On spatial conditional extremes for ocean storm severity

Shooter, Robert; Ross, Emma; Tawn, Jonathan A.; Jonathan, Philip

doi:10.1002/env.2562

Cited by 27 publications

(33 citation statements)

References 32 publications

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“…These choices were motivated by previous application studies including Shooter et al (2019), together with the known theoretical behaviours of α and β for d = 0 and d → ∞. This parametric form does not admit asymptotic dependence, however, since α(d, θ t ) = 1 for d > 0, although for suitably large A 1 and A 2 ≥ 2 then α(d, θ t ) ≈ 1 for d ≈ 0; a possible parametric form for α(d, θ t ) which permits asymptotic dependence is given by Wadsworth and Tawn (2019).…”

Section: Model Parameter Variation With Distance and Directionmentioning

confidence: 99%

“…In this case, a grouped adaptive MCMC algorithm based on Roberts and Rosenthal (2009) is used for parameter inference, described in Shooter et al (2019). Briefly, random search is used to find a reasonable starting solution.…”

Section: Parameter Estimationmentioning

confidence: 99%

“…The constraints are motivated by the fact that conditional quantiles (of one variable given a large value of another) under any form of asymptotic independence (α < 1) cannot be larger than under asymptotic positive dependence (α = 1). Details of the constraints applied in a spatial setting are given in the supplementary material of Shooter et al (2019), and summarised here in the Appendix.…”

Section: Parameter Estimationmentioning

confidence: 99%

“…For each storm-location combination, the direction (from which waves emanate, measured clockwise from North) at the time of the storm peak, referred to as the storm direction, was also retained. The spatial extremal characteristics of this sample have been examined previously in Ross et al (2017a) and Shooter et al (2019). At each location, marginal directional extreme value analysis of storm peak values was performed, and storm peak data transformed to standard Laplace marginal scale (see Ross et al 2017b).…”

Section: North Sea Storm Peak Significant Wave Heightmentioning

confidence: 99%

“…The model builds upon the work of Wadsworth and Tawn (2019) and Shooter et al (2019), adopting functional forms for SCE parameters. Shooter et al (2019) found that assuming a simple two-parameter for the decay of SCE slope parameter, α with distance was adequate to capture parameter behaviour adequately whilst reducing computational time for parameter estimation, since α would otherwise need to be estimated separately for pair of conditioning and remote locations. We build upon this idea by imposing either parametric or piecewise-linear forms for SCE parameters with distance and direction, motivated by theoretical considerations and evidence from preliminary analysis.…”

Section: Introductionmentioning

confidence: 99%

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Basin-wide spatial conditional extremes for severe ocean storms

et al. 2020

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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.

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Section: Model Parameter Variation With Distance and Directionmentioning

confidence: 99%

Section: Parameter Estimationmentioning

confidence: 99%

Section: Parameter Estimationmentioning

confidence: 99%

Section: North Sea Storm Peak Significant Wave Heightmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Basin-wide spatial conditional extremes for severe ocean storms

et al. 2020

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Simultaneous autoregressive models for spatial extremes

2020

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Motivated by the widespread use of large gridded data sets in the atmospheric sciences, we propose a new model for extremes of areal data that is inspired by the simultaneous autoregressive (SAR) model in classical spatial statistics. Our extreme SAR model extends recent work on transformed‐linear operations applied to regularly varying random vectors, and is unique among extremes models in being directly analogous to a classical linear model. An additional appeal is its simplicity; given a proximity matrix W, spatial dependence is described by a single parameter ρ. We develop an estimation method that minimizes the discrepancy between the tail pairwise dependence matrix (TPDM) for the fitted model and the estimated TPDM. Applying this method to simulated data demonstrates that it is able to produce good estimates of extremal spatial dependence even in the case of model misspecification, and additionally produces reasonable estimates of uncertainty. We also apply the method to gridded precipitation observations for a study region over northeast Colorado, and find that a single‐parameter extreme SAR model paired with a neighborhood structure which accounts for longer range dependence effectively models spatial dependence in these data.

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Spatial deformation for nonstationary extremal dependence

Richards

Wadsworth

2021

Environmetrics

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Modeling the extremal dependence structure of spatial data is considerably easier if that structure is stationary. However, for data observed over large or complicated domains, nonstationarity will often prevail. Current methods for modeling nonstationarity in extremal dependence rely on models that are either computationally difficult to fit or require prior knowledge of covariates.Sampson and Guttorp (1992) proposed a simple technique for handling nonstationarity in spatial dependence by smoothly mapping the sampling locations of the process from the original geographical space to a latent space where stationarity can be reasonably assumed. We present an extension of this method to a spatial extremes framework by considering least squares minimization of pairwise theoretical and empirical extremal dependence measures. Along with some practical advice on applying these deformations, we provide a detailed simulation study in which we propose three spatial processes with varying degrees of nonstationarity in their extremal and central dependence structures. The methodology is applied to Australian summer temperature extremes and UK precipitation to illustrate its efficacy compared with a naive modeling approach.

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On spatial conditional extremes for ocean storm severity

Cited by 27 publications

References 32 publications

Basin-wide spatial conditional extremes for severe ocean storms

Basin-wide spatial conditional extremes for severe ocean storms

Simultaneous autoregressive models for spatial extremes

Spatial deformation for nonstationary extremal dependence

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