1

Wildland Arson Crime Functions

David T. ButryNational Institute of

Standards and TechnologyGaithersburg, MD

Jeffrey P. Prestemon Southern Research Station

USDA Forest ServiceResearch Triangle Park, North

Carolina

and

2

Introduction There are 500,000 arson fires/year (wildland plus structural) in the

US, $3 billion in damages (National Fire Protection Association). Wildland arson is the leading single cause of wildfires in Florida. Arson ignitions on national forests have trended down over the past

1-2 decades, as have all causes. Area burned by accidental fire starts has trended upward over time,

apparently, in aggregate, although arson area burned has not trended.

Few have rigorously evaluated the underlying causes of short- or long-term temporal patterns.

3

Number of Ignitions by Fire Source on National Forests

0

2,000

4,000

6,000

8,000

10,00019

70

1974

1978

1982

1986

1990

1994

1998

2002

Lightning Ignitions

Other Ignitions

Arson Ignitions

4

Area Burned by Ignition Source on National Forests (FS + Protection)

9

10

11

12

13

14

15

1970

1974

1978

1982

1986

1990

1994

1998

2002

Ln

(Acr

es B

urn

ed)

Ln(Ligntning Acres)

Ln(Other Acres)

Ln(Arson Acres)

5

Crime and Arson It is apparent that arson is following

patterns similar to major crimes committed in the U.S.

Recent research shows that wildland arson is similar to violent crime in its response to law enforcement, criminal sanctions, and economic variables.

6

Crime Trend: Nationwide, Plus Wildland Arson on National Forests

0

1,000

2,000

3,000

4,000

5,000

6,000

7,00019

72

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

All-Crime Index

Violent CrimeIndex

Non-ViolentCrime Index

National ForestArson Index

7

Changes in Crime in Florida, 1972-2004

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.501

97

3

19

76

19

79

19

82

19

85

19

88

19

91

19

94

19

97

20

00

20

03

Murder Index

Rape Index

Robbery Index

Assault Index

Burglary Index

Larceny Index

MVT Index

Arson Index/10

Average

8

Today’s Presentation Provide background information on

Florida’s arson situation Outline our econometric models Report results Describe implications for fire forecasting

9

Why is Learning About Arson Important? Arson fires threaten large values

More often in the WUI Arson wildfires are part of a larger

ecological process Behave similarly in response to management,

weather, fuels Evidence suggests that arson fires appear

to be clustered in both time and space.

10

Background on Arson Wildland arson has a long history

Especially in the South Florida has over 1,400 arson ignitions and 45,000

arson-ignited burned acres per year

Wildland arson is linked to demographic factors Old research quantifying the role of law enforcement Research identifying some links to socioeconomic

factors

11

Background on Arson Recent research links Arson to physical factors

Arson fires follow other fires in timing: Mostly during fire season (January-July) Peak in ignition rate in mid-afternoon Are more common in dry weather Respond to previous wildfires in the area

But arson fires differ from others: More ignitions on weekends Concentrated in spatial distribution—perhaps, closer to roads

and urbanized areas

12

Arson wildfire theory Serial and copycat arson behaviors imply a contagion process.

Current arson could be explained by previous arson ignitions. Other research identifies these behaviors for other kinds of crimes.

Law enforcement may play a role. Florida’s number of police officers per capita increased 12% between 1982 and 2001 but has

declined by 2% since 1995; trends vary by county. Much recent research identifying a negative relationship between law enforcement and crime.

Weather and land management may affect it. Dry weather makes firesetting easier Fuels management can affect success rates and opportunities

Leisure time could help explain it. Socioeconomic factors should explain some of it.

Population level should be related—more people, more arsonists? Poverty has been linked to other crimes. Arson models should control for this. Labor factors might explain it—wages, unemployment—affecting crime opportunity costs

(Becker, new research in AER, elsewhere).

13

Crime Model (Becker)

Oi is the number of offenses committed

πi is the probability of being caught and convicted

fi is the wealth loss experienced by the criminal if caught and convicted

ui measures other factors influencing the decision and success of completion of the crime

),,( iiiii ufOO

The decision to commit a crime is described as:

14

Arsonist’s Expected Utility from a Successful Ignition (Becker)

)()1()),(()( iiiiiiiiiiiii cgUwWfcgUOEU

Oi is the number of offenses committed

πi is the probability of being caught and convicted

gi is the arsonist’s psychic and income benefits from illegal firesetting

ci is the production cost for the firesetting

fi(Wi,wi) is the loss from being caught and convicted of the crime is a positive function of income while employed

Wi is the employment status

wi is wage

15

TERM DEFINITION FUNCTION OF:

Probability of being caught Law enforcement

f Loss from being caught and convicted Wage rateEmployment status

c Production cost of firesetting Time available Unemployment statusFuels and weatherVariables related to

ignition success

g Psychic and income benefits

from illegal firesetting

16

Arson Poisson Autoregressive Model PAR(p) Daily Ignition Model

jtjeyYyEp

iij

p

iitjijtjtj

βx '

