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An improved energy balance model Goals: understand the effects of atmosphere and Greenhouse gases on the earth temperature.
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Summary: Earth Energy Balance Equation P in = P out P in = (1-A) S π R Earth 2, P out = 4 π R Earth 2 σ T Earth 4 T earth= 255K
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Q1 Planet-X is at a distance R=2R_earth from the sun. its temperature should be A) 2 T_earth; B) T_earth / 2; C) T_earth /\sqrt{2}; D) depends on the radius of X-planet.
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Earth Energy Budget Sheet
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Green house effect 1)Model one: Glass layer effects on the earth temperature; 2) An atmospheric model with Green house effect (with Green house gases).
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Q1 (facts) Atmosphere mainly A) reflects visible lights; B) absorbs infrared radiations from the earth; C) emits infrared radiation towards the earth; D) Both A), B) and C)
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One-layer atmosphere model Assumptions: a) Atmosphere absorbs all infrared radiation from the earth; So that earth radiation not seen from outside. b) Atmosphere emits blackbody radiation.
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Now the energy balance for the surface of the Earth is: P in = (1-A) S π R Earth 2 + σ T e 4 4π R Earth 2 P out = σ T s 4 4π R Earth 2 σ Te 4
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Now the energy balance for the surface of the Earth is: (1-A) S π R Earth 2 + σ T e 4 4 π R Earth 2 = σ T s 4 4π R Earth 2 T s 4 = (1-A) S / 4 σ + T e 4 = 2 T e 4 (Assuming T e = 255 K )
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You should get T s = 303 K = 30 ºC Not really – too hot! Issues: Is atmosphere a thin layer? Is it totally absorbing in infrared?
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Earth Energy Balance The more complex models involving multilayer atmosphere partially transparent in infrared come up with better estimates of temperatures of the surface of the Earth – about 15 ºC
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Different layers of the atmosphere
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Major green house gases
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