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Contents:
  1. Princeton Primers In Climate Series
  2. The Cryosphere
  3. Divecha Centre for Climate Change
  4. About this book

An illuminating case to consider is that of a satellite or space station in orbit around Earth; when an astronaut goes for a space walk from the space station, she appears to be weightless, with no forces whatsoever acting upon her figure 3. An astronaut orbiting Earth. But from the point of view of an observer rotating with the astronaut, the astronaut is stationary and therefore no net forces are acting upon her. Now we know that gravity is acting, pulling her toward Earth, and we say that this force is balanced by another force, centrifugal force, which is pushing her out.

The forces exactly balance, so the astronaut appears weightless; that is, in the rotating frame, the centripetal gravitational force pulling 66 A B r i e f I n t r o d u c t i o n to Dy n a m i c s her toward Earth is exactly balanced by the centrifugal force pushing her out. Because the centripetal force has magnitude X2r, the centrifugal force must have this magnitude also, and we conclude that in a rotating frame of reference, there appears to be an additional force, the centrifugal force, which acts to accelerate a body along a radius, outward from the axis of rotation.

The magnitude of the centrifugal force is X2r per unit mass, where r is the distance from the axis of rotation. There is no centrifugal force in inertial frames of reference. Coriolis force In this section, we give a mathematical, although elementary, derivation for the magnitude of the Coriolis force. As we saw in the previous section, in the rotating frame there is a centrifugal force of magnitude X2r trying to push the observer out, and in this case the centrifugal force is balanced by the friction between the observer and the disk.

Now let us suppose that the observer is passed by another body a cyclist, for example who is moving along a radius of the disk at a velocity u relative to the disk. Let us now consider how the forces and accelerations appear to the observer sitting in the rotating frame. The inward force on the cyclist is still Fc because the frictional force and the force due to the cyclist leaning in are still present. There is also an outward centrifugal force on the cyclist equal to MX2r because we are measuring everything in the rotating frame.

We reconcile ourselves to this mismatch by saying that, in the rotating frame, there is an additional force on a moving body equal to 2Xu per unit mass. This force is the Coriolis force, and it acts at right angles to a body moving in a rotating frame of reference. As in the previous section, we consider flow on a rotating disk for which meridional flow corresponds to radial flow. Suppose a body is sitting on the rotating disk and so is stationary in the rotating frame of reference, held in place by friction against the centrifugal forces pushing it out. Let us now suppose that we push it toward the axis of rotation.

The initial velocity is in the radial direction, so the tangential velocity is initially zero, but we may anticipate that the Coriolis force will deflect the body in the tangential direction. Let us differentiate equation 3. The derivative of r with respect to time is just v, the velocity in the radial direction, so that equation 3.

How do we interpret these forces? The first term is just the Coriolis force caused by the rotation of the disk itself; it is our old friend 2Xv, with the minus sign just giving us the direction of the force. We have thus shown that when a body moves in the radial direction it experiences a Coriolis force, equal to twice the angular velocity multiplied by the velocity in the radial direction. This force deflects the body in the 71 chapter 3 tangential direction, perpendicular to the direction in which the body is moving. We saw earlier in this chapter that when a body is moving in the tangential direction it experiences an apparent force in the radial direction, now equal to twice the rotation rate multiplied by the velocity in the tangential direction.

Now, the velocity in an arbitrary direction can always be decomposed into a velocity in the radial direction plus a velocity in the tangential direction, and we may conclude that, in general, a body moving in a rotating frame experiences a force at right angles to the direction of its velocity, and of magnitude equal to twice the rotation rate times the speed of the body. This force is the Coriolis force, and it deflects bodies to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. Mathematically we have, as in equation 3. The first of this pair of equations is the momentum balance in the zonal direction with x the distance toward the east : the Coriolis 72 A B r i e f I n t r o d u c t i o n to Dy n a m i c s force —fvg balances the pressure gradient force.

Similarly, the second equation is the momentum balance in the meridional y direction. These equations may be regarded as defining the geostrophic velocities ug and vg note the subscript g on the variables. Now suppose that we add a stress, x, to this balance. The stress is provided by the wind, and it diminishes with depth. The force is the vertical derivative of the stress so that equations 3. We rewrite equations 3.

If we integrate equations 3. Thus, we 73 chapter 3 see that a zonal wind stress i. That is, the average induced velocity in the Ekman layer—the Ekman transport—is perpendicular to the imposed wind stress at the surface. In the Northern Hemisphere where f is positive, if the stress is eastward i. For that reason, a useful philosophy is to begin with an austere picture of the phenomenon at hand and then gradually add layers of complexity and detail.

The first picture will be a simplification, but if it is based on sound scientific principles, then it will provide a solid foundation for what follows, and it will become possible to work toward an understanding of the system as it really is. In this chapter we apply this philosophy to try to understand the ocean circulation. What Makes the Ocean Circulate? What makes the ocean go around this way? Less obviously, the wind also plays a role in producing a deep, interhemispheric meridional overturning circulation, a circulation in which the water sinks near one pole and rises near the other.

