Statistical estimation of probable maximum precipitation

Abstract. Civil engineers design infrastructure exposed to hydrometeorological hazards, such as hydroelectric dams, using probable maximum precipitation (PMP) estimates. Current PMP estimation methods have several flaws: some required variables are not directly observable and rely on a series of approximations; uncertainty is not always accounted for and can be complex to quantify; climate change, which exacerbates extreme precipitation events, is difficult to incorporate; and subjective choices increase estimation variability. In this paper, we derive a statistical model from the World Meteorological Organization's PMP definition and use it for estimation. This novel approach leverages the Pearson Type-I distribution, a generalization of the Beta distribution over an arbitrary interval, allowing for uncertainty quantification and the incorporation of climate change effects. Multiple estimation procedures are considered, including the method of moments, maximum likelihood, and Bayesian estimation. However, statistical PMP estimation remains challenging because a short-tailed model is applied to typically heavy-tailed precipitation data. The performance of the proposed approach is assessed through a simulation study and applied to actual precipitation data from two nearby stations in Canada. Finally, we provide and discuss recommendations for best practices in PMP estimation.