Climate Modeling Primer

1. Climate Modeling Primer

2. Develop a model to predict the average surface temperature of Earth List 5 Factors Need to be Considered

3. Insolation: Energy from the Sun N solar radiation SUN

4. 6 X 10 Planck’s Law:  = 2897 / T max SUN Wien’s Law: T = 5780 K

5. SUN

6. Develop a model to predict the average surface temperature of Earth List 5 Factors Need to be Considered

7. Time Scales Focus on a particular time scale of interest Factors that change very slowly relative to that time scale can be considered constant Factors that are very fast relative to that scale can be considered to be in an “instantaneously” adjusting equilibrium called quasi steady state

8. Time Scales

9. Crudest, useful estimate of effective surface temperature of planet Te: Equate solar radiation it absorbs to the infrared radiation it emits incoming solar radiation T e 4  T e Rate at which object radiates is proportional to its area and to the fourth power of its absolute temperature (Stefan-Boltzman law)

10. Energy In Energy Out solar radiation terrestrial radiation Stored

11. DYNAMIC EQUILIBRIUM variable time

12. incoming solar radiation T e 4  T e Absorbed depends on: Solar Constant, Albedo (~0.3 for earth), Radius Emitted depends on: Effective Temperature, Radius, Stefan-Boltzmann Constant

13. earth e e e SUN 2 4 2 E = 4R T (1-A) SR Outgoing: Incoming: How much solar radiation does the earth intercept?

14. e e e SUN T = 255 K e 2 4 2 = 4R T (1-A) SR

15. Re-Radiated . Absorbed e 2 cT = (1-A) SR Model Refinement Radiation Temperature 2 4 - 4R T e e e

16. 6 X 10  = 2897 / T max Wien’s Law: T = 5780 K T = 255 K

17. e e e SUN T = 255 K e 2 4 2 = 4R T (1-A) SR

18. e e e incoming solar radiation T s 4 2 4 2  T = 4R T (1-A) SR e If the model equation for this system is given by: Then what has been assumed ?

19. Model Refinement

21. SUN reradiated incoming Greenhouse Effect CO2 Heating

22. SUN Box 2 Box 1 incoming Greenhouse Effect CO2 reradiated Heating

23. Energy In Energy Out Energy Out Energy In Energy Out Energy In Stored ATMOSPHERE BOX Stored SURFACE BOX

24. Consider an end-member atmosphere layer that’s opaque to infrared 4  T A 4 4  T  T A A incoming solar radiation T T A A = T effect T S 4 4  T =  T S S For radiative equilibrium: Incoming (sun) must = Outgoing (atmosphere) = 255 K If the atmosphere is at steady-state then incoming IR must equal outgoing

25.    incoming solar radiation T A T S  T = prediction is within 5% S Surface measurements show an average surface temperature of 288K

26. Model Refinement

27. Atmospheric Window for Infrared Radiation

28. 4 k T A 4 4 4 k T k) T k T S S A incoming solar radiation T A T S 4  T S

29. Ingregrate over all Bands

30.    T  eff incoming solar radiation T A 1/4  T = S T S  T = S Is this Really the Maximum Greenhouse Effect?

31. Model Refinement

32. Consider a 1-D column that represents the average vertical structure of the atmosphere of the entire planet Air layers containing CO2, H20… Global average albedo Transport of heat & chemical constituents between layers 50% of atmosphere is below 6km Atmosphere thins with elevation incoming solar radiation Space

33. SUN 4 4 4 4 4 4 T1 T1 T2 T2 T3 T3 4 TG Te = T1 Layer 1 Layer 2 Layer 3

34. 1/4 TG = (1+) Te SUN 4 4 4 4 4 4 T2 T1 T1 T3 T3 T2 1/4 T2 = (2) Te 1/4 T3 = (3) Te  4 1/4 TG TG = (4) Te Te = T1 Layer 1 Layer 2 Layer 3

35. Model Refinement

36. N solar radiation High Albedo e e e Low Albedo SUN 2 4 2 = 4R T (1-A) SR

37. N solar radiation High Albedo e e e Low Albedo SUN 2 4 2 = 4R T (1-A) SR f (Temperature)

38. 1 0 . e Albedo present day Temperature 2 cT = (1-A) SR f (Temperature) Big Deal or Small Deal? 2 4 - 4R T e e e

39. Re-Radiated . Absorbed e 2 cT = (1-A) SR Model Refinement Radiation Temperature 2 4 - 4R T e e e

40. . negative feedback e 2 cT = (1-A) SR f (Temperature) Model Refinement Re-Radiated Absorbed positive feedback Radiation Temperature 2 4 - 4R T e e e

41. Zonal Energy Balance Climate Model (cf. Budyko)

42. Model Refinement

45. Model Extension

46. Faint Young Sun

47. Faint Young Sun Paradox

48. Should We Expect Other Earth-like Planets At All? By Caleb A. Scharf “… long-term stability (read millions of years) of the Earth’s surface environment close to the ‘habitable’ state is a direct consequence of geophysical re-cycling.” “Geophysics is the dirty little secret here.”

49. Volcanic-Tectonic Driven Climate Model

50. from WHAK to BLAG