1. B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007 Remote Sensing I Summer 2007 Björn-Martin Sinnhuber Room NW1 - U3215 Tel. 8958 bms@iup.physik.uni-bremen.de www.iup.uni-bremen.de/~bms

2. B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007 Outline 1.Introduction 2.Electromagnetic Radiation 3.Radiative Transfer Through the Atmosphere 4.Weighting Functions and Retrieval Techniques 5.A Short Review of Spectroscopy

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

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

5. B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007 Radiative Transfer Without Scattering Remember RTE without scattering: (Also known as Schwarzschild equation.) With T(z,z´) the transmission between level z and z´

6. B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007 RTE for Satellite Nadir Sounder The RTE without scattering can be solved to give the upward directed radiance at the altitude z´ This is what a satellite nadir sounder in the microwave or infra-red spectral region will observe (for ).

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

8. B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007 Weighting Functions can be written as: with the Weighting Functions K(z) defined as: I.e., the measured radiance is determined by the thermal emission from the different levels, weighted by the Weighting Function.

9. B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007 Temperature Retrieval If the absorption results from a uniformly mixed compound (such as CO 2 or O 2 ), the absorption coefficient can be assumed to be of the form: with the number density profile n(z) decreasing exponentially with height (scale height H, typically about 7km) Thus:

10. B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007 Weighting Functions for Temperature Retrieval If then the transmission will be given by And the Weighting Functions are given by

11. B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007 Mathematical Discussion of Weighting Functions The weighting functions have their maximum at z max when At the maximum the weighting function have the value:

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