The radiation balance is a global phenomenon. The flows of radiant energy into and out of the upper edge of the Earth's atmosphere are approximately equal over a time scale of several years. This equilibrium state is the expected behavior for the climate system and a stable climate. The fluxes of energy may not balance over shorter periods, or a perturbation in the system may cause the climate system to seek a new equilibrium state. Whatever the condition of the global climate system, individual sites or regions typically experience an imbalance in radiation exchanges. Recognition of the global balance is an important initial step in understanding the global energy system and its related regional components.
The coupling of blackbody absorption and emission is fundamental to the Earth-atmosphere system radiation balance. The conservation of energy requires that the solar radiation absorbed must be balanced by the planetary radiation emitted. Although the Earth is not a perfect blackbody, it conforms closely with Equation 2.5. Therefore, the relationship between absorbed and emitted radiation for the Earth-atmosphere system is relatively straightforward. The planetary radiation balance is expressed as
where all the terms are defined for Equations 2.7 and 2.8. Using an albedo of 0.30 gives an emission temperature, or an effective radiation temperature, for the Earth without an atmosphere of255 K. This temperature represents the thermal state when the energy received by the Earth from the Sun balances the energy lost by the Earth back into space. However, the global observed mean surface temperature is 288 K, and a temperature of 255 K is characteristic for the atmosphere at an altitude of 5.5 km. These observations indicate additional factors must be considered in deriving the radiation balance for the Earth's surface, but the radiation balance for the top of the Earth's atmosphere is purely radiative.
Radiant energy absorbed and emitted at the top of the atmosphere varies geographically and seasonally. Zonal means of both fluxes based on latitude
T 250 E
Absorbed jf solar
T 250 E
Fig. 2.6. Annual mean absorbed solar radiation and emitted longwave radiation zonally averaged. (Data courtesy of the NASA Langley Research Center Atmospheric Science Data Center from their website at eosweb.larc.nasa.gov/.)
circles and calculated for a year or longer reveal the strong influence of the latitudinal gradient of insolation (Fig. 2.6). The curve for absorbed solar radiation is offset slightly to the Southern Hemisphere due to the eccentricity of the Earth's orbit around the Sun. It should be remembered that the absorbed solar radiation is the energy available for driving the Earth's atmospheric circulation (Peixoto and Oort, 1992). The emitted longwave radiation curve has a high plateau between about 30° N and 30° S with a slight dip over the equator. Emitted longwave radiation declines less abruptly at higher latitudes than absorbed solar radiation creating a region of energy surplus between about 40° N and 40° S. Energy deficit regions occur poleward of these latitudes in both hemispheres. To sustain an equilibrium between the radiative processes acting to warm the low latitudes and to cool the high latitudes, poleward heat transport by the atmosphere and the oceans is needed to offset the raidative differences (Trenberth and Solomon, 1994).
Sections 2.9 and 2.10 address the atmospheric response to solar and thermal radiant energy flows. Radiant energy absorption by the atmosphere means the atmosphere is a source of thermal radiant energy that augments solar heating of the Earth's surface. Consequently, the radiation balance for the atmosphere is not the same as the radiation balance for the Earth's surface.
Figure 2.3 quantifies the combined influences of atmospheric absorption of solar and thermal radiation summarized in Figure 1.4. The radiation balance at the top of the atmosphere is the same as that expressed in Equation 2.7, and the emission temperature is 255 K. The Earth's surface temperature must be warmer because it receives radiant energy from the Sun and radiant energy transmitted back to the surface from the atmosphere. These fluxes between the
Earth's surface and the atmosphere define the greenhouse effect resulting from the atmospheric response to radiant energy.
Assuming the Earth-atmosphere system is in thermal equilibrium, the radiation balance at the Earth's surface is expressed as
where rs is transmitted solar radiation, rt is transmitted thermal radiation, Tg is the emission temperature for the Earth's surface in K, and all other variables are defined for Equations 2.5 and 2.7. Values in Figure 2.3 support an approximate value for rs of 0.78 indicating strong transmission and weak absorption of solar radiation by the atmosphere. The value for rt is 0.17 indicating weak transmission and strong absorption of thermal radiation by the atmosphere (Andrews, 2000). Solving Equation 2.10 using these values results in a surface temperature of 283 K which is close to the observed mean value of 288 K. It is important to note that Figure 2.3 includes two non-radiative processes that contribute to heating the atmosphere. These energy transfers are expected to account for some of the difference between the observed temperature and the calculated temperature from Equation 2.10.
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