Outline

1. Remote Sensing ISummer 2007Björn-Martin SinnhuberRoom NW1 - U3215Tel. 8958bms@iup.physik.uni-bremen.dewww.iup.uni-bremen.de/~bms B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007

2. 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

3. Observed Radiance for an Infra-Red Nadir Sounder B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007

4. Example: TOVS: HIRS2 and MSU B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. Idealized Weighting Functions Scale height H=7km B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007