A Diagnostic Framework for Understanding Climatology of Tails of Hourly Precipitation Extremes in the United States

Abstract Hourly precipitation extremes are crucial in hydrological design. Their frequency and magnitude is encapsulated in the probability distribution tail. Traditional extreme‐analysis methods rely on theorems, like the Pickands‐Balkema‐de Haan, indicating specific type of tails assuming asymptotic convergence—a questionable assumption for real‐world samples. Moreover, popular stochastic models for hourly precipitation presume light‐tailed distributions to facilitate their mathematical formulation. In practice, limited information on hourly precipitation extremes makes identifying and quantifying their tail highly uncertain, especially on a station‐by‐station basis. Yet no comprehensive regional analysis of tails has been undertaken to quantify a climatology of tails for diagnostic and prognostic purposes. Here we undertake such an analysis for the conterminous United States. We introduce a novel Bayesian‐adjustment approach to assess the best model between power‐type and stretched‐exponential tails showing that the latter performs better. We present climatology of the tail and quantify its heaviness in over 4,000 hourly precipitation records across the United States and present three main conclusions. First, we show that hourly precipitation tails are heavier than those commonly used with important implications including underestimation of extremes. Second, we provide spatial maps of the tail behavior which reveal some strikingly coherent spatial patterns that can be used for inference in the absence of local observations. Third, we find a nonlinear increase in the tail heaviness with elevation and we formulate parametric functions to describe this law . These results can improve the accuracy of frequency analysis, probabilistic prediction, rainfall‐runoff modeling, and downscaling of historical observations and climate model projections.