federal department of home affairs fdha federal office of meteorology and climatology meteoswiss the...

Federal Department of Home Affairs FDHAFederal Office of Meteorology and Climatology MeteoSwiss

The covariation of windstorm frequency, intensity and loss over Europe with large-

scale climate diagnostics

15.05.2008

A collaboration between SwissRe,

MeteoSwiss, FP6 ENSEMBLES and NCCR Climate

2 Prediction of Winter Storm Risk

Paul Della-Marta, Mark Liniger, Christof Appenzeller

Outline

• The PreWiStoR project • Predictability of European winter storminess• Improved estimates of the European wind storm climate

• Storm selection method• Improved estimates of loss due to European wind storms

• The Swiss Re loss model• Calibration of ERA40, s2d and SwissRe storms

• The covariation of wind storm frequency, intensity and loss over Europe with large-scale climate diagnostics

• A bivariate extreme value peak over threshold model for wind storm intensity and loss



PreWiStoR: Prediction of winter Wind Storm Risk

• Problem: Observed records of wind storms are not long enough

• Solution: ~150 storms based on observations.• Use probabilistic modelling to generate synthetic storms

based on perturbed statistics• Calculate losses







• New approach to use ENSEMBLE prediction systems (seasonal to decadal, s2d)• Replace statistical perturbation with physics• Utilise around ~500 seasons of S2D data • Obtain a better estimate of wind storm risk and losses

See van den Brink et al. IJC (2005)



PreWiStoR: Data

• Seasonal to decadal (s2d) climate prediction models• Using the seasonal forecasting model of the ECMWF• A coupled ocean-atmosphere Global Circulation Model• 6-7 month forecast• Separate ocean analysis system to initiate the seasonal

forecasts• ENSEMBLE prediction system: Model is run many times

Initial conditions are perturbed Probabilistic Forecasts



Monthly mean Geopotential Height @850hPa (m) ONDJFMA

ERA40 SYS 3 Difference



Data Quality: Intercomparison of the 99th %-tile wind climate

Wind Gust

WG

Geostr. wind @ 850hPa

GWS

ERA40 ECMWF System 2 ECMWF System 3



An Extreme Wind Index (EWI)

• Spatial 95th percentile (calculated every 6 hours)• A measure of the extremity of lower bound of the spatial top

5% of wind • Applied to 850hPa Geostrophic Wind Speed (GWS)• Monthly averages taken for NDJFMA• Applied to ERA40 and Seasonal Forecasts



Probabilistic prediction skill: ECMWF Sys2

• Ranked Probability Skill Score (terciles)

• Bootstrap confidence intervals

Nov Dec Jan Feb Mar Apr MayLittle evidence of Predictabilty

Initial Condition Pred.



Improved estimates of the European wind storm climate

• Lack of predictability is disappointing, but the Seasonal Forecast data is still useful for risk assessment!

• Remove first month from seasonal forecasts independence of ensemble members

• Join multiple forecasts together to form an ONDJFMA season



Storm Selection Method

Index: Q95

Winter 1999/2000

95% threshold



Number of wind storms identified in ERA-40 and s2d

Example ERA-40 wind storm climatology



Comparison of wind storm frequency

• Wind storm climatologies are different in magnitude and shape

• All s2d models seem to have a less negative shape than ERA-40



Improved estimates of wind storm frequency and magnitude uncertainty

Return Level Return Period

95% Confidence interval (profile log-likelihood)



How can we compare the different climatologies?

• Apply a calibration technique to the Q95 relying on different assumptions

• Percentile based

• A high threshold based

• Mean based



Example: percentile calibration curves

SYS 3 SYS 2 DEMETER



Frequency calibration: aliasing the data…

• Each s2d dataset has a different temporal resolution of the Q95

• Has an effect on storm frequency, independent of model bias

• Solution: Alias ERA-40 to the same temporal res.

ERA-40, 6hr

SYS3, 12hr

SYS2, 12hr

DEMETER, 24hr



Percentile calibration and Aliasing



95th Percentile calibration and Aliasing



GPD Parameters after calibration

• Shape parameter is less negative

• Aliasing has helped the frequency of occurrence (lambda)



Summary: Storm intensity and storm frequency comparison

• Large differences in storm intensities between SwissRe, ERA40 and s2d need a calibration method... Necessarily a comprimise

• -or- you believe the raw output of GCMs

• Overall agreement in storm frequency between ERA40 and s2d, however, as shown before, aliasing of the signal is possible.



Swiss Re Wind Storm Loss Model(catXos)

• Vulnerability curve shows a cubic relation which is capped

• Portfolio value distribution is inhomogeous



The need for Calibration....

