Semi-parametric resampling with extremes

Abstract

Nonparametric resampling methods such as Direct Sampling are powerful tools to simulate new datasets preserving important data features such as spatial patterns from observed or analogue datasets while using only minimal assumptions. However, such methods cannot generate extreme events beyond the observed range of data values. We here propose using tools from extreme value theory for stochastic processes to extrapolate observed data towards yet unobserved high quantiles. Original data are first enriched with new values in the tail region, and then classical resampling algorithms are applied to enriched data. In a first approach to enrichment that we label "naive resampling", we generate an independent sample of the marginal distribution while keeping the rank order of the observed data. We point out inaccuracies of this approach around the most extreme values, and therefore develop a second approach that works for datasets with many replicates. It is based on the asymptotic representation of extreme events through two stochastically independent components: a magnitude variable, and a profile field describing spatial variation. To generate enriched data, we fix a target range of return levels of the magnitude variable, and we resample magnitudes constrained to this range. We then use the second approach to generate heatwave scenarios of yet unobserved magnitude over France, based on daily temperature reanalysis training data for the years 2010 to 2016.

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

“…Besides precipitation reanalyses, other types of interesting applications include resampling from regional or global climate model reanalyses or projections. The work of Opitz et al (2020) focused on spatial resampling of heatwaves in France; they combined a lifting step with nonparametric resampling techniques such as Multiple-Point Statistics (Mariethoz and Caers, 2014), and Direct Sampling in particular (Mariethoz et al, 2010), such that new profile processes inheriting spatial dependence patterns from the observed extreme episodes were sampled. The application of such resampling techniques allows for a strong increase in the variety of newly sampled extreme episodes and could be extended to our spatio-temporal setting, but it also implies additional (although rather mild) assumptions on the spatial and temporal structure of extremes.…”

“…On the other hand, generalized Pareto processes represent the original events that satisfy a threshold exceedance condition. For specific choices of marginal distributions, they can be represented constructively by multiplying a random scaling variable with a so-called spectral process, the latter characterizing the spatial variation in the extreme events (Ferreira and de Haan, 2014;Dombry and Ribatet, 2015;Thibaud and Opitz, 2015;Opitz et al, 2020).…”

Direct Sampling for Spatially Variable Extreme Event Generation in Resampling‐Based Stochastic Weather Generators

“…The main use of Direct Sampling is to provide statistically coherent simulations with a structure mimicking the one provided by a training image, whose main role in applications is to inform and include physical reality in stochastic modeling. Some Direct Sampling and Multi-point Geostatistics applications on the weather domain are on conditional stochastic rainfall (Wojcik et al, 2009), downscaling (Jha et al, 2013(Jha et al, , 2015, resampling extremes (Opitz et al, 2021), rainfall series generation (Benoit & Mariethoz, 2017;Oriani et al, 2014Oriani et al, , 2018 and conditional weather field generation (Oriani et al, 2017).…”

Gap-Filling Sentinel-1 Offshore Wind Speed Image Time Series Using Multiple-Point Geostatistical Simulation and Reanalysis Data

“…QS-and MPS in general-attempts to reconstruct image patterns by resampling values from the available training dataset. The simulation of values beyond the range of the TIs is thus not possible without involving parametric approaches [57]. This makes the algorithm inefficient when called to simulate extreme or rare events, as the pool of relative values in the TI set is small.…”