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Wildfire and Weatherin Southern California:

An exploratory quantitative analysis

Joanne Ho

Ph.D. defenseSchool of Forest Resources

University of WashingtonDecember 7, 2009

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What is wildfire?

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Fires > 250 acres (1980-2003)

Source: www.usgs.gov

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Southern California

San Francisco

Monterey

Lake Tahoe

Tijuana

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Research Question:

Is it possible set up an insurance scheme that will cover costs that exceed the budget allocation?

Traditional insurance

• Dollar-for-dollar payment for damages

• Insurance negligence

• Costly monitoring

• Payment based on proxy of damages

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Alternative insurance

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What causes fires?

Physical:

Weather:

fuel

ignition

temperaturemoisture wind

Weather Derivative

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Can weather derivatives cover costs that exceed the budget allocation?

Given known weather…

What is theprobability of ignition?

If ignition occurs, what is expected size of fire?

Find the best fit payoff function to pay for excess costs

Does the payoff function adequatelypay for excess costs?

Conclusions & further research

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Probability of ignition

Prob{Fireit 1 |weather} ( i 'wi i)Probit model

Logit model

Prob{Fireit 1 |weather} exp( i 'wi i)

1 exp( i 'wi i)

wi = temperature temperature2

relative humidity relative humidity2

vapor pressure deficit rainfall amount2

rainfall duration2

wind speed wind speed2

wi = temperature x relative humidity temperature x rainfall amount temperature x rainfall duration temperature x wind speed relative humidity x rainfall amount relative humidity x rainfall duration relative humidity x wind speed rainfall amount x rainfall duration rainfall amount x wind speed

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Expected size of fire

E[area_burned | ignition] 'wi "i iOrdinary least squares

wi = temperature temperature2

relative humidity relative humidity2

vapor pressure deficit rainfall amount2

rainfall duration2

wind speed wind speed2

wi = temperature x relative humidity temperature x rainfall amount temperature x rainfall duration temperature x wind speed relative humidity x rainfall amount relative humidity x rainfall duration relative humidity x wind speed rainfall amount x rainfall duration rainfall amount x wind speed

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Weather:• temperature• relative humidity• vapor pressure deficit• precipitation amount• precipitation duration• wind speed• wind direction

Data

Fire data:• date• Location• area burned• cost of suppression

Probit Model

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Results: estimated probability

Estimated Hectares Burned

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Residual hectares burned

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Res

idu

al

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Can weather derivatives cover costs that exceed the budget allocation?

Given known weather…

What is theprobability of ignition?

If ignition occurs, what is expected size of fire?

Find the best fit payoff function to pay for excess costs

Does the payoff function adequatelypay for excess costs?

Conclusions & further research

Gain from hedge ($)

$0

Option premium

slope = Y(i)

i

€

Y (imax )

€

Y (imin )

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Net cash flow for fire manager

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= -suppression costs + derivative compensations

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Conclusions

Can weather derivatives cover costs that exceed the budget allocation?

What is theprobability of ignition?

If ignition occurs, what is expected size of fire?

Find the best fit payoff function to pay for excess costs

Does the payoff function adequatelypay for excess costs?

Further research

Further Research

• Control for vegetation age & type

• Model patterns of human ignition

• Include population dynamics

• Understand spending structure

• Explore alternative insurance schemes

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Thank You!

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Acknowledgements

Committee• John Perez-Garcia• Ernesto Alvarado• Steve Harrell• Tom Hinckley• Dave Peterson

• USFS PNW PSW Fire lab• CINTRAFOR• MCCE IGERT• CSDE• Humboldt University at

Berlin• Dr. Martin Odening• Dr. Wei Xu• Silke Hüttel

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Literature

Fire prediction• NFDRS• Canadian Wildland

Fire Info System• Preisler et al. (2004)• Brillinger (2006)

Weather Derivative• Roll (1984) – Orange

juice, Florida• Turvey (2001,2006) –

Ice wine, Ontario• van Asseldonk et al.

(2003) – horticulture, Netherlands

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Framework of Dissertation

Question:

Can weather derivatives cover costs that

exceed the budget allocation?

Ch 2:

Weather-based estimation of wildfire risk

Ch 3:

Weather Derivatives for Specific Event Risks in California Wildfires

Ch 4:

Conclusion and

Further Research

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Logit & probit distributions

Bayesian Information Criterion

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BIC = −2ln(L) + [ln(N)]k