The meridional overturning circulation MOC , on the other hand, involves all three effects in an essential way. However, we will see that the MOC can only be maintained if either mixing or wind is present, for they enable the deep water to rise to the surface to begin circulating anew. Without them, the deep circulation would stagnate. The equatorial currents are different again, and we defer discussing them until chapter 6. Our idealized view of the gyres is illustrated in figure 4. The main questions we wish to answer are relatively simple: 1. What determines the way they go around and how strong they are?

The gyres exist because the mean winds provide a mechanical forcing, a stress, on the oceans, and this stress causes the water to accelerate. Frictional forces only arise when the water is in motion, so that if there is a wind blowing, then the ocean must be in motion, and an overall balance between the wind and the frictional forces ultimately comes about. For the sake of definiteness, we consider the subtropical gyre in a rectangular ocean—the lower gyre of figure 4. The winds blow eastward on the poleward side of the gyre these are the midlatitude westerly winds and westward at low latitude the tropical trade winds , and it seems entirely reasonable that the ocean should respond by circulating in the manner shown.

How does this description square with the notion of a gyre that seems to go around in the same direction as the wind? The mean winds are to the east in midlatitudes and to the west in the tropics and, as we showed in the section in chapter 3 on Ekman layers, there is a flow in the upper 79 chapter 4 winds Ekman transport gyre Ekman transport winds Figure 4. Production of gyres by winds. The winds blowing as shown induce a converging Ekman flow, causing the sea level to increase in the center, thus giving rise to a pressure gradient.

This gradient in turn induces a geostrophic flow around the gyre, in the same sense as the winds themselves. As illustrated in figure 4. This convergence pushes up the surface of the ocean, causing the sea surface to form a gentle dome, with the ocean surface at the center of the gyre a few tens of centimeters higher than at the edges.

The converging fluid must go somewhere, and the only place for it to go is downward. A complementary situation arises in the subpolar gyre, where the westerly eastward winds 80 T h e O c e a n C i r c u l at i o n are strongest on the equatorial side. Now the Ekman transport is directed away from the center of the gyre, and the sea level is depressed and upwelling occurs.

The doming of the sea surface produces a pressure gradient in the ocean, as illustrated in figure 4. Consider a horizontal plane at a level a little below the sea surface. The pressure at that level is produced by the weight of the fluid above it, as we discovered in the section in chapter 3 on hydrostatic balance, and so is higher where the sea surface is higher. This pressure gradient produces a geostrophic flow perpendicular to the pressure gradient, and so in the same direction as the wind that originally produced the doming.

Thus, when all is said and done, on a rotating planet the wind leads to the production of an ocean current that is aligned with the wind, rather as we would expect in the nonrotating case. However, the pressure gradients in the two cases are quite different because of the presence of the Coriolis force in the rotating case; note in particular that the horizontal pressure gradient produced by the doming extends all the way to the bottom of the ocean.

Thus, even though the direct effects of the wind stress are confined to the upper few tens of meters, the wind produces geostrophic currents that can extend to great depths. However, we do not need 81 chapter 4 a large change in the sea level to produce quite substantial flows, as we can see with a simple calculation. The geostrophic current is a balance between the Coriolis and pressure gradient forces, so that fu 1 2p t 2y 1 2p fv , t 2x. Thus, using equation 4. Thus far, our explanation would lead to gyres that look like those in the left panel of figure 4. The presence of the Gulf Stream has been known for a long time—Benjamin Franklin was one of the first people to chart it.

So our question is a simple one: why is the Gulf Stream in the west? It turns out that the cause of the western intensification is that, as we discussed in chapter 3, the magnitude of the effective rate of rotation specifically, the magnitude wind stress Figure 4. Two schematics of a subtropical gyre.

The left panel shows the basic response of the circulation to the winds shown, and the right panel shows the gyres in the presence of differential rotation, with western intensification.

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This differential rotation causes the gyres to have a marked east—west asymmetry, with the flow in the west squished up against the coast. As the effect is both important and hard to grasp, we give a couple of explications. For definiteness we focus on the subtropical gyre in the Northern Hemisphere, but the same principles apply to the other gyres.

Torques and interior flow If the wind stress acting on the ocean varies with latitude—as we see that it does in figure 4. In a steady state, not only do the forces on the ocean have to balance but so do the torques; otherwise the ocean would spin faster and faster. The torques on the ocean are provided by the wind, by friction, and by the Coriolis force the pressure gradient does not provide a torque. However, in the interior of the basin, frictional effects are in fact very weak and the spin provided by the wind stress is locally balanced by the effects of the Coriolis 84 T h e O c e a n C i r c u l at i o n force.

Now, the Coriolis parameter increases northward, and it turns out that to locally balance the wind torque, a meridional flow must be produced in the ocean interior. The direction of the meridional flow depends on the sense of the spin provided by the wind, but in the subtropical gyre the meridional flow turns out to be equatorward. Consider a parcel of fluid in the middle of the ocean, as illustrated in figure 4.

