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An improved energy balance model

An improved energy balance model. Goals: understand the effects of atmosphere and Greenhouse gases on the earth temperature. 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. Q1.

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An improved energy balance model

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  1. An improved energy balance model Goals: understand the effects of atmosphere and Greenhouse gases on the earth temperature.

  2. Summary: Earth Energy Balance Equation Pin = Pout Pin = (1-A) S π REarth2, Pout = 4π REarth2 σ TEarth4 Tearth= 255K

  3. 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.

  4. Earth Energy Budget Sheet

  5. Green house effect • Model one: Glass layer effects on the earth temperature; • 2) An atmospheric model with Green house effect • (with Green house gases).

  6. 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)

  7. 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.

  8. σ Te4 Now the energy balance for the surface of the Earth is: • Pin = (1-A) S π REarth2+σ Te4 4π REarth2 • Pout = σ Ts4 4π REarth2

  9. Now the energy balance for the surface of the Earth is: (1-A) S π REarth2+σ Te4 4π REarth2= σ Ts4 4π REarth2 • Ts4 = (1-A) S / 4σ + Te4 = 2 Te4 (Assuming Te = 255 K )

  10. You should get Ts = 303 K = 30 ºC • Not really – too hot! Issues: • Is atmosphere a thin layer? • Is it totally absorbing in infrared?

  11. 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

  12. Different layers of the atmosphere

  13. Major green house gases

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