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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
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
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
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)
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
7 Prediction of Winter Storm Risk
Paul Della-Marta, Mark Liniger, Christof Appenzeller
Monthly mean Geopotential Height @850hPa (m) ONDJFMA
ERA40 SYS 3 Difference
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. wind @ 850hPa
GWS
ERA40 ECMWF System 2 ECMWF System 3
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
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 MayLittle evidence of Predictabilty
Initial Condition Pred.
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
12 Prediction of Winter Storm Risk
Paul Della-Marta, Mark Liniger, Christof Appenzeller
Storm Selection Method
Index: Q95
Winter 1999/2000
95% threshold
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
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
15 Prediction of Winter Storm Risk
Paul Della-Marta, Mark Liniger, Christof Appenzeller
Improved estimates of wind storm frequency and magnitude uncertainty
Return Level Return Period
95% Confidence interval (profile log-likelihood)
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
17 Prediction of Winter Storm Risk
Paul Della-Marta, Mark Liniger, Christof Appenzeller
Example: percentile calibration curves
SYS 3 SYS 2 DEMETER
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
DEMETER, 24hr
19 Prediction of Winter Storm Risk
Paul Della-Marta, Mark Liniger, Christof Appenzeller
Percentile calibration and Aliasing
20 Prediction of Winter Storm Risk
Paul Della-Marta, Mark Liniger, Christof Appenzeller
95th Percentile calibration and Aliasing
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)
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.
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
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
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
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)
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)
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)
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
30 Prediction of Winter Storm Risk
Paul Della-Marta, Mark Liniger, Christof Appenzeller
Monthly mean Geopotential Height @850hPa (m) ONDJFMA
ERA40 SYS 3 Difference
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
32 Prediction of Winter Storm Risk
Paul Della-Marta, Mark Liniger, Christof Appenzeller
PC Loadings (EOF) GPH@850hPa anomalies ONDJFMA
ERA40 SYS 3 Difference
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)
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
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
36 Prediction of Winter Storm Risk
Paul Della-Marta, Mark Liniger, Christof Appenzeller
Storm Frequency Model: ERA40
D.F. Smoother = 1 D.F. Smoother = 2
37 Prediction of Winter Storm Risk
Paul Della-Marta, Mark Liniger, Christof Appenzeller
Storm Frequency Model: SYS 3
D.F. Smoother = 1 D.F. Smoother = 2
?
38 Prediction of Winter Storm Risk
Paul Della-Marta, Mark Liniger, Christof Appenzeller
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
39 Prediction of Winter Storm Risk
Paul Della-Marta, Mark Liniger, Christof Appenzeller
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
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
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
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
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)
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
45 Prediction of Winter Storm Risk
Paul Della-Marta, Mark Liniger, Christof Appenzeller
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
46 Prediction of Winter Storm Risk
Paul Della-Marta, Mark Liniger, Christof Appenzeller
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?)
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
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
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
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)
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?
52 Prediction of Winter Storm Risk
Paul Della-Marta, Mark Liniger, Christof Appenzeller
PC Loadings (EOF) equivalent potential temperature @850hPa anomalies ONDJFMA
ERA40 SYS 3 Difference
Influence of additional latent heat flux from the gulf stream?
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 relationshipD.F. Smoother = 2 D.F. Smoother = 2
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 relationshipD.F. Smoother = 2
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
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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