The wind blows zonally with a stronger eastward wind to the north and so provides a clockwise torque. We can balance this torque by a Coriolis force if there is a southward flow of water in the interior. In that case, the Coriolis force provides a westward force on all the parcels of fluid moving south. However, the force is stronger on the fluid that is in the northern part of the domain because the Coriolis parameter increases northward , so the spin provided to the fluid is counterclockwise, opposing that spin provided by the wind.

The southward flow adjusts itself so that the spin provided by the varying Coriolis force just balances the spin provided by the wind. However, only if the boundary layer is in the west as illustrated in the right panel of figure 4. The production of a western boundary current. Schematic of the torques namely, the spin-inducing forces: the wind, W; Coriolis, C; and friction, F acting on parcels of water in the ocean interior center and western and eastern boundary layers left and right , in a Northern Hemisphere subtropical gyre.

In the interior, friction is small and the torques balance if the flow denoted V is southward. If the northward return flow is in the west, then a balance can be achieved between friction and Coriolis forces, as shown. If the northward return flow is in the east, no balance can be achieved. If the return flow were to be in the east, then the flow would, perversely, be circulating in the opposite sense to the torque provided by the wind, and no balance could be achieved. A local view of how the torque balances work in the boundary layer is provided in figure 4.

Suppose that the wind blew the opposite way. The balance of the wind torque and the Coriolis effect can now be achieved if interior flow is northward, and this is the case 86 T h e O c e a n C i r c u l at i o n in the subpolar gyres. For the overall flow to have the same sense as the wind torque, the return flow still has to be in the west. Thus, we see that western boundary currents are a consequence of the differential rotation of Earth, not the way the wind blows. If Earth rotated in the opposite direction, the boundary currents would be in the east.

Westward drift In this section, we give a slightly different explication of why the boundary current is in the west.

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It is not really a different explanation because the cause is still differential rotation, but here we think about it quite differently. The spin is also called the vorticity. Now consider a parcel of fluid sitting in the ocean. It may be spinning from two causes, namely, because it is spinning relative to Earth and because Earth itself is spinning. If that parcel moves and if no external forces act upon it, then the total spin of the fluid parcel is preserved. Suppose we displace parcel A northward. B A Later displacement Figure 4. If parcel A is displaced northward, then its clockwise spin increases, causing the northward displacement of parcels that are to the west of A.

A similar phenomenon occurs if parcel B is displaced south. Thus, the initial pattern of displacement propagates westward. This spin has the effect of moving the fluid that is just to the west of the original parcel northward, and then this fluid spins more clockwise, moving the fluid to its left northward, and so on. The northward displacement thus propagates westward, whereas parcels to the east of the original displacement are returned to their original position so that there is no systematic propagation to the east.

Similarly, a parcel that is displaced southward parcel B also causes the pattern to move westward. This is an idealized example—in fact we have just described the westward propagation of a simple Rossby wave—but the same effect occurs with more complex patterns and in particular, with the gyre as a whole. Thus, imagine that an east—west symmetric gyre is set up, as in the left panel 88 T h e O c e a n C i r c u l at i o n of figure 4. Differential rotation then tries to move the pattern westward, but of course the entire pattern cannot move to the west because there is a coastline in the way!

The gyre thus squishes up against the western boundary in the manner illustrated in the right panel figure 4. This way of viewing the matter serves to emphasize that it is not the frictional effects that cause western intensification; rather, frictional effects allow the flow to come into equilibrium with an intense western boundary current, with the ultimate cause being the westward propagation caused by differential rotation.

The Overturning Circulation The other main component of the ocean circulation is the meridional overturning circulation MOC , circulation essentially occurring in the meridional plane. There are two rather distinct aspects to this circulation, but they each have a common feature, namely the sinking of dense water at high latitudes and its subsequent rise to the surface elsewhere.

The buoyancy gradients themselves are produced by variations in temperature and salinity, and so the circulation is also sometimes known as the thermohaline circulation. The two different aspects are the processes that keep the 89 chapter 4 water circulating. The buoyancy or Archimedean force The force due to buoyancy is one of the most familiar forces occurring in a fluid and, rather famously, was known to Archimedes. It is the force that, among other things, allows objects to flow in water. Consider a container of still water and focus attention on a particular piece of water that is fully surrounded by other fluid.

The parcel has a finite weight, of course, and it does not sink to the bottom of the container because it is held up by the pressure force provided by the rest of the fluid in the container. Because none of the water is moving, the weight of the parcel its mass times the acceleration due to gravity, acting downward must exactly equal the upward pressure forces provided by the rest of the fluid. Now, let us replace the parcel with a solid object of the same shape and size.

If the solid object is lighter than the weight of the fluid 90 T h e O c e a n C i r c u l at i o n displaced, then there is a net upward force on it, and the object moves upward until it floats on the surface. If the solid object is heavier than the fluid displaced, the object sinks. These considerations apply to water itself. If we cool the water at the surface of the ocean, or add salt to it, it becomes more dense and therefore sinks—and it can sink quite quickly.

A parcel of water that is negatively buoyant at the surface of the polar ocean can sink to considerable depth in a concentrated convective plume in a matter of hours to days, with a corresponding vertical velocity of a few centimeters per second.

