Vegetation Radiative Transfer Modelling (Nadine Gobron) - PEER

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Conservation of radiant energy in a slab Δz We obtain the two-stream equations ∂I ↓ ∂z (z) = −KI ↓ (z) − SP ↓↑ I ↓ (z) + SP ↑↓ I ↑ (z) ∂I ↑ ∂z (z) = + KI ↑ (z) + SP ↑↓ I ↑ (z) − SP ↓↑ I ↓ (z) coefficients of absorption, K (in m -1 ) and scattering S (in m -1 ) Pinty, B. and M. M. Verstraete (1998) `Introduction to Radiation <strong>Transfer</strong> Modeling in Geophysical Media’, in From Urban Air Pollution to Extra-Solar Planets, ERCA Volume 3 Edited by C. Boutron, EDP Sciences, Les Ulis, France, 67-87. 14
Asymmetry factor for scattering processes •We have for isotropic medium: P ↑↓ = P ↓↑ •The asymmetry factor g is a single number, defined as the mean cosine of the scattering angle (-1 or +1 in our case): ↓↓ ↓↑ g = ( + 1)P + ( −1) P •Typically: g = +1 for strict downward scattering, g=-1 for strict upward scattering and, g=0 for isotropic scattering. •For the above set of equations, we have: P ↑↓ P ↓↓ = P ↑↑ ↑↑ ↓↑ ↓↓ + P = P + P = 1 P ↑↓ = P ↓↑ = (1 − g) / 2 P ↑↑ = P ↓↓ = (1 + g) / 2 15
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Page 3 and 4: Satellites have different “eyes
Page 5 and 6: Model of radiation transfer • Sin
Page 7 and 8: Outline • Radiative Transfer Equa
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Page 13: Conservation of radiant energy for
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Page 19 and 20: Two-stream equations • In a more
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Vegetation Radiative Transfer Modelling (Nadine Gobron) - PEER

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