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Federal Department of Home Affairs FDHA Federal Office of Meteorology and Climatology MeteoSwiss The covariation of windstorm frequency, intensity and loss over Europe with large- scale climate diagnostics A collaboration between SwissRe, MeteoSwiss, FP6 ENSEMBLES and NCCR Climate

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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

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3 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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

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4 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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

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5 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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)

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6 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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

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7 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Monthly mean Geopotential (m) ONDJFMA ERA40SYS 3 Difference

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8 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Data Quality: Intercomparison of the 99th %-tile wind climate Wind Gust WG Geostr. 850hPa GWS ERA40 ECMWF System 2 ECMWF System 3

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9 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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

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10 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Probabilistic prediction skill: ECMWF Sys2 Ranked Probability Skill Score (terciles) Bootstrap confidence intervals Nov Dec Jan Feb Mar Apr May Little evidence of Predictabilty Initial Condition Pred.

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11 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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

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12 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Storm Selection Method Index: Q95 Winter 1999/ % threshold

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13 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Number of wind storms identified in ERA-40 and s2d Example ERA-40 wind storm climatology

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14 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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

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15 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Improved estimates of wind storm frequency and magnitude uncertainty Return LevelReturn Period 95% Confidence interval (profile log-likelihood)

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16 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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

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17 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Example: percentile calibration curves SYS 3SYS 2DEMETER

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18 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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 DEMET ER, 24hr

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19 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Percentile calibration and Aliasing

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20 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 95 th Percentile calibration and Aliasing

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21 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller GPD Parameters after calibration Shape parameter is less negative Aliasing has helped the frequency of occurrence (lambda)

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22 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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.

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23 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Swiss Re Wind Storm Loss Model ( catXos ) Vulnerability curve shows a cubic relation which is capped Portfolio value distribution is inhomogeous

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24 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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

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25 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller CALIB1: ERA40 GWS SwissRE (*me2) Adjustment curve: CDF(SwissRE)-CDF(ERA40) Set to values greater than zero to zero

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26 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller CALIB2: Sys3 GWS ERA40 GWS Adjustment curve: CDF(ERA40)-CDF(Sys3 GWS)

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27 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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)

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28 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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)

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29 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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

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30 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Monthly mean Geopotential (m) ONDJFMA ERA40SYS 3 Difference

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31 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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

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32 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller PC Loadings (EOF) anomalies ONDJFMA ERA40 SYS 3Difference

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33 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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)

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34 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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

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35 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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

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36 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Storm Frequency Model: ERA40 D.F. Smoother = 1D.F. Smoother = 2

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37 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Storm Frequency Model: SYS 3 D.F. Smoother = 1D.F. Smoother = 2 ?

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38 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Storm Frequency Model: ERA40 Call: vglm(formula = COUNT ~ PC1 + PC2 + PC3 + PC4 + PC5 + SEAS.CYC, family = poissonff, data = datadf) Pearson Residuals: Min 1Q Median 3Q Max log(mu) Coefficients: Value Std. Error t value (Intercept) PC PC PC PC PC SEAS.CYC

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39 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Storm Frequency Model: SYS 3 Call: vglm(formula = COUNT ~ PC1 + PC2 + PC3 + PC4 + PC5 + SEAS.CYC, family = poissonff, data = datadf) Pearson Residuals: Min 1Q Median 3Q Max log(mu) Coefficients: Value Std. Error t value (Intercept) PC PC PC PC PC SEAS.CYC

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40 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Storm Frequency Model: ERA40 Conditional frequency plots: Number of wind storms per month Seasonal cycle held constant

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41 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Storm Frequency Model: ERA40 Conditional frequency plots: Number of wind storms per month 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

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42 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Storm Frequency Model: SYS 3 Conditional frequency plots: Number of wind storms per month

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43 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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)

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44 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Storm Instensity Model: ERA40 Gamma Generalised Linear Model Gamma distribution VGLM model VGAM model Y= Monthly mean wind storm Q95

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45 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Storm Intensity Model: ERA40 Call: vglm(formula = INTENSITY ~ PC1 + PC2 + PC3 + PC4 + PC5 + SEAS.CYC, family = gamma2, data = datadf) Pearson Residuals: Min 1Q Median 3Q Max log(mu) log(shape) Coefficients: Value Std. Error t value (Intercept): (Intercept): PC PC PC PC PC SEAS.CYC PC4: Negative influence of blocking

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46 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Storm Intensity Model: SYS 3 Call: vglm(formula = INTENSITY ~ PC1 + PC2 + PC3 + PC4 + PC5 + SEAS.CYC, family = gamma2, data = datadf) Pearson Residuals: Min 1Q Median 3Q Max log(mu) log(shape) Coefficients: Value Std. Error t value (Intercept): (Intercept): PC PC PC PC PC SEAS.CYC PC3: EAL significant PC4: not significant (blocking biases in SYS3?)

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47 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Storm Intensity Model: ERA40 Conditional intensity plots: Monthly average Q95 (ms^-1) of wind storms

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48 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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

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49 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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

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50 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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)

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51 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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?

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52 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller PC Loadings (EOF) equivalent potential anomalies ONDJFMA ERA40 SYS 3Difference Influence of additional latent heat flux from the gulf stream?

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53 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Storm Frequency & Intensity Model: ERA40 Storm Frequency Storm Intensity Non-linearity in the relationship D.F. Smoother = 2

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54 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller Storm Frequency & Intensity Model: ERA40 Storm Frequency Storm Intensity Non-linearity in the relationship D.F. Smoother = 2

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55 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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

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56 Prediction of Winter Storm Risk Paul Della-Marta, Mark Liniger, Christof Appenzeller 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

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