MODEL APPROXIMATION OF ANGULAR-DEPENDENCE IN AVHRR BRIGHTNESS TEMPERATURES OVER A BLACK SURFACE

Brightness temperatures t(i)(m) in spectral channels i = 3 (3.7 mu m), 4 (10.8 mu m), and 5 (12 mu m) of the Advanced Very High Resolution R adiometer (AVHRR) and the Along Track Scanning Radiometer (ATSR) were calculated for a variety of viewing directions 1 less than or equal to m less than or equal to 3 (m = sec theta; theta is the satellite zeni th angle), and for a representative set of surface-atmosphere conditio ns (-2 less than or equal to t(s) less than or equal to 35 degrees C, 0.2 less than or equal to W less than or equal to 5.4 g cm(-2); where t(s) and W are the surface temperature and the column water vapour con tent). The assumption that the surface is a blackbody is used in order to analyse the atmospheric effect in detail, and to provide a backgro und for further incorporation of the surface emissivity. t(i)(m) are a pproximated with a polynomial t(i)(m) = a(0)(i) + a(1)(i)m + ... + a(j )(i)m(i)(j = 1, 2, and 3, for linear, quadratic, and cubic fits, respe ctively). Linear fit provides standard errors of sigma less than or eq ual to 0.07 and sigma less than or equal to 0.4-0.5 degrees C at 3.7 a nd 10.8-12 mu m, respectively. Using a quadratic fit reduces these err ors to sigma less than or equal to 0.01 and sigma less than or equal t o 0.04-0.06 degrees C. The information content of the fit parameters i s analysed in this Letter. The value of a(0) is within a few degrees o f t(s). The values of sigma, (a(0)-t(s)), a(j) strongly correlate with the factor W Delta t = W(t(s) - (t) over bar(a)), where (t) over bar( a) is the effective temperature of the atmosphere. These results are u seful for better understanding recent empirical studies of the angular effect in AVHRR brightness temperatures, and for developing algorithm s for t(s) and W retrieval using spectral methods for the cross-scanni ng AVHRR, and angular methods for the ATSR.