Very_Basic_Climate_Modeling_F10_Lect5

Very_Basic_Climate_Modeling_F10_Lect5 - Very Basic Climate...

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Very Basic Climate Modeling Fall 2010, Lecture 5 1
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Radiation Balance The temperature of any body, including earth, is determined by a balance between incoming radiation and outgoing radiation This is similar to a bank account F in = F out F in is the incoming energy flux F out is the outgoing energy flux 2
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Intensity of Incoming Energy Sunlight, at the earth’s distance from the sun, has an intensity, I, given by: I in = 1350 w/m 2 Some of the incoming radiation is reflected back into space – reflectivity is called the albedo , denoted α (Greek alpha) For earth, average albedo is about 0.33 3
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Corrected I in Correcting for reflection, we get I in = 1350 w/m 2 (1 – α) = 1000 w/m 2 We must correct this for the area of the earth which receives solar illumination Only half of the earth is at any given time, and sunlight near the poles is much weaker than near the equator 4
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Flux in Watts In order to measure the flux in watts, rather than watts/m 2 , we need to multiply by the area The illuminated area is actually that of a circle A[m 2 ] = πr 2 earth (Greek pi) So the incoming flux in watts becomes F in = πr 2 earth (1-α) I in 5
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Computing F out Next we need to compute the outbound energy flux, F out In order to do this, we use the Stefan- Boltzmann equation for a blackbody radiator 6
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Stefan-Boltzmann Equation I = εσT 4 I is the Intensity of emitted radiation ε is the emissivity (Greek epsilon) o ε is a number between 0 and 1 o If a blackbody is perfect, ε = 1 σ is a fundamental constant of physics called the Stefan-Boltzmann constant (Greek sigma) T is absolute temperature (K) Note that intensity varies as the fourth power of the absolute temperature 7
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F out 8 The earth radiates over the entire surface The area of the earth is given by A = 4πr 2 earth F out is computed by F out = AεσT 4 earth = 4πr 2 earth εσT 4 earth
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