Wildfire management can be a complex decision-making process involving uncertain and dynamic conditions, and requiring rapid assimilation of multiple types of information from various sources [1
]. Operations research (OR) models can be used to help integrate fire data, suggest management strategies, and conduct tradeoff analysis to assist fire decision processes [3
]. OR models developed for wildfire management can take many forms, ranging from pre-fire applications determining optimal investment portfolios in prevention/suppression activities along with optimal stationing and deployment rules for suppression resources [7
], to post-fire applications determining optimal mitigation strategies for reducing debris flow risk [13
Of interest here are OR models built for incident-level fire operations that endogenously determine suppression resource demands in relation to fire or landscape characteristics, and that assign suppression resources to support various tactical response decisions. We specifically focus our model on the objective of minimizing economic losses from an escaped fire, which is a common but non-exclusive fire management objective. Operationally, the tactics employed to meet this objective include any combination of direct, indirect or contingency line construction, as well as point protection of highly valued resources or assets. Both ground resources (e.g., fire engines, hand crews, bulldozers) and aerial resources (e.g., helicopters, fixed-wing aircraft) can support these tactics through various tasks, broadly intended to delay, stop, or extinguish a fire. Specific task typically includes advanced preparation and in situ point protection, containment line construction, burnout preparation and implementation, line holding (i.e., improving and patrolling) and mopping up. Delaying fire spread and reinforcing containment lines with aerial resources are also common tasks that help minimize losses. Published OR modeling research is reflective of these realities, focusing on construction of containment lines to manage the extent and location of burned areas [14
], and the allocation of resources to point protect structures such as homes [17
Here we present a mixed integer program (MIP) model where the decision variables relate to constructing fire line and protecting structures, and where objective functions could be designed to best balance the positive and negative wildfire effects, the expenditures from responding to wildfire, or the potential hazard to fire responders. Our primary research objectives are to develop OR models that: (1) are relevant to on-the-ground fire operations; (2) readily integrate with existing incident decision support systems; (3) improve assessment of incident-specific wildfire risk; and (4) ultimately, improve upon previous spatial response optimization work by incorporating additional probabilistic and time-sensitive information. Contextually we leveraged decision support products that are widely used by fire managers in the western USA, although the broad contours of the model are likely applicable elsewhere. Furthermore, we grounded our model development in risk management principles, increasingly being adopted by the wildland fire management community, which notably emphasize more proactive assessment and planning as a basis for supporting incident decisions, i.e., “engaging the fire before it starts” [20
Regarding our first objective, we developed a network of pre-identified potential wildland fire operational delineations (PODs) as primary management units and decision variables. PODs are landscape polygons whose boundaries are features that are relevant to fire containment operations, such as roads, ridgetops, fuel transitions, water bodies, etc., within which risks, opportunities, and response strategies can be summarized [23
]. PODs can be built using a combination of geospatial analysis and local expert knowledge, often with supporting analytical products identifying suppression opportunities and potential control locations (PCLs) [24
]. PODs have been used to summarize suppression difficulty and protection demand [26
], to optimize fuel treatment placement across a landscape [27
], and, most relevant for our purposes, to optimize creation of clustered, or aggregated, response PODs (rPODs) for real-time incident support [28
]. It is worth emphasizing that PODs are more than an academic concept; locally developed PODs were used for real-time decision support during the 2017 fire season on the Tonto National Forest in Arizona, USA [22
], and analytical products serving as the building blocks of PODs [23
] were delivered for real-time decision support for fifteen large fires across the western USA during the 2017 fire season [Risk Management Assistance Teams (RMAT) website, https://wfmrda.nwcg.gov/RMAT.html
]. Furthermore, as of this writing, POD development to support spatial fire planning has already been carried out or is actively proceeding on National Forest System and adjacent lands in Arizona, California, Colorado, Montana, New Mexico, Oregon, and Washington, USA.