1,

1,,1,,

,1]|[

yj,t is a vector of daily arson ignitions for location j

xj,t is a vector of independent variables (including a constant)

βj is a vector of associated parameters

j,i’s are the autoregressive parameters

17

Empirical Models County-level daily time scale Poisson Autoregressive models of

order p, PAR(p) Five high-arson county pairs in Florida 1994-2001

Locational daily time scale PAR(p) with spatio-temporal components Six high-arson Census tracts in Florida 1994-2001

Annual fixed-effects cross-section time series panel Poisson model Most Florida Counties 1994-2001

California national forests daily time scale PAR(p) 1993-2002

18

Study Locations

Spatio-temporal Analyses

19

Daily Time Series Model: Spatio-Temporal Analysis

The PAR(p) relates current day’s fires to Previous days’ fires, Presence of neighboring arson

Local—arson in surrounding Census tracts Regional—arson in Census tracts in same and

surrounding counties Long-term annual wildfires in the area (1-12 yr), Prescribed fire permits in the area (0-2 yr lags), Current fire danger index (KBDI), Seasonal factors: days of the week, months Socioeconomic factors: population, full-time equivalent

police officers per capita, poverty rate

20

Data Wildfire and prescribed fire from the

Florida Division of Forestry Socioeconomic data

U.S. Bureau of the Census University of Florida-Bureau of Economic

and Business Research Florida Department of Law Enforcement

Climate and weather from NOAA

21

Daily Locational Model Results Broadly significant variables

(significant across 3 or more models) Previous ignitions (up to 4 days) Previous local ignitions (up to

11 days) Previous regional ignitions (up

to 4 days) KBDI Some months Previous wildfire area (up to 5

years)

Significant variables

(significant across 1 or 2 models) Weekend days Poverty rate Unemployment rate Retail Wage Police Some months Previous prescribed fire

22

Daily Pooled Model Results*

Significant variables Previous ignitions (up to 10 days) Previous local ignitions (up to 11

days) Previous regional ignitions (1 day) KBDI Saturday Most months Previous prescribed fire (up to 1

year)

Insignificant variables Sunday Population Poverty rate Unemployment rate Retail wage Previous wildfire

*All variables interacted with population except AR terms, local ignitions, and regional ignitions.

23

Daily Model Results: Daily Autocorrelations

24

Simulated Outbreak Response Assume one unexpected arson ignition occurred

on April 30, 2005 Analyze using the pooled model results and with

continuous variables set at the pooled model means

Examine variation in response when outbreak occurs at different locations Same Census tract Local Census tract Regional Census tract

25Day after outbreak

Simulation—Response of an unexpected arson ignition on April 30, 2005.

26

Response to Outbreak 15.7 additional arson ignitions when

outbreak occurs in same Census tract 18.3 additional arson ignitions when

outbreak occurs in a neighboring “local” Census tract

17.6 additional arson ignitions when outbreak occurs in a neighboring “regional” Census tract

27

We Also Evaluated Effects of Law Enforcement Saturation Strategies

Ongoing work is seeking to develop hot-spotting models for law enforcement

28

Summary We have extended results from newly published

work in AJAE: wildland arson, at least in Florida, is spatially and temporally autoregressive.

Hence, wildland arson is a predictable process after an ignition occurs, potentially allowing for successful and effective law enforcement action.

Also implies that ignitions should be modeled that recognizes at least temporal and probably spatio-temporal autocorrelation (depends on the spatial scale of modeling) within daily time frames.

29

Questions

30

Law Enforcement Saturation Given an outbreak, examine how varying

levels law enforcement saturation affects future arson Levels of saturation are consecutive days,

following the outbreak, of arson prevention Saturation supposes perfect ability to control

arson ignitions (i.e., when there’s saturation, no arson ignitions occur)

31

Law Enforcement Saturation

32

Effect of Saturation Although an outbreak can have long-lasting effects

(several weeks), eleven days of saturation prevents any new arson ignition

Saturation has different effects depending on locational source of the outbreak (significance of differences across neighboring locations not evaluated)

On average, the following number of ignitions are prevented for each day of saturation 1.4 if outbreak occurred in same Census tract 1.7 if outbreak occurred in neighboring “local” Census

tract 1.6 if outbreak occurred in neighboring “regional”

Census tract

33

Law Enforcement Implications Focus enforcement on locations with recent and nearby arson

fires. Concentrate enforcement where arson fires have been ignited in last

ten days. Concentrate enforcement around where arson fires have been

ignited in last 2 days. Pay attention to weather trends.

Periods of hot, dry weather associated with higher arson risk Perhaps this is associated with the success of ignition, lower

expected “time and effort needed to obtain a successful ignition. There is a Saturday effect.

Count on Saturdays—lower opportunity costs of firesetting? This result is consistent with an economic model of crime, at least

for this variable.

34

Fire Management Implications

The use of prescribed fire is not found to be associated with lower arson risk

Locations with lots of wildfire are at lower arson ignition risk.

As other ignition risks, arson risk is closely tied to time of year and fuel flammability.