The Response of the SSM/I to the Marine Environment. Part I: An Analytic Model for the Atmospheric Component of Observed Brightness Temperatures

A comprehensive closed-form parameterization has been developed for the contribution of the nonprecipitating marine atmosphere to microwave brightness temperatures observed by the Special Sensor Microwave/Imager (SSM/I). The variables considered in this model include viewing angle, integrated water vapor amount and scale height, effective tropospheric lapse rate and new-surface temperature, total cloud liquid water, effective cloud height, and surface pressure. First an approximate closed-form formula is derived for the efficient calculation of upwelling brightness temperature at the top of the atmosphere and the downwelling brightness temperature at the surface. The independent variables include the viewing angle, separate optical depths and absorption scale heights for dry air and water vapor, effective surface temperature lapse rate, cloud height, and cloud optical depth. This parameterization is valid for all microwave frequencies for which the total optical depth of the atmosphere, excluding cloud liquid water, is less than unity. Second, the dependence of the radiative variables listed above on meteorological variables is determined for each of the SSM/I frequencies 19.35, 22.235, 37.0, and 85.5 GHz, based on the values computed from 16 893 maritime temperature and humidity profiles representing all latitude belts and all seasons. Comparisons of the brightness temperatures predicted by the complete brightness-temperature model with brightness temperatures obtained by direct numerical integration of the radiative transfer equation for the radiosonde-profile dataset yield rms differences well below 1 K for all four SSM/I frequencies. Finally, the global radiosonde dataset is used to compute expectation values and standard deviations of selected atmospheric variables on which the brightness-temperature model depends. These statistics are intended for use in constrained nonlinear retrieval algorithms and similar applications.