Planetary albedo is the ratio of radiation reflected into space divided by the total incident solar radiation S. Radiative equilibrium then requires that the absorbed solar irradiance is the same as the emitted irradiance E and is given by:
E = (1-A)S/4
where A is the planetary albedo and S is the solar irradiance incident on earth which
is
1380 Wm^-2. The factor of one quarter arises because the cross sectional area of the earth
disc exposed to solar radiation ( (pi)r2) is one quarter of the area of the earth's
radiating
surface (4 (pi)r2). Thus if the earth's albedo is 30%, then E = 241 W m^-2. From the
Stefan-Boltzmann law, the equivalent blackbody temperature corresponding to this emitted
irradiance is found to be T(equivalent) = 255 K.
"The circulation of the earth's atmosphere and oceans can be envisioned as if
powered by a heat engine. The shortwave radiation from the sun provides the fuel supply,
while the infrared radiation heat loss to space from the earth's surface and atmosphere is
the exhaust. The engine is throttled, to a large extent, by storms and oceanic
disturbances associated with the transformation of radiative heat to latent and sensible
heat." from Smith (1985), p.395.
For the earth, there is a balance (radiative equilibrium) between incoming solar
radiation, the main energy source, and energy sinks including absorption, reflection,
re-emission at infrared wavelengths, and so on. The result of this balance is that the
earth's mean temperature is fairly stable, although natural or anthropogenically induced
changes in the earth's atmosphere, its cloud cover or albedo might upset the sensitive
radiation balance and lead to changes in mean temperature and in climate.
Figure 13 below shows some of the complicated interactions between the atmosphere and
electromagnetic radiation. The composition of the atmosphere, the existence of surface
vegetation and cloud cover are some of the critical factors which affect the rate of
incoming solar radiation and emitted longwave radiation.
Figure 13: Some of the interactions between the atmosphere and incoming or outgoing electromagnetic radiation. From Smith (1985), p395 - after Kellogg (1982).
The global energy balance is determined by many important radiative processes which include:
For a more quantitative appreciation of the earth's radiation budget it is noted that the net radiation (N) is given by the difference between the absorbed solar radiation Q = (1-A)S/4 and the outgoing longwave radiation R(LW). Thus
N = (1-A)S/4 - R(LW)
where A is the planetary albedo, S is the solar irradiance, and the factor 4, as before, results from the cross-sectional area of the earth's disc being only one quarter of the surface area of one hemisphere. For a given location on earth, the radiation budget equation can be re-written with S/4 replaced by Scos theta where is the local solar zenith angle, at a given time. A is then termed the bidirectional reflectance of the earth-atmosphere for a given time and location, as distinct from the planetary albedo.
From the above equation, radiative heating occurs whenever there is a net gain (N positive), and radiative cooling occurs in regions where N is negative.
For a given time and location on earth, the above equation may result in a different net radiation. For example, bidirectional reflectances for a certain area depend on surface properties, cloud cover, latitude, etc. Also the incoming solar radiation varies with season due to the changing distance of the earth from the sun. The variation of incoming solar radiation with latitude determines climatic zones on earth. However when the above equation is integrated over a long period of time, for the whole earth, the net radiation must be zero if the earth is to remain at a constant temperature.
The importance of clouds in the radiation budget is shown in Figure 14 below. The variations of R(LW) and of absorbed solar radiation with cloud amount and for various cloud heights are shown.
Figure 14: Absorbed solar radiation [Q = (1-A)S/4] and emitted longwave radiation (R(LW)) both as a function of cloud amount for the four cloud heights as shown. The net radiation (N) is given by the difference between absorbed and emitted radiation as discussed in the text. From Smith (1985), p401.
Increasing cloud height or cloud amount results in a decrease in RLW because clouds radiate at lower temperatures as height above the (warmer) surface of the earth increases. Also, increasing cloud cover results in a decrease in absorbed solar radiation because clouds generally have higher albedos for solar radiation than the earth's surface. Note that RLW is equal to the absorbed solar radiation (which defines a global radiation balance) for a mean cloud height of 5.5km when the average cloud amount is 50 per cent.
Figure 15 below summarises the mean global energy balance for the earth-atmosphere system and indicates some of the main processes in action.
Figure 15: Summary of the mean global energy balance for the earth-atmosphere system. Numbers are percentages relative to the 100 units of incoming solar irradiance at the top left of the Figure. From Wallace and Hobbs (1977), p321.
Note that the incoming solar radiation at the top of the earth's atmosphere, which is an irradiance of S/4 = 1380/4 = 345 Wm^-2, is represented by 100 units of solar radiation in the upper left of the Figure.
In examining Figure 15 the following points are worthy of mention:
Dr D C Griersmith
