A moment-based polarimetric radar forward operator for rain microphysics

There is growing interest in combining microphysical models and polarimetric radar observations to improve our understanding of storms and precipitation. Mapping model-predicted variables into the radar observational space necessitates a forward operator, which requires assumptions that introduce uncertainties into model-observation comparisons. These include uncertainties arising from the microphysics scheme a priori assumptions of a fixed drop size distribution (DSD) functional form, whereas natural DSDs display far greater variability. To address this concern, this study presents a moment-based polarimetric radar forward operator with no fundamental restrictions on the DSD form by linking radar observables to integrated DSD moments. The forward operator is built upon a dataset of >200 million realistic DSDs from one-dimensional bin microphysical rain-shaft simulations, and surface disdrometer measurements from around the world. This allows for a robust statistical assessment of forward operator uncertainty and quantification of the relationship between polarimetric radar observables and DSD moments. Comparison of ''truth'' and forward-simulated vertical profiles of the polarimetric radar variables are shown for bin simulations using a variety of moment combinations. Higher-order moments (especially those optimized for use with the polarimetric radar variables: the sixth and ninth) perform better than the lower-order moments (zeroth and third) typically predicted by many bulk microphysics schemes.