Spectral radiance-temperature conversions for measurements by AVHRR thermal channels 3,4,5
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Spectral radiance-temperature conversions for measurements by AVHRR thermal channels 3,4,5

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    This report reviews the relationship between spectral radiance and brightness temperature for the Advanced Very High Resolution Radiometer (AVHRR) Chs. 3, 4, 5 of the NOAA-7, -9, -10, -11, -12 satellites. The impact on the Ch.3 radiance of the solar spectral irradiance and reflectance is examined as well. All information necessary for easy generation of detailed spectral radiance tables for brightness temperatures to any desired thermal resolution is provided for each of the thermal channels on the five satellites. By generating appropriate spectral radiances for each 0.1 degree, temperature (in tenths of degree) becomes an index for extremely rapid computer conversions (table look-up) of spectral radiances. Use of the same table for converting radiances (based on measured counts) to brightness temperatures requires a table search for each radiance. Abbreviated tables, equally spaced in temperature, of spectral radiances and brightness temperatures are presented for each of the thermal channels, along with the unique effective wavenumber that links each pair of variables through the Planck function. Precise calculations for any radiance/temperature can be made from the Planck function by using the appropriate effective wavenumber as a function of the brightness temperature (for calculating spectral radiance given the brightness temperature) and as a linear function of the logarithm of the spectral radiance (for calculating brightness temperature given the measured radiance). However, more efficient precise calculations are achieved by replacing the variable effective wavenumber with a fixed centroid wavenumber for each channel, along with the associated effective temperatures for the brightness temperatures. Thus, the Planck function (or its inverse), together with three tabulated constants for each channel (the fixed centroid wavenumber and the slope and intercept of the linear relation between effective temperature and brightness temperature) is recommended for all precise spectral radiance or brightness temperature calculations. Filtered Ch.3 solar spectral irradiances for each satellite have been specified to enable the determination of top-of-the- atmosphere scene reflectance for Ch.3, once the thermal emission for daytime Ch.3 is removed from the measured spectral radiance. Thermal limitations of Chs.3,4,5 measurements are discussed.
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