STOCHASTIC MODELING OF HURRICANE DAMAGE UNDER CLIMATE CHANGE

Transcription

1 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 Web site: Talk:

2 QUOTE Emil Gumbel (1941): "Il est impossible que l'improbable n'arrive jamais."

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5 OUTLINE (1) Economic Damage from Hurricanes (2) Stochastic Model for Damage (3) Effects of El Niño (4) Trends in Extreme Hurricanes (5) Unresolved Issues

6 (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

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8 (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

9 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 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

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14 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)

15 (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)

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18 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

19 (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

20 Hurricane Damage Data -- U. S. National Hurricane Center most damaging hurricanes ( ) Unadjusted damage data (Only corrected for inflation, 2004 US billion $) Adjusted damage data (Adjusted for both inflation & changes in societal vulnerability)

21 Unadjusted Hurricane Damage 40 Damage (billion $) Year

22 Adjusted Hurricane Damage 100 Damage (billion $) Year

23 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 = ( 1.2 % per yr increase) LRT: P-value 0.057

24 Adjusted Hurricane Frequency 4 3 Frequency Year

25 Adjusted Hurricane Frequency 4 Observed Poisson trend 3 Frequency Year

26 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)

27 Adjusted Hurricane Damage: Q-Q Plot Katrina Observed Damage (billion $) Expected Damage (billion $)

28 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 = billion $ per yr LRT: P-value (Shape parameter ξ 0.5)

29 (5) Unresolved Issues Trends -- Meteorology versus impacts El Niño Effects -- Frequency effect stable -- Damage effect unstable?