Measurements of upwelling and downwelling rain brightness temperatures show significant differences between horizontal and vertical polarization, which depend on wavelength and rain rate. These measurements are related to the first and second Stokes parameter. Also, the third Stokes parameter of atmospheric microwave emission will have measurable values under certain conditions. A polarimetric model for the description of the microwave emission and scattering by hydrometeors, including all four Stokes parameters, is presented. This model is applied to the scenario of plane layers of ice crystals and rain above a rough surface. The magnitudes of the third Stokes parameter for microwave emission from oriented nonspherical rain drops and for scattering by ice crystals are estimated. It is shown that the third Stokes parameter for rain is dominated by the first azimuthal harmonic of the emission vector. Finally, an algorithm for the computation of polarized brightness temperatures emanating from cylindrical rain cells above a surface is developed. ¿ 1998 American Geophysical Union