• ERA40 850hPa Geostrophic wind fields are different from SwissRe wind fields

• SwissRe loss model is calibrated for use with SwissRe wind fields



CALIB1: ERA40 GWS SwissRE (*me2)

• Adjustment curve: CDF(SwissRE)-CDF(ERA40)• Set to values greater than zero to zero



CALIB2: Sys3 GWS ERA40 GWS

• Adjustment curve: CDF(ERA40)-CDF(Sys3 GWS)



Comparison of Loss Return Periods

• Calibrated wind storm wind fields including information on their duration is used as input to catXos

• Error estimates from the calibration methodology can be used to estimate errors in loss

• All loss return periods are expressed in %Total Insured Value (%TIV)



Summary: Comparison of Loss Return Periods

• All s2d datasets and ERA40 tend to indicate that the SwissRe underestimated the return period of loss between 1-5 years

• For return periods > 40 years there is a tendency for SwissRe to overestimate the risk of loss

• Uncertainty in the calibration estimates leads to large uncertainties in loss bypass calibration by altering the vunerabilty in catXos

• However, the use of s2d data has replaced statistical perturbation of storms (SwissRE) with dynamical perturbations (s2d)



The covariation of wind storm frequency, intensity and loss over Europe with large-scale climate diagnostics

• Hypothesis: Large-scale atmospheric state has an influence the frequency and magnitude of wind storms

• As prediction of large-scale circulation improves in seasonal forecast models improved estimates of storminess, a type of potential predictabilty...

• S2d data maybe useful to determine the relationships since these relationships are determined using ERA40 or e.g. HadSLP i.e. Shorter than s2d

• The chicken or the egg? circular arguments



Monthly mean Geopotential Height @850hPa (m) ONDJFMA




Parameters of the PCA

• Performed on anomalies monthly mean (previous slides) subtracted

• Grid-points latitude weighted by the • Covariance matrix• pcaXcca CATtool• Five PCs chosen (will perform a Rule N check later)• PC loadings (EOFs) are scaled such that:

• The length of the eigenvectors = eigenvalues• The PCs have mean of zero and a s.d of 1



PC Loadings (EOF) GPH@850hPa anomalies ONDJFMA




Vector Generalised Linear Models (VGLMs)

• Extension of GLMs in that multivariate responses can be used• Allows modelling of the parameter of a chosen distribution as a

function of the covariates• Applicable to distributions such as: Poisson, Gamma, GEV and

GPD• R package VGAM, Yee & Stephenson (2007)



A VGLM model of applied to the r-th largest GEV distribution

• ERA40 data• Could be used to explore observed variability (EMULATE)

and decadal variability in s2d or C20C



Exploratory analysis using Vector Generalised Additive Models (VGAMs)

• Fit a smooth function in the vector generalised linear model• Allows non-linearity in relationships to be seen

VGAM model

VGLM model



Storm Frequency Model: ERA40

D.F. Smoother = 1 D.F. Smoother = 2



Storm Frequency Model: SYS 3

D.F. Smoother = 1 D.F. Smoother = 2

?



Storm Frequency Model: ERA40Call:vglm(formula = COUNT ~ PC1 + PC2 + PC3 + PC4 + PC5 + SEAS.CYC, family = poissonff, data = datadf)

Pearson Residuals: Min 1Q Median 3Q Maxlog(mu) -1.569 -0.5951 -0.07564 0.4592 2.612

Coefficients: Value Std. Error t value(Intercept) -0.744843 0.16803 -4.4329PC1 0.291205 0.04045 7.1993PC2 0.038500 0.04053 0.9499PC3 0.237290 0.04117 5.7643PC4 0.008085 0.04215 0.1918PC5 0.023258 0.04248 0.5475SEAS.CYC 0.647527 0.07881 8.2163



Storm Frequency Model: SYS 3Call:vglm(formula = COUNT ~ PC1 + PC2 + PC3 + PC4 + PC5 + SEAS.CYC, family = poissonff, data = datadf)

Pearson Residuals: Min 1Q Median 3Q Maxlog(mu) -1.771 -0.6984 -0.1361 0.5543 4.712

Coefficients: Value Std. Error t value(Intercept) -1.01632 0.06254 -16.2516PC1 0.14956 0.01766 8.4693PC2 0.01769 0.01646 1.0744PC3 0.18474 0.01682 10.9811PC4 -0.01294 0.01722 -0.7512PC5 0.00913 0.01679 0.5436SEAS.CYC 0.82837 0.03274 25.3049




• Conditional frequency plots: Number of wind storms per month

• Seasonal cycle held constant





• Remaining variable held constant

• Given it is January: mean occurrence is ~2.4

• If PC1 is forecasted to be +2

• Then number of wind storms is likely to be ~ 4



Storm Frequency Model: SYS 3




Summary: Storm frequency models

• The NAO and the EAL are important for wind storm frequency• SYS 3 EAL is more strongly connected with storm freq. than

ERA40• SYS 3 NAO is less strongly connected with storm freq. than

ERA40

• Formal likelihood ratio tests show that the seasonal cycle improves models

• In the literature there is no framework on how to measure the “explained variance” of a GLM and VGLM/VGAM models, will investigate further cross-validation

