Analysis of the mean raindrop shape model for dual polarization radar rainfall estimation

Information about the shape of raindrops is critical for estimating rainfall rate with dual polarization radar. 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 nonlinear fourth-order polynomials. In fact, there is still no consensus regarding the most appropriate equation to use to describe the shape-size relation. Moreover, while non-linear equations are important for studying raindrop shape, it is not clear that they are needed to estimate an integral quantity such as rainfall rate. 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 is examined. Proposed rain algorithms based on the estimation of the drop shape are compared with algorithms that assume specific a-priori fixed drop shape-size relations expressed by a fourth order polynomial. Reconstructed rain and radar measurement profiles obtained from real radar observations were used to this purpose. Results show that 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.