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
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.
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)
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.
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
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.
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
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
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.
Region 4: Northeast Coast Region 3: Southeast Coast Region 2: Florida Region 1: Gulf Coast Hourly interpolated hurricane positions (1851-2004)
Bayesian Model for Coastal Hurricane Winds 2 Hurricane Intensity Component Hurricane Frequency Component Covariate Component Observed maximum wind speed. True maximum wind speed.
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
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)
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
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( )