Probability-distribution uncertainty in seasonal SPI and SSI forecasting for the Netherlands

Abstract. Probability distributions used to standardize hydroclimatic variables can influence estimated drought magnitude and classification, but their effect on seasonal forecast skill remains poorly understood. We examine how distribution choice propagates through Standardized Precipitation Index (SPI) and Standardized Streamflow Index (SSI) monitoring and forecasting systems for the Netherlands. Five candidate distributions were fitted by maximum likelihood for each grid cell, calendar month, and accumulation period. Selection robustness was assessed using 500 bootstrap samples and Akaike Information Criterion test. Parameters derived from ERA5-Land precipitation and EFAS v5.0 discharge reanalysis were subsequently applied, without refitting, to SEAS5 precipitation and EFAS seasonal discharge hindcasts. Forecast performance using the selected distributions was evaluated with the Continuous Ranked Probability Score, root mean squared error, and bias, and compared with an otherwise identical Gamma-based workflow. Distribution suitability varied strongly with variable and accumulation period. Weibull was most frequently selected for SPI-1, while Pearson Type III dominated SPI-3, SPI-6, and SPI-12. SSI selection was more heterogeneous and generally less stable, although Weibull occurred most frequently for SSI-1 and SSI-3. Forecast skill declined with lead time and was generally higher for longer accumulation periods. Selected and Gamma distributions produced similar aggregate forecast performance beyond the shortest leads, despite differences in individual standardized values. These differences were generally small for SPI but larger and strongly seasonal for SSI-1, with maximum historical differences reaching 1.69 SSI units. Nevertheless, drought-class and threshold disagreements remained uncommon. The findings demonstrate that greatest relevance of historical distribution fit is at short accumulation periods, in low-confidence locations and seasons, and when index magnitude near a decision threshold matters. However, distribution fit does not automatically translate into improved long aggregate seasonal forecast skill. For Dutch drought management, Gamma can therefore remain a consistent national reference, while distribution-selection confidence and local sensitivity should be reported where index values approach warning thresholds.