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Similarly, if we warm the water that is at the bottom of the ocean, it will become lighter and rise, although this tends to be a much slower process, spread out over a wide area. The overturning circulation maintained by mixing How do the above considerations apply to the circulation of the ocean? For simplicity, we consider only the effects of temperature and not of salinity, and a schema of the circulation is given in the top panel of figure 4.

The ocean, is, roughly speaking, a big basin of water for which the temperature of air just above the sea surface decreases with latitude. Air—sea exchange of heat heats or cools the water at the sea surface so that it has, approximately and on average, the temperature of the air above it. Schema of the two main components of the MOC. Top: The mixing-maintained circulation.

Dense water at high latitudes sinks and moves equatorward, displacing warmer, lighter water. The cold, deep water is slowly warmed by diffusive heat transfer mixing from the surface in mid- and low latitudes, enabling it to rise and maintain a circulation. In the absence of both wind and mixing, the abyss would fill up with the densest available water and the circulation would cease. This is just what happens to water at high latitudes, especially in winter in the North Atlantic and near Antarctica, and this process is known as convection. Some lighter water at depth comes up to the surface to take the place of the dense, sinking water, as indicated by the dashed lines in figure 4.

What happens then? Recall that the pressure at some level in a fluid is equal to the weight of the fluid above that level, so that if a column of fluid is cold and therefore dense, then the column weighs more than does a column of lighter fluid. Thus, the pressure in the deep ocean is largest at the high latitudes because the cold water weighs more than the warmer water at low latitudes. Thus, in the deep ocean there is a pressure force acting to push fluid from high latitudes to low latitudes, and the water begins to circulate, flowing at depth from high latitudes to low latitudes.

If no other physical processes occurred, the dense water would displace light water until the entire deep ocean were filled up with cold, dense water with polar origins. Nearer the surface, there would be a region of strong vertical temperature gradients, linking the low temperature of the abyss with the warmer surface waters.

However, the deep, abyssal waters would eventually stop circulating because the water in the deep ocean would be as cold and dense as the coldest and densest waters at high latitudes at the surface. That is, the surface water 93 chapter 4 would no longer be denser than the water beneath it, and convection and the deep circulation would cease. So what enables a deep circulation to continue? The circulation continues because the deep water in low and midlatitudes is continually, albeit weakly, warmed by the transport of heat from the surface. This warming enables the water to rise and the circulation to continue.

If there were no such heat transport, the deep ocean would simply fill up with cold, dense polar water. There would then be no convection because the cold surface waters at high latitudes would not be negatively buoyant. Thus, although the circulation can be thought of as being set up by a buoyancy gradient at the surface, its continuation relies on the effect of transport of heat down into the abyss, and without that, this part of the overturning circulation could not be maintained.

What physical process causes the downward heat transfer? In a quiescent fluid, the heat is transferred by molecular diffusion, in which molecules of water pass on their energy to neighboring molecules without any wholesale transport of fluid itself. However, the molecular diffusivity is very small and molecular diffusion is a slow process indeed, requiring thousands of years for a significant amount of heat to be diffused from the surface to the abyss.

This process is sometimes called turbulent diffusion because the process is similar to that of molecular diffusion but with parcels of 94 T h e O c e a n C i r c u l at i o n water replacing individual molecules. Turbulent diffusion arises in large part from internal gravity waves that break and mix the fluid.

Such waves, analogous to waves on the surface of the ocean but interior to the fluid, are generated by mechanical forcing—by the winds and the tides. Thus, without the effects of mechanical forcing, this component of the MOC would be weak indeed because the diffusion would be small. Thus, to summarize, the following two effects combine to give an overturning circulation.

Without this warming, the abyss would fill with cold, dense water and circulation would cease. It is natural to think of the meridional buoyancy gradient as being between the equator and the pole, mainly caused by temperature falling with latitude. Salty water is heavier than freshwater at the same temperature, so adding salt can have a similar effect to that of cooling the surface. However, variations in salinity turn out to be the key difference in the overturning circulation of the Atlantic and the Pacific—the North Atlantic is saltier than the North Pacific, and so it can more easily maintain an overturning circulation.

The overturning circulation maintained by wind The second mechanism that can lead to a deep overturning circulation relies, in its simplest form, on the presence of strong zonal wind blowing over the ocean surrounding Antarctica, as illustrated in the lower panel of figure 4. Unlike an ocean basin, the ocean surrounding Antarctica is effectively a channel, for it has no meridional boundaries and so no real gyres. The 96 T h e O c e a n C i r c u l at i o n wind around Antarctica blows in a predominantly zonal direction, toward the east. As one might expect, the wind generates a mean current in the same direction— the Antarctic Circumpolar Current, or ACC.

However, because Earth is rotating, the wind stress generates an Ekman flux as described in chapter 3 that is perpendicular to the wind, and so northward the Coriolis force deflects bodies to the left in the Southern Hemisphere , as illustrated in figure 4.

