An exploration of the relationship between productivity and diversity in British Grasslands

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(No Transcript)
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Climate change, extreme sea levels
hydrodynamical models
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Introduction

• Quantifying the impacts of climate change upon
  extreme sea levels.
• Spatial variation in impacts.
• Scientific tools -
• Observational data,
• Process knowledge,
• Numerical models
• Statistical tools
• Extreme value theory,
• Spatial statistics,
• Nonparametric regression
• Multivariate analysis

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Hydrodynamical models
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North Sea models
lt 35km NEAC grid lt 12km NISE grid
V V
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Scientific problems

• Observational climate data
• Observational climate data for 1970-1999.
• Model output verified against observational sea
  level data.
• Test for evidence for temporal change in extreme
  values.
• Numerical climate model
• Generate 30-year long stationary sequences of sea
  level data.
• Climate input data generated using ECHAM-4
  climate model under two scenarios current CO2,
  double current CO2.
• Interest is in comparing extremal characteristics
  of the spatio-temporal fields generated under
  the two scenarios.

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Previous findings

• Surge residuals
• Annual maxima
• Univariate extreme value modelling for each site
• Use the GEV (Generalized Extreme Value)
  distribution

Changes in 50 year surge residuals (in cm) as a
result of a doubling of CO2 levels
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Statistical methods for spatial extremes

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An example

• Spatial variability
• Spatial coherence
• Residual spatial dependence

Initial location 0, Scale 1, Shape
-0.35, Dependence 0.7
Insert a map here simulated parameter surface
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Methods

Insert a diagram here
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Multivariate extremes

• General theory
• Componentwise maxima
• Multivariate extreme value distribution
• Modelling of marginal and dependence
  characteristics
• Parameter linking
• Inference
• 2-step likelihood estimation
• Independence working assumption
• Sandwich variance estimator
• Fix margins, transform and estimate ?
• 1-step likelihood estimation.

BEVL (Bivariate Extreme Value
Logistic) distribution
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A local grid-based method

Grid Evaluation points
Kernels
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Acknowledgements

• Supervisors
• Janet Heffernan
• Jonathan Tawn
• Assistance and advice
• Johan Segers, Vadim Kuzmin, Alexandra Ramos,
• Christopher Ferro, Alec Stephenson, Matthew
  Killeya
• Images
• Web sources (list available on request)
• Lamb, H. (1991) Historic storms of the North Sea,
  British Isles and Northwest Europe, CUP,
  Cambridge.

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Apparent independence