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Extreme Hurricane Winds in the United States Thomas H. Jagger & James B. Elsner Department of Geography Florida State University http://garnet. fsu . edu/~jelsner/www University of Florida’s Winter Workshop on Environmental Statistics January 12, 2007 Gainesville, FL
Coastal hurricanes are a serious social and economic concern for the United States.
Strong winds, heavy rainfall, and storm surge kill people and destroy property.
Hurricane destruction rivals that from earthquakes.
Historically, 80% of all U.S. hurricane damage is caused by 20% of the most intense hurricanes.
The rarity of severe hurricanes implies that empirical estimates of return periods likely will be unreliable.
Extreme value theory provides models for rare wind events and a justification for extrapolating to levels that are much greater than have already been observed.
Stuart Coles “An Introduction to the Statistical Modeling of Extreme Values”
Definitive answers to questions about whether hurricanes will be more intense or more frequent in a future of global warming require long records .
The expected worse case indicates a 94% probability of at least some loss during a year.
The expected worse case amount is $23.7 billion.
The expected best case indicates a 53% probability of at least some loss.
The expected best case amount is $1.1 billion.
The maximum 50-year single event loss under the worse case is $630 billion.
The maximum 50-year single event loss under the best case is $10 billion.
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Poisson Regression 1993 Regression Tree 1996 Discriminant Model 1997 Time Series Model 1998 Single Change Point Model 2000 Weibull Model 2001 Space Time Model 2002 Extreme Value Model 2006 Cluster Model 2003 Time Series Regression 2008 Multiple Change Point Model 2009 Space Time Regression 2010 Hurricane Type (Paths, Origin) Hurricane Rate (Counts) Hurricane Strength (Intensity) Regional Hurricane Activity Large Scale Predictors (AMO, NAO, ENSO) Regional Scale Predictors (SST, SLP, etc)
Darling (1991): empirical model to estimate local probabilities of hurricane wind speeds exceeding specified thresholds.
Rupp and Lander (1996): method of moments on annual peak winds over Guam to determine the parameters of an extreme value model leading to estimates of recurrence intervals for extreme typhoon winds.
Heckert et al. (1998): peaks-over-threshold method and a reverse Weibull distribution to obtain mean recurrence intervals for extreme wind speeds at consecutive mileposts along the U.S. coastline.
Chu and Wang (1998): various parametric distributions to model return periods for tropical cyclone wind speeds in the vicinity of Hawaii.
Jagger et al. (2001): maximum likelihood (ML) estimation to determine a linear regression for the scale and shape parameters of the Weibull distribution for hurricane wind speeds in coastal counties.
Pang et al. (2001): Bayesian approach to estimating parameters from a Weibull distribution using wind speed data.
Interpolating 6-hourly positions and intensities hourly.
For each tropical storm in each region, find maximum wind speed using interpolated values.
Interpolation remove some boundary bias.
Examining the effect of climate variables on the distribution of extreme winds.
The model employed by Jagger et al. (2001) captures the variation of hurricane frequency as a function of climate variables using the Weibull distribution, which is appropriate for wind speeds above some threshold but not necessarily for the most extreme winds.
Here we attempt to put extreme hurricane winds in the context of climate variability and climate-change.
Demonstrating the feasibility of a Bayesian approach for adding older, less reliable, data into the analysis.
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Results: Models for Extremes Curves are based on an extreme value model and asymptote to finite levels as a consequence of the shape parameter having a negative value. Parameter estimates are made using the ML approach. The thin lines are the 95% confidence limits. The return level is the expected maximum hurricane intensity over p -years. Points are empirical estimates and fall close to the curves. Return level plots by region
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Return level plots for the entire U.S. coast (Region 4) by climate factors. Curves are based on an extreme value model using a ML estimation procedure. Data is partitioned separately by predictor. Red (blue) lines and points indicate above (below) normal climate conditions for each predictor. 15
Theoretical predictions of the influence of global warming on hurricane activity suggest:
Increased maximum intensity.
Increased level of storminess is uncertain .
Impact of Global Warming? Return Level (kt) Warm years Cold years For a given return period (> 5 yr), warm years result in higher return levels.