In a gyre, the return flow could be at the surface in a western boundary current, but none exist in the ACC and the flow must therefore return at depth, where friction along the bottom enables the flow to be nongeostrophic, or the presence of topography allows zonal pressure gradients to be maintained. Where does the deep water ultimately come from? One option would be that the flow simply circulates locally in the Southern Hemisphere.

However, if the water in the Northern Hemisphere is sufficiently dense, then it will be drawn into the Southern Hemisphere and into and across the ACC, where it can come up to the surface. Thus, the presence of winds in the Southern Ocean generates an interhemispheric meridional overturning circulation, in which water sinks at high northern latitudes 97 chapter 4 Ekman drift wind stress ACC Antarctica ACC wind stress Ekman drift Figure 4. The wind predominantly blows in a zonal direction around the Antarctic continent, generating an Ekman flow toward the north and a net loss of water from the channel.

The water returns at depth, generating a deep overturning circulation, as illustrated in the bottom panel of figure 4. The two can exist side by side, and the overturning circulation in the Atlantic Ocean is schematically illustrated in figure 4. Some of the water that sinks in the North Atlantic moves across into the Southern Hemisphere and upwells in the ACC enabled by the wind , and some upwells and returns in the North Atlantic itself enabled by mixing.

The water that sinks in the North Atlantic forming the North Atlantic Deep Water does not in fact extend all the way to the bottom of the ocean because there is some even denser water beneath it—Antarctic Bottom Water, which comes from high southern latitudes and circulates through the effects of mixing. Which component of the circulation is dominant? Only careful observations can tell us, although currently it is often believed that the wind component is stronger than the mixing component in the Atlantic Ocean. Note finally that the horizontal velocities in the abyssal ocean are usually quite small, on the order of 1 mm s—1, and at this speed it would take some 99 Depth chapter 4 D.

South Equator North Figure 4. Schematic of the meridional overturning circulation, most applicable to the Atlantic Ocean D. The arrows indicate water flow, and dashed lines signify water crossing constant-density surfaces, made possible by mixing. The upper shaded area is the warm water sphere, including the subtropical thermocline and mixed layer, and the lower shaded region is Antarctic Bottom Water. The bulk of the unshaded region in between is North Atlantic Deep Water. Embedded within the circulation are smaller T h e O c e a n C i r c u l at i o n mesoscale eddies, which actually contain the bulk of the kinetic energy of the ocean and which are analogous to atmospheric weather systems.

This Ekman flow in turn causes the sea surface to slope and produces a geostrophic flow, which is the main component of the gyres and which extends down several hundred meters. Two processes bring deep water up to the surface: mixing and the wind. It is a response both to wind and to the meridional temperature gradient. Appendix A: Mathematics of Interior Flow in Gyres Suppose that the wind blows zonally across the ocean, with a stronger eastward wind to the north, as in figure 4.

The balance between the varying wind and the meridional flow embodied in equation 4.

But only if the flow returns in the western boundary current can the frictional effects balance the wind stress curl overall, for then the flow overall has the same sense as the wind. In addition, the ocean generally has a lower albedo than land, so that if all the ocean were replaced by land, the planet as a whole would be cooler.

In some contrast, when the ocean freezes it forms sea ice, which has a generally high albedo. The Moderating Influence of the Ocean Perhaps the most obvious effect that the ocean has on climate is its moderating effect on extremes of temperature, both diurnally i. We focus on the effects on the annual cycle because these tend to be on a larger scale and more befitting a book with climate in the title, but much the same principles and effects apply to the diurnal cycle. First we take a look at the observations to confirm that there is a moderating influence from the ocean.

One wonders if the respective climate extremes affect or even effect the different personalities of New Yorkers and Californians. For each city, we plot the average low temperature and the average high temperature for each month. Note the much bigger range in New York and the maximum earlier in the year, in July rather than September. In contrast, the winds have blown over the Pacific Ocean before arriving at San Francisco.

So why does the ocean moderate the climate? It is in part because water has a relatively high heat capacity, compared to the material that makes land e. First of all, the higher the heat capacity of a body, the more heat is needed to change its temperature.


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Thus, if an object is being cyclically heated and cooled, as in a seasonal cycle, then the change in its temperature is much smaller if its heat capacity is higher. Now, to what depth in the land and ocean does the heat penetrate over the course of a seasonal cycle? Rather, regarding the ocean, just that part that is turbulently mixed by the effects of wind and in part by heating and cooling itself fully partakes in the annual cycle, namely the mixed layer, which we discussed in chapter 2.

Although its character varies from place to place in the ocean, it has a typical depth of about 50— m. That is, the effective heat capacity of the ocean is approximately that of a body of water 50— m deep. This heat capacity is quite large, and for comparison, the heat capacity of the atmosphere corresponds to a depth of just 3 m of water. What is the effective heat capacity of land? Two effects make it much less than that of water.

First, the specific heat of dry land is about 4 times less than that of water for wet land, the factor is about 2. The heat can penetrate only by conduction, and because the earth soil has rather low thermal conductivity, only the top few meters are significantly heated and cooled over the course of a season.

