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Introduction to Climate and Energy Balance Models
Samantha OestreicherUniversity of Minnesota
July 22, 2013
Outline
What is Climate?How do we observe climate?An Overview of Earth’s Climate
System.Types of RadiationEnergy Balance Model
◦ Stefan-Boltzmann◦ Budyko-Sellers
What is Climate?
Climate := 30 year average of weather.
Weather:Do I need an umbrella today?
Climate:Do I need to own an
umbrella?
http://www.dartmouth.edu/~mpayres/People/Sharon.7506.web.jpghttp://www.whoi.edu/ooi_cgsn/auvs-gliders?tid=1621&cid=137956&article=95673
How do we observe climate?
How do we model climate?There are two main view on how to model climate:
1. “No detail is too small!”Leads to all-inclusive Global Climate Models
2. “The rest is details”Leads to simpleConceptual Climate Models
www.pmel.noaa.gov/foci/ice06/FOCI_Ice2006_phytoplankton.html
www.nasa.gov/vision/earth/lookingatearth/ice_clouds.html
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
Global Climate Models
How do we model climate?There are two main view on how to model climate:
1. “No detail is too small!”Leads to all-inclusive Global Climate Models
2. “The rest is details”Leads to simpleConceptual Climate Models
www.pmel.noaa.gov/foci/ice06/FOCI_Ice2006_phytoplankton.html
www.nasa.gov/vision/earth/lookingatearth/ice_clouds.html
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?
Types of RadiationPlank’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.
http://www2.webster.edu/~barrettb/courses/mediaproduction.htm
Types of Radiation
The Earth gives off longwave radiation or
infared.
The Sun gives off shortwave radiation or ultraviolet.
Energy Balance ModelsIn 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 = sTeq
4
or(342/s)1/4=Teq
Thus Earth’s temperature is modeled to be
Teq = 279K = 6 °C = 43 °F
4TQdt
dTR
Energy Balance ModelsTeq = 279K = 6 °C = 43 °F
But the observed temperature of Earth is onlyT = 14 °C
Stefan-Boltzmann is black body radiation. We need to include albedo.
http://www.cocorahs-albedo.org/
Globally 30% of insolation is reflected back into space.
Energy Balance ModelsThus the improved energy balance model is:
Which has equilibrium solution:Q (1- a) = sTeq
4
or(342*(1-0.3)/s)1/4=Teq
Thus Earth’s temperature is modeled to beTeq = 255K = -18 °C = 0 °F
Question:Why isn’t the Earth a snowball?
4)1( TQdt
dTR
Energy Balance ModelsBudyko - 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
photospheretemperature
global meansurface temperature
4)1( TQdt
dTR
)()1( BTAQdt
dTR
Question: What is happening in the atmosphere to cause this discrepancy?
Energy Balance Models
)()1( BTAQdt
dTR
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%?
B
AQTeq
)1(
32.0
62.0
ocean
ice
Budyko 1969