where we have inserted numbers setting Te = 255K. Thus for every 1 Wm-2 increase in the forcing of energy balance at the surface, Ts will increase by about a quarter of a degree. This is rather small when one notes that a 1 Wm-2 change in surface forcing demands a change in solar forcing of about 6Wm-2, on taking into account geometrical and albedo effects (see Problem 7 at the end of this chapter).
A powerful positive climate feedback results from the temperature dependence of saturated water vapor pressure, es, on T; see Eq. 1-4. If the temperature increases, the amount of water that can be held at saturation increases. Since H2O is the main greenhouse gas, this further raises surface temperature. From Eq. 1-4 we find that
^ = 0T, ee and so, given that p = 0.067°C-1, a 1°C change in temperature leads to a full 7% change in saturated specific humidity. The observed relative humidity of the atmosphere (that is the ratio of actual to the saturated specific humidity; see Section 5.3) does not vary significantly, even during the seasonal cycle when air temperatures vary markedly. One consequence of the presence of this blanket of H2O is that the emission of terrestrial radiation from the surface depends less on Ts than suggested by the Stefan-Boltzmann law. When Stefan-Boltzmann and water vapor feedbacks are combined, calculations show that the climate sensitivity is dTs r K
which is twice that of Eq. 2-15.
The albedos of ice and clouds also play a very important role in climate sensitivity. The primary effect of ice cover is its high albedo relative to typical land surfaces or the ocean (see Table 2.2 and Fig. 2.5). If sea ice, for example, were to expand into low albedo regions, the amount of solar energy absorbed at the surface would be reduced, causing further cooling and enhancing the expansion of ice. Clouds, because of their high reflectivity, typically double the albedo of the Earth from 15% to 30%, and so have a major impact on the radiative balance of the planet. However it is not known to what extent the amount or type of cloud (both of which are important for climate, as we will see in Chapter 4) is sensitive to the state of the climate or how they might change as the climate evolves over time. Unfortunately our understanding of cloud/radiative feedbacks is one of the greatest uncertainties in climate science.
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