A radiative-transport model has been developed to study the emitted radiation from variable cloud and rain systems at the frequencies of the special sensor microwave imager (SSM/I). The model is based on the matrix operator method and takes into account multiple scattering as well as polarization. The simulations are based on a multivariate approach using globally distributed atmospheric profiles of pressure, temperature, humidity, and different cloud types in multiple layers. The inhomogeneous vertical distributions of water and ice in clouds and rain are modeled by bulk analytical formulae. Fractional coverages of cloud and rain clusters are incorporated into the analysis to account for the low spatial resolution of microwave radiometers, which decreases the correlations between the brightness temperatures and the microphysical parameters. Retrieval algorithms are developed for the water vapor, total water, and ice paths as well as for surface rain rates. By the exclusion of strong convective conditions, the retrieval of ice paths is found to be problematic owing to the strong gradient of scattering efficiency with sizes.

The water vapor paths are also derived for cloudy and raining conditions with limited spatial coverages. The theoretical standard errors of the retrievals lie in the range of 0.1--0.2 g/cm2 for vapor paths of 0--7 g/cm2, 0.02--0.03 g/cm2 for total water paths of 0--1.2 g/cm2, 0.015 g/cm2 for ice paths of 0--0.25 g/cm2, and 1.3 mm/h for rain rates of 0--30 mm/h. The algorithms are applied to global sets of SSM/1 data for August 1987. The resulting fields of monthly rain amounts are compared to those of satellite infrared measurements, a surface climatology, and a general circulation model (GCM) experiment. The results are found to be mainly consistent with the climatology, whereas the IR data and the GCM experiment produce questionable inconsistencies. The water vapor path estimations are compared to colocated radiosonde measurements showing deviations below 0.78 g/cm2 including cloudy and rainy situations, whereas our total water path estimations show the best results for inhomogeneous scenes compared to those calculated by algorithms taken from the literature. ¿ American Geophysical Union 1993