An Examination of the Validity of the Mean Raindrop-Shape Model for Dual-Polarization Radar Rainfall Retrievals

Information about the shape of raindrops is critical for the retrieval of rainfall rate from dual-polarization radar measurements. As described in the literature, the relation describing drop oblateness as a function of its equivolumetric diameter is nonlinear. There are several relations that express the shape-size dependence as a nonlinear fourth-order polynomial that has five coefficients or 5 DOF. While these are important for studying raindrop shape, it is not clear that they are needed to estimate an integral quantity such as rainfall rate. This paper examines the validity of using a simple equivalent linear shape-size model based on the principle of the mean-value theorem for estimating rain from dual-polarization radar measurements. Assuming Rayleigh-Gans scattering for spheroids to describe raindrop scattering and drop oblateness described by a linear relation between axis ratio and equivolumetric diameter, a general self-consistency equation relating reflectivity factor, differential reflectivity, specific differential phase shift, and slope of the shape-size relation is obtained for each radar operating frequency. In this 4-D space, relations for estimating rainfall rate without requiring an assumption of a specific drop-shape model from polarimetric radar measurements were obtained. To study all the implications arising from electromagnetic and microphysical aspects, reconstructed rain and radar measurement profiles obtained from real radar observations were used to test the performance of the proposed rain estimation procedure. The performance is compared with algorithms derived assuming specific a priori fixed drop-shape-size relations expressed by a fourth-order polynomial. Results show that, in general, the proposed rain algorithms perform better or at least equal to the algorithms derived assuming a priori fixed shape-size models, demonstrating that the prevailing model directly derived from data is suitable for rainfall retrieval purposes.