Statistical Post-Processing of Forecasts for Extremes Using Bivariate Brown-Resnick Processes with an Application to Wind Gusts

TL;DR

This paper develops a bivariate Brown-Resnick process model to enhance the statistical post-processing of weather forecast extremes, specifically wind gusts, by capturing spatial dependencies between observations and forecasts.

Contribution

It introduces a new parametric model for pseudo cross-variograms of bivariate Brown-Resnick processes, advancing theoretical understanding and practical application in weather extremes forecasting.

Findings

The model effectively captures spatial dependence in wind gust extremes.

Application to real data improves forecast calibration and accuracy.

Theoretical insights into pseudo cross-variogram behavior are provided.

Abstract

To improve the forecasts of weather extremes, we propose a joint spatial model for the observations and the forecasts, based on a bivariate Brown-Resnick process. As the class of stationary bivariate Brown-Resnick processes is fully characterized by the class of pseudo cross-variograms, we contribute to the theorical understanding of pseudo cross-variograms refining the knowledge of the asymptotic behaviour of all their components and introducing a parsimonious, but flexible parametric model. Both findings are of interest in classical geostatistics on their own. The proposed model is applied to real observation and forecast data for extreme wind gusts at 119 stations in Northern Germany.