1. Climate Modeling Theory - 2
Module 5
Climate Modeling Theory - 2
William J. Gutowski, Jr.
Iowa State University

2. Climate Modeling Theory - 2
Module 5
Climate Modeling Theory - 2
GOAL:
Understand basis for modeling climate from (almost) first principles

3. Climate Modeling Theory - 2
Module 5
Climate Modeling Theory - 2
Review (Part 1):
Symbolism
Conservation Laws
mass (r, rq)
thermodynamic energy (T, q)
momentum ( )
Equation of State (p = rRT)
Water in the Atmosphere

4. Climate Modeling Theory - 2
Module 5
Climate Modeling Theory - 2
OUTLINE (Part 2):
Radiation
Surface Processes
Earth System

5. RNET
FSH
RNET

6. Climate Modeling Theory - 2
Module 5
Climate Modeling Theory - 2
OUTLINE (Part 2):
Radiation

7. Radiation Spectrum Black Body Curves Emission 255 K 6,000 K
Wavelength [m]

8. Radiation Spectrum Solar (shortwave, visible) Terrestrial
Black Body Curves
Emission
6,000 K
255 K
Wavelength [m]
Solar
(shortwave, visible)
Terrestrial
(longwave, infrared)

9. Radiation Spectrum Solar Terrestrial Absorption [%] Wavelength [m]
Entire atmosphere
Absorption [%]
Above km
Wavelength [m]
Solar
Terrestrial

10. Radiation Spectrum Solar Terrestrial CH4 N2O Absorptivity [%] O2 & O3
CO2
H2O
Wavelength [m]
Solar
Terrestrial

11. Energy Balance for Earth

12. Energy Balance for Earth
Planetary Albedo

13. Energy Balance for Earth

14. Energy Balance for Earth

15. Solar Constant
At photosphere surface, solar flux ~ W-m-2

16. Solar Constant At photosphere surface, solar flux ~ 6.2.107 W-m-2
At Earth’s orbit, solar flux ~ 1360 W-m-2

17. Daily Solar Radiation at Top of Atmos.
[106 J-m-2]
Note high latitude annual cycle, esp. maximum values in summer.
This is at top of atmosphere. This is not radiation reaching the surface. Raidation reaching the surface is reduced from this by reflection. High-latitude reflection will be larger because (1) large amount of snow and ice cover and (2) oblique angle of incoming radiation.

18. Planetary Albedo Scattering: air molecules, aerosols
Reflection: clouds
Surface albedo
Ocean %
Snow %
Crop %
Forest %
Cities %

19. What is Earth’s temperature?
Balance: Radiation in = Radiation out a
Incoming = 1360 W-m-2 x (1-albedo) x (area facing sun)
= 1360 x (1-0.3) x pa2
= W

20. What is Earth’s temperature?
Balance: Radiation in = Radiation out a
Incoming = 1360 W-m-2 x (1-albedo) x (area facing sun)
= 1360 x (1-0.3) x pa2
= W
Outgoing = sT4 x (area emitting) ; i.e., black body
= sT4 x 4 pa2

21. What is Earth’s temperature?
Balance: Radiation in = Radiation out a
Incoming = 1360 W-m-2 x (1-albedo) x (area facing sun)
= 1360 x (1-0.3) x pa2
= W
Outgoing = sT4 x (area emitting) ; (i.e., black body)
= sT4 x 4 pa2
Balance implies
T = {0.7(1360 W-m-2)/4s}1/4 = 255 K = -18 oC

22. What is Earth’s temperature?
Balance: Radiation in = Radiation out a
Balance implies T = -18 oC
Observed surface T = +15 oC
Difference? Must account for atmosphere (greenhouse effect).

23. What is Earth’s temperature?
Balance: Radiation in = Radiation out a
Balance implies T = -18 oC
Observed surface T = +15 oC
Difference? Must account for atmosphere (greenhouse effect).
Perspective 1.
Atmosphere reduces effective emissivity of surface.
Use radiation = esT4. Then e = (255/288)4 = 0.61

24. What is Earth’s temperature?
Balance: Radiation in = Radiation out a
Balance implies T = -18 oC
Observed surface T = +15 oC
Difference? Must account for atmosphere (greenhouse effect).
Perspective 1.
Atmosphere reduces effective emissivity of surface.
Use radiation = esT4. Then e = (255/288)4 = 0.61
Perspective 2.
Where is T = 255 K? (Effective black body level)
Approximately 5 km above surface (above most q).

25. Greenhouse Effect IR radiation absorbed & re-emitted,
partially toward surface
Solar radiation penetrates

26. Greenhouse Effect IR radiation absorbed & re-emitted,
partially toward surface
Net IR: ~ W-m
Emitted IR: ~ W-m

27. Radiative Cooling vs. Height

28. Absorbed Solar Radiation
High influx in tropical oceans, esp. where cloud cover low.
Rapdi drop with latitude: high zenith angle, ice/snow cover

29. Outgoing Terrestrial Radiation
Note effect of high clouds in the tropics.
Variation with latitude (temperature), but weaker gradient than absorbed solar. Also, net surface longwave (not shown) has even less of a gradient.

