Introduction to Climate and Energy Balance Models

Introduction to Climate and Energy Balance ModelsSamantha OestreicherUniversity of Minnesota

July 22, 2013

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 desireI hold with those who favor fire.But if it had to perish twice,I think I know enough of hateTo say that for destruction iceIs also greatAnd would suffice.2OutlineWhat is Climate?How do we observe climate?An Overview of Earths Climate System.Types of RadiationEnergy Balance ModelStefan-BoltzmannBudyko-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.pngHow 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=95673How do we observe climate?

How do we observe climate?

How do we observe climate?

nicl-smo.unh.edu

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

nicl-smo.unh.edu

The cores ALSO show something different is happening to the atmospheric CO2.14An Overview of Earths Climate System

9:35How do we model climate?

http://www.prism.washington.edu/story/Earth+System+ModelsHow 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 detailsLeads to simpleConceptual Climate Models

www.pmel.noaa.gov/foci/ice06/FOCI_Ice2006_phytoplankton.html

www.nasa.gov/vision/earth/lookingatearth/ice_clouds.htmlGlobal Climate Models

Complicated 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, PDEsGlobal Climate Models

Global Climate Models - Simulation

Global Climate Models - PredictionIPCC Report AR4The cores ALSO show something different is happening to the atmospheric CO2.22

9:50How 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 detailsLeads to simpleConceptual Climate Models

www.pmel.noaa.gov/foci/ice06/FOCI_Ice2006_phytoplankton.html

www.nasa.gov/vision/earth/lookingatearth/ice_clouds.htmlEnergy Balance ModelsTemperature Change = Energy In Energy OutEnergy 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/m2Question:What kind of energy is the Sun radiating?

http://www2.webster.edu/~barrettb/courses/mediaproduction.htmTypes of Radiation

Types of RadiationPlanks Function gives a distribution of wavelengths based on the temperature of the body. Weins 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.htmTypes of RadiationThe 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.

Earths Insolation = 342 W/m2 = Q

Thus the simplest energy balance model is:

Temperature change = energy in energy out

Which has equilibrium solution:Q = sTeq4or(342/s)1/4=Teq

Thus Earths temperature is modeled to be

Teq = 279K = 6 C = 43 F

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) = sTeq4or(342*(1-0.3)/s)1/4=Teq

Thus Earths temperature is modeled to beTeq = 255K = -18 C = 0 F

Question:Why isnt the Earth a snowball?

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

Question: What is happening in the atmosphere to cause this discrepancy?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 Earths albedo was not 30%?

Budyko 1969

Last Question:Extras