Report

US Hurricanes and economic damage: an extreme value perspective Nick Cavanaugh, futurologist Dan Chavas, tempestologist Christina Karamperidou, statsinator Katy Serafin, bathy queen Emmi Yonekura, landfaller ASP 2011 Summer Colloquium Project 23 June 2011 Outline • Motivation • Previous work • Methodology and results – Economic data: absolute vs. relative damages – GPD without physical covariates – GPD with physical covariates – Application to GFDL current vs. future hurricanes • Conclusions and future work Motivation: society GDP: 1o x 1o Atlantic hurricane tracks (1900+) (Yale G-Econ) (NHC Best Track) 63% of global insured natural disaster losses caused by US landfalling hurricanes (Source: Rick Murnane, last week) http://gecon.yale.edu http://gcaptain.com/wp-content/uploads/2010/09/Atlantic_hurricane_tracks.jpg Motivation: science • Objectives: – Combine physical storm characteristics with statistics of damages in an extreme value theory framework – Reduce the sensitivity of statistical analysis of damage to economic vulnerability at landfall Recent work • Katz (2002), Jagger et al (2008,2011) • Jagger et al (2008,2011): Generalized Pareto Distribution (GPD) is appropriate for modeling extreme events involving large economic losses However, inclusion of physical characteristics of storms as covariates has not been tried Methodology I: absolute vs. relative damage Economic data: Pielke et al., 2008 • Base year and normalized (2005$) economic damages for 198 storms (pre-threshold) from 1900-2004 Histogram of Coastal GDP 60 50 40 Coastal Points But are variations in damages representative of the damage threat from a hurricane or rather of the large variation in economic value along the coast? 30 20 10 0 0 100 200 300 GDP 400 500 600 Distribution of GDP (bil $) in 1o x 1o boxes along US coast Methodology I: absolute vs. relative damage Physical characteristics of storms and economic value at landfall should be independent Neumayer et al. (2011) Physical * Economic corr = -.1 Damage Index (DI) Fraction of possible damage [0,1] i.e. “damage capacity” of storm Goal: remove from our damage database the variability in damages due to variations in economic value along the coast Results Damages vs. DI: histograms Histogram of Total Damage: Histogram of Damage Index: 120 150 100 80 count count 100 60 40 50 20 0 0 0 50 100 Total.Damage Max = $150 bil 150 0.0 0.2 0.4 DamageIndex Max = .89 0.6 0.8 Results Damages vs. DI: no covariates Damage Index (DI): [0,1] Total Damage: (bil 2005$) 0.8 Bret .89 0 0.4 0.0 0.2 50 Billion $ Damage Index 100 0.6 150 Great Miami $156 bil 1900 1920 1940 1960 1980 Top 10 by Damage: 2000 1900 1920 1940 1960 Top 10 by DI: 1980 2000 Results Damages vs. DI: no covariates Damage Index (DI): [0,1] 30 28 29 Profile Log-likelihood -148 -150 -152 Profile Log-likelihood -146 31 -144 Total Damage: (bil $) 0.0 0.5 Shape Parameter ξ>0 1.0 -0.2 0.0 0.2 0.4 Shape Parameter ξ~0 0.6 0.8 1.0 Results Damages vs. DI: no covariates Quantile Plot 0 0.0 0.2 50 100 Empirical 0.6 0.4 Total Damage Model 0.8 150 1.0 Probability Plot 0.2 0.4 0.6 0.8 1.0 20 60 80 Return LevelPlot Plot Probability Density Plot Quantile Plot 10 0.4 100 0.6 1000 1.0 0.8 ReturnEmpirical period (years) 0.4 0.00 0.2 0.04 Empirical f(x) 0.21 100 0.6 0.08 0.8 0.12 Model 0.6 0.8 1.0 80000 120000 0.1 0.0 40 Empirical 0.4 0 0.2 40000 Damage Index (DI) Modellevel Return 0.0 00.1 0.2 500.3 0.41000.5 x Model 0.6150 0.7 Methodology II: physical covariates Want to capture physical characteristics of individual storms that are relevant to its capacity to cause damage Hurricane Katrina 8:15p CDT Aug 28 2005 Hurricane Katrina 8:15p CDT Aug 28 2005 Eye Hurricane Katrina 8:15p CDT Aug 28 2005 Eyewall Hurricane Katrina 8:15p CDT Aug 28 2005 R34 Methodology II: physical covariates Causes of damage Wind Sensitive to: - Wind speed (Vmax) - Size (R34) Storm surge Sensitive to: - Wind speed (Vmax) - Size (R34) - Bathymetry (seff) - Translation speed - Landfall angle See Irish