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Introduction to Climate and Energy Balance Models. Samantha Oestreicher University 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 Radiation Energy Balance Model - PowerPoint PPT Presentation
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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