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Spatial oceanographic extremes Adam Butler (Lancaster University), talk at RSC2003

Spatial oceanographic extremes Adam Butler (Lancaster University), talk at RSC2003 Coworkers: Janet Heffernan, Jonathan Tawn, Roger Flather Data supplied by Proudman Oceanographic Laboratory (POL). Introduction: SSTO data. SSTO data - S ynthetic S patio- T emporal O ceanographic data.

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Spatial oceanographic extremes Adam Butler (Lancaster University), talk at RSC2003

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  1. Spatial oceanographic extremes Adam Butler (Lancaster University), talk at RSC2003 Coworkers: Janet Heffernan, Jonathan Tawn, Roger Flather Data supplied by Proudman Oceanographic Laboratory (POL)

  2. Introduction: SSTO data • 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.

  3. Data example: the dataset • 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

  4. Methodology: classical EVT models • 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

  5. Data example: classical EVT models Need to add indications as to how extremes get extracted etc. etc.

  6. Data example: nonstationarity & dependence

  7. Methodology: 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.

  8. Methodology: the Heffernan-Tawn model • 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.

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