Physically-based passive microwave precipitation retrieval algorithms require a set of relationships between satellite observed brightness temperatures (TB) and the physical state of the underlying atmosphere and surface. These relationships are typically non-linear, such that inversions are ill-posed especially over variable land surfaces. In order to better understand these relationships, this work presents a theoretical analysis using brightness temperature weighting functions to quantify the percentage of the TB resulting from absorption/emission/reflection from the surface, absorption/emission/scattering by liquid and frozen hydrometeors in the cloud, the emission from atmospheric water vapor, and other contributors. The results are presented for frequencies from 10 to 874 GHz and for several individual precipitation profiles as well as for three cloud resolving model simulations of falling snow. As expected, low frequency channels (<89 GHz) respond to liquid hydrometeors and the surface, while the higher frequency channels become increasingly sensitive to ice hydrometeors and the water vapor sounding channels react to water vapor in the atmosphere. Low emissivity surfaces (water and snow-covered land) permit energy downwelling from clouds to be reflected at the surface thereby increasing the percentage of the TB resulting from the hydrometeors. The slant path at a 53deg viewing angle increases the hydrometeor contributions relative to nadir viewing channels and show sensitivity to surface polarization effects. The TB percentage information presented in this paper answers questions about the relative contributions to the brightness temperatures and provides a key piece of information required to develop and improve precipitation retrievals over land surfaces
