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# Lesson14 Band Model.pdf

Lesson14 Band Model.pdf

## Statistical

Statistical Band Model (Goody)• Goody studied the water-vapor bands and noted theapparent random line positions and band strengths.• Let us assume that the interval contains n linesof mean separation d, i.e. =nd• Let the probability that line i has a line strength S ibe P(S i ) where0P(S)dS1• P is normally assumed to have a Poisson• P is normally assumed to have a Poissondistributioni

Statistical Band Model (Goody)• For any line the most probable value of S isgiven bySP( S)dSS0 0 )0P( S dS• The transmission T over an interval is givenbyTi01 d P(Si)ekiudSi

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