1. Forest Fire Detection Economics David L. Martell Faculty of Forestry University of Toronto Robert S. McAlpine Ontario Ministry of Natural Resources Fire Detection Workshop Hinton, Alberta March 25, 2003

2. 2 Overview Basic Concepts Basic Concepts Detection Methods Detection Methods Detection Patrol Routing Problem Detection Patrol Routing Problem Detection/Initial Attack System Model Detection/Initial Attack System Model Conclusion Conclusion

3. 3 Life Cycle of a Forest Fire

4. 4 Value of Detection System Need to assess detection system from an overall system perspective Need to assess detection system from an overall system perspective Detection system objective is to find fires such that they can be controlled at reasonable cost and impact Detection system objective is to find fires such that they can be controlled at reasonable cost and impact Value of the detection system is the net reduction in total cost plus loss Value of the detection system is the net reduction in total cost plus loss

5. 5 Detection Considerations   Value of the resource protected   Visibility   Probability of a fire occurring   Expectations of fire behavior   Potential for fire spread   Coverage by unorganized detection

6. 6 Detection Probability Partition the protected area into many small cells Partition the protected area into many small cells is the probability you find the fire when you look in a cell Detection probability Detection probability

7. 7 Detection Methods Lookout Towers Aircraft

8. 8 Strategic Decisions 1. How many towers? 2. What locations?

9. 9 Fire Lookout Tower Location Models Partition protected area into a large number of small rectangular cells Identify potentially good tower sites

10. 10 Tower Location Models 1. Minimize the number (or cost) of towers required to cover all cells to cover all cells - may require double coverage for triangulation 2. Maximize the number of cells seen by a specified number of towers - use potential damage estimates to weight cells

11. 11 Aircraft Strategic Decisions 1. How many aircraft? 2. What hours? 3. What type?

12. 12 Aircraft Tactical Decisions 1. When to dispatch 2. Where to fly

13. 13 Detection Patrol Routing Problem Partition the protected area into a large number of small rectangular cells Partition the protected area into a large number of small rectangular cells Predict the expected number of fires or probability of fires in each cell Predict the expected number of fires or probability of fires in each cell Use vegetation, fire weather and “ values at risk ” map to identify potentially critical cells that “ must ” be visited Use vegetation, fire weather and “ values at risk ” map to identify potentially critical cells that “ must ” be visited Develop the “ best ” patrol route(s) to visit all the cells that must be visited Develop the “ best ” patrol route(s) to visit all the cells that must be visited

14. 14 Simple Detection Patrol Routing Problem 1. Should you dispatch a detection patrol? detection patrol? 2. If you dispatch detection patrol, at detection patrol, at what time? what time?

15. 15 Simplifying Assumptions 1) Fire Started at 08:00 hours 2) Forward Rate of Spread of the Fire = 36 m/h 3) Fire Damage = $200 per hectare burned up until the time of detection

16. 16 Fire Loss Assuming Fire is Circular Time Fire is FoundHoursArea Burned (ha) Fire Cost ($) 10:0021.6320 12:0046.51,300 14:00614.72,940 16:00826.15,220 18:001040.78,140 20:001258.611,720

17. 17 Detection Probability Function LookAircraftPublic TimeDetection Probability 10:000.2- 12:000.4- 14:000.6- 16:000.8- 18:000.6- 20:00-1.0

18. 18 Detection Patrol Routing Problem Suppose you look at 10:00 Expected Cost =(1,000 + 320 )×0.2 (find at 10:00) + Loss +(1,000 + 11,720)×(1-0.2) (public at 20:00) + Loss +(1,000 + 11,720)×(1-0.2) (public at 20:00) = 10,440 = 10,440 Look TimeFlying CostExpected Cost+ Loss 10:00100010,440 12:0010008,552 14:0010007,452 OPTIMUM 16:0010009,856 20:00011 720 (DO NOT FLY)

19. 19 Detection Patrol Routing Problem

20. 20 Towers vs Aircraft Towers fixed fixed expensive expensive constant surveillance constant surveillance Aircraft flexible flexible inexpensive inexpensive intermittent surveillance intermittent surveillance Use in high value forest if have a large detection budget Use in low value forest with small detection budget

21. 21 Measures of Detection System Effectiveness Cost per unit area protected Cost per unit area protected (minimize with NO effort) Cost per fire detected Cost per fire detected (let the public find them all) Hours flown per fire detected Hours flown per fire detected (minimize with NO effort) Percent of fires detected by airborne observers with the public) (compete Average size at detection Average size at detection (ignores travel time, spread rate, etc.) Find fires so you can put them out at reasonable cost and damage (detection cost, suppression cost, fire damage) Find fires so you can put them out at reasonable cost and damage (detection cost, suppression cost, fire damage)

22. 22 Detection/Initial Attack System Model Model that predicts the final sizes of historical fires given: Actual fire report record Actual fire report record Actual fuel and fire weather information Actual fuel and fire weather information Suppression by a perfect hypothetical initial attack crew Suppression by a perfect hypothetical initial attack crew Model provides an objective relative measure of how well the detection system worked on a single fire or collection of fires Does not indicate how well the system should perform

23. 23 Fire Behaviour Fire Shape:wind driven ellipse model Fire Shape:wind driven ellipse model Fire Growth: FBP to predict area, perimeter Fire Growth: FBP to predict area, perimeter Fire declared held when the fire line constructed equals 50% of the fire perimeter Fire declared held when the fire line constructed equals 50% of the fire perimeter

24. 24 Fire Suppression Rate of Line Construction: RLC = B 0 + B 1 × FI by fuel type

25. 25 Simple Containment Model Hypothetical Final Size: Predicted final size of a fire given the fire conditions and a hypothetical perfect initial attack crew that is dispatched as soon as the fire is reported Predicted final size of a fire given the fire conditions and a hypothetical perfect initial attack crew that is dispatched as soon as the fire is reported Perfect Final Size: Final size of a fire given detection as soon as the fire starts, and a hypothetical perfect initial attack crew that is dispatched as soon as the fire starts Final size of a fire given detection as soon as the fire starts, and a hypothetical perfect initial attack crew that is dispatched as soon as the fire starts Detection Loss = HF - PF(ha per fire)

26. 26 Average Annual Results (1980 - 85) Year to year comparisons (e.g., before and after detection program changes) are valid Year to year comparisons (e.g., before and after detection program changes) are valid Direct comparison between regions questionable (values at risk and fire loads differ) Direct comparison between regions questionable (values at risk and fire loads differ) REGIONNWNCNONE HF4.471.611.630.84 PF0.380.160.260.12 N (fires/year)343187118300 N × (HF-PF) (loss) 1403271162216

27. 27 How Well Should the Detection System Perform? Depends Upon: Values at risk Values at risk Number of fires per year Number of fires per year Fire behaviour Fire behaviour Public detection system Public detection system Detection budget Detection budget

28. 28 Thank You Discussion