Retrieving the hail size distribution from C-band radar Doppler spectra

Hailstorms can cause significant damage to personal property and public infrastructure. Yet, the distribution of hailstone sizes and shapes at the ground and aloft is not well understood and quantified. Some in situ sensors, for example, can record the impact energy of falling hailstones, which can then be used to estimate the hail size distribution based on the sampled hailstones. But these sensors only record a small number of hailstones during short hail showers and thus fail to reliably capture large hailstones that occur infrequently and can still cause substantial damage in their impact zones. Polarimetric radars, on the other hand, scan a large atmospheric volume, but only allow for deriving a characteristic hail size, such as the maximum estimated hail size, thereby ignoring other important hailstorm attributes such as the overall shape of the hail size distribution.
This presentation introduces a method for retrieving the full hail size distribution from C-band radar Doppler spectra, collected with the research radar of the German Meteorological Service (DWD, Deutscher Wetterdienst) in pre-alpine southern Germany. The retrieval method builds on the spectral processing techniques developed for the operational vertically-pointing birdbath scan of DWD's dual-polarization C-band Doppler radar network. Here, hail Doppler spectra are isolated in the birdbath scan output beyond the radar near-field at a Doppler velocity resolution of about 2.6 cm/s and a vertical resolution of 25 m. Exploiting previously published hail size-to-fall-velocity relationships, the Doppler velocities can be converted into hailstone diameters; and the obtained Doppler power spectra can be translated into hail size (frequency) distributions, after quantifying the radar backscatter cross-section for each hail size, i.e., each velocity bin, based on T-matrix calculations for mixtures of (dry) hard and soft ice spheroids with realistic hail aspect ratios and densities. Crucial steps in the retrieval algorithm are (i) how the Doppler velocities can be corrected for vertical air motion, (ii) which hail size-to-fall-velocity relationship is selected, and (iii) what assumptions are made about ice spheroid mass and shape.
A comparison of our radar retrievals for a hailstorm from spring 2021 with the hail size spectrum derived from a co-located, automatic in situ hail impact sensor yields insights into the shape of the hail size distribution and the maximum hail size. The hail size distribution estimated from the C-band radar Doppler spectra shows a relatively constant plateau for small hail before declining sharply at intermediate hail sizes. This general shape of the hail size distribution is also observed in the population of about 200 hailstones sampled by the in situ sensor during the 5-min hail shower. In contrast to the agreement on the general shape of the hail size distribution, the maximum hail size estimated from the Doppler spectra agrees better with manual measurements of the maximum hailstone dimension at the ground of 2 to 2.5 cm than the maximum hailstone diameter of less than 1.5 cm registered by the in situ sensor.