Scale dependence of precipitation structure using Tweedie Poisson–Gamma scaling: an Estonian case study from radar composites and gauges

Abstract. We characterize precipitation structure over Estonia and the surrounding region using Tweedie Poisson–Gamma scaling, with Tweedie power as a descriptor of aggregation-dependent mean–variance behaviour in zero-inflated, heavily-positive-skewed precipitation. The study extends existing Tweedie precipitation analysis to the joint examination of temporal aggregation, seasonality, spatial variability, and observing-system differences. The analysis uses a 1 km, 5 min radar composite derived from the two Estonian C-band radars together with an OTT Pluvio² L gauge network over September 2020 to August 2024. For accumulation lengths from sub-hour to daily windows, is estimated from block-wise mean and variance statistics using ordinary least squares, with availability filtering to handle missing radar timestamps and matched window sampling for radar–gauge comparison.

Across all data sources, p increases with accumulation length, showing that temporal aggregation changes precipitation mean–variance scaling. Seasonal separation is also clear, with generally highest in summer and lowest in winter, and winter showing the strongest increase with accumulation. Spatially, the all-year radar fields show strong scale dependence but only weak geographical contrasts at fixed accumulation length, whereas seasonal maps show clearer heterogeneity at longer windows. Radar-based at station locations is generally higher than gauge-based estimates, and the magnitude and spread of the differences depend on accumulation length and gauge temporal resolution. These results show that should not be used as a fixed precipitation parameter transferable across durations, seasons, space, or products. Instead, it provides a scale-aware benchmark for evaluating precipitation consistency in generated, corrected, or forecast products, such as quantitative precipitation estimation, downscaling, and nowcasting.