Calculate the "steady state” numerical values of the earth’s ground temperature Ts and the atmospheric temperature Ta taking into account the “greenhouse effect” of atmospheric infrared absorption and emission described above.
Earth absorbs solar energy and radiates infrared energy. The intensity of the solar radiation incident on earth is J = 1350 Wm-2, also known as the solar constant. Assume earth’s surface (ground) temperature to be uniform at Ts, and that the ground and atmosphere are black (emissivity = 1) for infrared radiation. The radius of the earth is 6.378 x 106 m.
The diagram shows the ground at the surface temperature Ts and the atmosphere, represented as a thin black layer, at temperature Ta . Suppose the atmosphere absorbs 100% of the infrared radiation emitted by the ground. Assume that the ground absorbs 47.5% of the incident solar energy, and that the atmosphere absorbs 17.5% of the incident solar energy (for a total of 65% absorbed by the planet).
Calculate the "steady state” numerical values of the earth’s ground temperature Ts and the atmospheric temperature Ta taking into account the “greenhouse effect” of atmospheric infrared absorption and emission described above.
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