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

1. 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 15.05.2008

2. 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

3. 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

4. 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

5. 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)

6. 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

7. Monthly mean Geopotential Height @850hPa (m) ONDJFMA ERA40 Difference SYS 3

8. Data Quality: Intercomparison of the 99th %-tile wind climate ERA40 ECMWF System 2 ECMWF System 3 Wind Gust WG Geostr. wind @ 850hPa GWS

9. 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

10. Probabilistic prediction skill: ECMWF Sys2 • Ranked Probability Skill Score(terciles) • Bootstrap confidence intervals Little evidence of Predictabilty Initial Condition Pred. Nov Dec Jan Feb Mar Apr May

11. 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

12. Storm Selection Method Index: Q95 95% threshold Winter 1999/2000

13. Number of wind storms identified in ERA-40 and s2d Example ERA-40 wind storm climatology

14. 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

15. Improved estimates of wind storm frequency and magnitude uncertainty 95% Confidence interval (profile log-likelihood) Return Level Return Period

16. 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

17. Example: percentile calibration curves SYS 3 SYS 2 DEMETER

18. 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

19. Percentile calibration and Aliasing

20. 95th Percentile calibration and Aliasing

21. GPD Parameters after calibration • Shape parameter is less negative • Aliasing has helped the frequency of occurrence (lambda)

22. 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.

23. Swiss Re Wind Storm Loss Model(catXos) • Vulnerability curve shows a cubic relation which is capped • Portfolio value distribution is inhomogeous

24. 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

25. CALIB1: ERA40 GWS  SwissRE (*me2) • Adjustment curve: CDF(SwissRE)-CDF(ERA40) • Set to values greater than zero to zero

26. CALIB2: Sys3 GWS  ERA40 GWS • Adjustment curve: CDF(ERA40)-CDF(Sys3 GWS)

27. 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)

28. 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)

29. 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

30. Monthly mean Geopotential Height @850hPa (m) ONDJFMA ERA40 Difference SYS 3

31. 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

32. PC Loadings (EOF) GPH@850hPa anomalies ONDJFMA ERA40 SYS 3 Difference

33. 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)

34. 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

35. 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

36. Storm Frequency Model: ERA40 D.F. Smoother = 1 D.F. Smoother = 2

37. Storm Frequency Model: SYS 3 D.F. Smoother = 1 D.F. Smoother = 2 ?

38. 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) -1.569 -0.5951 -0.07564 0.4592 2.612 Coefficients: Value Std. Error t value (Intercept) -0.744843 0.16803 -4.4329 PC1 0.291205 0.04045 7.1993 PC2 0.038500 0.04053 0.9499 PC3 0.237290 0.04117 5.7643 PC4 0.008085 0.04215 0.1918 PC5 0.023258 0.04248 0.5475 SEAS.CYC 0.647527 0.07881 8.2163

39. 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) -1.771 -0.6984 -0.1361 0.5543 4.712 Coefficients: Value Std. Error t value (Intercept) -1.01632 0.06254 -16.2516 PC1 0.14956 0.01766 8.4693 PC2 0.01769 0.01646 1.0744 PC3 0.18474 0.01682 10.9811 PC4 -0.01294 0.01722 -0.7512 PC5 0.00913 0.01679 0.5436 SEAS.CYC 0.82837 0.03274 25.3049

40. Storm Frequency Model: ERA40 • Conditional frequency plots: Number of wind storms per month • Seasonal cycle held constant

41. 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

42. Storm Frequency Model: SYS 3 • Conditional frequency plots: Number of wind storms per month

43. 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)

44. Storm Instensity Model: ERA40 Gamma Generalised Linear Model • Y= Monthly mean wind storm Q95 Gamma distribution VGLM model VGAM model

45. 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) -1.978 -0.6599 -0.1958 0.5165 5.133 log(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 63.6085 PC1 0.014859 0.003678 4.0397 PC2 0.004446 0.003686 1.2060 PC3 0.004940 0.003784 1.3054 PC4 -0.010739 0.003703 -2.9004 PC5 -0.001216 0.003713 -0.3276 SEAS.CYC 0.033483 0.004177 8.0156 PC4: Negative influence of blocking

46. 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) -1.996 -0.7339 -0.1486 0.5368 7.478 log(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 159.880 PC1 0.004222 0.001478 2.856 PC2 -0.003797 0.001438 -2.641 PC3 0.007121 0.001451 4.907 PC4 -0.001576 0.001490 -1.058 PC5 -0.002902 0.001459 -1.989 SEAS.CYC 0.031910 0.001200 26.593 PC3: EAL significant PC4: not significant (blocking biases in SYS3?)

47. Storm Intensity Model: ERA40 • Conditional intensity plots: Monthly average Q95 (ms^-1) of wind storms

48. 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

49. 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

50. 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)