1. Introduction to Climate and Energy Balance Models
July 22, 2013
Samantha Oestreicher
University of Minnesota

2. “Some say the world will end in fire…”
Some say the world will end in fire, Some say in ice. From what I've tasted of desire I hold with those who favor fire. But if it had to perish twice, I think I know enough of hate To say that for destruction ice Is also great And would suffice. 

3. Outline What is Climate? How do we observe climate?
An Overview of Earth’s Climate System.
Types of Radiation
Energy Balance Model
Stefan-Boltzmann
Budyko-Sellers

5. What is Climate?
Climate := 30 year average
of weather.

6. What is Climate? Climate := 30 year average of weather. Weather:
Do I need an umbrella today?

7. What is Climate? Climate := 30 year average of weather. Weather:
Do I need an umbrella today?
Climate:
Do I need to own an umbrella?

8. People have been making observations for hundreds of years.
How do we observe climate?
People have been making observations for hundreds of years.

9. How do we observe climate?

10. How do we observe climate?

11. How do we observe climate?

12. How do we observe climate?

13. How do we observe climate?
The cores ALSO show something different is happening to the atmospheric CO2.
nicl-smo.unh.edu

14. How do we observe climate?
The cores ALSO show something different is happening to the atmospheric CO2.
nicl-smo.unh.edu

15. An Overview of Earth’s Climate System
9:35

16. How do we model climate?

17. How do we model climate?
There are two main view on how to model climate:
“No detail is too small!”
Leads to all-inclusive
Global Climate Models
“The rest is details”
Leads to simple
Conceptual
Climate Models

18. Complicated choices starting from how to grid the globe.
Global Climate Models
Complicated choices starting from how to grid the globe.

19. Global Climate Models

20. Global Climate Models Global Climate Models require: Physical sciences
Physical, chemical, biological processes
Computer science
Data mining, coupling non-similar grids, error analysis, parallel processing, time optimization
Statistics
Extreme events, trends, and averaging
Mathematics
Data assimilation, numerical znalysis, PDEs

21. Global Climate Models - Simulation

22. Global Climate Models - Prediction
The cores ALSO show something different is happening to the atmospheric CO2.
IPCC Report AR4

23. 9:50

24. How do we model climate?
There are two main view on how to model climate:
“No detail is too small!”
Leads to all-inclusive
Global Climate Models
“The rest is details”
Leads to simple
Conceptual
Climate Models

25. Energy Balance Models Temperature Change = Energy In – Energy Out
Energy Out using Stefan-Boltzmann Law:
Temperature of the Sun = 5,778 K
Power flux (W/m2) = (5.67 x10-8 )*(5778)4 = 6.33x107 W/m2
Question:
What kind of energy is the Sun radiating?

26. Types of Radiation

27. Types of Radiation
Plank’s Function gives a distribution of wavelengths based on the temperature of the body.
Wein’s Law tells us the maximum frequency is inversely proportional to the temperature. ie: Hotter bodies produce shorter wavelengths.
The Sun gives off shortwave radiation or ultraviolet.
The Earth gives off longwave radiation or infared.

28. Types of Radiation
The Sun gives off shortwave radiation or ultraviolet.
The Earth gives off longwave radiation or infared.

29. Energy Balance Models
In the “Global Energy Balance Models and the Goldilocks Zone” section of the MATLAB guide, you will use the Stefan-Boltzmann Law to derive the average incoming solar radiation (or insolation) to Earth.
Earth’s Insolation = 342 W/m2 = Q
Thus the simplest energy balance model is:
Temperature change = energy in – energy out
Which has equilibrium solution:
Q = sTeq4 or
(342/s)1/4=Teq
Thus Earth’s temperature is modeled to be
Teq = 279K = 6 °C = 43 °F

30. Energy Balance Models Teq = 279K = 6 °C = 43 °F
But the observed temperature of Earth is only
T = 14 °C
Stefan-Boltzmann is black body radiation. We need to include albedo.
Globally 30% of insolation is reflected back into space.

31. Energy Balance Models

32. Energy Balance Models Thus the improved energy balance model is:
Which has equilibrium solution:
Q (1- a) = sTeq4 or
(342*(1-0.3)/s)1/4=Teq
Thus Earth’s temperature is modeled to be
Teq = 255K = -18 °C = 0 °F
Question:
Why isn’t the Earth a snowball?

33. Energy Balance Models
Budyko - Sellers Suggest new outgoing longwave radiation (OLR) formulation:
OLR = A + BT
A and B are determined from satellite observations.
T is surface temperature (in Celsius).
A = 202 W/m B =1.90 W/m K
Dynamics
photosphere
temperature
global mean
surface temperature
Question:
What is happening in the atmosphere to cause this discrepancy?

34. Energy Balance Models Budyko-Sellers Energy Balance Model is:
With equilibrium solution
This equilibrium solution is stable with eigenvalue –B. (Recall B>0.)
Question:
What if Earth’s albedo was not 30%?
Budyko 1969

35. Last Question:

36. Extras