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

Remote Sensing I

Summer 2007

Björn-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

Outline

1. Introduction

2. Electromagnetic Radiation

3. Radiative Transfer Through the Atmosphere

4. Weighting Functions and Retrieval Techniques

5. A Short Review of Spectroscopy

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

Observed Radiance for an Infra-Red Nadir Sounder

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

Example: TOVS: HIRS2 and MSU

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

Radiative Transfer Without Scattering

LI

LIdz

dI

Remember RTE without scattering:

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

z

z

zdzzzT exp,

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

RTE for Satellite Nadir Sounder

z

zdz

zzTzTLzTIzI

0

,,00

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 ).z

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

Side Remark: Case with no atmosphere

surfaceTL

If atmospheric absorption (and thus emission) can be neglected,the observed radiance is given by the emission from the surface:

0

01

,,00 zd

z

zTzTLTII

For known emissivity ε this can be inverted to get thesurface temperature Tsurf.

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

Weighting Functions

0

,00 dzzKzLTII

can be written as:

z

zTzK

,

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.

z

zdz

zzTzTLzTIzI

0

,,00

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

Temperature Retrieval

znz

If the absorption results from a uniformly mixed compound(such as CO2 or O2), the absorption coefficient can be assumedto be of the form:

H

znzn exp0

H

zz exp0

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

HzzT exp,

If

H

zz exp0

then the transmission will be given by

And the Weighting Functions are given by

Hzzz

zTzK

exp,

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

Mathematical Discussion of Weighting Functions

HzzzK exp

The weighting functions

have their maximum at zmax when

HHzHz v 0ln1 maxmax

km/05.01

max eH

zK

At the maximum the weighting function have the value:

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

Idealized Weighting Functions

Scale height H = 7km