Statistical Analysis of Extreme Wind in Regional Climate Model

SimulationsEMS 2013

Stephen Outten

Motivation

Statistical methods

Extreme winds in RCMs

Practical application

Overview

Hardanger Bridge

Photo from: Norwegian Public Roads Administration

Hardanger bridge

Utsira

Current Procedure1. Obtain observations for short

time series at bridge and long time series at lighthouse

2. Relate short and long term time series to create long series at bridge and obtain distribution

3. Derive return events with associated uncertainties at bridge from current distribution

3. Derive return events with associated uncertainties at bridge from current distribution???

ENSEMBLES Project◦ Regional downscaling of IPCC models◦ Multiple RCMs employed◦ 25 km horizontal resolution◦ European domain◦ Uniform grid◦ Future A1B scenario

RCM Data

e q lo n = 18.0000 , eq la t = 50 .750 0, p o llo n = -162 .000, p o l la t = 3 9.2500s ta r tlo n = -21 .7200 , s ta rtla t = -20.680 0 , e n d lo n = 15.4600 , e n d la t = 20.9000ie = 170, je = 190 , d e l ta = 0 .2200 00, N G = 32300 , N G 10= 39900

e q lo n = 18.0000, eq lat = 50 .7500, p o l lo n = -162 .000, p o l la t = 39.2500s tartlo n = -21.6100, s tartla t = -20.5700, e n d lo n = 15.3500, e n d lat = 20 .7900ie= 85 , je = 95, d e lta= 0.440000, N G = 8075, N G 10= 12 075

0.44 degr ee (50km) grid mesh0.22 degr ee (25km) grid mesh

ENSEMBLES RCM Minim um Ar ea

4 downscalings◦ 2 GCMs x 2 RCMs◦ Maximum daily wind speeds

Statistical Methods

Theorem 1◦ The maxima of multiple samples of data converge

to a Generalised Extreme Value (GEV) distribution

Theorem 2◦ The exceedances over a suitably chosen threshold

converge to a Generalised Pareto Distribution (GPD)

Extreme Value Theory

BCM/HIRHAM5 : Bergen : 1961-1990

GEV GPD

BCM/HIRHAM5 : Bergen : 50 year return

R50 : 19.61 ms-1 R50 : 19.58 ms-1

GEV GPD

CI99% : 18.05 ms-1

30.07 ms-1

CI99% : 18.12 ms-1

26.10 ms-1

Parameter Space for Bergen

GEV GPD

Likelihood contours from inside to outside: 90%, 95%, 98%, and 99%

GEV : Parameter Sensitivity

R50: 19.61 ms-1

R50: 28.60 ms-1

Generalised Extreme Value Family

Generalised Extreme Value Distribution

σ k μ

(reversed) Weibull

Gumbel Fréchet

k<0 k=0 k>0

Gumbelσ μ

Likelihood Ratio TestCompares the fit of two models, one of which is a special case of the other

Procedure:• Fit both models to the data• Calculate test statistic from

log-likelihoods• Use a Chi-squared to

determine if fits are significantly different

Applying Approach to BergenGEV GPD

GumbelConfidence Interval at 99% level GEV : 18.05 ms-1 to 30.07 ms-1

GPD : 18.12 ms-1 to 26.10 ms-1

Gumbel : 18.33 ms-1 to 22.86 ms-1

Proposed Procedure1. Obtain observations for short time series at bridge and

long time series at lighthouse2. Relate short and long term time series to create long

series at bridge and obtain distribution3. Use statistical tests to select the appropriate distribution

to minimise the uncertainty

4. Derive return events with associated uncertainties at bridge from current distribution

Extreme Winds in Regional Climate Models

Model Resolution

Hardanger bridge

Utsira

e q lo n = 18.0000 , e q la t = 50 .7500, p o l lo n = -162 .00 0, p o l la t = 39.2500s ta r tlo n = -21 .7 200 , s ta rtla t = -20.6800 , e n d lo n = 1 5.4600 , e n d la t = 20.9 000ie = 1 70, je = 190 , d e l ta = 0 .2 20000, N G = 323 00 , N G 10= 39 900

e q lo n = 18.0000, e q lat = 50 .7500, p o llo n = -162.000, p o l la t = 39.2500s tartlo n = -21.6100, s tar tla t = -20.5700, e n d lo n = 15.3500, e n d la t = 20.7900ie= 85 , je = 95 , d e lta = 0.440000, N G = 8075, N G 1 0= 12075

