2. Meridional atmospheric structure; heat and water transport

The equator-to-pole temperature difference DT was stronger during the last glacialmaximum, with polar temperatures down by at least twice as much as equatorial onescompared to the present day. Some paleoclimate evidence also suggests that DT has beenweaker in the past than today, including high-latitude incidence of temperate flora andfauna (50-70 MY) and low-latitude glaciations (600-700 MY, ~2GY?). Temperaturegradients are connected to energy transport via conservation laws, as well as winds onEarth due to its rotation. Today’s surface temperature ranges from ~27C at the equator to~-30C (on average) at the poles (see Fig. 1)

Energy balance models

Recall that the most primitive equilibrium climate model can be written

(S/4)(1-A) = esTS4, (1)

where S is the solar constant (1365 W/m2 today), A is the planetary albedo (about 30%today), s is the Stefan-Boltzmann constant, TS the mean surface temperature (about 288Ktoday), and e is an effective emissivity for earth (about 0.61 today) that decreases asatmospheric infrared opacity increases, due to the lower temperature as one goes up inthe atmosphere (which produces Earth’s greenhouse effect).

We could write this as a function of latitude f:

(S(f)/4)(1-A(f)) = e(f)sTS(f)4 + H(f) (2)

where we have to add a transport term H(f) because energy can accumulate at certainlatitudes due to transport by the atmosphere or ocean. Specifically, H µ -—⋅F where F isthe horizontal flux of moist static energy carried within the atmosphere, ocean, and solidearth. We can calculate S(f) and observe A(f) and e(f) accurately from space today; ifwe plug these into (2), neglect H, and solve for an equilibrium TS(f), we find an equator-to-pole temperature gradient about twice as big as currently observed. That means that Fis directed from warm to cold regions (as expected) and carries enough energy to reducetoday’s meridional gradient of TS to half the radiative equilibrium value. Directlyobserving F is difficult; current estimates are that between 1/4 and 1/3 is carried in theoceans, the rest in the atmosphere (virtually none in the solid earth). Today’satmospheric component is split about 50/50 between dry static energy (F1) and latent heat(water vapor) transport (F2), though this would change in different climates.

A question central to climate change is how F(f) depends on TS(f). No definitive generaltheory has yet been developed, but GCM simulations can be used as a guide to behavior.Simple scaling arguments suggest that F1 ~ (DT)2, which would tend to preventsignificant changes in DT. F1(f) probably also depends on other things like orography.

Even without a stabilizing dependence of F on DT, climate responses to global changes inS, A or e would according to (2) be similar at all latitudes. You need latitudinallyvarying changes in these parameters to change DT, and the more sensitive F is to DT, thelarger these need to be. A at high latitudes should depend on ice cover; since ice shouldgrow with decreasing T, this leads to a positive feedback that can produce “polaramplification,” or greater T changes at high latitudes than at low latitudes. Cloud covercan potentially change e and A in latitudinally varying ways, but no theories exist topredict this quantitatively.

The latent heat flux F2 depends on the amount of water vapor in the atmosphere. Astemperatures increase, water vapor content increases at 6-13%/C, which will tend to driveF2 higher with higher global T regardless of DT. This is another important source of“polar amplification,” which becomes more important in warmer climates (where the ice-albedo feedback becomes inoperative) but less important in colder climates.

The thermal wind balance and zonal winds

Observations from the last glacial maximum (LGM) indicate stronger winds at midlatitudes. This is consistent with larger DT, according to a relationship known as thethermal wind balance.

The average air flow over long time scales (days) above the surface is approximately ingeostrophic balance. This means that the Coriolis force (which points to the right/left inthe northern/southern hemisphere) opposes the force due to pressure gradients in theatmosphere. With little net force, the air cruises along on a path with gentle (average)curvature. The pressure gradients are caused by temperature gradients. With warmtropics (positive DT), pressure decreases more slowly with height (due to the reduceddensity of warm air) than at high latitudes. This leads to a pressure surplus in the tropicsat higher levels, which pushes air toward the poles. Steady state occurs when the airbegins moving eastward fast enough for the Coriolis force to counteract this push. LargerDT requires stronger flow; a faster rotation rate requires weaker flow.

