Selecting the best distribution for modeling trends in low, medium, and extreme daily precipitation under climate change

Abstract. Changes in mean precipitation and the frequency and intensity of extreme precipitation represent one of the most consequential aspects of anthropogenic climate change. This study evaluates a set of statistical distributions for modeling trends across the full precipitation spectrum (low, medium, and extreme daily quantiles). Modeling with a single flexible distribution ensures statistical consistency, thereby avoiding the artificial separation and discontinuity inherent in multi-model approaches. We used time as a covariate for dry-day frequency and sea surface temperature for the wet-day distribution parameters. We applied the methodology to a dense network of over 900 meteorological stations in France, offering a wide variety of climatic regimes, allowing for a robust conclusion. We employed a multi-criterion approach to select the best model, in the first step using the Akaike Information Criterion, and then based on their ability to flexibly capture trends across low, medium, and extreme precipitation quantiles. Our findings highlight that three-parameter distributions (generalized gamma and extended generalized Pareto distribution), particularly with evolving shape parameters, are essential for accurately capturing observed differential changes across the full precipitation spectrum, a flexibility that the two-parameter gamma distribution notably lacked. Although AIC generally favored generalized gamma, both generalized gamma and the extended generalized Pareto distribution demonstrated robust performance. This research underscores the critical need for a multi-criterion model identification framework in nonstationary trend analysis to provide reliable insights essential for hydrological and climate impact assessments.