Conditional simulation of max-stable processes

TL;DR

This paper introduces a new framework for conditional simulation of max-stable processes, enabling accurate modeling of spatial extremes like rainfall and temperature, with practical applications demonstrated in Switzerland.

Contribution

It provides closed-form solutions for Brown-Resnick and Schlather processes and demonstrates their effectiveness on real and simulated data.

Findings

Accurate conditional simulations of spatial extremes.

Framework handles real-sized problems efficiently.

Effective modeling of environmental extremes like rainfall and temperature.

Abstract

Since many environmental processes such as heat waves or precipitation are spatial in extent, it is likely that a single extreme event affects several locations and the areal modelling of extremes is therefore essential if the spatial dependence of extremes has to be appropriately taken into account. This paper proposes a framework for conditional simulations of max-stable processes and give closed forms for Brown-Resnick and Schlather processes. We test the method on simulated data and give an application to extreme rainfall around Zurich and extreme temperature in Switzerland. Results show that the proposed framework provides accurate conditional simulations and can handle real-sized problems.