On spatial extremes: with application to a rainfall problem

TL;DR

This paper applies advanced spatial extreme value theory to analyze 30 years of daily rainfall data across 32 stations in North Holland, estimating rare event rainfall thresholds using simulations and continuous stochastic process models.

Contribution

It introduces a novel application of spatial extreme value theory to rainfall data, combining recent theoretical developments with computational simulations.

Findings

Estimated 100-year rainfall threshold for North Holland.

Demonstrated the effectiveness of spatial extreme value models.

Provided a methodology for similar spatial extreme analyses.

Abstract

We consider daily rainfall observations at 32 stations in the province of North Holland (the Netherlands) during 30 years. Let $T$ be the total rainfall in this area on one day. An important question is: what is the amount of rainfall $T$ that is exceeded once in 100 years? This is clearly a problem belonging to extreme value theory. Also, it is a genuinely spatial problem. Recently, a theory of extremes of continuous stochastic processes has been developed. Using the ideas of that theory and much computer power (simulations), we have been able to come up with a reasonable answer to the question above.