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 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

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 1)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. 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

9. 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 )

10. 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?

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