Statistical dynamical model to predict extreme events and ...
Statistical Analysis of Extreme Wind in Regional Climate Model Simulations
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Transcript of Statistical Analysis of Extreme Wind in Regional Climate Model Simulations
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