Constraining Frequency Distributions with the Probable Maximum Precipitation for the Stochastic Generation of Realistic Extreme Events

Abstract

Stochastic weather generators are widely used to produce large ensembles of climate time series for assessing risk-based environmental impacts. However, they often perform poorly at generating extreme values since the fitting of traditionally used distribution functions is limited by short historical records. In such cases, extreme values are generated by extrapolating the fitted distributions far outside of observations, and can result in values outside of the physically possible range. This work uses a curve-fitting approach constrained on the probable maximum precipitation (PMP) to allow for the generation of realistic precipitation over the entire range of daily precipitation amounts. The method differs from the traditional parametric approach which assumes that the daily precipitation follows a specific probability distribution. Instead, the curve-fitting approach uses a second-degree polynomial to fit the Weibull experimental frequency distribution of observed daily precipitation. In this process, the PMP is specifically represented with its associated probability of occurrence, thus ensuring the realistic representation of extreme precipitation events. The proposed algorithm is compared to three distribution functions (of varied complexity) for simulating daily precipitation amounts at 35 stations dispersed across central and southern Quebec, Canada. The curve-fitting approach is presented in two versions: with and without constraint on the PMP. The results show that compound distribution functions perform better than their single distribution counterparts at representing the overall distribution of daily precipitation amounts, especially when simulating the upper tail. The unconstrained curve-fitting approach consistently performs better than all of the distribution functions with respect to preserving the statistical characteristics (e.g., mean, standard deviation and overall distribution) of daily precipitation amounts. Constraining the second-degree polynomial to the PMP is an effective way to generate the entire range of daily precipitation amounts with no risk of generating physically impossible values for events with extremely small probability. However, its overall performance is slightly less than that of its unconstrained counterpart.