Spatial oceanographic extremes

Adam Butler (Lancaster University), talk at RSC2003Coworkers: Janet Heffernan, Jonathan Tawn, Roger Flather

Data supplied by Proudman Oceanographic Laboratory (POL)

SSTO data - • Synthetic Spatio-Temporal Oceanographic data.• Generated from deterministic models.• Lattice-based spatio-temporal data.• Large, high resolution datasets.• Variables: surge height, wave height,

surge direction,… • Possibly multivariate.

Extremal properties of SSTO data • Extremes are linked to risk.• Key: estimating extreme return levels of a single

variable at a single site.• Fundamentally about extrapolation.• Extremes of derived variables.• Spatial aggregation: regional risk assessment.• Temporal evolution of extremal properties.

Introduction: SSTO data

• Variable: surge level• Region: NE Atlantic• Period: 1955-2001• Spatial resolution: 35km• Temporal resolution: 1hr • Generating model: NEAC• Met input data: DNMI• Data provided by: POL

Data example: the dataset

Why use EVT for modelling ? • EVT = Extreme Value Theory...• Modelling choice between EVT approach and

process approach• EVT-based models rely upon very weak

assumptions• The price of this is inefficiency• For SSTO data, the choice is pathological.

Which EVT model to use ? • Classical: univariate models for extremes,

assuming independence.• Asymptotically motivated models• Main approaches: blockwise maxima, threshold

exceedance

Methodology: classical EVT models

Data example: classical EVT models

Need to add indications as to how

extremes get extracted etc. etc.

Data example: nonstationarity & dependence

Nonstationarity • Nonstationarities of known form: straightforward• Nonstationarities of unknown form: harder !• SSTO: nature of nonstationarity usually unknown• SSTO: spatial nonstationarity is dominant• SSTO: temporal nonstationarities are subtle

Dependence • Very strong spatial and temporal dependence• Avoiding temporal dependence via aggregation• e.g. Peaks over Threshold (POT) model• Modelling spatial dependence via multivariate

extremes • e.g. Multivariate threshold exceedance models...• Chapter 2 of my thesis - simulation studies.

Methodology: nonstationarity & dependence

Heffernan and Tawn (2003) • A semi-parametric model for

multivariate extremes• No strong a priori assumptions about

the form of extremal dependence• Relatively parsimonious• Extremal dependence parameters

Spatial extension• Reduce number of dependence parameters• Adjust for temporal dependence • Add spatial nonstationarity via local likelihood• Chapters 3-5 of my thesis.

Methodology: the Heffernan-Tawn model