The same can be said for the major ice sheets over land, such as those over Greenland and Antarctica: they have large mass but low thermal conductivity. Thus, combining the effects of a larger heat capacity and a larger effective depth, the ocean has an effective heat capacity that is about times greater than that of land. This high heat capacity considerably attenuates the seasonal cycle and is a good part of the reason for the large difference between San Francisco and New York.

San Francisco is a rather extreme case because not only is the summer temperature moderated by the ocean, but also the interminable fog that blows in from the ocean and covers the city like a wet blanket keeps the summer temperatures miserably low and makes them seem even lower, as Mark Twain perhaps felt. However, the heat capacity effect does occur on very large scales. Amplitude and lag of the annual cycle in the Northern and Southern hemispheres, as a function of latitude. The lag is the time, in days, from the maximum solar insolation to the maximum temperature.

Source: Trenberth, The lag in the seasons The observant reader noted in figure 5. Suppose that a system is heated externally e. If the system has a very small heat capacity, then the heating and cooling must balance each other at all times. A consequence of this is that the cooling is greatest when the heating is greatest, and so the temperature itself is highest when the sun is highest in the sky. Indeed, we find that in continental climates the temperature is highest fairly soon after the summer solstice and coldest soon after the winter solstice: In Fig.

If a system has a large heat capacity, it takes some time to warm up and cool down, and so the maximum temperatures occur some time after the maximum insolation and thus later in the summer. The same effect occurs on a daily basis: inland, the maximum daily temperature occurs shortly after noon, whereas at the seaside the maximum temperature is later in the afternoon. On a large scale, in the Northern Hemisphere midlatitudes, the maximum temperature occurs on average about 30 days after the maximum solar insolation, whereas in the more maritime Southern Hemisphere, the maximum occurs about 45 days after peak insolation figure 5.

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At very high latitudes, where the Southern Hemisphere is covered by land Antarctica but the Northern Hemisphere by ocean the Arctic Ocean , the lag is longer in the Northern Hemisphere. A mathematical demonstration of this effect is given in appendix A of this chapter. We talk more about the mechanisms that give rise to climate variability in the next chapter, but for now let us just suppose that the climate system excluding the ocean is able to vary on multiple timescales, from days to years.

Then, just as the ocean is able to damp the seasonal variability, the ocean damps variability on all these timescales. However, the ocean does not damp the variations equally on all timescales; rather, because on longer timescales the ocean itself can heat up or cool down in response to climate variations, the damping effects are larger on shorter timescales. We give a brief mathematical treatment of this argument in the next section, and a more complete treatment in appendix A of this chapter.

Mathematical treatment of damping The surface temperature of the ocean and the land are maintained by a balance between heating and cooling. The heating occurs both by solar radiation and by downward longwave radiation from the atmosphere and is proximately independent of the temperature of the surface itself. The cooling, on the other hand, increases with the temperature—a hot object cools down faster than a warm one.

The parameter C is the heat capacity of the system, and m is a constant that determines how fast the body cools when it is hot. Obviously, this equation is too simple to realistically describe how the surface temperature varies it ignores lateral variations, for one thing , but it illustrates the point we wish to make. That is to say, the ocean mixed layer can absorb or give out heat on the timescale of about a year. Variability on timescales significantly longer than this is not greatly damped by the presence of an ocean mixed chapter 5 layer because on these timescales the mixed layer itself heats up and cools down and so provides no damping to the system.

However, on timescales much shorter than this, the mixed layer absorbs heat from a warm atmosphere, or alternatively gives up heat to a cold atmosphere, thus damping the variability that the atmosphere otherwise might have. There is thus a much smaller damping effect over land than over the ocean. The situation is not quite as straightforward as this argument suggests. A complicating factor is that the entirety of the ocean mixed layer does not respond to fast variations in the atmosphere.

Thus, for example, only the top few meters of water may respond to diurnal variations in temperature, and such variations are therefore damped less than one might expect. Nevertheless, the overall effect is clear: The heat capacity of the ocean mixed layer damps variations on timescales up to and including the annual variations.

Interested readers can find a more complete description of this effect in appendix A of this chapter. Ocean Heat Transport The other great effect that the oceans have on the mean climate is that they transport heat, usually poleward, thus cooling the tropics and subtropics and warming high latitudes. How much? On average, both the atmosphere and the ocean transport heat poleward, and this transport is illustrated in figure 5.

The total transport of the atmosphere plus the ocean may be determined fairly directly from satellite measurements. Over the whole planet, there is a balance between the incoming solar radiation and outgoing longwave radiation, and if there were no heat transport, the incoming solar radiation would equal the outgoing infrared radiation at each latitude—a state of pure radiative balance. In fact, at low latitudes there is an excess of incoming solar radiation, whereas at high latitudes there is an excess of outgoing infrared radiation, meaning that at low high latitudes Earth is colder warmer than it would be if it were in pure radiative balance.

The imbalance arises because heat is transported poleward by the motion of the atmosphere and ocean, and if we measure the imbalance at each latitude, then we obtain the total heat transport by the atmosphere and ocean. Perhaps needless to say, this measurement is easier said than done, but the advent of modern satellites that make separate measurements of solar and infrared radiation makes it possible. The most accurate estimates come from the period of the Earth Radiation Budget Experiment, in particular over the period —, when intense observations were made, but data continue to be gathered.

