2370 Integrated spatial fire and forest management planning Can. J. For. Res. Downloaded from cdnsciencepub.com by 3.236.70.69 on 09/28/22 For personal use only. Mauricio A. Acuna, Cristian D. Palma, Wenbin Cui, David L. Martell, and Andres Weintraub Abstract: Forest management planners usually treat potential fire loss estimates as exogenous parameters in their timber production planning processes. When they do so, they do not account for the fact that forest access road construction, timber harvesting, and silvicultural activities can alter a landscape’s vegetation or fuel composition, and they ignore the possibility that such activities may influence future fire losses. We develop an integrated fire and forest management planning methodology that accounts for and exploits such interactions. Our methodology is based on fire occurrence, suppression, and spread models, a fire protection value model that identifies crucial stands, the harvesting of which can have a significant influence on the spread of fires across the landscape, and a spatially explicit timber harvest scheduling model. We illustrate its use by applying it to a forest management unit in the boreal forest region of the province of Alberta in western Canada. We found that for our study area, integrated fire – forest management planning based on our methodology could result in an 8.1% increase in net present value when compared with traditional planning in which fire loss is treated as an exogenous factor. Résumé : Les aménagistes forestiers considèrent habituellement l’estimation des pertes potentielles causées par le feu comme un paramètre exogène dans leurs processus de planification de la production de matière ligneuse. Ce faisant, ils ne tiennent pas compte du fait que la construction de routes d’accès en forêt, la coupe de bois et les travaux sylvicoles peuvent modifier la végétation ou la composition des combustibles d’un paysage et ils ignorent la possibilité que de telles activités puissent influencer les pertes futures causées par le feu. Nous avons développé une méthodologie intégrée de planification de l’aménagement forestier et de la gestion du feu qui tient compte de ces interactions et les exploite. Notre méthodologie est basée sur des modèles d’occurrence, de suppression et de propagation des feux, un modèle de la valeur de la protection contre le feu qui permet d’identifier les peuplements cruciaux dont la coupe peut avoir une influence significative sur la propagation des feux dans le paysage, ainsi qu’un modèle spatialement explicite pour établir le calendrier des coupes de bois. Nous illustrons son utilisation en l’appliquant à une unité d’aménagement forestier dans la région de la forêt boréale de la province d’Alberta, au Canada. Dans notre aire d’étude, nous avons constaté que la planification intégrée de l’aménagement forestier et de la gestion du feu basée sur notre méthodologie produisait une augmentation de 8,1 % de la valeur actualisée nette comparativement à la planification traditionnelle dans laquelle les pertes causées par le feu sont traitées comme un facteur exogène. [Traduit par la Rédaction] Introduction Fire is a natural component of many forest ecosystems and is particularly important in the boreal forest region of Canada. Although fire does have beneficial impacts on many natural forest ecosystem processes, it also poses threats to public safety, property, and other forest values. During each year, fire burns large portions of Canada’s forested areas, and fire management agencies spend significant amounts of money on efforts to limit its destructive impact (Martell 1994). Fire and forest managers seek to achieve an appropriate balance between the detrimental impacts of fire on public safety, property, and forest resources, the beneficial impacts of fire on natural forest ecosystem processes, and the cost of achieving that balance (Martell et al. 2004). In Canada, fire managers have traditionally focused on fire prevention, detection, and suppression, and to a lesser extent, they have worked with others to manipulate forest vegetation or fuels to reduce the likelihood of fires occurring and to decrease the rate of spread and intensity of any fires that do occur. Forest managers typically view fire management (including fuel management) as an exogenous activity that can produce reductions in burned area that contribute to enhanced indus- Received 20 June 2010. Accepted 9 July 2010. Published on the NRC Research Press Web site at cjfr.nrc.ca on 17 November 2010. M.A. Acuna. CRC for Forestry, University of Tasmania, Private Bag 12, Hobart, TAS, 7001, Australia. C.D. Palma. Department of Forest Resources Management, University of British Columbia, Vancouver, BC V6T 1Z4, Canada. W. Cui1 and D.L. Martell.2 Faculty of Forestry, University of Toronto, Toronto, ON M5S 3B3, Canada. A. Weintraub. Department of Industrial Engineering, University of Chile, P.O. Box 2777, Santiago, Chile. 