A regional and nonstationary model for partial duration series of extreme rainfall

Abstract

Regional extreme value models for estimation of extreme rainfall intensities are widely applied, but their underlying assumption of stationarity is challenged. Many recent studies show that the rainfall extremes worldwide exhibit a nonstationary behavior. This paper presents a spatiotemporal model of extreme rainfall. The framework is built on a partial duration series approach with a nonstationary, regional threshold value. The model is based on generalized linear regression solved by generalized estimation equations. It allows a spatial correlation between the stations in the network and accounts furthermore for variable observation periods at each station and in each year. Marginal regional and temporal regression models solved by generalized least squares are used to validate and discuss the results of the full spatiotemporal model. The model is applied on data from a large Danish rain gauge network for four durations ranging from 10 min to 24 h. The observation period differs between stations, and the number of stations with more than 10 years of observations has increased over the years. A spatiotemporal model for the threshold is suggested, applying the mean annual precipitation and time as the explanatory variables in the regional and temporal domain, respectively. Further analysis of partial duration series with nonstationary and regional thresholds shows that the mean exceedances also exhibit a significant variation in space and time for some rainfall durations, while the shape parameter is found to be constant.

A review of methods to account for impacts of non-stationary climate data on extreme rainfalls for design rainfall estimation in South Africa

“…In Denmark, a spatio-temporal model of extreme rainfall for short durations was developed using a non-stationary POT approach. The model was determined to be highly qualified to model spatio-temporal variability in the parameters of the GP distribution (Gregersen et al 2017). The results of that study show that extreme precipitation can be underestimated using the assumption of stationarity, thus highlighting the importance of updating design strategies for hydraulic infrastructure in changing climatic conditions (Sarhadi & Soulis 2017).…”

Nordic contributions to stochastic methods in hydrology

“…The approach was further developed and evaluated in Madsen et al (2002). Gregersen et al (2013aGregersen et al ( , 2017 used generalized linear modelling to assess the value of spatial and temporal explanatory variables for the IDF estimation and found mean summer temperature and precipitation particularly useful. Recently, non-stationarity has been introduced in the regionalization for Denmark due to indications of increasing extremes (Arnbjerg-Nielsen 2006).…”

“…Recently, non-stationarity has been introduced in the regionalization for Denmark due to indications of increasing extremes (Arnbjerg-Nielsen 2006). Gregersen et al (2017) extended the method of Gregersen et al (2013a) to allow for non-stationarity also considering more parameters. Madsen et al (2017) related PDS parameters to daily gridded rainfall statistics, including non-stationarity as an additional source of uncertainty.…”

Principles for Distributing Infiltration-Based Stormwater Control Measures in Series

“…We set up a hypothetical case study including three sub-catchments in series (Figure 2). We ran continuous simulations using a rainfall time series from Kløvermarken, Copenhagen, Denmark, which is part of the rain gauge system run by The Water Pollution Committee of The Society of Danish Engineers [32,33]. The rainfall time series is identical to the one used by [8], covering 1979-2019 inclusive for this study with a time step of one minute.…”