Fig 1.
Study area in the Red Rock-Prairie Creek region, Alberta, Canada.
Base map data used: administrative boundaries [62]; historic fires [63,64], waterways [65]; digital elevation model [66]. Mapping software used: ESRI ArcMap 10.
Fig 2.
Wind rose diagrams for the study area: a) prevailing winds; b) fire spread indicators qij between node pairs i, j derived from the fire growth model outputs.
Table 1.
Summary of the model variables and parameters.
Fig 3.
Delineating a fireplain: a) simulated wildfire perimeters with the ignition points in node i; b) delineating the fireplain Ωi around node i.
All nodes j within a fireplain Ωi around i are assigned the unary fire spread indicators qij; c) estimating the fire spread probabilities pij from node i to nodes j from the perimeters of simulated fires (an example of three simulated fires over 100 independent replications of a burn year); d) equivalent removal of nodes vs. edges to allocate a linear firebreak segment.
Fig 4.
Landscape network G: a) nodes i; b) edges ij; c) fire spread probabilities pij between node pairs i, j.
The pij values between the adjacent nodes are not shown. Patch-based fire hazard measures, φi: d) burn probability; e) the likelihood of fuel presence within a 500-m radius of a given site (rescaled to 0-1 range); f) fireplain size. The network node data can be found in S2 Appendix. Mapping software used: Python Matplotlib 3.4 library.
Table 2.
Optimal firebreak models 1-6.
Fig 5.
Using the edge removal problem 3 solution to warm start node removal problem 1.
Fig 6.
Distributions of the simulated fire sizes and the fire spread vector lengths between node pairs i, j in network G: a) simulated fire size distribution; b) distribution of fire spread distances between node pairs i, j, weighted by the estimated fire spread probabilities between i and j, pij.
Table 3.
Firebreak allocation summaries in problems 1-6 optimal solutions.
Fig 7.
Optimal node and edge removal solutions with treatment budgets of 25, 50 and 80 removed nodes (or equivalently, 62, 125 and 250 removed edges).
The cost ratio between the removal of a node in the CNDP solutions and an edge in the CERP solutions is 2.5:1. The background maps show the fireplain size for each node after the treatments. The network node data can be found in S2 Appendix.
Fig 8.
Objective value vs. the treatment budget.
X-axis denotes the treatment budget level in the equivalent number of treated edges. The removed node budgets in the problem 1, 2 and 6 solutions were converted to the equivalent numbers of removed edges using a 2.5:1 cost ratio: a) spread potential of large fires; b) the largest fireplain size (characterizes the worst-case outcome of the spread of large fires); c) mean fireplain size (characterizes the average reduction of the potential fire spread area). Lower values on Y-axis indicate better outcomes.
Fig 9.
The trade-off between the capacity to reduce the spread potential of large fires vs. the reduction of the largest fireplain size.
The treatment budget level: a) 25 nodes/ 62 edges; b) 50 nodes/ 125 edges; c) 80 nodes/ 200 edges. Callout I shows the trade-off between the problem 3 solution that minimizes the spread potential of large fires and the problem 5 solution that minimizes the largest fireplain size.