Regarding our second objective, we leveraged functionality from the Wildland Fire Decision Support System (WFDSS), a web-based platform developed in the USA that combines fire behavior modeling, economic principles, geospatial analysis, and information technology to support fire response decisions [30
]. Specifically, we used the Fire Spread Probability (FSPro) model, which ingests topography, fuel data and daily fire weather forecasts during a fire event to stochastically simulate fire spread [31
]. Results from those simulations are used to predict time-based burn probability contours or polygons, along with fire arrival times across the landscape, which we used as inputs to our MIP model. Although FSPro enables quantification of the exposure of highly valued resources and assets (HVRAs) in relation to burn probability, it does not estimate fire intensity or fire effects, which may inhibit analysis of tradeoffs across firefighter safety, suppression expenditures, and fire impacts to HVRAs [32
This leads us to our third objective, better characterizing incident risk to HVRAs. As a basis we used a landscape-scale risk assessment framework that evaluates both the hazard (fire likelihood and intensity) and vulnerability (exposure and susceptibility) of HVRAs at every location (i.e., each grid cell) across a landscape [33
]. The framework outlined in [35
] is generalizable and scalable, such that risk assessment results can be used for a variety of purposes, including strategic budgeting, fuel treatment prioritization, and incident decision support [27
]. In a pre-fire landscape-scale risk assessment, the fire likelihood and intensity estimates used to calculate expected net value change (eNVC
) are commonly generated by a stochastic simulator such as FSim [37
]. FSim’s fire behavior results do not model the weather at the time and place of any actual wildfire. Instead, they reflect the full range of weather conditions that exist across a relatively large landscape and during an entire fire season. For a risk assessment on an ongoing wildfire, an improvement could be made by generating fire likelihoods and intensities that are sensitive to the weather conditions likely to occur during the event. As described above, we used FSPro to generate fire likelihoods (burn probabilities), but not flame length probabilities (or intensity results of any kind). Instead, we used a deterministic modeling process called Flep-Gen (for Flame-Length Exceedance Probability Generator [38
]) to estimate, for each grid cell, the probability that flame length will fall into each of six fire intensity levels (as is common with risk assessment, see [34
]). Flame length classes used here are 0–0.61 m (0–2 ft), 0.61–1.22 m (2–4 ft), 1.22–1.83 m (4–6 ft), 1.83–2.44 m (6–8 ft), 2.44–3.66 m (8–12 ft), and >3.66 m (12 ft). By combining these incident-specific fire behavior simulations with pre-existing risk assessment data that characterize the location, susceptibility, and importance of HVRAs, we are able to calculate incident-specific eNVC
Lastly, we aim to capitalize on enhanced fire modeling integration to improve upon earlier work demonstrating the optimal rPOD concept. Our recent study [28
] used a deterministic MIP model to integrate point protection decisions with strategic fire containment boundary design by aggregating pre-identified PODs into larger fire containers, i.e., rPODs. That approach defined a response strategy as the combination of fire line construction along rPOD containment boundaries and point protection assignments within that rPOD, and illustrated how optimal strategies varied with fire weather and budget constraint scenarios. However, the model used a conditional
net value change layer assuming the entire selected rPOD burns under the specified weather scenario, meaning it did not consider fire spread probabilities. Nor did it consider the timing of line construction in relation to fire arrival times. Here, we expand the set of data inputs to include GIS raster layers of simulated burn probability, flame length (meter) probability, fire arrival time (day), and expected net value change, all calculated using common weather forecast data. To reiterate, the use of common weather data across fire modeling systems ensures that the same set of stochastic weathers were used to support FSPro fire simulations, estimation of expected fire loss/benefit, flame length probability prediction, and to support suppression decisions during a large fire event. Furthermore, we developed a secondary optimization model that, for a given optimal rPOD, dictates the timing of fire line construction activities to encourage completion of containment line prior to fire arrival along specific rPOD edges.
In the following sections we present our methods and results, tailored to a case study based on the simulations of the 2017 Sliderock Fire in Montana, USA. Both the inherent uncertainties in wildfire behaviors and fire manager’s different risk preferences could influence the selection of fire containment strategies. We generated alternative rPOD response strategies that vary with managerial risk preferences around cost and firefighter safety, and present a conceptual decision tree to demonstrate how such a tool could be used to facilitate tradeoff analysis and strategy selection. We further illustrate use of the model to develop a contingency strategy, which is consistent with the idea of re-running the tool in response to changes in factors such as fire weather, line effectiveness, and suppression resource availability. After presenting results we discuss model insights, limitations, and possible extensions. Through this study, we hope to demonstrate the potential of using OR models to integrate probabilistic data and to provide easily accessible response strategy suggestions that accord with fire manager’s risk preferences and that ultimately improve response safety and efficiency.
