Statistical estimation of probable maximum precipitation

Abstract. Civil engineers design infrastructures exposed to hydrometeorological hazards, such as hydroelectric dams, using the estimation of probable maximum precipitation (PMP). The World Meteorological Organization (WMO) defines PMP as the maximum amount of water that can physically accumulate over a given time period and region, depending on the season and without considering long-term climate trends. Current methods for calculating PMP have many flaws: some variables used are not directly observable and require a series of approximations to be used; uncertainty is not always taken into account and can sometimes be complex to determine; climate change, which exacerbates extreme precipitation events, is difficult to incorporate into the calculations and subjective choices increases estimation variability. The goal of this work is to propose a statistical and objective method for estimating PMP that meets the WMO definition and allows for uncertainty estimation and climate change incorporation. This novel approach leverages the Pearson Type I distribution, a generalization of the Beta distribution over an arbitrary interval. The proposed method is applied to estimate the PMP at two meteorological stations in Québec, Canada.