Radar-derived variability of ice water content (IWC), total number concentration (Nt), and mean volume diameter (Dm) for improved parameterizations

Radar polarimetry and recently developed microphysical retrievals offer great potential for evaluating and improving the parameterizations of numerical models. In this study, we intend to inform the subgrid parameterizations of the ICON general circulation model (ICON-GCM), in particular to assess and improve the spatial heterogeneity of ice water content at ICON subgrid scales. Quasi-vertical profiles (QVPs) generated by azimuthal averaging of various polarimetric radar variables from Plan Position Indicators (PPIs) acquired during standard conical scans at antenna elevation angles of 18° successfully reduce statistical errors, especially for phase-based measurements such as specific differential phase (KDP). This methodology provides the ideal data basis for various robust polarimetric microphysical retrievals of IWC, Nt, and Dm. However, the use of QVPs reduces the information on sub-grid scale variability compared to higher-resolution PPIs. Thus, an important question is how much averaging is required for robust estimates of IWC, Nt, and Dm and how we can separate spatial variability from noise. Spatial variabilities or azimuthal standard deviations and statistical errors of different retrievals are analyzed using measurements of the polarimetric X-band radar in Bonn, Germany (BoXPol). Statistical errors are quantified by the standard error of the mean (σ_mean), calculated via Gaussian error propagation using Bienaymé's law. σ_mean is used to investigate the extent to which the azimuthal window size of 360° in the QVP methodology can be reduced while still ensuring acceptable statistical errors of IWC, Dm, and Nt. Range-defined QVPs (RD-QVPs), a variant making use of different antenna elevation angles, can further reduce the statistical errors due to the larger sample size. Shannon's information entropy is exploited within a new method to test the distributions of polarimetric variables and retrievals for homogeneity within PPIs. This is key for the use of σ_mean to ensure that samples are drawn from the same distribution. Statistics of a large BoXPol data set are presented and compared to simulations of ICON-GCM. Finally, an attempt is made to improve the specific threshold used in ICON-GCM for the onset of aggregation (particle diameters > 0.1 mm are defined as snow) by estimating the particle size distributions (PSDs) assuming an exponential function.