Large fire managers must make response decisions in a timely manner, limiting opportunities to examine an extensive suite of rPOD options. Additionally, large fire suppression decisions often involve stakeholders with different values, incentives and risk preferences and suppression decisions could be heavily influenced by social-political factors, public opinions, media reports, etc. [44
]. In this study, we tested several fire manager’s preference scenarios. Fire managers could design and evaluate more scenarios by extending the use of this model to preseason fire risk analyses or fire management training programs, for example, considering a range of possible landscapes, ignition locations, weather conditions, risk preferences, and resource availability situations (see [28
]). Important variables to consider in pre-season, cross-boundary fire planning may also include ownership patterns, the extent and proximity of community and structures, the degree of pre-existing collaboration, and potential for conflict. Adopting thematic “archetypes” for community attributes [45
] along with fire transmission and exposure pathways [46
] could also prove useful for guiding and informing such planning efforts. Integrating those considerations into scenarios and using OR models to provide alternative containment suggestions would allow managers to understand the tradeoffs of different management policies and actions on various stakeholders. Ultimately, this may help provide better communication and facilitate negotiations between stakeholders as optimal response strategies are determined. A strength of the scenario-based planning is that it provides an opportunity to infuse and enrich discussions with a broader set of qualitative concerns in relation to a frontier of response options. In a recent fire planning workshop hosted in Estes Park, Colorado, USA, for example, responders from a variety of response agencies considered potential scenarios where a fire that ignited in Rocky Mountain National Park could spread into adjacent communities. The team collectively discussed fire containment options, structure density and protection need, evacuation concerns, smoke exposure, and tourism impacts, all in relation to design of large fire containment strategies.
Our goal is to keep improving the OR model and eventually to integrate it into or use it as an extension of the existing wildfire decision support systems to support transparent and data driven large fire suppression decisions. WFDSS is the most extensively used large fire decision support system in the U.S. OR approaches such as the two-step model described herein will remain external to this system at this time given WFDSS’ structure and capability, but by explicitly using data products already integrated in WFDSS to support our model would be relatively easy as an external extension. For example, WFDSS already uses FSPro runs and predicts probabilistic fire spread and intensity maps. Fire analysts with GIS or fire behavior background could run FSPro multiple times across multiple weeks during a large fire event to provide updated fire simulation information. They could potentially generate the probability of fire at different intensity levels using tools such as Flep-Gen, which is currently not available within WFDSS. By combining burn probability and fire intensity probability with existing quantitative wildfire risk assessments we could calculate the expected fire loss and benefits for a specific fire event using consistent information used by local and regional fire staff. Our OR model could use these data layers to provide large fire containment suggestions by iteratively running the two-step containment optimization at multiple decision points during the incident. The model would then provide fire suppression suggestions at the beginning of the incident as well as at key strategic decision points. Each iteration builds on updated fire footprints, fire probabilities, fire intensity distributions, fire weather forecast, or changing resource availability situations. Consistency in use of decision support information reduces confusion and limits the potential for decision makers to disregard model results during the decision process. An advantage of keeping the OR model as an external extension of WFDSS is that the model could more easily access GIS data that are not embedded in WFDSS, for example, landscape risk layers, potentially SDI and PCL layers, in the future, and improved POD delineation data. Regardless of the different implementation pathways, future development of this model would require close collaboration with fire managers. We are currently testing the model based on two other fires, the Lolo Fire [28
] and the Ferguson Fire [47
]. More tests would be required to further improve the model.
