Generalized Pareto processes for simulating space-time extreme events: an application to precipitation reanalyses

Abstract

To better manage the risks of destructive natural disasters, impact models can be fed with simulations of extreme scenarios to study the sensitivity to temporal and spatial variability. We propose a semi-parametric stochastic framework that enables simulations of realistic spatio-temporal extreme fields using a moderate number of observed extreme space-time episodes to generate an unlimited number of extreme scenarios of any magnitude. Our framework draws sound theoretical justification from extreme value theory, building on generalized Pareto limit processes arising as limits for event magnitudes exceeding a high threshold. Specifically, we exploit asymptotic stability properties by decomposing extreme event episodes into a scalar magnitude variable (that is resampled), and an empirical profile process representing space-time variability. For illustration on hourly gridded precipitation data in Mediterranean France, we calculate various risk measures using extreme event simulations for yet unobserved magnitudes, and we highlight contrasted behavior for different definitions of the magnitude variable.

Semi-parametric resampling with extremes

“…We use lower case letters for scalars, dummy variables as well as for datasets and realizations of random values and random functions. Extreme value theory for stochastic processes provides an asymptotic decomposition Y I d = Sη I of extreme events Y I into a scale variable S and a normalized profile process η I for certain choices of marginal distribution in data, with scale and profile being stochastically independent (Ferreira and de Haan, 2014;Thibaud and Opitz, 2015;Dombry and Ribatet, 2015;Opitz et al, 2015;de Fondeville and Davison, 2018;Engelke et al, 2019a;Palacios-Rodriguez et al, 2019). The processes presenting such factorization of scale and profile are known as Pareto processes.…”

“…Our approach thus combines nonparametric methods able to account for complex dependence structures with a theoretically founded parametric model to properly account for univariate extremes. Previous approaches to lifting observed extreme episodes, using extreme-value theory similar to our method but without further resampling steps, have been proposed in Ferreira and de Haan (2014); Chailan et al (2017); Palacios-Rodriguez et al (2019).…”

Identification of regions with a robust increase of heavy precipitation events

“…In order to develop adaptation strategies to hazards of heavy precipitation, reliable (i.e. robust) knowledge about affected Aalbers et al (2018) and Rajczak and Schär (2017) and ii) the peak-over-threshold method (POT) as in Palacios-Rodríguez et al (2020) and Berg et al (2019). BMM (also called the Annual Maximum Method) determines the annual maximum values over a certain period of time and then fits an extreme value distribution (EVD) to these annual maximum values.…”

Modelling extremes of spatial aggregates of precipitation using conditional methods

“…Coles and Tawn (1996) used this formulation to derive closed form results for the tail behaviour of R A where the tail parameters are determined by the marginal GPD parameters of {Y (s)} and its dependence structure ;Ferreira, de Haan and Zhou (2012) formalise these results and provide some non-parametric extensions. Further extensions of this framework by Engelke, De Fondeville and Oesting (2018) relate not only the extremal behaviour of {Y (s)} and the aggregates R A , but also the joint behaviour of aggregates over different regions, A. de Fondeville and Davison (2021) use functional Pareto processes to model the dependence in {Y (s)} and Palacios-Rodríguez et al (2020) illustrate non-parametric Pareto process modelling to simulate extreme precipitation fields, re-sampling event profiles from observed, gridded data. All of these modelling approaches rely on the marginal shape parameters of {Y (s)} to be spatially homogeneous i.e., ξ(s) = ξ for all s ∈ A, for each A of interest.…”