| 01 Jul 2026
Retrieval of the hail size number distribution from polarimetric radar data using the double-moment normalization
Abstract. Estimating the distribution of hail sizes is essential for assessing potential damage to infrastructure, vehicles, and agriculture. In this study, we introduce a novel technique for retrieving the hail size number distribution (HSND) from polarimetric C-band radar data. Our approach uses a generalized additive model (GAM) to estimate two empirical moments of the HSND, which is then reconstructed using the double-moment normalization technique, exploiting the relative invariance of the normalized HSND. The model is trained using data from the Swiss automatic hailsensor network (August 2018–September 2025) across three hail-prone regions. Hundreds of polarimetric features are extracted from a high-resolution 3D radar composite combining data from the five operational, dual-pol Swiss radars. Among these, the most predictive features selected by the model include the volume of the region where the cross-correlation coefficient ρHV falls below 0.97 and the horizontal reflectivity ZH is above 50 dBZ in a vertical column of 1 km radius, the maximum value of vertical reflectivity ZV in a column of 1 km radius, the integral of ZV in a column of 1 km radius. HSND estimates derived from radar show strong agreement with independent hailsensor measurements. Additional validation is performed using photogrammetric drone surveys and crowd-sourced hail reports. The radar-retrieved HSND closely matches the shape of drone-based HSND for the two events, while overestimating the number of hailstones per diameter bin due to melted hailstones prior to drone observations and to the nature of the training data used (a minimum number of 30 hailstones must have been measured by a sensor for a single event to be used). Radar-based percentile diameters of the retrieved HSND exhibit a slightly higher Pearson correlation and lower bias with crowd-sourced hail reports compared to the MESHS (Maximum Expected Severe Hail Size) product operated by MeteoSwiss. The main advantage of the presented technique is that it enables high-resolution (1 km, 5 min) retrievals of the full HSND and related features, such as kinetic energy, potentially providing valuable insights for real-time hail monitoring, nowcasting and long-term statistical assessments of hail features across Switzerland. The proposed model could be easily adapted to other countries, though the invariance of the normalized HSND outside Switzerland should be verified. Because hail is rare, further ground hail observations remain crucial for refining the HSND retrievals, ensuring a more comprehensive evaluation of the proposed approach, and properly assessing the associated uncertainty.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Atmospheric Measurement Techniques.
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