STOCHASTIC MODELING OF HURRICANE DAMAGE UNDER CLIMATE CHANGE Rick Katz Institute for Study of Society and Environment National Center for Atmospheric Research Boulder, CO USA Email: rwk@ucar.edu Web site: www.isse.ucar.edu/hp_rick.html Talk: www.isse.ucar.edu/hp_rick/pdf/lsce.pdf
QUOTE Emil Gumbel (1941): "Il est impossible que l'improbable n'arrive jamais."
OUTLINE (1) Economic Damage from Hurricanes (2) Stochastic Model for Damage (3) Effects of El Niño (4) Trends in Extreme Hurricanes (5) Unresolved Issues
(1) Economic Damage from Hurricanes Data -- Pielke and Landsea (1998) Web site: sciencepolicy.colorado.edu/homepages/roger_pielke/ hp_roger/hurr_norm/data.html Normalized Data -- Adjusted for inflation & changes in societal vulnerability -- Residual intended to reflect only climate
(2) Stochastic Model for Damage Random Sum Model -- Embrechts et al. (1997): Bread and butter of insurance mathematics Number of Events -- Poisson distribution (Trend? Covariates?) Damage for Individual Storm -- Lognormal distribution (Trend? Covariates?) -- Generalized Pareto distribution for upper tail
Statistics of Random Sums -- Notation N(t) number of events in tth yr X k damage from kth event in tth yr (i. i. d.) S(t) = X 1 + X 2 + + X N(t) total damage in tth yr -- Mean of total annual damage E[S(t)] = E[N(t)] E(X k ) -- Variance of total annual damage Var[S(t)] = E[N(t)] Var(X k ) + Var[N(t)] [E(X k )] 2
Heavy Tail -- Estimated shape parameter of GP distribution 0.5 Origin of Heavy Tail -- Underlying geophysical phenomenon? -- Inherent feature of distribution of income or wealth? (Recall origin of Pareto distribution) Chance Mechanisms -- Mixture of light-tailed distributions can induce heavy-tailed distribution (e. g., exponential to Pareto)
(3) Effects of El Niño El Niño Phenomenon -- Statistical characteristics ( quasi-periodic ) -- Teleconnections (interannual variability) Connections to Hurricane Statistics -- Hurricane frequency -- Hurricane intensity -- Hurricane path (North Atlantic Oscillation)
Tail Dependence on El Niño State -- Unable to detect effect on parameters of generalized Pareto distribution -- Unable to detect effect on frequency of high damage (parameter of Poisson distribution) Inconsistency between Extremal & Non-Extremal Modeling -- Issue of parsimony -- Chance mechanisms -- Penultimate approximations
(4) Trends in Extreme Hurricanes Background -- Trend in frequency of intense hurricanes (Along with trends in Sea Surface Temperature) Damage Data -- Adjusted for inflation & societal vulnerability -- Lack of any apparent trend
Hurricane Damage Data -- U. S. National Hurricane Center www.nhc.noaa.gov/gifs/table3b.gif -- 30 most damaging hurricanes (1900 2004) Unadjusted damage data (Only corrected for inflation, 2004 US billion $) Adjusted damage data (Adjusted for both inflation & changes in societal vulnerability)
Unadjusted Hurricane Damage 40 Damage (billion $) 30 20 10 0 1900 1920 1940 1960 1980 2000 Year
Adjusted Hurricane Damage 100 Damage (billion $) 80 60 40 20 0 1900 1920 1940 1960 1980 2000 Year
Annual Number of Events (Adjusted Damage) -- Poisson distribution (With trend?) Rate parameter λ(t): log λ(t) = λ 0 + λ 1 t MLE of λ 1 = 0.012 ( 1.2 % per yr increase) LRT: P-value 0.057
Adjusted Hurricane Frequency 4 3 Frequency 2 1 0 1900 1920 1940 1960 1980 2000 Year
Adjusted Hurricane Frequency 4 Observed Poisson trend 3 Frequency 2 1 0 1900 1920 1940 1960 1980 2000 Year
Adjusted Damage for Individual Storm -- Generalized Pareto (GP) distribution for upper tail Excess in adjusted damage over threshold of $10 billion (17 storms) Heavy upper tail: Shape parameter ξ 0.3 (If include damage from Hurricane Katrina in 2005: ξ 0.5)
Adjusted Hurricane Damage: Q-Q Plot Katrina Observed Damage (billion $) 100 80 60 40 20 0 0 20 40 60 80 100 Expected Damage (billion $)
Trend in Adjusted Damage -- GEV distribution fit to damage for all 30 storms (Rather than GPD to highest 17 storms) Linear trend in location parameter μ(t): μ(t) = μ 0 + μ 1 t MLE of μ 1 = 0.037 billion $ per yr LRT: P-value 0.133 (Shape parameter ξ 0.5)
(5) Unresolved Issues Trends -- Meteorology versus impacts El Niño Effects -- Frequency effect stable -- Damage effect unstable?