Forest Fire Detection EconomicsForest Fire Detection Economics

David L. MartellDavid L. Martell

Faculty of Forestry University of TorontoFaculty of Forestry University of Toronto

Robert S. McAlpineRobert S. McAlpine

Ontario Ministry of Natural ResourcesOntario Ministry of Natural Resources

Fire Detection WorkshopFire Detection WorkshopHinton, AlbertaHinton, Alberta

March 25, 2003March 25, 2003

22

Overview Overview

Basic ConceptsBasic Concepts

Detection MethodsDetection Methods

Detection Patrol Detection Patrol Routing ProblemRouting Problem

Detection/Initial Detection/Initial Attack System Attack System ModelModel

ConclusionConclusion

33

Life Cycle of a Forest FireLife Cycle of a Forest Fire

44

Value of Detection SystemValue of Detection System

Need to assess detection system from Need to assess detection system from an overall system perspectivean overall system perspective

Detection system objective is to find Detection system objective is to find fires such that they can be controlled fires such that they can be controlled at reasonable cost and impactat reasonable cost and impact

Value of the detection system is the Value of the detection system is the net reduction in total cost plus lossnet reduction in total cost plus loss

55

Detection ConsiderationsDetection Considerations

Value of the resource protected Visibility Probability of a fire occurring Expectations of fire behavior Potential for fire spread Coverage by unorganized detection

66

Detection ProbabilityDetection Probability

Partition the Partition the protected area into protected area into many small cellsmany small cells

is the probability you find the fire when is the probability you find the fire when you look in a cellyou look in a cell

Detection Detection probabilityprobability

77

Detection MethodsDetection MethodsLookout TowersLookout Towers AircraftAircraft

88

Lookout TowersLookout Towers

Strategic Strategic DecisionsDecisions

1. How many towers?1. How many towers?

2. What locations?2. What locations?

99

Fire Lookout Tower Location Fire Lookout Tower Location ModelsModels

Partition protected area into a large number of small rectangular cells

Identify potentially good tower sites

1010

Tower Location ModelsTower Location Models

1. Minimize the number (or cost) of towers required1. Minimize the number (or cost) of towers required

to cover all cellsto cover all cells

- may require double coverage for triangulation- may require double coverage for triangulation

2. Maximize the number of cells seen by a specified 2. Maximize the number of cells seen by a specified number of towersnumber of towers

- use potential damage estimates to weight cells- use potential damage estimates to weight cells

1111

AircraftAircraft

Strategic Strategic DecisionsDecisions1. How many 1. How many aircraft?aircraft?

2. What hours?2. What hours?

3. What type?3. What type?

1212

AircraftAircraft

TacticalTactical DecisionsDecisions

1. When to dispatch1. When to dispatch

2. Where to fly2. Where to fly

1313

Detection Patrol Routing Detection Patrol Routing ProblemProblem

Partition the protected area into a large Partition the protected area into a large number of small rectangular cellsnumber of small rectangular cells

Predict the expected number of fires or Predict the expected number of fires or probability of fires in each cellprobability of fires in each cell

Use vegetation, fire weather and “values at Use vegetation, fire weather and “values at risk” map to identify potentially critical cells risk” map to identify potentially critical cells that “must” be visitedthat “must” be visited

Develop the “best” patrol route(s) to visit all Develop the “best” patrol route(s) to visit all the cells that must be visitedthe cells that must be visited

1414

Simple Detection Patrol Routing Simple Detection Patrol Routing

ProblemProblem

1. Should you dispatch 1. Should you dispatch aa

detection patrol?detection patrol?

2. If you dispatch2. If you dispatch

detection patrol, atdetection patrol, at

what time?what time?

1515

Simplifying AssumptionsSimplifying Assumptions

1) Fire Started at 08:00 hours1) Fire Started at 08:00 hours

2) Forward Rate of Spread of the Fire = 36 m/h2) Forward Rate of Spread of the Fire = 36 m/h

3) Fire Damage = $200 per hectare burned up 3) Fire Damage = $200 per hectare burned up until the time of detectionuntil the time of detection

1616

Fire Loss Assuming Fire is Fire Loss Assuming Fire is CircularCircular

Time Fire is Found

Hours Area Burned (ha)

Fire Cost($)

10:00 2 1.6 320

12:00 4 6.5 1,300

14:00 6 14.7 2,940

16:00 8 26.1 5,220

18:00 10 40.7 8,140

20:00 12 58.6 11,720

1717

Detection Probability FunctionDetection Probability Function

Look Aircraft Public

Time

Detection

Detection

  Probability

Probability

10:00

0.2 -

12:00

0.4 -

14:00

0.6 -

16:00

0.8 -

18:00

0.6 -

20:00

- 1.0

1818

Detection Patrol Routing Detection Patrol Routing ProblemProblem

Suppose you Suppose you look at 10:00look at 10:00

Expected Cost =Expected Cost = (1,000 + 320 )(1,000 + 320 )××0.20.2 (find at 10:00)(find at 10:00)

