On tail trend detection: modeling relative risk

TL;DR

This paper develops a statistical model to detect changes over time in the probability of extreme environmental events, such as heavy rainfall, without needing to specify a particular threshold, and applies it to European rainfall data.

Contribution

It introduces a threshold-free method for modeling and testing trends in the probability of extreme events, with estimation procedures and simulation validation.

Findings

Trend depends on proximity to the sea.

Method successfully detects trends in rainfall extremes.

Application to European stations shows regional differences.

Abstract

The climate change dispute is about changes over time of environmental characteristics (such as rainfall). Some people say that a possible change is not so much in the mean but rather in the extreme phenomena (that is, the average rainfall may not change much but heavy storms may become more or less frequent). The paper studies changes over time in the probability that some high threshold is exceeded. The model is such that the threshold does not need to be specified, the results hold for any high threshold. For simplicity a certain linear trend is studied depending on one real parameter. Estimation and testing procedures (is there a trend?) are developed. Simulation results are presented. The method is applied to trends in heavy rainfall at 18 gauging stations across Germany and The Netherlands. A tentative conclusion is that the trend seems to depend on whether or not a station is close to the sea.