et al. (2008) http://myfloridapa.com/type%20of%20claims.html Methodology II: physical covariates • Wind speed Vmax: HURDAT Best Track 1900-2004 • Storm size R34: Extended Best Track (CSU) 1988-2005 • Bathymetry: gridded 1-min res altimetry data 100 km seff Methodology II: physical covariates Bathymetry Methodology III: GPD fit PDF -1-1/x ì æ ö x u ) ï 1 ç1+ x ( ÷ ïs è s ø P ( x x > u) = í æ ( x - u) ö ï 1 expç÷ ïî s s è ø ,x ¹ 0 ,x = 0 With Multiple Possible Covariates lns = s 0 + s1Vmax + s 2 seff + s 3 r34 x = x 0 + x1Vmax + x 2 seff + x 3 r34 Results Damage: with covariates Damages lns = s 0 + s1Vmax + s 2 seff Residual Probability Plot 3 0.8 Likelihood - ratio test for s1 = 0 : .62(.28) 2 Empirical 1 0.4 Model 0 ln .58(1.05) .015(.009) Vmax 0.2 u $5 billion(42pts) 0.0 p - value(seff ) = 0.79 0.6 p - value = 0.1 Likelihood - ratio test for s 2 = 0 : 4 1.0 x = x 0 + x1Vmax + x 2 seff Residual Quantile Plot (Exptl. Scale) 0.0 0.2 0.4 0.6 0.8 1.0 0 Empirical 1 2 Model Damage = f(Vmax) *Using 1900-2004 data r34 : not enough data shape parameter left constant 3 Results DI: with covariates Damage Index lns = s 0 + s1Vmax + s 2 seff 4 1.0 Residual Quantile Plot (Exptl. Scale) Empirical 0 ln 2.650.64 0.010.005 Vmax 0.10.036 seff 0.10.17 2 3 0.8 0.6 1 u 0.06 (41pts) 0.4 (s 2 = 0) p - value = 0.02 (s1 and s 2 vs. s 2 ) p - value = 0.056 (s1 = 0, s 2 = 0) p - value = 0.003 0.2 Likelihood -ratio test (s1 = 0) p - value = 0.08 Model x = x0 Residual Probability Plot 0.0 0.2 0.4 0.6 0.8 1.0 0.0 1.0 Empirical 2.0 3.0 Model DI = f(seff, Vmax) *Using 1900-2004 data r34 : not enough data shape parameter left constant Methodology IV: Future Climate • Statistical-Deterministic Hurricane model (Emanuel et al. 2006) – downscaled from GFDL CM2.0 model: 1981-2000 and 2081-2100 (A1b) climates • Modeled values of Vmax and seff => GPD Results: Future Climate GPD PDF of US Hurricane Damage Index Add all PDFs and re-fit GPD for each climate 6 0.4 0.3 density 4 model density 5 model 0.2 A1B ctrl A1B ctrl 3 0.1 2 0.0 0.5 0.6 0.7 DamageIndex 1 0 0.2 0.4 0.6 DamageIndex 0.8 1.0 0.8 0.9 1.0 Results: Future Climate Local Distribution of Scale Parameter Change Scale Parameter Shift 45 Δσlocal =Δ exp( σ0 + σ1Vmax + σ2seff) 0.04 40 0.03 0.02 lat 35 0.01 30 0 25 −0.01 −0.02 20 −100 −95 −90 −85 −80 lon −75 −70 −65 Conclusions • Damage Index, which seeks to remove economic vulnerability from damages, appears to better capture role of physical characteristics of storm in causing damage than actual damages • Bathymetry, wind speed found to be useful covariates whose relationships are consistent with physical intuition • Changes in scale parameter in the future indicate a shift to higher probability of extreme damage events locally and globally, though we haven’t proven differences are statistically significant Future work ideas • Find means of relating back to actual economic damages • Try rmax for size • Account for uncertainty • Try out a deterministic damage index and apply GPD to that? Thanks! Comments/suggestions welcome Results Damages vs. damage index Residual Quantile Plot (Exptl. Scale) 0 0.2 1 0.4 2 Model Empirical 0.6 3 4 0.8 5 1.0 Residual Probability Plot 0.0 0.2 0.4 0.6 0.8 1.0 Empirical 0.0 1.0 2.0 Model DI = f(seff) 3.0 Results Damages vs. damage index Residual Quantile Plot (Exptl. Scale) 2 0 0.2 1 0.4 Model Empirical 0.6 3 0.8 4 1.0 Residual Probability Plot 0.0 0.2 0.4 0.6 0.8 1.0 Empirical 0.0 1.0 2.0 Model DI = f(Vmax) 3.0 Results: Future Climate 0.012 0.010 density 0.008 model A1B control 0.006 0.004 0.002 0.000 50 100 vmax 150 0.6 0.5 density 0.4 model 0.3 A1B control 0.2 0.1 0.0 2 4 6 8 gfdl.all$shelf 10 12 14 Top 10 by Wind Speed: Example 1: Katrina vs. Camille NOAA SLOSH model KATRINA (2005) Peak storm surge = 8.5 m CAMILLE (1969) Peak storm surge = 6.9 m …yet Katrina produced much higher storm surge because it was twice as large http://www.wunderground.com/hurricane/camille_katrina_surge.png http://www.nhc.noaa.gov/HAW2/english/surge/slosh.shtml