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Remote Sensing I Summer 2007 Björn-Martin Sinnhuber Room NW1 - U3215 Tel. 8958 [email protected] www.iup.uni-bremen.de/~bms. Outline. Introduction Electromagnetic Radiation Radiative Transfer Through the Atmosphere Weighting Functions and Retrieval Techniques

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Remote Sensing ISummer 2007Björn-Martin SinnhuberRoom NW1 - U3215Tel. [email protected]/~bms

B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007


Outline
Outline

  • Introduction

  • Electromagnetic Radiation

  • Radiative Transfer Through the Atmosphere

  • Weighting Functions and Retrieval Techniques

  • A Short Review of Spectroscopy

B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007


Observed radiance for an infra red nadir sounder
Observed Radiance for an Infra-Red Nadir Sounder

B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007


Example tovs hirs2 and msu
Example: TOVS: HIRS2 and MSU

B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007


Radiative transfer without scattering
Radiative Transfer Without Scattering

Remember RTE without scattering:

(Also known as Schwarzschild equation.)With T(z,z´) the transmission between level z and z´

B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007


Rte for satellite nadir sounder
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 ).

B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007


Side remark case with no atmosphere
Side Remark: Case with no atmosphere

If atmospheric absorption (and thus emission) can be neglected,

the observed radiance is given by the emission from the surface:

For known emissivity ε this can be inverted to get the

surface temperature Tsurf.

B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007


Weighting functions
Weighting Functions

can be written as:

with the Weighting FunctionsK(z) defined as:

I.e., the measured radiance is determined by the thermal emissionfrom the different levels, weighted by the Weighting Function.

B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007


Temperature retrieval
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:

B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007


Weighting functions for temperature retrieval
Weighting Functions for Temperature Retrieval

If

then the transmission will be given by

And the Weighting Functions are given by

B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007


Mathematical discussion of weighting functions
Mathematical Discussion of Weighting Functions

The weighting functions

have their maximum at zmax when

At the maximum the weighting function have the value:

B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007


Idealized weighting functions
Idealized Weighting Functions

Scale height H=7km

B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007


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