30. What if temperature decreases?
The same:
Incoming = W
Outgoing = sT4 x (area emitting)
= sT4 x 4 pa2

31. What if temperature decreases?
These are the same:
Incoming = W
Outgoing = sT4 x (area emitting)
= sT4 x 4 pa2
But for T < 255 K:
imbalance
Incoming solar exceeds outgoing IR
net energy input
T increases
~ Negative Feedback ~

32. Climate Modeling Theory - 2
Module 5
Climate Modeling Theory - 2
BREAK

33. Climate Modeling Theory - 2
Module 5
Climate Modeling Theory - 2
OUTLINE (Part 2):
Radiation
Surface Processes

34. Key Energy Fluxes at Surface
Net Radiation
Sensible Heat
Latent Heat
Deep Soil/Ocean

35. Key Energy Fluxes at Surface
Sensible Heat
FSH = r Cp(wT)s
Tair Ts

36. Key Energy Fluxes at Surface
Sensible Heat
FSH ≈ - r CpCH(Tair-Ts)
CH = CH(V, zo, dq/dz)
FSH = r Cp(wT)s
Tair Ts

37. Key Energy Fluxes at Surface
Latent Heat
Note various water pathways.
Magnitude of ET depends on land use (vegetation) and soil type.

38. FLH ~ - rCpCW{eair-esat(Ts)}
Key Energy Fluxes at Surface
FLH ~ - rCpCW{eair-esat(Ts)}
Latent Heat
Note various water pathways.
Magnitude of ET depends on land use (vegetation) and soil type.

39. FLH ~ - rCpCW{eair-esat(Ts)}
Key Energy Fluxes at Surface
FLH ~ - rCpCW{eair-esat(Ts)}
Latent Heat
CW = CW(V, zo, dq/dz)
but also
CW = CW(physiology)
soil moisture
CW µ leaf temp.
sunlight
CO2 level
Note various water pathways.
Magnitude of ET depends on land use (vegetation) and soil type.

40. Key Energy Fluxes at Surface
Deep Ocean
Deep Soil
Important for global climate
Generally small

41. Cycles Diurnal FLH FSH FSH FLH Grassland - Net Radiation Dry Lake
Note magnitudes of fluxes.
FLH

42. Cycles Diurnal FLH FSH Less cooling by evaporation Ts increases FSH
Grassland
- Net Radiation
Cycles
FLH
FSH
Diurnal
Dry Lake
- Net Radiation
Less cooling by evaporation
Ts increases
FSH larger
FSH
Note magnitudes of fluxes.
FLH

43. Cycles Annual Soil Temperature at depths marked
Note magnitudes of fluxes.

44. Cycles
Annual
Note magnitudes of fluxes.

45. Subsurface Water Root Zone Vadose Zone Ground Water Impermeable Layer
Note effect of high clouds in the tropics.
Variation with latitude (temperature), but weaker gradient than absorbed solar. Also, net surface longwave (not shown) has even less of a gradient.
Water Table
Ground Water
Impermeable Layer

46. Subsurface Water

47. Water Cycle Q Q P P E E
River flow (dishcarge) can pool, creating inland bodies of water that produce ET.
Groundwater can also give groundwater-supported ET, when water table is near surface. R

48. Climate Modeling Theory - 2
Module 5
Climate Modeling Theory - 2
OUTLINE (Part 2):
Radiation
Surface Processes
Earth System

49. Earth Climate System Q P E E R

50. Plant B Plant A Scales of Climate Human Influences Global
Regional Regional Regional Regional
Microscale Microscale Microscale Microscale Microscale Microscale Microscale Microscale Microscale
Microclimate A
Microclimate B
Microclimate C
Air-Transported
Pathogen B
Air-Transported
Pathogen A
CO2, CO, NOx,SO2,
trace gases, shading,
H2O, temperature,
Solar, IR, wind,
particulate matter
CO2, CO, NOx,SO2,
trace gases, shading,
H2O, temperature,
Solar, IR, wind,
particulate matter
CO2, CO, NOx,SO2,
trace gases, shading,
H2O, temperature,
Solar, IR, wind,
particulate matter
Surface slope, IR Radiation, Evaporation, Biogeochemicals
Crop A
Crop B
Chemicals
Chemicals
Chemicals
Plant A
Plant B
Human
Influences
Insect A
Management
Management
Particulate Deposition, Precipitation, Solar Radiation, IR
Insect B
Soil Pathogen B
Erosion
Chemicals
Soil Pathogen D
Detritus
Soil A
H2O, temperature,
nutrients, microbes,
soil carbon, trace chemicals
Soil A
H2O, temperature,
nutrients, microbes,
soil carbon, trace chemicals
Soil C
H2O, temperature,
nutrients, microbes,
soil carbon, trace chemicals
Soil B
H2O, temperature,
nutrients, microbes,
soil carbon, trace chemicals
Soil B
H2O, temperature,
nutrients, microbes,
soil carbon, trace chemicals
Hydrology, Soil Microbiology, Soil Biochemistry
Field Field Field Field Field Field Field Field Field Field
Regional Regional Regional Regional
Continental
Scales of Landforms

51. Climate Modeling Theory
Modules 3 & 5
Climate Modeling Theory
Acknowledgements
Dingman (1994) Physical Hydrology
Haltiner (1971) Numerical Weather Prediction
Holton (1992) An Introduction to Dynamic Meteorology
Oort & Peixoto (1992) Physics of Climate
Wallace & Hobbs (1977) Atmospheric Science: An Introductory Survey
Colleagues at Iowa State University