3. complete problem 3-1 in dingman (2nd edition, given below). contrast with the analysis in trenberth et al 3-1: use the model described in box 3-1 to explore and compare the sensitivity of planetary temperature (tp) to changes in (a) planetary albedo (ap); and (b) the solar flux (s). for comparisons, it is most meaningful to express sensitivity in relative terms, as the fractional change in tp in response to a given fractional change in ap and s 4. again, revisit the following question: what are the connections between the terrestrial water balance and the terrestrial energy balance? 3.1 basic aspects of global climate 39 box 3-1 energy-balance model of global radiational temperature we can apply some of the basic physics of energy trans fer discussed in section d.1 to develop a simple "zero- dimensional" energy-balance model of the temperature of the earth-atmosphere system. the long-term average rate of energy input to this system, e t1, equals the solar flux, s (e t1, minus the fraction, a, of this arriving energy that is reflected by the system equating i and q and solving for s: (1-4) yields (381-3) equation (3b1-3) shows how the radiating temperature of the earth-atmosphere system (called the planetary temperature) depends on the solar constant and the re- flectivity of the system (called the planetary albedo) s.(1-a) (3b1-1) s-1 .74x1017 w, ơ 5.78x10-8 w m-2 k-4, and a is 5.10x10 m2.from figure 3-2, we see that the value of a, is 0.3. inserting these values in equation (381-3) gives t, 253.6 k, which is quite close to the value of 253 k quoted in the text. (the difference is due to round- ing errors in the numbers in figure 3-2 and to uncertain- tyìn the true value of a to maintain equilibrium, the average rate at which the system radiates energy to outer space, q, must equal from the stefan-boltzmann law (equation d-1) this rate is (381-2) where σ is the stefan-boltzmann constant. t, is the effective radiating temperature of the system (assum- ing an emissivity of 1), and a is the surface area of the exercise 3-1 gives you an opportunity to explore this question by using this simple model. a simple model for calculating the earth's surface temperature is de- scribed in box 3-2 system.