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Weighting Functions for Microwave and Infra-Red Satellite Nadir Sounding

Weighting Functions for Microwave and Infra-Red Satellite Nadir Sounding. Remote Sensing I Lecture 7 Summer 2006. Radiative Transfer Without Scattering. Remember RTE without scattering:. (Also known as Schwarzschild equation.) With T(z,z´) the transmission between level z and z´.

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Weighting Functions for Microwave and Infra-Red Satellite Nadir Sounding

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  1. Weighting Functions for Microwave and Infra-Red Satellite Nadir Sounding Remote Sensing I Lecture 7 Summer 2006

  2. Radiative Transfer Without Scattering Remember RTE without scattering: (Also known as Schwarzschild equation.)With T(z,z´) the transmission between level z and z´

  3. RTE for Satellite Nadir Sounder The RTE without scattering can be solved to give the upwarddirected radiance at the altitude z´ This is what a satellite nadir sounder in the microwave orinfra-red spectral region will observe (for ).

  4. Weighting Functions For a nadir looking satellite sensor this can be written as: with the Weighting Functions K(z) defined as: I.e., the measured radiance is determined by the thermal emissionfrom the different levels, weighted by the Weighting Function.

  5. Temperature Retrieval If the absorption results from a uniformly mixed compound(such as CO2 or O2), the absorption coefficient can be assumedto be of the form: with the number density profile n(z) decreasing exponentiallywith height (scale height H, typically about 7km)Thus:

  6. Weighting Functions for Temperature Retrieval If then the transmission will be given by And the Weighting Functions are given by

  7. Mathematical Discussion of Weighting Functions The weighting functions have their maximum at zmax when At the maximum the weighting function have the value:

  8. Idealized Weighting Functions for Temperature Retrieval Scale height H=7km

  9. Idealized Weighting Functions for Temperature Retrieval

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