Rob Shooter

This paper details a methodology proposed for the EVA 2021 conference data challenge. The aim of this challenge was to predict the number and size of wildfires over the contiguous US between 1993 and 2015, with more importance placed on extreme events. In the data set provided, over 14% of both wildfire count and burnt area observations are missing; the objective of the data challenge was to estimate a range of marginal probabilities from the distribution functions of these missing observations. To enable this prediction, we make the assumption that the marginal distribution of a missing observation can be informed using non-missing data from neighbouring locations. In our method, we select spatial neighbourhoods for each missing observation and fit marginal models to non-missing observations in these regions. For the wildfire counts, we assume the compiled data sets follow a zero-inflated negative binomial distribution, while for burnt area values, we model the bulk and tail of each compiled data set using non-parametric and parametric techniques, respectively. Cross validation is used to select tuning parameters, and the resulting predictions are shown to significantly outperform the benchmark method proposed in the challenge outline. We conclude with a discussion of our modelling framework, and evaluate ways in which it could be extended.

This paper details a methodology proposed for the EVA 2021 conference data challenge. The aim of this challenge was to predict the number and size of wildfires over the contiguous US between 1993 and 2015, with more importance placed on extreme events. In the data set provided, over 14\% of both wildfire count and burnt area observations are missing; the objective of the data challenge was to estimate a range of marginal probabilities from the distribution functions of these missing observations. To enable this prediction, we make the assumption that the marginal distribution of a missing observation can be informed using non-missing data from neighbouring locations. In our method, we select spatial neighbourhoods for each missing observation and fit marginal models to non-missing observations in these regions. For the wildfire counts, we assume the compiled data sets follow a zero-inflated negative binomial distribution, while for burnt area values, we model the bulk and tail of each compiled data set using non-parametric and parametric techniques, respectively. Cross validation is used to select tuning parameters, and the resulting predictions are shown to significantly outperform the benchmark method proposed in the challenge outline. We conclude with a discussion of our modelling framework, and evaluate ways in which it could be extended.

The extremal spatial dependence of significant wave height in the North East Atlantic is explored using Joint Altimetry Satellite Oceanography Network satellite altimeter observations for the period 2002–2018, and a spatial conditional extremes model motivated by the work of Heffernan and Tawn. The analysis involves (a) registering individual satellite passes onto a template transect, (b) marginal extreme value analysis at a set of locations on the template transect and transformation from physical to standard Laplace scale, (c) estimation of the spatial conditional extremes model for a set of locations on a template transect, and (d) comparison of extreme spatial dependence for different template transects. Inferences for two transects considered are qualitatively similar; however, for the “normal ascending” transect running approximately south‐west to north‐east lying between Iceland and the United Kingdom, extremal spatial dependence is found to decay more quickly than for the second “opposite descending” transect running approximately north‐west to south‐east to the west of Ireland.

Physical considerations and previous studies suggest that extremal dependence between ocean storm severity at two locations exhibits near asymptotic dependence at short inter-location distances, leading to asymptotic independence and perfect independence with increasing distance. We present a spatial conditional extremes (SCE) model for storm severity, characterising extremal spatial dependence of severe storms by distance and direction. The model is an extension of Shooter et al. 2019 (Environmetrics 30, e2562, 2019) and Wadsworth and Tawn (2019), incorporating piecewise linear representations for SCE model parameters with distance and direction; model variants including parametric representations of some SCE model parameters are also considered. The SCE residual process is assumed to follow the delta-Laplace form marginally, with distance-dependent parameter. Residual dependence of remote locations given conditioning location is characterised by a conditional Gaussian covariance dependent on the distances between remote locations, and distances of remote locations to the conditioning location. We apply the model using Bayesian inference to estimates extremal spatial dependence of storm peak significant wave height on a neighbourhood of 150 locations covering over 200,000 km² in the North Sea.

We describe a model for the conditional dependence of a spatial process measured at one or more remote locations given extreme values of the process at a conditioning location, motivated by the conditional extremes methodology of Heffernan and Tawn. Compared to alternative descriptions in terms of max‐stable spatial processes, the model is advantageous because it is conceptually straightforward and admits different forms of extremal dependence (including asymptotic dependence and asymptotic independence). We use the model within a Bayesian framework to estimate the extremal dependence of ocean storm severity (quantified using significant wave height, H_S) for locations on spatial transects with approximate east–west (E‐W) and north–south (N‐S) orientations in the northern North Sea (NNS) and central North Sea (CNS). For H_S on the standard Laplace marginal scale, the conditional extremes “linear slope” parameter α decays approximately exponentially with distance for all transects. Furthermore, the decay of mean dependence with distance is found to be faster in CNS than NNS. The persistence of mean dependence is greatest for the E‐W transect in NNS, potentially because this transect is approximately aligned with the direction of propagation of the most severe storms in the region.