphere in the same way as they do at low levels, in response to differential heating at the surface. As a result, the high-level circulation at any one moment hardly ever has a pattern as simple as that in figure 4.5b, which is a simplified diagram corresponding, more or less, with the long-term average.

Consider how highs and lows affect the wind. What happens in the Northern Hemisphere is shown in figure 4.7. Figure 4.7a shows the isobars of an anticyclone, resembling the contours of a hill; if it were not for the rotation of

Figure 4.7 (a) An anticyclone and (b) a cyclone, both in the Northern Hemisphere, at an elevation above the friction layer at 1,000 m above the surface. The closed loops are isobars; the winds (arrows) are parallel to them.

NORTH

Figure 4.8. Details of one wave of the polar jet stream. Dashed arrows show the wind direction; the fine lines are isobars. (a) Here the jet blows around a ridge of high pressure, turning to the right. (b) Here it blows around a trough of low pressure, turning to the left. The solid and open arrows show the wave's two components: the solid arrows show the Corio-lis effect as it would be in the absence of local pressure differences; it is stronger at high latitudes than at low. The open arrows show the wind directions resulting from the local pressure gradients, which happen to be steeper around the low than around the high.

Figure 4.8. Details of one wave of the polar jet stream. Dashed arrows show the wind direction; the fine lines are isobars. (a) Here the jet blows around a ridge of high pressure, turning to the right. (b) Here it blows around a trough of low pressure, turning to the left. The solid and open arrows show the wave's two components: the solid arrows show the Corio-lis effect as it would be in the absence of local pressure differences; it is stronger at high latitudes than at low. The open arrows show the wind directions resulting from the local pressure gradients, which happen to be steeper around the low than around the high.

the earth, causing the Coriolis effect, the winds would blow out radially in all directions "down the hill." Because of the Coriolis effect however, they are deflected to the right until Coriolis effect and pressure gradient are in equilibrium, at which stage they blow parallel with the isobars clockwise round the high. Figure 4.7b shows a cyclone; the pressure is lowest at the center, the isobars mimic the contours of a depression, the winds blow inward, "downhill," and deflection to the right turns them into counterclockwise winds.

Now consider how all this affects the flow of the polar jet stream. Visualize the jet in the subarctic as it approaches a ridge of high pressure extending northward from a localized anticyclone farther south (see fig. 4.8). The jet is deflected to the right (clockwise) by the anticyclone, boosting the Coriolis deflection already forcing it to blow toward the east. The enhanced deflection sends the jet southeastward, into lower latitudes. Sooner or later it encounters a trough of low pressure, which forces it leftward (counterclockwise) with sufficient strength to overcome its tendency to turn to the right. The jet now blows northeastward, toward an encounter with the next ridge of high pressure, where it will turn southeastward again. And so on, around the world.

In this way the jet stream carries cold air from polar latitudes toward the tropics and warm air back again, moderating temperature extremes worldwide.

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