PowerPoint Presentation Shifts In U'S' Hurricane Landfall P

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Climate signals in US hurricane losses
2nd International Summit on Hurricanes and
Climate Change
June 2nd, 2009 Corfu, Greece
Thomas H. Jagger James B. Elsner Department of
Geography Florida State University http//myweb.f
su.edu/jelsner Support from RPI and NSF with
thanks to
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Research Questions

• Do climate signals exist in hurricane loss data?
• If so, can we develop loss models using
  historical loss events and climate variables that
  can be used to predict
• This seasons hurricane loss?
• The largest loss in the next 50 years?

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Specific Questions of Interest

• What evidence exists to show that hurricane
  losses are conditioned by climate?
• Under what climate conditions would we expect the
  most/least damage in a given year?
• How does the yearly distribution of loss change
  as we move from least favourable to most
  favourable climate conditions?
• How do the return levels of damage change under
  different climate conditions?

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Climate Conditioning Summary
Hurricane losses are conditioned by
climate... Scenarios created using maximum /
minimum historical values for climate variables

• Under worst case scenario 99 probability of at
  least one loss during one year. Median loss 188
  billion.
• The median 50-year maximum storm is 793 billion.
• Under best case scenario 63 probability of at
  least some loss during one year. Median loss .12
  billion.
• The median 50-year maximum storm is 18 billion.
• Mean values are much larger, e.g. mean loss 2
  trillion for 50-year maximum storm size under
  worst case scenario.

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Loss Data

• Loss Data set by Collins and Lowe (CL)
• From 1900-1999
• Extended through 2005 using insured losses from
  U.S. Property Claims Service.
• 2006 - 2008 data from NHC storm summaries.
• Collins, D.J., and S.P. Lowe, 2001 A macro
  validation dataset for U.S. hurricane models.
  Casualty Actuarial Society, Winter Forum,
  217252.
• Raw Data is extrapolated to 2005 dollars for
• Inflation
• Wealth
• Population
• Data similar to that by Pielke and Landsea (PL)
• Total loss data available.
• Includes losses due to tropical storms.
• Pielke, R.A., Jr., and C.W. Landsea, 1998
  Normalized hurricane damages in the United
  States, 192595. Wea. Forecasting, 13, 621631.

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Loss Data by Event
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Yearly CL Total Loss Data
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Removal of Tropical Storm Loses
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• To be useful to risk models, the relationship
  between climate and hurricane activity needs to
  be forecast in advance of the season.

Fortunately, four important climate variables
related to hurricanes can be used in a prediction
model but each variable enters the prediction
model in a unique way.
NAO May-June, precursor signal to hurricane
activity.
SST Aug-Oct, Slowly varying (persistent
predictable)
SOI Aug-Oct, Can be predicted with some skill by
dynamical models. Pressure component of ENSO
SSN Sept. Sun Spot Number. Very predictable once
cycle starts.
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Seasonal Predictors
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Evidence for Climate Effects
ENSO (as SOI) ratio switch from 50 to 99 All
variables related to loss, ratio different than
1.0.
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Damage Models

• Two damage models
• Yearly loss model
• Predict current year US Hurricane losses.
• Not designed to estimate extreme losses as an
  extreme value distribution not used to model
  losses.
• Extreme loss model
• Predict extreme losses under different climate
  scenarios.
• Not designed to estimate yearly losses as small
  losses are removed from model.
• Conditional marked Poisson process assumption
• Process Series of storm losses
• Counts Total number of yearly storm losses
• Follow climate conditioned Poisson distribution
  by assumption
• Counts independent given Poisson rate.
• Marks Losses associated with each storm
• Follow climate conditioned parametric
  distribution.
• Marks independent given parameters.

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Yearly Loss Model

• Tropical storms removed
• Damages split into small and large sets
• Used 1 Billion to separate Hurricanes into small
  and large losses.
• Log(Hurricane losses) are normally distributed.
• 210 Storms, 151 Hurricanes, 85 large, 66 small
• Large set contains 94 of hurricane losses.
• Marked Poisson point process approach
• Independently model small and large losses.
• Bayesian analysis used to estimate the posterior
  distributions of model parameters and predicted
  yearly losses.