Winds near the surface are more complicated, since friction enters in to slow down thewinds and provide a third force. The net result is that wind is nearly geostrophic, butblows toward low surface pressure. That tends to equalize surface pressures compared towhat one finds aloft. The combined result at the surface is relatively weak winds that donot obey thermal wind balance. However, it appears that in midlatitudes upper-levelwinds basically pull the surface air along but at a slower speed, so that surface windsshould be at least qualitatively related to DT aloft. Also, geostrophic balance is closeenough so that you can tell the winds pretty well by looking at a sea-level pressure chart.

The mean winds in the troposphere and stratosphere are dominated by the midlatitudejets, which peak near 10 km and decrease toward the surface (see fig. 2). The jets arestrongest at the edge of the tropics because the Coriolis force is weakest near the equator(requiring stronger winds to generate the same force). In the tropics the temperature

gradients break down and become very small, leading to decreased winds. Close to theequator, Coriolis forces vanish and geostrophic balance itself no longer applies.

Surface pressure maps reflect the strong mid-latitude “westerlies” (means blowing fromthe west), by indicating low pressure poleward and high pressure in the subtropics (seeFig. 3). The low pressure is concentrated in two centers in the northern hemisphere,known as the Aleutian and Icelandic lows. In the southern hemisphere there is a zonalstrip of very low pressure near the border of Antarctica. In the tropics there are surfaceeasterlies (“trade winds”). Poleward of the jets, winds are generally weaker and can beeither direction.

The thermal wind balance is also relevant to the polar night jet, a wind thatcircumnavigates the winter stratospheric polar vortex. This becomes stronger when thevortex is colder. Cold temperatures lead to ozone-destroying clouds. In the northernhemisphere, variability from the troposphere disturbs the polar night jet, limiting ozonedestruction.

Mechanisms of meridional energy transport

In a completely thermal-wind balanced atmosphere, the winds would all be zonal andthere would be no meridional energy transport. In reality, eddies occur which transportheat. In the tropics, there is a big, overturning eddy called the Hadley circulation (seeFigure 5). Air rises in the summer hemisphere near the equator and sinks in the wintersubtropics, carrying moist static energy into the winter hemisphere. The Hadleycirculation exists because of the weak Coriolis force near the equator.

Beyond 25 degrees latitude, the Hadley circulation abruptly gives way to a mainly zonalcirculation. The net overturning circulation outside the Hadley circulation is weak andunimportant. Further poleward transport occurs in transient, quasi-horizontal eddies(transient means their wind averages to zero over time). These eddies tilt upward awayfrom the equator, owing to the steep slope of the isentropic (constant potentialtemperature) surfaces (Figure 5). This is because air will conserve potential temperaturewhen adiabatically moved to a different pressure. This upward slope means that air in theupper troposphere communicates with the tropical, near-surface atmosphere, not only inthe tropics itself (via deep convection) but at all latitudes (via transient eddies). In thetropics, lapse rates are (thought to be) controlled purely by local thermodynamics, but athigh latitudes they may be altered by low-latitude temperature changes via eddy transport(for example, a warmer tropics would tend to warm the mid-troposphere at mid-latitudes,making the lapse rate less negative). All of this applies particularly to the winterhemisphere; the summer hemisphere behaves a bit more like the tropics.

Atmospheric energy balance and radiation

The atmosphere is always losing infrared radiation to space. It must be heated bytransport from the surface, which is mostly released as condensational heating(conversion of latent heat in water vapor). This is proportional to rainfall. Thus, Earth’s

hydrologic cycle is controlled largely by atmospheric radiative cooling. A warmeratmosphere tends to cool faster, leading to more global rainfall (an alternative way tothink of this is that with a highly absorbing greenhouse atmosphere, more of the radiationto space, which is the same according to eq. (1), comes from the atmosphere). In a verycold climate, condensational heating would eventually no longer dominate theatmospheric heat budget, which would decouple the hydrological cycle from atmosphericradiation.

Water vapor is currently the strongest greenhouse gas in Earth’s atmosphere. Normally,a warmer object radiates more energy. However, water vapor concentrations increasewith T. Consequently, in the (saturated) absorbing bands of water vapor, the emission tospace depends only on relative humidity rather than temperature. This makes climatemore sensitive, and can even lead to a runaway greenhouse if water vapor concentrationsbecome sufficient to saturate enough of water vapor’s vibration-rotation spectrum (this isrelated to the Kombayashi-Ingersoll limit discussed by Pierrehumbert (2002) and mayhave occurred on Venus).

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