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Abstract

Extreme rainfalls of short time scales (from a few minutes to one hour) are often required for the design of urban infrastructures. However, these data are often limited or unavailable at the location of interest while those for the daily scale are widely available. Hence, it is important to develop a modeling method that could describe accurately the statistical properties of the extreme rainfall processes over a wide range of time scales so that short-duration rainfalls can be estimated from those of longer durations. Scale-invariance (or scaling) models such as the scaling Gumbel (GUM) and Generalized Extreme Value (GEV) models have been proposed for addressing this issue. These models have been developed based on the scaling properties of the computed ordinary moments or non-central moments (NCMs) of the observed extreme rainfalls. However, the probability weighted moments (PWMs) have been known to provide more robust estimates of extreme variables for small sample sizes. Therefore, this study introduces a novel PWM-based scaling GEV distribution model (GEV/PWM). The general mathematical framework and the scaling properties of the proposed model were described using both NCMs and PWMs. The feasibility and accuracy of the proposed GEV/PWM mode were assessed using the long records of short-duration extreme rainfall data from a network of 74 raingauges located across Canada. Results of this numerical application have indicated that the extreme rainfall estimates given by the GEV/PWM model are the most accurate as compared to those given by other existing scaling models such as GEV/NCM, GUM/NCM, and GUM/PWM.