1SOC 30/09/04

Problem Areas (?)

& Possible Approaches (?)

in Ocean Extremes

Clive AndersonUniversity of Sheffield, UK

2SOC 30/09/04

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

3SOC 30/09/04

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?

4SOC 30/09/04

tX X X X

transect times

Intermittency problem

a) over-threshold observations unlikely to be storm peaks

b) many storms likely to be missed

5SOC 30/09/04

• Data from numerical models

- reconcile with observations at extremes?

- assimilate observations at extremes?

6SOC 30/09/04

Approaches (?) 1

• Data from multiple sources - combine? via joint likelihoods

- conflicts? Model relationships of

to underlying variable (Hs say) and incorporate

into likelihoods

Generic form for relationship?

7SOC 30/09/04

Approaches (?) 2

• Satellite data - intermittency and spatial resolution

x

Wave heights: NE Pacific

X

8SOC 30/09/04

tX X X X

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.

9SOC 30/09/04

- 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

10SOC 30/09/04

4. Structural model representing storms (above-threshold obs.)

3. Moving max models (de Heuvels, Smith & Weissman, Zhang)

11SOC 30/09/04

Atlantic Storm, 1st – 9th December 1997: 6-hourly views

12SOC 30/09/04

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

13SOC 30/09/04

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 inadequacyGaussian process?

14SOC 30/09/04

Geosat 10 day ERS-1 & ERS-2 35 day

ERS-1 168 day