Lecture 11: Meridonal structure of the atmosphere

Transcription

1 Lecture 11: Meridonal structure of the atmosphere September 28, Meridional structure of the atmosphere In previous lectures we have focussed on the vertical structure of the atmosphere. Today, we will begin to discuss the horizontal structure. We shall see that geometrical effects play a major role in setting the observed horizontal distribution of temperature and pressure. The spherical Earth intercepts an essentially parallel beam of solar radiation and so the incoming flux per unit surface area is greater at the equator than at the pole. But the outgoing terrestrial radiation per unit area is much more weakly dependent on latitude. Although outgoing radiation balances incoming radiation when integrated over the globe, there is a net heating in the tropical belt and a net cooling over the polar caps. Thus the atmosphere in the equatorial belt is warmer (and hence moister) than the atmosphere over the polar caps. These horizontal temperature gradients induce, by hydrostatic balance, horizontal pressure gradients and hence winds. The resulting wind patterns (along with ocean currents) act to transport heat meridionally, cooling the tropics and warming the pole, allowing a steady state to be achieved. More detailed notes can be found in Chapter Temperature It is: warm in tropics cold in polar latitudes WHY? 1

2 Figure 1: Geometrical effects play a major role in setting the observed horizontal distribution. The spherical Earth intercepts an essentially parallel beam of solar radiation and so the incoming flux per unit surface area is greater at the equator than at the pole see Fig.1 and Problem Set 4 but the outgoing terrestrial flux depends only weakly on latitude. The annual average latitudinal distribution of incoming solar radiation at the top of the atmosphere is shown in Fig.2. Its distribution is a consequence of the spherical geometry of the earth and the tilt of the earth see Fig.3. The average incident flux at the equator is S = 1367 =435Wm 2,because the flux is intercepted over a strip of size 2aδy andisthusspreadbythe rotation of the Earth over a surface area of 2πaδy (here δy is the meridional π π width of the strip and a is the radius of the earth) see Fig.5: flux intercepted area = 2aδyS 0 2πaδy = S 0 π = 1307 π =435w/m2 The globally averaged incident solar flux is S 4 =341Wm 2 because: flux intercepted area = πa2 S 0 4πa = S = 1307 =341Wm 2. 4 Note that the incoming flux has fallen to S 4 at, roughly, a latitude of 30 N (this latitude divides the hemisphere into two equal parts) and continues to fall to the pole. 2

3 Figure 2: Distribution of annual mean and solstice (see Fig.3) incoming solar radiation. The slight dip in the distribution at, for example, the winter solstice in the southern hemisphere, corresponds to edge of the polar day. Figure 3: Earth describes an elliptical orbit around the Sun and is closest to the Sun at the winter solstice. The point on its orbit when the Earth is farthest from (closest to) the Sun is known as the Aphelion (Perihelion). The seasons are labelled for the Northern hemisphere. 3

4 Figure 4: The earth s axis tilts at 23.5 and, at the present time in its history, points towards the North Star. We sketch the incoming solar radiation at summer solstice. a y Figure 5: 4

5 Figure 6: Annual mean absorbed solar, OLR and net radiation The net radiative budget of the Earth-atmosphere system, averaged over the year, is shown in Fig.6. The absorbed solar (incoming minus reflected) has a strong maximum in the tropics, where it is about 6 times larger than at the poles. The emitted longwave, however, is much flatter, implying that the actual pole-to-equator temperature difference is much less than if the atmosphere were to be in radiative balance at each latitude, column by column. The slight dip in OLR at the equator is due to radiation from the (cold) tops of deep convecting clouds. From Fig.6 we can deduce that, averaged over the year, there is a net surplus of incoming radiation in the tropics, and a net deficit at high latitudes - in the troposphere it is indeed hotter at the equator than at the poles. Look at the observed T and θ in Figs.7 and Pressure and geopotential height What is the consequence of a warm tropics and a cold pole on the pressure field expanding/contracting columns of air and hence lateral pressure gradients. These will drive winds. Height of pressure surfaces: p z = ρg = gp RT 5

6 Figure 7: The zonally averaged annual mean temperature in C. Figure 8: The zonally averaged annual mean potential temperature. 6

7 using p = ρrt. So z p = RT gp z (ln p) = RT g = H the scale height discussed in Chapter 4 If T = constant, H= constant and z varies like ln(p), which implies that p decays expotentially within height see Chapter 3. Integrating up: Z z(p) =R p s p T dp g p wherewehavesetz(p s )=0.z(p) is called the geopotential height. The thickness of a layer of atmosphere sandwiched between two pressure surfaces is: and if T=constant Z z z z 1 = R p 1 p 2 T dp g p z z z 1 = RT g ln(p 1 ) p 2 as derived before in an earlier lecture. Thus: If T warm cold =30 C, p s p 500 z warm cold = =2,then much as is observed see Fig.9. R T warm cold g z is 608m ln µ ps p 7

8 Figure 9: Zonal-mean geopotential height (m) for annual mean conditions. Values are departures from a horizontally uniform reference profile. 8