In the article \"The Climatic Effects of Nuclear War\" (Scientific American, Aug

Question

In the article "The Climatic Effects of Nuclear War" (Scientific American, August 1984), the authors calculate a global energy balance corresponding to the first few months following a 9,000-megaton nuclear exchange. The resulting smoke and dust in the atmosphere absorb 75 percent of the incoming sunlight (257 W/m2), while the albedo is reduced to 20 percent. Convective and evaporative heating of the atmosphere from the Earth's surface is negligible, as is the energy reflected from the Earth's surface. The Earth's surface radiates 240 W/m2 all of which is absorbed by the atmosphere. Assuming that the Earth can be modeled as a blackbody emitter as shown below, find the following (equilibrium) quantities: 6. a. The temperature of the surface of the Earth (this is "nuclear winter) b. X, the rate at which radiation is emitted from the atmosphere to space c. Y the rate of absorption of short-wavelength solar radiation at the Earth's surface d. Z, the rate at which the atmosphere radiates energy to the Earth's surface Incoming 342 W/m2 Radiated to space Reflected Reflected 69 Atmosphere Convection, evaporation Absorbed 257 Radiated to ground Radiated, 240 Win Absorbed

Explanation / Answer

Total incoming irradience = 342w/m2

reflecteed by atmosphere = 69

absorbed by atmosphere = 257

reflected by earth atmosphere = 0

(Y)absorbed by earth surface = 342- 257-69-0 = 16 w/m2

Radiated by earth = Y + Z

240 = 16+ Z

Z= 224 w/m2 radiated to ground

X( radiated to space) = atmospheric absorbtions - radiated to ground (z)

X = 257 + 240 -224 = 273 w/m2

radiated power = sigma x T4

240 w/m2= 5.67 x 10-8w/m2- k4 x T4

T4 = 42.328 x 108 k4

T = 2.55 x 100 k

T= 255 k

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