+ Loss ++ Loss + (1,000 + 11,720)(1,000 + 11,720)××(1-0.2)(1-0.2) (public at 20:00)(public at 20:00)

= = 10,44010,440

Look Time Flying Cost

Expected Cost+ Loss

10:00 1000 10,440

12:00 1000 8,552

14:00 1000 7,452 OPTIMUM

16:00 1000 9,856

20:00 0 11 720 (DO NOT FLY)

1919

Detection Patrol Routing Detection Patrol Routing ProblemProblem

2020

Towers vs AircraftTowers vs Aircraft

TowersTowers fixedfixed

expensiveexpensive

constant surveillanceconstant surveillance

AircraftAircraft flexibleflexible

inexpensiveinexpensive

intermittent intermittent surveillancesurveillance

Use in high value Use in high value forest if have a forest if have a large detection large detection budgetbudget

Use in low value Use in low value forest with small forest with small detection budgetdetection budget

2121

Measures of Detection System Measures of Detection System EffectivenessEffectiveness

Cost per unit area protected Cost per unit area protected (minimize with NO (minimize with NO effort)effort)

Cost per fire detected Cost per fire detected (let the public find them all)(let the public find them all)

Hours flown per fire detected Hours flown per fire detected (minimize with NO (minimize with NO effort)effort)

Percent of fires detected by airborne observersPercent of fires detected by airborne observers

with the public)with the public)

(compete(compete

Average size at detectionAverage size at detection(ignores travel time, (ignores travel time, spreadspreadrate, etc.)rate, etc.)

Find fires so you can put them out at reasonable Find fires so you can put them out at reasonable cost and damage (detection cost, suppression cost and damage (detection cost, suppression cost, fire damage)cost, fire damage)

2222

Detection/Initial Attack System Detection/Initial Attack System ModelModel

Model that predicts the final sizes of historical fires Model that predicts the final sizes of historical fires given:given: Actual fire report recordActual fire report record Actual fuel and fire weather informationActual fuel and fire weather information Suppression by a perfect hypothetical initial attack Suppression by a perfect hypothetical initial attack

crewcrew

Model provides an objective relative measure of how Model provides an objective relative measure of how well the detection system worked on a single fire well the detection system worked on a single fire or collection of firesor collection of fires

Does not indicate how well the system should Does not indicate how well the system should performperform

2323

Fire BehaviourFire Behaviour

Fire Shape:Fire Shape: wind driven ellipse modelwind driven ellipse model Fire Growth:Fire Growth: FBP to predict area, FBP to predict area,

perimeterperimeter

Fire declared held when the fire line Fire declared held when the fire line

constructed equals 50% of the fire perimeterconstructed equals 50% of the fire perimeter

2424

Fire SuppressionFire Suppression

Rate of Line Construction:Rate of Line Construction:RLC = BRLC = B00 + B + B11 ×× FI by fuel type FI by fuel type

2525

Simple Containment ModelSimple Containment Model

Hypothetical Final Size:Hypothetical Final Size:

Predicted final size of a fire given the fire Predicted final size of a fire given the fire conditions and a hypothetical perfect conditions and a hypothetical perfect initial attack crew that is dispatched as initial attack crew that is dispatched as soon as the fire is reportedsoon as the fire is reported

Perfect Final Size:Perfect Final Size:

Final size of a fire given detection as soon Final size of a fire given detection as soon as the fire starts, and a hypothetical as the fire starts, and a hypothetical perfect initial attack crew that is perfect initial attack crew that is dispatched as soon as the fire startsdispatched as soon as the fire starts

DetectionDetection Loss = HF - PF Loss = HF - PF (ha per fire)(ha per fire)

2626

Average Annual Results Average Annual Results (1980 - (1980 -

85)85)

Year to year comparisons (e.g., before and after Year to year comparisons (e.g., before and after detection program changes) are validdetection program changes) are valid

Direct comparison between regions questionable (values Direct comparison between regions questionable (values at risk and fire loads differ)at risk and fire loads differ)

REGION NW NC NO NE

HF 4.47 1.61 1.63 0.84

PF 0.38 0.16 0.26 0.12

N (fires/year) 343 187 118 300

N × (HF-PF) (loss) 1403 271 162 216

2727

How Well Should the Detection How Well Should the Detection System Perform?System Perform?

Depends Upon:Depends Upon: Values at riskValues at risk

Number of fires per yearNumber of fires per year

Fire behaviourFire behaviour

Public detection systemPublic detection system

Detection budgetDetection budget

2828

Thank YouThank You

DiscussionDiscussion