1. 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

8. 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)

12. P ( x > v | x > u ) v [kt]

17. Atlantic Sea Surface Temperature (SST) ºC

18. Hurricane Season Global Warming

19. 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

20. 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

22. 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

27. 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

29. 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.

32. Posterior Densities

34. Regions Parameters Covariates + Intercept

35. Region 4: Northeast Coast Region 3: Southeast Coast Region 2: Florida Region 1: Gulf Coast Hourly interpolated hurricane positions (1851-2004)

36. Bayesian Model for Coastal Hurricane Winds 2 Hurricane Intensity Component Hurricane Frequency Component Covariate Component Observed maximum wind speed. True maximum wind speed.

37. 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

38. 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

42. Predicting Insured Losses 21

43. 22 Peaks Over Threshold

44. 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

45. 24 Large Loss Potential Evenly Distributed

46. 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

47. + NAO, -SST - NAO, +SST 26 Yearly Insured Losses Depends on Climate

48. 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(  )

53. Increasing Radius beginning at 45 km