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In this paper we suggest that brightness temperature from the band radiance measured by a thermal sensor using Planck's law can be obtained along with effective parameters adequate for a given band, and a given temperature range. We propose an accurate algorithm to obtain these parameters (effective wavenumber or effective wavelength), which is based on Taylor's expansion of the exponential function that appears in Planck's equation. The dependence of the effective wavenumber on temperature has been investigated and the advantages of working with large temperature ranges have been analysed. We have compared the effective wavenumbers obtained with this algorithm to the parameters provided by NOAA/NESDIS and the maximum difference obtained has been 0.5 cm-1. The method has been applied to Landsat-Thematic Mapper band-6 and the results indicate that the error in temperature determination of the method is less than 0.01 K. A comparison with other published algorithms is also included.
Sospedra et al. (1998) studied this question.