Estimation of the Peak over Threshold-Based Design Rainfall and Its Spatial Variability in the Upper Vistula River Basin, Poland

Abstract

The proper assessment of design rainfalls with long return periods is very important because they are inputs for many flood studies. In this paper, estimations are performed on daily design rainfall totals from 16 meteorological stations located in the area of the Upper Vistula River Basin (UVB), Poland. The study material consists of a historical series of daily rainfall totals from the period of 1960–2021. The peak over threshold (POT) method is used, and the rainfall depth over threshold is assumed to follow the generalized Pareto distribution (GPD) with parameters estimated from Hill statistics. Alternatively, the competitive method based on annual maxima (AM) is applied. The theoretical distribution of AM is assumed to follow a theoretical distribution function selected by using the Akaike information criterion (AIC) from a family of seven candidate distributions, the parameters of which are estimated by using the maximum likelihood method. The two methods are compared by using the root mean square error (RMSE) and the mean deviation error (MDE) criteria. It is found that the POT-based method with GPD and Hill estimators outperform the AM-based method when considering the highest rainfall events. The confidence intervals of the design rainfalls, derived by using the Monte Carlo simulation method, reflects their large spatial diversity across the UVB. It is shown that the station’s altitude strongly correlates with the threshold, variance, and design rainfall depth of the GPD. This proves the advantage of the GPD with Hill estimates, namely that it can accurately reflect the spatial properties of rainfall and its variability in the UVB. Results can be applied in water-management applications related to floods.