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Yearly Loss Model Fits

• Model Distributions with WinBugs code
• log10(loss) Truncated normal, u9 (log(1
  Billion))
• Small Losses LSdnorm(mS,sS) T(0,u)
• mS 9.54 , sS 1.11
• Large Losses LLdnorm(mL,s) T(u,8)
• mL 9.04 .981
  SST sL .810
• Storm Rate Poisson
• Small Losses NSdpois(?S)
• log(?S) -.543
  .00898(Year-1954)
• Large Losses NLdpois(?L)
• log(?L ) -.140 1.22
  SST - .160 NAO
• 
  .420 SOI - .00448 SSN
• Uninformative priors used for model parameters.
• DIC used for Model Selection.
• Parameter estimates shown here are posterior
  means.

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Yearly Losses Depend on Climate
SST-.52, NAO2.9, SOI-2.3, SSN236
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SST.61, NAO-2.7, SOI2.61, SSN0
0
Probability of loss free year
Damage increases with increasing SST, SOI
and with decreasing NAO, SSN
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GPD Distribution
Extreme Loss Model

• In most cases, the largest observations follow a
  Generalized Pareto Distribution.
• Distribution has three parameters
• threshold (u)
• scale(s)
• shape(x)
• LL dGPD(u,s,x)
• Threshold is
• set at 9.0 (log10(1 Billion)
• set so remaining data follow GPD.
• determined using graphical tools
• Mean residual life plot,
• Parameters versus threshold plot,
• Return level plots

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Extreme Loss Model
Peaks-over-threshold
(POT)

• Peaks Logarithm of large Losses follows GPD
• Log scale (s) regressed onto NAO and SST.
• Shape (x) regressed onto SOI.
• Counts Yearly counts of extreme hurricane
  losses have Poisson distribution
• Logarithm Poisson rate (?) regressed onto NAO,
  SST, SSN, SOI.
• Bayesian analysis used to estimate the posterior
  distributions of regression coefficients and
  predicted loss.
• Best model selected by minimizing DIC over all
  reasonable sets of regression coefficients, that
  is over sets of covariate sets
• Our case s NAO,SST, x SOI,
  ?NAO,SST,SSN,SOI
• Quantile equation is used to calculate return
  levels which are
• Nonlinear functions of model parameters s, x, ?
• random variables since regression coefficients
  are random.

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Extreme Loss Model

• Model Distributions
• log(loss) GPD
• LLdGPD(u,?,?)
• u9 (log(1 Billion))
• Rate Poisson
• NNdpois(?)
• log(?) .0014 .640 SST - .123 NAO
• ? -.504 -.138 SOI
• log(?) -.142 1.21 SST - 0.161 NAO
• .420 SOI - .00442
  SSN
• Uninformative priors used for parameters.

SST NAO
SSN
LL
NN
as coded in OpenBUGS Set RP to RP-.5 for year to
year rl.
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Extreme Losses Depend on Climate
Return level quantiles for different climate
regimes
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Results using CL loss data

• Climate signals exist in loss data!
• Predictive models were easily created by assuming
  losses follow a conditionally marked Poisson
  process.
• Bayesian framework. Model selection based on DIC.
• Yearly Loss Model, important regression
  covariates
• SST log10(large loss), mL and large storm rate,
  log(?L)
• SOI,NAO, SSN Large storm rate, log(?L)
• Yr Small storm rate, log(?S)
• No important covariates for log10(small loss), mS
  .
• No covariates used for variance parameters sL
  and sS .
• Extreme Loss Model, important covariates
• Log(losses) gt 9 assumed to have GPD
• NAO and SST Storm rate, log(?) and GPD scale,
  log(s)
• SOI Storm rate, log(?) and GPD shape, ?
• SSN Storm rate, log(?)

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Comments on POT BUGS Models

• Bayesian Modeling with OpenBUGS
• Model mixes well.
• Model must be initialized carefully.
• MLE is estimated from posterior sample values at
  minimum deviance.
• Posterior mean and MLE often very different.
• Return level samples useful only for fixed
  climate predictors.
• DIC used for model selection.
• Demo and R/OpenBUGS code available.
• Yearly model and extreme model code available.
• Insured loss and total loss data examined.

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More Information

• Google hurricane climate
• http//myweb.fsu.edu/jelsner
• jelsner_at_fsu.edu tjagger_at_fsu.edu
• Forecasting U.S. insured hurricane losses
• Thomas H. Jagger, James B. Elsner and Mark A.
  Saunders in Climate Extremes and Society by
  Cambridge University Press
• Environmental signals in property damage due to
  hurricanes
• Thomas H. Jagger and James B. Elsner, Submitted
  To Natural Hazards by Springer

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