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Entire coast 137 kt Magnitude of the difference in return level is consistent with climate models Warm Years Cold Years Saffir-Simpson Category 14 yr No change in frequency of weaker hurricanes 11 Hurricane Katrina
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Bayesian Extreme Value Models Hurricane Intensity Component Hurricane Frequency Component Covariate Component Observed maximum wind speed. True maximum wind speed. Bayesian model for coastal hurricane wind speeds Intercept: j=1 X[,1]=1 for all
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How Gibbs Sampling Works Gibbs sampling algorithm in two parameter dimensions starting from an initial point and completing three iterations. (0) (1) (2) (3) The contours in the plot represent the joint distribution of and the labels (0) , (1) etc., denote the simulated values. One iteration of the algorithm is complete after both parameters are revised. Each parameter is revised along the direction of the coordinate axes---problematic if the two parameters are correlated (contours compressed) as movement along the axes tend to produce small changes in parameter values.
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Region 4: Northeast Coast Region 3: Southeast Coast Region 2: Florida Region 1: Gulf Coast Hourly interpolated hurricane positions (1851-2004)
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Bayesian Model for Coastal Hurricane Winds 2 Hurricane Intensity Component Hurricane Frequency Component Covariate Component Observed maximum wind speed. True maximum wind speed.
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Results: Raw Climatology P( >0) = 0.22 P( >0) < 0.01 P( >0) < 0.01 P( >0) < 0.01 Assuming the model is correct, the data support a super-intense hurricane threat only in the Gulf of Mexico. Region 1: Gulf Coast: Shape Region 2: Florida: Shape Region 3: Southeast: Shape Region 4: Northeast: Shape Probability that hurricane intensity is unbounded Frequency Distribution Frequency Distribution
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Important Results: Conditional Climatology log( ) log( ) log( ) log( ) log( ) log ( ) Frequency Distribution Frequency Distribution Region 1: AMO: Scale Region 3: AMO: Threshold Region 1: NAO: Threshold Region 2: NAO: Threshold Region 1: SOI: Threshold Region 3: SOI: Threshold Stronger Hurricanes More Hurricanes More Hurricanes More Hurricanes More Hurricanes More Hurricanes
A Monte Carlo procedure is employed on the posterior samples to generate a large number (50K) simulated hurricane seasons based on sampled covariate and parameter values.
Results from the Gulf Coast show that the simulated data match the empirical data through Category 4 wind speeds but for winds in excess of 135 kt (68 m/s) the simulated data indicate a higher frequency (by a factor of 2 to 3). *mean annual exceedence rate Region 1: Gulf Coast 0.015 0.028 0.054 0.143 0.279 0.423 0.469 Simulation* 0.007 0.007 0.037 0.142 0.313 0.418 0.463 Empirical data* 170 150 135 114 96 83 80 Threshold (kt) V++ V+ V IV III II > I Category (SS)
Modeled 100-year return levels do not appear to match empirical evidence.
Might be a problem with the regression structure of the shape parameter. Using simpler models where we replace the covariates with discrete factors (above/below normal) we produce a better match.
Convergence is not guaranteed when modeling the log( ) and scale as a linear combination of covariates.
Problem in region 4 (NE) where there are fewer hurricanes.
Threshold is not estimated in the current model.
Behrens, Lopes and Gamerman(2004)
"Bayesian analysis of extreme events with threshold estimation“
Statistical Modelling, 4, 227-244.
The nature of the shape parameter is such that its value is a function of the support of the underlying distribution.
Attempts to model this using a Reversible Jump Markov Chain MC approach reduces this problem but introduces significant autocorrelation into the sampler.
Model assigns positive probability for discrete values of xi, uses RJMCMC
To be useful to risk models, the relationship between climate and hurricane activity needs to be forecast in advance of the season.
Fortunately, three important climate variables related to hurricanes can be used in a prediction model; but each variable enters the prediction model in a unique way.
NAO : Natural precursor signal to hurricane activity.
SST : Slowly varying (persistent).
ENSO : Can be predicted with some skill by dynamical models.
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Small Loss Events (36.5%) Large Loss Events (63.5%) 99.4% Losses 0.6% Losses Reference line indicates 80/17 split We split losses (red line: $100 Million) Allows us to examine significant events Splitting Insured Losses
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SST SST 25 Preseason Predictors Insured Loss Model Model Distributions : log(loss): Truncated Normal . dnorm( ,1/ 2 ) Rate: Poisson dpois( ) May June averaged values of predictors
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SST 27 Extreme Loss Model and Results Predictors set at maximum values of covariates with least favorable climate: +NAO, +SOI -NAO, -SOI Model Distributions : log(loss): GPD distribution . dGPD(u, , ) u=9 (log(1 Billion)) Rate: Poisson dpois( )
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