One way to then determine the total heat transport by the atmosphere at a given latitude is to sum up the product of the temperature and meridional velocity over all longitudes and over the entire depth of the atmosphere. Given the heat transport by both the atmosphere and by the atmosphere—ocean system, the heat transport by the ocean follows by simple subtraction, and this transport is shown in the dashed line in figure 5. It is also possible to calculate the ocean transport directly, using in situ ocean measurements; the advantage is that one may be able to elucidate the individual mechanisms of ocean heat transport rather than just the overall effect.

Such direct measurements tend to be less accurate than the residual method because of the sparsity of measurements in the ocean, but the two methods are broadly consistent. Upper panel: Heat transport in the total atmosphere— ocean system solid line , in the ocean dashed line , and in the atmosphere dotted line. Lower panel: Oceanic heat transport, subdivided into the various basins. Source: Trenberth and Caron, As for the ocean overall, and as we might expect, it transports heat poleward in both hemispheres. The transport is associated with a release of heat into the atmosphere at high latitudes, whereas the ocean is being heated by the atmosphere at low latitudes.

Another notable feature about the ocean transport is that the poleward transport is much larger in the Northern Hemisphere than in the Southern. Such a transport is quite remarkable, for it implies that the ocean is not being thermally driven by the meridional temperature gradient alone which would transport heat from hot places to cold places. What could be the driving force?

If we consider the North Atlantic as an example, poleward heat transport occurs because the western boundary current the Gulf Stream in this case brings warm water up from the tropics along the eastern seaboard of the United States, releasing heat especially in winter when the warm water comes into contact with the colder air coming off the cold continental land mass. Such a release of heat occurs at the western edges of all the major ocean basins in midlatitudes, for example, off the coasts of Japan, the Eastern United States, South America south Brazil, Uruguay, and Argentina and southeastern Australia.

The poleward flow of the western boundary currents is balanced by equatorial flow in the middle of the gyres that brings cold water equatorward, although the flow is broader and weaker so that chapter 5 the transport of cool water equatorward is spread over a large area. The transport occurs in both the Pacific and the Atlantic, and in both the Northern and Southern hemispheres.

The subpolar gyres in the Northern Hemisphere also transport poleward, but they are less well defined than the subtropical gyres and cover less of the ocean so that their heat transport is somewhat weaker than that of the subtropical gyres. The net effect of this circulation is a poleward transport of heat that would be, in the absence of other effects, roughly equal in magnitude in the two hemispheres. We see from this figure that there is a large northward, and so poleward, heat transport in the Northern Hemisphere because the equatorward moving water has come from high northern latitudes and is correspondingly cold, and the poleward moving water nearer the surface is warmer.

In the Southern Hemisphere, however, the southward moving water is colder than the northward moving water because the cold North Atlantic Deep Water continues its path into the Southern Ocean and the water moving northward near the surface is relatively warm. That is, the water moving equatorward is generally warmer than the water moving poleward! Thus, the heat transport in the Atlantic from the deep circulation is northward in both hemispheres. What are the gross effects of the ocean heat transport on the climate? The main effect is simply that the high latitudes, especially the high latitudes in the Northern Hemisphere, are warmer than they would be if the oceans were not present.

How much warmer is a question that we cannot answer with armchair reasoning. We would need to perform detailed calculations with comprehensive climate models of the type used to predict the weather or used for global warming experiments. One such set of experiments was performed by M. Winton of the Geophysical Fluid Dynamics Laboratory in Princeton, and we briefly describe some of the results found Winton Climate models solve the equations that determine the temperature and motion of both the atmosphere and the ocean. The models also have representations of sea ice and cloudiness and of their effects on the incoming solar radiation and outgoing infrared radiation.

Thus, for example, snow and ice cover reflects solar radiation back to space, making the climate cooler than it would be in their absence.

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If the ice sheets were for some reason to expand, the climate would cool, the ice sheets would further expand, and the climate would further cool—an example of a positive feedback, in this case the ice—albedo feedback. When the ocean heat transport is removed, the atmosphere tries to compensate for this change by transporting more heat poleward itself. What seems to happen is the following. Although the atmosphere is able to partially compensate for the lack of an ocean transport, the atmospheric transport naturally occurs at a higher elevation than the ocean transport. The lack of an ocean heat transport enables sea ice to grow, and once the ice begins to grow, the positive ice—albedo feedback comes into play and the ice grows more.

The detailed mechanism for the strong effect of the ocean seems to involve the upward convective flux of heat in the wintertime: The meridional overturning circulation leads to convection at high latitudes, with cold water parcels sinking and being replaced by slightly warmer parcels, which then release heat into the atmosphere. Thus, the story goes, the Gulf Stream brings warm water from Florida up the eastern seaboard of the United States and then across the Atlantic in the North Atlantic Drift to the shores of Britain and Ireland, hence moderating the otherwise cold winters.