0.44 degr ee (50km) grid mesh0.22 degr ee (25km) grid mesh

ENSEMBLES RCM Minim um Ar ea

25 km resolution 1.3 km bridge2-3 km wide fjord

Proposed Procedure1. Obtain observations for short time series at bridge and

long time series at lighthouse2. Relate short and long term time series to create long

series at bridge and obtain distribution3. Use statistical tests to select the appropriate distribution

to minimise the uncertainty4. Obtain regional climate model data at lighthouse location

for reference and future periods

5. Relate the future distribution at the lighthouse to the bridge

6. Derive return events with associated uncertainties at bridge from current distribution

Future Change : Bergen○ : BCM-HIRHAM5 Current∗ : BCM-HIRHAM5 Future

○ : BCM-RCA3 Current∗ : BCM-RCA3 Future

○ : ECHAM5-RCA3 Current∗ : ECHAM5-RCA3 Future

○ : ECHAM5-HIRHAM5 Current∗ : ECHAM5-HIRHAM5 Future

Models and Extreme Winds

Source: Knutson et al. 2008

Models at UtsiraBCM/HIRHAM5 BCM/RCA3

Proposed Procedure1. Obtain observations for short time series at bridge and long

time series at lighthouse2. Relate short and long term time series to create long series

at bridge and obtain distribution3. Use statistical tests to select the appropriate distribution to

minimise the uncertainty4. Obtain regional climate model data at lighthouse location for

reference and future periods5. Combine projected change from models with observations

from lighthouse to create future wind speed distribution at lighthouse *

6. Relate the future distribution at the lighthouse to the bridge7. Derive return events with associated uncertainties at bridge

from current and future distributions

* Holland G. and Suzuki-Parker A, Journal of Climate, (submitted)

Practical Application

1. Obtain observations for short time series at bridge and long time series at lighthouse

2. Relate short and long term time series to create long series at bridge and obtain distribution

3. Use statistical tests to select the appropriate distribution to minimise the uncertainty

4. Obtain regional climate model data at lighthouse location for reference and future periods

5. Combine projected change from models with observations from lighthouse to create future wind speed distribution at lighthouse *

6. Relate the future distribution at the lighthouse to the bridge7. Derive return events with associated uncertainties at bridge

from current and future distributions

Proposed Approach

* Holland G. and Suzuki-Parker A, Journal of Climate, (submitted)

Application to Utsira Lighthouse

WS50 = 37.9 ms-1

WS50 = 38.2 ms-1

WS50 = 38.2 ms-1

WS50 = 38.6 ms-1

WS50 = 38.1 ms-1

Instanes A. and Outten S, Journal of Bridge Engineering, (to be submitted)

Developed method for including projected changes in extreme winds into the design process

Future changes in extreme winds are generally smaller than the uncertainty involved in estimating the extreme event

Inter-model spread is the largest source of uncertainty

Vital to assess uncertainties in estimates of extreme events

Summary

Thank You

Extra SlidesMore statistics and Winds over Europe

BCM/HIRHAM5 : 50 year returnReference

(1961-1990)Future

(2070-2099)

Outten & Esau, Atmos. Chem. Phys., 2013

DMI/BCM : Future Change

Outten & Esau, Atmos. Chem. Phys., 2013

BCM/HIRHAM5: Uncertainty-Future Change

Outten & Esau, Atmos. Chem. Phys., 2013

BCM ECHAM5GCM

HIRHAM5

RCA3

RCM

BCM ECHAM5GCM

HIRHAM5

RCA3

RCM