A regional peaks-over-threshold model in a nonstationary climate

Regional frequency analysis is often used to reduce the uncertainty in the estimation of distribution parameters and quantiles. In this paper a regional peaks-over-threshold model is introduced that can be used to analyze precipitation extremes in a changing climate. We use a temporally varying threshold, which is determined by quantile regression for each site separately. The marginal distributions of the excesses are described by generalized Pareto distributions (GPD). The parameters of these distributions may vary over time and their spatial variation is modeled by the index flood (IF) approach. We consider different models for the temporal dependence of the GPD parameters. Parameter estimation is based on the framework of composite likelihood. Composite likelihood ratio tests that account for spatial dependence are used to test the significance of temporal trends in the model parameters and to test the IF assumption. We apply the method to gridded, observed daily precipitation data from the Netherlands for the winter season. A general increase of the threshold is observed, especially along the west coast and northern parts of the country. Moreover, there is no indication that the ratio between the GPD scale parameter and the threshold has changed over time, which implies that the scale parameter increases by the same percentage as the threshold. These positive trends lead to an increase of rare extremes of on average 22% over the country during the observed period.
We apply the method to gridded, observed daily precipitation data from the Netherlands for the winter season. A general increase of the threshold is observed, especially along the west coast and northern parts of the country. This implies, that moderate extremes have increased over the observed time period. Moreover, the positive trend in the threshold induces an increase in the scale parameter of the GP distribution owing to the IF assumption. There is no additional trend in the scale parameter and the trend in the shape parameter is not significant.