04-Planck

# 04-Planck - ESM 266: Remote Sensing of Environment Jeff...

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ESM 266: Remote Sensing of Environment Lab 4, Infrared remote sensing Jeff Dozier & Karl Rittger April 21, 2008 Due April 29, 2008 Objectives To gain proficiency with concepts of electromagnetic radiation. To understand relationship between brightness temperature and kinetic temperature. Background Surfaces are generally not blackbodies, but have wavelength-dependent reflectivities and emissivities, whereby, by Kirchhof’s Law, r λ λ =1. Generally in the infrared wavelengths ε is almost 1.0, but not quite and not for some constituents. In the microwave wave- lengths, which we will study later, emissivity can be substantially lower. A modified form of Planck equation calculates spectral emitted radiance from a surface at kinetic temperature T (absolute): 2 5 2 ( ) ( ) , where ( 1)     x hc hc Lx e k T Planck’s constant 34 6.62606896 10 Js. h  Speed of light 299,792,458 m/s. c Boltzmann’s constant 23 1.3806504 10 J/deg. k To make the exponent x dimensionless, wavelength must be in meters. T is in degrees Kelvin. The brightness temperature T B is then defined as the equivalent blackbody temperature, i.e. a substance with ε =1 that would emit the same amount of radiation:   2 5 2 ( ) , where ( B B x B hc hc e k T   2 5 so 2 ln 1 B hc T hc k L    22 55 Moreover ( ) ( ( B x x hc hc ee   T B

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## This note was uploaded on 08/06/2008 for the course ESM 266 taught by Professor Dozier during the Spring '08 term at UCSB.

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04-Planck - ESM 266: Remote Sensing of Environment Jeff...

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