Certainly, the surface temperature of the eastern North Atlantic is a few degrees warmer than the water at the same latitude off the coast of Newfoundland, as figure 2. Although this difference does have some effect on the temperature differences between the two locations, Britain and Ireland have a moderate winter climate primarily as a consequence of the fact that they are next to the ocean, with the ocean on their west. Even if there were no gyres in the ocean at all, the climate of these parts would be much more moderate than the climate at similar latitudes on the eastern sides of continental land masses.

Thus, Britain and Ireland have a much more similar climate to British Columbia, at a similar latitude on the west coast of Canada, than they do to Newfoundland and Labrador on the east coast. If the ocean were to cease circulating altogether— that is, both the gyres and the meridional overturning circulation were to cease—then the high latitudes would generally get colder, as we discussed in the previous section, and possibly freeze over.

If the oceans did not freeze, western Europe would still have a maritime climate and a more moderate seasonal cycle than the eastern United States and eastern Canada. Appendix A: The Mathematics of the Relationship between Heating and Temperature In this appendix, we give an elementary mathematical treatment of the relationship between heating and temperature.

We will explain two things: why the temperature range is smaller if a body has a larger heat capacity and why there is a lag between heating and temperatures. We model the system with the simple equation C dT dt S mT. Substituting into equation 5. If the heat capacity is large or the frequency is high, then T. Because high frequencies are damped more than low frequencies, we say that the variations are reddened. Note too that the temperature variations are now out of phase with the heating. Thus, the maximum temperature occurs when the heating is least. It is this effect that accounts for the delay in the maximum temperature in maritime climates, with the hottest part of the year occurring in late summer or even the beginning of autumn.

In this chapter we look at climate variability, and in particular climate variability that is associated in one way or another with the ocean. This condition is not very restrictive because nearly all forms of climate variability on timescales of months to decades are affected by, or even caused by, the ocean. Even in cases in which the underlying cause of the variability is nonoceanic, the ocean may modulate the variability and determine its timescale, and in many ways we can think of the ocean as the pacemaker of climate.

Climate and Weather What is the difference between climate and weather? But what precisely? There is no ideal definition of climate, but a useful working notion is that climate is the statistics of the weather—the mean, the standard deviation, and so forth. However, this notion slightly begs the question of how we calculate the statistics—how do we take the mean, for example? And if climate is a time average of the weather, then how can climate have any temporal variability? Although it is rather fanciful, it is useful to envision a thought experiment in which we take the ensemble average of the weather.

Thus, we envision a large number of identical planet Earths, forced the same way, but each one started out in a slightly different way so that each has different weather. We could then unambiguously define the climate to be the average, along with other relevant statistical quantities like the variance, over the ensemble of planet Earths. If the forcing were to change, perhaps because the CO2 levels in the planets were to increase, then the climate of the ensemble would also change. The problem with this definition is that it is not practical, there is no such ensemble in reality.

We could then define climate as the average of the weather over a time period long enough so that weather fluctuations are averaged out but variability on longer timescales is still allowed. Weather typically varies on timescales of a few days to a few weeks, so that we might define climate as the average weather over time periods longer than a month, say. In practice, this time period is too short for many purposes because the monthly average temperature still fluctuates considerably, and a more common definition takes the climate to be the average along with other statistical quantities over a period of a few years, with the precise averaging period depending on what quantity is of interest.

We might choose to take the average over a particular time of year—only over the winter months, for example, and so obtain a winter climatology. If we are interested in how climate varies across ice ages, then averaging over a period of centuries or even millennia might be appropriate, but if we are interested in whether climate changed over the course of the twentieth century, a much shorter period is obviously more appropriate. The moral of the above discussion is that, although it is useful to think of the climate as some kind of average, there is no compact single definition of climate that is useful and appropriate for all purposes, and we are often better served by talking about the climate with reference to a particular timescale.

Climate varies on more than one timescale—indeed, there may be no timescale on which we can say there is no climate variation. The mechanism that gives rise to weather resides in the atmosphere, and it is the consequence of a fluid instability called baroclinic instability. This instability can be thought of as a type of convective instability in which if a fluid is heated from below it expands, becomes lighter than its surroundings, and therefore rises. It takes a parcel moving at this speed a little more than a day to travel 1, km, hence accounting for the typical timescale of days to weeks.

The axis of rotation of Earth is chapter 6 fixed relative to the distant stars, so that as Earth moves around the sun, the North Pole points generally toward the sun giving the Northern Hemisphere summer , away from the sun giving the Northern Hemisphere winter or somewhere in between, as illustrated in figure 1. If we think of a season as lasting roughly three months, are there any climate phenomena that have timescales between the weather timescale and the seasonal timescale?

The NAO is a phenomenon at the interface between weather and climate that dictates variability on a monthly timescale over the North Atlantic and surrounding regions, thus from the eastern seaboard of the United States, over Greenland, to Europe, and from the Arctic region to the Canaries. There is an analogue of the NAO in the Southern Hemisphere called the Southern Annular Mode , although it has a more hemispheric extent, and a somewhat similar pattern in the Pacific Basin called the Pacific—North American pattern , but none are quite as well studied as the NAO, so let us focus on that.

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