• Calculation of conditional exceedance probabilities • Storm seriality: over-dispersion parameter of the Poisson GLM• Reperform calculations with the new storm selection (next section)• Adjust storm selection parameters so that ERA40 does not have

as many storms (due to the 6hour time resolution)



Storm Instensity Model: ERA40 Gamma Generalised Linear Model

Gamma distribution

VGLM model

VGAM model

• Y= Monthly mean wind storm Q95



Storm Intensity Model: ERA40Call:vglm(formula = INTENSITY ~ PC1 + PC2 + PC3 + PC4 + PC5 + SEAS.CYC, family = gamma2, data = datadf)

Pearson Residuals: Min 1Q Median 3Q Maxlog(mu) -1.978 -0.6599 -0.1958 0.5165 5.133log(shape) -14.816 -0.1006 0.4248 0.6416 0.707

Coefficients: Value Std. Error t value(Intercept):1 2.393119 0.121266 19.7345(Intercept):2 5.641005 0.088683 63.6085PC1 0.014859 0.003678 4.0397PC2 0.004446 0.003686 1.2060PC3 0.004940 0.003784 1.3054PC4 -0.010739 0.003703 -2.9004PC5 -0.001216 0.003713 -0.3276SEAS.CYC 0.033483 0.004177 8.0156

PC4: Negative influence of blocking



Storm Intensity Model: SYS 3Call:vglm(formula = INTENSITY ~ PC1 + PC2 + PC3 + PC4 + PC5 + SEAS.CYC, family = gamma2, data = datadf)

Pearson Residuals: Min 1Q Median 3Q Maxlog(mu) -1.996 -0.7339 -0.1486 0.5368 7.478log(shape) -29.975 -0.1507 0.3969 0.6383 0.707

Coefficients: Value Std. Error t value(Intercept):1 2.443144 0.037800 64.634(Intercept):2 5.642231 0.035290 159.880PC1 0.004222 0.001478 2.856PC2 -0.003797 0.001438 -2.641PC3 0.007121 0.001451 4.907PC4 -0.001576 0.001490 -1.058PC5 -0.002902 0.001459 -1.989SEAS.CYC 0.031910 0.001200 26.593

PC3: EAL significant

PC4: not significant (blocking biases in SYS3?)



Storm Intensity Model: ERA40

• Conditional intensity plots: Monthly average Q95 (ms^-1) of wind storms



Summary: Storm intensity models

• In ERA40: +NAO and -blocking pattern are related to + storm intensity

• In SYS 3: +NAO and +EAL pattern are related to + storm intensity

• Differences could be due to longer dataset or biases in SYS 3?

• Generally the statistical significance of intensity models is lower than with the frequency models



Storm Loss Model: ERA40 Gamma Generalised Linear Model

• Express total monthly loss as %TIV• Transform the loss data by the cube root (very long tailed

dist)• Apply Gamma Generalised Linear Model



Storm Loss Model: ERA40 & SYS 3

• Conditional loss plots: Monthly total cube-root of %TIV

Lower influence of NAO on loss in SYS 3 (right) compared with ERA40 (left)



Summary: Storm loss models

• In ERA40: +NAO and +EAL are related to + storm intensity• In SYS 3: +NAO and +EAL and a - blocking pattern are

related to + storm intensity• SYS 3 NAO relationship much weaker than in ERA40• Differences could be due to longer dataset or biases in SYS

3?



PC Loadings (EOF) equivalent potential temperature @850hPa anomalies ONDJFMA


Influence of additional latent heat flux from the gulf stream?



Storm Frequency & Intensity Model: ERA40

Storm Frequency Storm Intensity

Non-linearity in the relationshipD.F. Smoother = 2 D.F. Smoother = 2



Storm Frequency & Intensity Model: ERA40

Storm Frequency Storm Intensity

Non-linearity in the relationshipD.F. Smoother = 2



Extensions of the Method

• Reason the GPD and GEV are not suitable is that the monthly mean wind storm intensity is not GPD distributed!

• Investigate other distributions for loss data, currently we need a cube-root transformation!

• Compute conditional exceedence probabilities• E.g. What is the probability of 5 or more wind storms occuring in a

particular month conditional on PC1 score being x?• Apply it to grid point statistics• Assess the added accuracy in the relationships as a result of using

s2d data



A bivariate extreme value peak over threshold model for wind storm intensity and loss• Using the methodology in Coles (2001) and the evd R -

package• Fitted to ERA40 wind storm Q95 and the transformed %TIV• Could be used to define the vulnerability with real loss data

federal department of home affairs fdha federal office of meteorology and climatology meteoswiss the...

Documents

wind storm intensity

wind storm climatology

mark liniger

records of wind storms

christof appenzeller

q95 winter

risk assessment

loss slide