The effect of clouds on the surface temperature can be illustrated using the heuristic example given below. The models described here are over-simplified, but nevertheless serve to illustrate the main principle of the role of low and high clouds. The difference between these two types is important for the models of solar-terrestrial links, including the hypothesis proposed by Svensmark and Friis-Christensen (1997).
A simple model based on energy balance considerations and a given atmospheric lapse rate (rate of change of temperature with height r = dT/dz) is derived below. The equations are based on radiative energy balance from the schematic diagrams for low and high clouds shown in Figure 7.2.
The cloud top of low clouds may be assumed to have similar temperature to the ground, Tct « Ts + Tz, z « 0. Tct is the temperature of the cloud top and Ts is the surface temperature. Using this approximation and re-arranging equation (7.1), the surface temperature can be expressed in terms of the TSI and albedo:
Thus, the effect of low clouds on the surface temperature can be inferred from the difference between the emission temperatures derived from a cloud-
free ocean surface and an ocean surface covered by low clouds (equation (7.2)).
The albedo for cloud tops is assumed to be Act = 0.5, whereas the ocean surface reflects less radiation, Aoce=0.1. The solar constant is taken as 1370 Wm-2, and the Stefan-Boltzmann constant is a = 5.67 x 10-8Wm-2 K-4. Hence, the effect of the low clouds compared to cloud-free ocean surface is to reduce the surface temperature: ATs(low) « — 37 K. This estimate is clearly unrealistically high," but nevertheless points to the importance of the clouds.
For high clouds, the cloud top temperature is substantially lower than the surface temperature.
The long-wave radiation emitted to space by the clouds (aT^) is equal to the amount directed back to Earth's surface. It is assumed that the cloud does not absorb solar radiation, and the only source of energy for the cloud is therefore long-wave radiation from Earth's surface (aT4):
A radiative equilibrium between the insolation and Earth's black body radiation can be expressed as:
By using equation (7.3), the cloud top temperature can be substituted by the surface temperature:
The estimated effect of high clouds on the surface temperature is:
This estimate is of course a crude simplification, but serves as a simple demonstration of why the high clouds are believed to have a warming effect on the surface.
a The radiative forcing is just one of several factors affecting the surface temperature.
The effect of radiative forcing associated with variations in the cloud cover depends on the cloud height. Low clouds tend to cool the surface because more solar energy is reflected back to space than upwelling long-wave radiation is absorbed and re-emitted back down to Earth. High clouds, on the other hand, increase the surface temperature (Ts) because the enhanced greenhouse effect is stronger than the albedo effect. Another factor playing a role is the number of cloud drops, as many small cloud drops have higher effective surface area than few large drops, given the same amount of water. Cloud thickness is also a factor affecting the radiation balance, with thick clouds being more important than thin clouds.
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