1Present address: Forest Analysis and Modelling Unit of the Forests Branch of the Ontario Ministry of Natural Resources, 70 Foster Drive, Suite 400, Sault Ste Marie, ON P6A 6V5, Canada. 2Corresponding author (e-mail: martell@smokey.forestry.utoronto.ca). Can. J. For. Res. 40: 2370–2383 (2010) doi:10.1139/X10-151 Published by NRC Research Press Can. J. For. Res. Downloaded from cdnsciencepub.com by 3.236.70.69 on 09/28/22 For personal use only. Acuna et al. trial forest productivity. Thus, although fire and forest managers do collaborate to some extent, they largely work independently of each other. Forest managers typically call for fire protection in areas where they plan to harvest or have made silvicultural investments, and fire managers in turn use such priorities to influence the development and implementation of their fire management strategies. In recent years, fire and forest managers have recognized the need for integrated fire and forest management. Integrated approaches to fuel and forest management (which Hirsch et al. (2001) refer to as FireSmart forest management) address the fuel management implications of harvesting and silviculture at the same time as they address traditional timber production objectives. Hirsch et al. (2001) describe FireSmart forest management as the ‘‘use of forest management practices (e.g., site preparation, regeneration, stand tending, harvest scheduling ... block layout and design, and road construction) in a proactive and planned manner to reduce both the area burned by undesirable wildfires and the risk associated with the use of prescribed fire.’’ The premise underlying this concept is that timber harvesting and other land management activities (e.g., road construction) can alter forest fuel complexes in ways that contribute to decreases in the number and size of escaped fires and area burned. Such reductions in the flammability of the forest landscape can augment the value of existing fire management programs that produce a reduction in burned area with an enhanced secondary reduction in burned area above and beyond the primary reduction that results from the fire management program itself. Put simply, the harvesting and regeneration of a forest stand may reduce the flammability of the landscape and future forest-level fire losses and thereby contribute to a secondary increase in the annual allowable cut (AAC) (Palma et al. 2007). Several authors have suggested that fuel breaks can and should be used to fragment high-risk forest landscapes (e.g., Agee et al. 2000; Finney 2001; Hirsch et al. 2001; Finney and Cohen 2003; Wei et al. 2008). A fuel break can, for example, be created by replacing strips of flammable forest with vegetation that does not burn, or by cutting a strip of forest from below to reduce the amount of fuel available for combustion or to increase the height to crown base and thereby decrease a forest stand’s crown fire potential. Others have investigated the impact of forest management practices on fire behaviour. Harvesting, for example, has been shown to reduce fire spread across a landscape, and its spatial location appears to be a key factor that contributes to reductions in the risk of large fires (Johnson et al. 1998; Gustafson et al. 2004; González et al. 2005). Hirsch and Pengelly (1997) suggested that the timing and placement of roads and harvest blocks could reduce fire losses. In other words, the strategic fragmentation of the forest that results from road construction and other harvesting activities can produce firebreaks and other changes in a landscape’s fuel mosaic that may reduce its flammability and burned area. Thinning and other fuel management practices have also been shown to be effective in reducing fire hazard (e.g., Stephens 1998; Graham et al. 1999; Pollet and Omi 2002). The effect of exogenous reductions in the average annual 3 Also, 2371 burn fraction on the AAC of a forest has been studied using, for example, forest level simulation, linear programming, and stochastic programming timber harvest scheduling models (e.g., Van Wagner 1979; Reed and Errico 1986; Martell 1994; Boychuk and Martell 1996) that can be used to assess how fire management or the level of fire protection influences timber production. However, these models do not