Uncertainty analysis for design rainfall estimation using peaks-over-threshold model and specially formulated pivotal quantities

Abstract

Uncertainties associated with the estimated design rainfall depths are difficult to quantify, especially if the uncertainties of the threshold used in the traditional peaks-over-threshold model need to be quantified and included. In this paper, we propose a data-based framework to quantify all the sources of uncertainties associated with the estimation of design rainfall. Three pivotal quantities are formulated to assess the uncertainties of parameters used in generalized Pareto distributions. The frequency distributions of thresholds are determined based on goodness-of-fit tests. The proposed framework is applied at 42 precipitation stations in the Yangtze River Delta region of China. Interval estimates of distribution parameters and design rainfall depths are obtained at these stations. The results show that the spatial distributions of the parameter uncertainties are complex. At some areas, the design rainfall depths and their uncertainties are both high, leading to poor reliability of estimated design rainfall depths. Compared with the conventional bootstrap and Bayesian methods, the pivotal quantity method can provide more reliable results on the estimations of the joint distributions of parameters. The proposed framework is demonstrated to be useful and effective for all the 42 stations and is recommended for use in other areas.