In addition to creating an operationally relevant OR model aligned with existing decision support tools and systems, we were interested in improving upon previous spatial response optimization research. This study accomplishes this by considering firefighter safety through expanding time buffers between line construction and fire arrival (larger buffer mimics indirect attack; zero or very smaller time buffer allows direct attack) and allowing explicit consideration of fire fighter safety by using flame length probability data along potential control lines. By organizing different fire containment alternatives through a decision tree, we were able to reflect various fire management scenarios. Despite these improvements, alternative modelling strategies may also produce valuable results. For example, one could use a stochastic programming (SP) model to incorporate multiple future fire development scenarios and corresponding probabilities directly into the model formulation. Building and solving a large SP model with many stochastic scenarios would be computationally challenging but could provide one robust containment option suitable for all considered scenarios. Fire suppression SP models [10
] have been built to solve small- to moderate-sized problems; they often rely on heuristics to control model size and find “good” instead of optimal solutions. A potential future research direction could be building SP models to capture fire uncertainties and implement efficient solution algorithms to solve those models. Alternatively, one could also design and test heuristic methods. For example, we may build and solve many smaller SP models to identify different line construction strategies and integrate those selected control lines by voting to form a selected rPOD. We can then test a large set of stochastic fire scenarios to evaluate the overall effectiveness of the selected rPOD by referencing certain large fire suppression key performance indicators (KPIs) [52
], such as expected fire losses, rate of fire line engaged, held, and burned over, or fire fighter exposure rate to high flame length lines etc. Another simpler future model improvement to deal with the line holding uncertainty could be expanding the objective function of the current model to minimize the probability of any line breaching along the entire rPOD boundary using the PCL estimates.
Future improvements are still needed to make the model and its supporting data better reflect the real-world fire suppression practices. For example, the current model assumes that line construction along each boundary between two adjacent PODs needs to be finished within one suppression management period (i.e., one day). During actual fire suppression, however, night shift and multiday lines are possible. From the input data management perspective, delineating a landscape into smaller PODs or splitting POD boundaries into shorter control line segments can help alleviate this model limitation. Using smaller PODs would also give the model more options of forming better rPODs. Another way to address this model limitation would be directly revising the model formulation to allow for multiday lines, which we believe is viable but needs more investigations.
Many of the challenges in using OR models to support fire suppression are related with data availability and quality. For example, one of the key data requirements in building suppression models is the productivity of suppression resources along potential fire containment lines. Line construction productivity varies by crew type and capacity, topography, vegetation, accessibility, weather and fire intensity situations [53
]. As suppression decisions can be highly sensitive to the rates of fireline production [54
], it would be necessary to collect verified, locally specific empirical suppression data to more accurately parameterize decision support models [56
]. In this study, many simplifications were made, for instance, using the availability of Type I hand crew only as the resource availability measurement. Large fire suppression, however, often involves the collaboration between multiple types of crew, engines, helicopters and aircrafts. Data currently collected on the synergies between firefighting resources and resource effectiveness are very limited [54
]. A potential future research could focus on classifying the line construction or point protection tasks into more specific subtasks, i.e., spraying water, removing fuels, burning out, wrapping, setting up sprinkler system, etc.; we can then build statistics models to predict the productivity rate of using each resource type to achieve each subtask under different fire suppression situations such as terrain, weather, or fuel types. Future rPOD optimization model would then be able to focus on how to most efficiently assign resources to finish the more specific subtasks in order to build firelines and achieve point protect objectives. Future refinements of input data could also focus on better reflecting the relative workload associated with line width. There may be a non-linear relationship, where more sawyers are necessary for wider lines, and this could be informed by local data on vegetation as well.
Similar challenges exist with fire behavior modeling, including improving spatially explicit fuel modeling, diversifying wind and weather conditions across landscapes, and improving fire behavior algorithms. Fire arrival time is a key factor influencing the selection of timing and locations of fire line construction. Validation of fire arrival time modeling based on locally collected data either by fire fighters on the ground or through satellites or drones would be an important future research direction to improve the reliability of data and the model suggested suppression decisions based on those data.
Leveraging existing networks of PODs created by the U.S. National Forest fire and land management planners for spatial response optimization research offers a new frontier in OR modeling with direct relevance to on-the-ground management. In this study, we used a network of existing PODs built from prominent ridges and major water features. Fire and forest staff continue to develop POD networks across forested landscapes in the western USA, offering new insights and innovations not currently used in our model. For example, suppression difficulty index (SDI) [24
] and potential control line atlases (PCLs) [25
] are routinely integrated with local knowledge to determine POD boundaries with the highest likelihood of holding as a containment line. These risk analysis products and the resulting POD boundaries more accurately represent expected large fire response, will help parameterize large fire optimization models, and help identify those lines at highest risk of breaching for contingency planning. We expect to continue to observe improvements in creating POD networks and as these model inputs continue to improve, so too will the results from our OR model. We cannot overstate the importance of integrating advanced analytics with local, field-based knowledge to determine optimal response strategies that balance firefighter safety, probability of control, and protection of values at risk.