Abstract
The potential for changes in environmental extremes is routinely investigated by fitting change-permitting extreme value models to long-term observations, allowing one or more distribution parameters to change as a function of time or some other covariate. In most extreme value analyses, the main quantity of interest is typically the upper quantiles of the distribution, which are often needed for practical applications such as engineering design. This study focuses on the changes in quantile estimates under different change-permitting models. First, metrics which measure the impact of changes in parameters on changes in quantiles are introduced. The mathematical structure of these change metrics is investigated for several change-permitting models based on the Generalised Extreme Value (GEV) distribution. It is shown that for the most commonly used models, the predicted changes in the quantiles are a non-intuitive function of the distribution parameters, leading to results which are difficult to interpret. Next, it is posited that commonly used change-permitting GEV models do not preserve a constant coefficient of variation, a property that is typically assumed to hold for environmental extremes. To address these shortcomings a new (parsimonious) model is proposed: the model assumes a constant coefficient of variation, allowing the location and scale parameters to change simultaneously. The proposed model results in changes in the quantile function that are easier to interpret. Finally, the consequences of the different modelling choices on quantile estimates are exemplified using a dataset of extreme peak river flow measurements in Massachusetts, USA. It is argued that the decision on which model structure to adopt to describe change in extremes should also take into consideration any requirements on the behaviour of the quantiles of interest.
Highlights
There is widespread interest in quantifying the impacts of climate and other anthropogenic changes on the likelihood of very extreme natural hazards (IPCC 2012)
Throughout the paper only univariate parametric models have been discussed, the results can be extended to the case of multivariate and non-parametric models
All analysis and calculations have been carried out assuming a Generalised Extreme Value (GEV) distribution, the findings could be useful for other distributions whose quantile function has the same structure as the one in Eq (2), such as the Generalised Pareto distribution which is typically employed when analysing peaks-over-threshold records and has been used to detect changes in environmental extremes (Silva et al 2016, 2017)
Summary
There is widespread interest in quantifying the impacts of climate and other anthropogenic changes on the likelihood of very extreme natural hazards (IPCC 2012). Several studies in the literature, including those listed, carry out some investigation of the implied impact on the magnitude of estimated quantile of using change-permitting models against results obtained when assuming constant parameters. The analytical study of the change criteria shows that a minority of model structures results in simple definitions of change in the quantile function. GEV Generalised Extreme Value distribution variation, enforcing a change in the scale of the distribution when the location is allowed to change Such models are not commonly used in the investigation of changes in extremes, even though a constant coefficient of variation is a common characteristic of estimates based on environmental extremes records (Overeem et al 2009; Menabde et al 1999; Serago and Vogel 2018; Blanchet et al 2009). The maximum likelihood estimation framework is adopted throughout the manuscript, some of the concepts discussed would apply to models estimated within a Bayesian framework
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