Optimizing the implementation of a forest fuel break network

Methods and models to design, prioritize and evaluate fuel break networks have potential application in many fire-prone ecosystems where major increases in fuel management investments are planned in response to growing incidence of wildfires. A key question facing managers is how to scale treatments into manageable project areas that meet operational and administrative constraints, and then prioritize their implementation over time to maximize fire management outcomes. We developed and tested a spatial modeling system to optimize the implementation of a proposed 3,538 km fuel break network and explore tradeoffs between two implementation strategies on a 0.5 million ha national forest in the western US. We segmented the network into 2,766 treatment units and used a spatial optimization model to compare linear versus radial project implementation geometries. We hypothesized that linear projects were more efficient at intercepting individual fire events over larger spatial domains, whereas radial projects conferred a higher level of network redundancy in terms of the length of the fuel break exposed to fires. We simulated implementation of the alternative project geometries and then examined fuel break-wildfire spatial interactions using a library of simulated fires developed in prior work. The results supported the hypothesis, with linear projects exhibiting substantially greater efficiency in terms of intercepting fires over larger areas, whereas radial projects had a higher interception length given a fire encountered a project. Adding economic objectives made it more difficult to obtain alternative project geometries, but substantially increased net revenue from harvested trees. We discuss how the model and results can be used to further understand decision tradeoffs and optimize the implementation of planned fuel break networks in conjunction with landscape conservation, protection, and restoration management in fire prone regions.

Ground-based logging activities were assumed in stands with an average slope <35%.
Harvest cost estimates were adopted from Rainville et al. [1].Cable-based logging activities were assumed in stands with an average slope >35%.Harvest cost estimates were adopted from Rainville et al. [1].

Hauling costs
Timber hauling costs were calculated from each individual stand to the nearest wood processing facility and were estimated using the road network classified by driving speed.Round-trip travel time between each stand and the nearest processing facility was computed for the shortest path using travel distance and road-specific speed [2] (Table A3).Round trip costs per cubic meter of timber were estimated using travel time, truck hourly cost of $100 at 10 hours per day, and truckload capacity of 12 m 3 .One additional hour of delay time was added for loading, unloading and wait times.Note that hauling cost was only included in the net revenue calculation for stands that generated more than 35 m 3 ha -1 of merchantable timber, and reflected the round trip distance to the nearest mill.
Hauling costs were calculated as:

Revenue from treatments Harvested timber volume from fuel treatments
We attributed the FBN segments with forest vegetation data by intersecting the 300 m wide FBN with the Forest vegetation polygons [3].Inventory data for each stand was obtained from the Forest Service FSVeg inventory data system [3].The vegetation polygons were originally delineated from photointerpretation and follow natural breaks in vegetation type and changes in stand structure from past management activities and disturbance.As noted in the methods, we did not distinguish the road surface area in the spatial configuration since roads are represented as line features in the forest GIS layers.This results in a small bias in the area calculations that does not significantly affect the results or conclusions.The resulting stand polygon layer that intersected the FBN contained 57,606 features, ranging in size from 0.00001 ha to 16.84 ha with an average of 3.0 ha.Seven stand slivers in the initial dataset had no calculable area and were excluded from the analysis.The final FBN segment polygon layer contained a total of 2766 features, ranging in size from 33.0 ha to 106.1 ha, with an average size of 71.3 ha.
Harvested volume was estimated by simulating treatments designed by the forest fuels planner (Stinchfield pers comm.) with the Forest Vegetation Simulator Blue Mountains variant (Keyser and Dixon, 2015).The thinning treatment consisted of a thin from below followed by a pile and burn and was assigned to all stands with canopy cover exceeding 15%.Thinning from below prioritized removal of smaller trees of targeted fire-intolerant species (e.g., grand fir) and reduced ladder fuels to prevent torching and crowning fire behavior.Grand fir was thinned from below up to a maximum DBH of 76.2 cm, while the maximum harvested tree size for other species was set to 53.3 cm to meet late-old structure objectives [4].Conifer stands that did not meet the canopy cover threshold, but had a 20% or greater chance of > 1.2 m flame lengths received a pile and burn treatment consisting of hand or machine piling of harvest residue and downed woody material as practiced on the Forest, at a cost of $1110/ha.The pile and burn treatments were simulated using the FuelMove keyword, which has the same effect as the pile burn process in terms of removing fuels from the site.Note that the thinning prescription is specific to fuel breaks and outside of these areas treatments are customized to individual plant association groups to meet restoration objectives [5].

Log Values
Average pond values by species and small end diameter for all dimensional timber mills within the study area were collected from timber sales specialists on the Umatilla National Forest, and updated in 2020 (Tables A3, A4).We calculated the small end diameter of each harvested tree by bucking the stem and generating logs using the economics extension of FVS [6].

Optimization model
We used the ForSys model developed from the Landscape Treatment Designer [LTD, 8,9].The input file consisted of a shapefile containing the outputs from treating each 300 m segment of the fuel break and a matrix of adjacency for each segment.The program then tests each segment as a seed for a project (1200 ha of treatments) and adds adjacent segments.Intersections provide a choice for the algorithm.The process is repeated for each segment and the project that maximizes the objective value is reported.
Subject to: where C is a global constraint of 1200 ha, Z is a vector of binary variables indicating whether the jth segment is treated (e.g., Z j = 1 for treated segments and 0 for untreated segments),   is the contribution to objective i in segment j if treated, and A is the area of the jth treated stand.W i is a weighting coefficient that can be used to emphasize the objective versus distance from the project centroid (seed polygon) thus creating different levels of linearity.We prioritized projects and noted the point at which 1200 ha of adjacent segments were not available for each scenario.Constraint slack was set to 400 ha so that every segment was prioritized into a project if it could sum to a minimum of 800 ha treated.

Fig S1. 1 .
Fig S1.1.Decision-tree used to assign treatment prescription to each stand based on stand canopy closure (CC), merchantable volume, net revenue and flame length likelihood.Adapted from Belavenutti et al. [7].

Table S1 .
1. Ground-based logging activity cost ($/m 3 ) by tree size class and number of cut trees per acre used to estimate harvesting costs for each simulated project area.

Table S1 .
2. Cable-based logging activity cost ($/m 3 ) by tree size class and number of cut trees per acre for each simulated project area.

Table S1 .
4. Delivered log values ($/m 3 ) by species and size class used in the estimation of revenues from thinning treatments for the northern Umatilla National Forest.

Table S1 .
5. Delivered log values ($/m 3 ) by species and size class used in the estimation of revenues from thinning treatments for the southern Umatilla National Forest.