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
solar radiation
Objects above 0K can emit radiation
Max possible radiation for given temperature is blackbody
Plancks law gives blackbody curves

4. Planck’s Law: SUN Wien’s Law:  = 2897 / T T = 5780 K max 6 X 10
Objects above 0K can emit radiation
Max possible radiation for given temperature is blackbody
Plancks law gives blackbody curves

5. SUN

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

7. Focus on a particular time scale of interest
Time Scales
Focus on a particular time scale of interest
Factors that change very slowly relative to that time scale can be considered constant
Stop and Think 03
DEMO: pendulum
Momentum goes from + to - and 0
Same for angular
When a ball hits a bat where doe the momentum go?
What is “the system”
Momentum goes to string to ceiling to earth
Earth gets what pendulum looses
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
 T 4 e T e
incoming solar radiation
Rate at which object radiates is proportional to its area and to the
fourth power of its absolute temperature (Stefan-Boltzman law)

10. solar radiation
terrestrial radiation
Energy In
Energy Out
Stored

11. DYNAMIC EQUILIBRIUM
variable
time

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

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

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

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

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

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

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

19. Model Refinement

21. SUN Greenhouse Effect CO2 Heating reradiated incoming
Haze Effect vs Greenhouse Effect
Heating

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

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

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

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

26. Model Refinement

27. Atmospheric Window
for Infrared Radiation

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

29. Ingregrate over all Bands

30.  T   T  T =  T  T = A
  T S
incoming solar radiation
 T =
1/4 S
 T
eff
 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…
incoming
solar radiation
Transport of heat & chemical constituents between layers
Global
average
albedo
50% of atmosphere is below 6km
Atmosphere thins
with elevation
Space

33. SUN Te = T1 T1 Layer 1 T2 Layer 2 T3 Layer 3 TG 4 4 4 4
Haze Effect vs Greenhouse Effect
TG 4
Layer 3

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

35. Model Refinement

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

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

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

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

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

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
Walket Hayes and Kasting
Berner Lasaga and Gerrels

51. Coupled Volcanic-Tectonic Evolution and
Climate Evolution Model

52. Solid Planet
Dynamics Model
Climate Model
CO2 Cycling

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

54. Mantle Heat ProductionQs
Surface Mantle
Heat Flux H H
Mantle Heat Production

55. an expression for this is the key to this modeling exercise Ur =
cV T = Qs
Convective
Flux Qs
Surface Mantle
Heat Flow
an expression for this is the key
to this modeling exercise
Mantle Heat
Production H H Qs
Ur =
Ur=
Continents back =

56. Carbonate-Silicate Weathering Cycle
Tectonics + Hydrologic Cycle
Cycles are dynamic- Fluxes are critical. What does a snapshot say about a cycle?
Tectonic factors - volcanism, uplift, and exposure - affect atmospheric pCO2 , but ultimately the stabilizing influence is the sensitivity of weathering rates to atmospheric pCO2 . Increases in relief in tectonically active regions increase Aex , and thus cause CO2 draw-downs. The attendant climate change reduces chemical weathering rates elsewhere, returning the carbonate-silicate cycle to steady state (Kump & Arthur 1997).
The major effect of CO2 on weathering is indirect, and involved the greenhouse effect of atmospheric pCO2 on temperature and net precipitation.
Kump et al., 2000