The equations of the radar covariances and cross covariances for linear vertical and horizontal polarization, slant linear +45¿ and -45¿ polarization, and left-hand and right-hand circular polarization are presented for a model medium containing spheroidal particles. This model takes into account the distribution of canting angles but assumes the uniformity of the distribution function along the propagation path. Assuming the particles to be locally equioriented, equations for the intrinsic differential reflectivity and the mean canting angle are derived. Furthermore, for particles having the same orientations throughout the region of precipitation, the total differential phase shift is obtained. Reflectivity and depolarization ratios are also considered. A comparison of the three polarization schemes from a theoretical point of view is made and illustrated with data from the DLR C band Doppler and polarimetric weather radar. Since the DLR radar did not record the magnitude of the covariances and cross covariances, the comparison is only partially complete. The data confirm the theoretical prediction that depolarization is stronger in circular and slant linear polarization than in linear horizontal/vertical polarization. ¿ 1998 American Geophysical Union