Introduction to Climate and Energy Balance Models

Samantha OestreicherUniversity of Minnesota

July 22, 2013

“Some say the world will end in fire…”

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.

What is Climate?

Climate := 30 year average

of weather.

Weather:Do I need an umbrella

today?

What is Climate?

Climate := 30 year average of weather.

Weather:Do I need an umbrella today?

Climate:Do I need to own an

umbrella?

People have been making observations for hundreds of

years.

How do we observe climate?

How do we observe climate?

http://spaceplace.nasa.gov/earth-card-game/terra-lrg.en.png

How do we observe climate?

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 observe climate?

How do we observe climate?

nicl-smo.unh.edu

How do we observe climate?

nicl-smo.unh.edu

An Overview of Earth’s Climate System

9:35

How do we model climate?

http://www.prism.washington.edu/story/Earth+System+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

Global Climate ModelsComplicated

choices starting from how to grid the globe.

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

Global Climate Models

Global Climate Models - Simulation

Global Climate Models - Prediction

IPCC Report AR4

9:50

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?

http://www2.webster.edu/~barrettb/courses/mediaproduction.htm

Types of Radiation

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 Models

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

Last Question:

Extras