Bulk-Density Representations of Branched Planar Ice Crystals: Errors in the Polarimetric Radar Variables

The increased availability of polarimetric weather radar observations at wavelengths of X, C, and especially S band has prompted interest in interpreting these observations in ice precipitation. The potential for evaluating recently-developed microphysical models that evolve ice particle aspect ratios and densities continuously has also increased efforts toward developing forward models to map the model output to the polarimetric radar variables. Because of their relative simplicity and computational efficiency, analytical calculations for homogeneous spheroids are often used to calculate the polarimetric radar variables at long wavelengths. As such, branched planar crystals with complex internal structures are modeled as homogeneous particles with an effective density reduced from that of pure ice. We show that this assumption leads to significant errors in the backscatter cross sections at horizontal and vertical polarizations, as well as the differential reflectivity at frequencies of X band and lower. These errors are shown to occur because homogeneous particles underestimate the interactions between the small ice regions in branched planar ice crystals that scatter as electric dipoles. In an effort to maintain relatively simple forward models for the polarimetric radar variables associated with ice, we introduce empirical relations to map natural and model-simulated branched planar crystals to solid ice spheroids with similar scattering properties. Uncertainty estimates in the simulated polarimetric radar variables using this method are also given.