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induce including the process of obtaining Solution Ys and Ya

induce including the process of obtaining Solution Ys and Ya

Applications and Investigations in Earth Science (9th Edition)
Applications and Investigations in Earth Science (9th Edition)
9th Edition
ISBN:9780134746241
Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Chapter1: The Study Of Minerals
Section: Chapter Questions
Problem 1LR
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please induce including the process of obtaining Solution Ys and Ya
Selective Absorption and Transmission Assume that the earth behaves like a blackbody and that the atmosphere has an absorptivity as for incoming solar radiation and a for outgoing longwave radiation. Let Y, be the irradiance emitted by the atmosphere (both upward and downward); Ys the irradiance emitted from the earth's surface; and E the solar irradiance absorbed by the earth-atmosphere system. Then, radiative equilibrium requires E-(1-a) Y - Y₁ = 0, at the top of the atmosphere, (1-as) E-Y + Y₁ = 0, at the surface. Solving yields Ys Y₁ = (2-as) (2-a₁) Y₁ = E, and (2-a)-(1-a)(2-as) (2-a₁) Since a> as, the irradiance and hence the radiative equilibrium temperature at the earth surface is increased by the presence of the atmosphere. With a = .8 and as = .1 and E = 241 Wm 2, Stefans Law yields a blackbody temperature at the surface of 286 K, in contrast to the 255 K it would be if the atmospheric absorptance was independent of wavelength (as = a). The atmospheric gray body temperature in this example turns out to be 245 K E.
Transcribed Image Text:Selective Absorption and Transmission Assume that the earth behaves like a blackbody and that the atmosphere has an absorptivity as for incoming solar radiation and a for outgoing longwave radiation. Let Y, be the irradiance emitted by the atmosphere (both upward and downward); Ys the irradiance emitted from the earth's surface; and E the solar irradiance absorbed by the earth-atmosphere system. Then, radiative equilibrium requires E-(1-a) Y - Y₁ = 0, at the top of the atmosphere, (1-as) E-Y + Y₁ = 0, at the surface. Solving yields Ys Y₁ = (2-as) (2-a₁) Y₁ = E, and (2-a)-(1-a)(2-as) (2-a₁) Since a> as, the irradiance and hence the radiative equilibrium temperature at the earth surface is increased by the presence of the atmosphere. With a = .8 and as = .1 and E = 241 Wm 2, Stefans Law yields a blackbody temperature at the surface of 286 K, in contrast to the 255 K it would be if the atmospheric absorptance was independent of wavelength (as = a). The atmospheric gray body temperature in this example turns out to be 245 K E.
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