Download extreme sea levels

Climate change, extreme sea levels
& hydrodynamical models
Introduction
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Quantifying the impacts of climate
change upon extreme sea levels.
Spatial variation in impacts.
Scientific tools • Observational data,
• Process knowledge,
• Numerical models
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Statistical tools
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Extreme value theory,
Spatial statistics,
Nonparametric regression
Multivariate analysis
Hydrodynamical models
North Sea models
< 35km NEAC grid <
12km NISE grid
V
V
Scientific problems
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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.
Previous findings
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Surge residuals
Annual maxima
Univariate extreme
value modelling for
each site
Use the GEV
(Generalized
Extreme Value)
distribution
   ( x   ) 1/  
F ( x)  exp  1 
 

 
 
Changes in 50 year surge residuals (in cm) as
a result of a doubling of CO2 levels
Statistical methods for spatial extremes
An example
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Spatial variability
Spatial coherence
Residual spatial dependence
Insert a
map here:
simulated
parameter
surface
Initial location = 0,
Scale = 1,
Shape = -0.35,
Dependence = 0.7
Methods
Insert a
diagram here
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 
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1-step likelihood estimation.
BEVL (Bivariate Extreme
Value Logistic) distribution

F ( x, y)  exp  x
1/ 
y

1/  
A local grid-based method
l ( , ; y) 
w l
jN m ( y )
j m
( ; x j )  ld  , ; t ( xi ) : xi  N d ( y)
Kernels
Grid
Evaluation
points
Acknowledgements
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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.
Apparent independence