Double moment normalization of hail size distributions and retrieval of its moments from polarimetric radar measurements

The development of algorithms for estimating hail size distributions (HSD) from radar data can be limited by the availability of direct hail size measurements at the ground. The deployment of a network of 80 automatic hail sensors over Switzerland made possible the investigation of the link between polarimetric radar variables and the HSD. After selecting a set of 118 significant hail events, the technique of double moment normalization has been used to reconstruct the HSD from two known moments. By assuming that the normalized distribution over the region of interest (Switzerland) is approximately invariant, a single fit can be performed for all the events. A generalized gamma distribution has been chosen for this double-moment normalized HSD, and all combinations of two moments between the first and the seventh one have been tested. Using the resulting estimate of the normalized distribution it is possible to reconstruct the HSD and compare it to the one measured by the hail sensors. The metrics chosen for this comparison are root mean square error, bias, relative bias, and Pearson correlation coefficient. Only two moments of the HSD are needed for this reconstruction, making these moments the ideal candidates for the retrieval from polarimetric radar measurements (as has been proposed for the raindrop size distribution). A series of 3-dimensional cone-shaped regions above the locations of the hail sensors has been extracted from the scans of the MeteoSwiss operational radars in Switzerland.
The network includes five C-band Dual-polarization weather radars, which perform Plan Position Indicator (PPI) scans at 20 elevations every five minutes. The relationship between the moments of the HSD recorded at the ground and the polarimetric radar variables within the cones are under investigation: preliminary results will be presented and discussed at the conference.