Analytically derived conversion of spectral band radiance to brightness temperature

Simple analytic expressions for brightness temperature have been derived in terms of band response function spectral moments. Accuracy measures are also derived. Application of these formulas to GOES-12 Sounder thermal infrared bands produces brightness temperature residuals between −5.0 and 2.5 mK for a 150-400 K temperature range. The magnitude of residuals for the five ASTER Radiometer thermal infrared bands over the same temperature range is less than 0.22 mK.