1. SOC 30/09/04 1 Problem Areas (?) & Possible Approaches (?) in Ocean Extremes Clive Anderson University of Sheffield, UK

2. SOC 30/09/04 2 The Overall Problem Estimate extremes in presence of seasonal variability possible long-term trend possible relation to other climate variables dependent observations on the basis of possibly sparse and irregular data and give realistic assessment of uncertainty of result

3. SOC 30/09/04 3 Problem Areas Data from multiple sources - how combine? - how reconcile potential conflicts? How extreme? - Description, extrapolation, both? Satellite data - how use to augment other data? (as above) - how use alone? * intermittency * spatial resolution, spatial dependence * infer average extreme characteristics?

4. SOC 30/09/04 4 t XX XX transect times Intermittency problem a) over-threshold observations unlikely to be storm peaks b) many storms likely to be missed

5. SOC 30/09/04 5 Data from numerical models - reconcile with observations at extremes? - assimilate observations at extremes?

6. SOC 30/09/04 6 Approaches (?) 1 Data from multiple sources - combine? via joint likelihoods - conflicts? Model relationships of to underlying variable (H s say) and incorporate into likelihoods Generic form for relationship?

7. SOC 30/09/04 7 Approaches (?) 2 Satellite data - intermittency and spatial resolution x Wave heights: NE Pacific X

8. SOC 30/09/04 8 t XX XX transect times Intermittency problem a) over-threshold observations unlikely to be storm peaks b) many storms likely to be missed X             Handled (crudely) by an asymptotically-justified approximation. Technical improvements appear possible.

9. SOC 30/09/04 9 - How to utilize nearby data? some form of spatio-temporal model needed Possibilities: 1.ad hoc weighted (log-)likelihood: likelihood contributions from distant data down-weighted. 2.hierarchical model: if assume Generalized Pareto, conditionally independent, and a space-time random field fitting via MCMC, predictions by simulation

10. SOC 30/09/04 10 4. Structural model representing storms (above-threshold obs.) 3. Moving max models (de Heuvels, Smith & Weissman, Zhang)

11. SOC 30/09/04 11 Atlantic Storm, 1 st – 9 th December 1997: 6-hourly views

12. SOC 30/09/04 12 4. Structural model - representing tracks, sizes, intensities of storms as stochastic elements. cf Cox & Isham, Smith, Coles, de Haan - fitting via MCMC, predictions by simulation

13. SOC 30/09/04 13 Approaches (?) 3 Numerical model data - reconcile with/assimilate real data, emphasizing extremes cf model uncertainty/calibration/assimilation at non- extreme levels (PC/SOC, Sheffield, Durham approach uses model emulator based on Gaussian Process) ? for extremes would emulator based on max-stable process be appropriate? model emulator model inadequacy Gaussian process?

14. SOC 30/09/04 14 Geosat 10 day ERS-1 & ERS-2 35 day ERS-1 168 day