Radiative Transfer Radiative transfer equation (RTE) - IAP ...

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Transmission of Earth atmosphere Microwave regime 1 Zenith Microwave Transmittance <strong>RTE</strong> Transmittance 0.9 0.8 0.7 0.6 0.5 0.4 H 2 O O 2 O 2 H 2 O Dry (0 kg/m 2 ) Polar (3.1 kg/m 2 ) Midlatitude (21.3 kg/m 2 ) Tropical (53.6 kg/m 2 ) Beer’s law Abs. cross section Opacity & Transmission Mean free path Scattering Schwarzschild eq. 0.3 0.2 0.1 0 0 50 100 150 200 250 300 Frequency [GHz] copied from Petty, Atmospheric radiation
Mean free path of a photon What happens to a photon launched from a particular point in a medium? → We cannot say what happens to a particular photon → We can determine what happens in a statistical sense What is the probability that a photon propagating along the x-axis is absorbed between x and x + ∆x? Given by the integral of a probability density function p(x) <strong>RTE</strong> Beer’s law Abs. cross section Opacity & Transmission Mean free path Scattering Schwarzschild eq. ∫ x+∆x x p(x) dx where ∫ x+∞ x p(x) dx = 1 Assume exponential attenuation according Beers law → probability photon is not absorb over distance x is e −kax → probability photon is not absorb over distance x + ∆x is e −ka(x+∆x) → probability photon is absorb over interval ∆x is difference ∫ x+∆x x p(x)dx = e −kax − e −ka(x+∆x)
Page 1 and 2: Radiative Transfer Radiative transf
Page 3 and 4: Absorption by a non homogeneous med
Page 5 and 6: Opacity and transmittance Atmospher
Page 7: Transmission of Earth atmosphere Mi
Page 11 and 12: Scattering of radiation ◮ In addi
Page 13 and 14: Example of scattering efficiency RT
Page 15 and 16: Schwarzschild equation The atmosphe
Page 17 and 18: Schwarzschild equation The net chan
Page 19: Radiative transfer equation Line by

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