General moment-based methods for DSD normalization and a polarimetric radar forward operator

Description

Knowledge of drop size distributions (DSDs) is critical for parameterizing microphysical process rates in bulk schemes, interpreting remote sensing observations, and ultimately understanding precipitation’s role in the climate system. Natural DSDs exhibit large variability that depends on environmental and forcing factors. However, most microphysical models assume a fixed DSD functional form a priori, limiting the ability of models to capture natural variability and leading to large uncertainties in the simulation of microphysical processes and cloud system behavior. We have developed a bulk microphysics scheme that does not make a priori assumptions on the DSD; additionally, we have developed a DSD normalization that is generalizable to any number and/or choice of prognostic DSD moments, as well as a polarimetric radar forward operator that directly relates these prognostic DSD moments to the radar variables ZH, ZDR, and KDP. Here we develop a general method for characterizing DSDs using any number and combination of reference DSD moments without assuming any particular DSD functional form, extending previous normalization approaches. This method allows for any unknown DSD moment to be derived from any set of known reference moments, as well as an estimate of the uncertainty in the derived moment. We test the method using a big data approach: we use nearly 200 million DSDs from bin model simulations and DOE ARM disdrometer observations covering a large parameter space. We show that three reference moments can in general well characterize DSDs, and quantify the value of including various observed references moments for deriving unknown moments. This work is relevant to remote sensing retrievals and bulk microphysics schemes that do not impose a functional form for the DSD, such as our new parameterization approach (BOSS). In contrast, traditional bulk microphysics schemes that impose a fixed DSD functional form and that predict a finite number of DSD moments cannot capture inherent natural DSD variability, leading to a form of structural uncertainty in forward-simulated radar variables. Our new polarimetric radar forward operator addresses this uncertainty using our large DSD dataset, allowing for a novel and robust statistical assessment of forward operator uncertainty. Comparison of "truth" and forward-simulated vertical profiles of the polarimetric radar variables are shown for bin simulations, including an assessment of error statistics.