account for the fact that the timing and location of some forest management activities such as access road construction, harvesting, and silviculture can influence fire spread and landscape flammability, and their potential impact on fire loss should be assessed endogenously. The spatial and temporal optimization of fuel management activities poses very difficult mathematical modelling challenges due to the spatial nature of the problem (which typically calls for the development of large integer or mixed integer programming models that are difficult to solve) and the fact that fire occurrence, control, and spread are stochastic or random processes. We developed a spatially explicit methodology that fire and forest managers can use to develop and evaluate FireSmart strategies, and we illustrate its use by describing how we applied it to a portion of a forest management unit in the province of Alberta and the results that we obtained when we did so. Methods Study area Our methods were applied to a subset of Millar Western Forest Products Ltd.’s Forest Management Agreement area (FMA 97-0034), located near the community of Whitecourt in west-central Alberta, Canada (Fig. 1). Millar Western’s FMA falls within the Foothills and Boreal Forest natural regions of Alberta (Natural Regions Committee 2006). The total forested area in our 20 790 ha study area was 12 964 ha, and the rest of our study area was classed as roads, rivers, lakes, urban communities, and other non-flammable cover types. Millar Western’s 1997–2006 detailed Forest Management Plan describes the 1961–1998 fire activity observed in a 3.7 million ha area (5388’N–5585’N and 1148W–1178W) in which our study area was embedded. The study area was divided into a regular grid of 231 000 cells (30  30 m or 0.09 ha each), and a digital map coverage of the forested area was used to display a cover-type map that was used to subjectively aggregate the forested cells into 464 harvest blocks. The harvest blocks were homogeneous with respect to forest cover type and age class and ranged in size from 13 to 46 ha, averaging 27.9 ha. Overview of our integrated fire – forest management planning system We have developed an integrated iterative fire – forest management planning system3 that models the interaction between fire and forest management (Fig. 2). Our suppression planning system has three primary components: (i) a fire ignition, suppression, and spread model, (ii) a heuristic procedure for estimating stand fire protection values (FPV) that reflect the extent to which harvesting each stand will reduce the flammability of the landscape, and (iii) referred to as FireSmart forest management planning system throughout the paper. Published by NRC Research Press 2372 Can. J. For. Res. Vol. 40, 2010 Can. J. For. Res. Downloaded from cdnsciencepub.com by 3.236.70.69 on 09/28/22 For personal use only. Fig. 1. Map of the study area. a spatial harvest scheduling model that maximizes economic returns but ensures that some of the harvesting activity will contribute to reducing landscape flammability and well as timber production. Both the cell burn probabilities (step i) and the FPVs (step ii) are input into the spatial harvest planning model. Fire ignition, suppression, and spread model The fire ignition, suppression, and spread model uses historical fire occurrence data and descriptions of the fuel, weather, and topographical features of the landscape to predict where fires might occur and how they might spread across the landscape. It produces estimates of the time required for a fire to spread from the cell in which it starts to a cell that contains a forest value and cell burn probabilities (burn fractions (BFs)), the annual probability that any cell on the landscape will burn given its current vegetation or fuel mosaic (Sanchez-Guisandez et al. 2007). Fire protection value assessment heuristic This is a heuristic procedure that produces an estimate of the ‘‘value’’ of harvesting a block based on the extent to which it will ‘‘cool’’ the forest by interrupting crucial paths along which fire can spread across the landscape (Palma et al. 2007). A block’s FPV is assessed by estimating the extent to which harvesting it will force fires that may spread through it to follow longer paths, which will reduce the flammability of the landscape. Spatial forest planning model Our spatial harvest planning model is a mixed integer programming model that specifies when and where to harvest cut blocks to maximize the present net worth (PNW) of the timber harvested over the planning horizon. It includes a fire protection constraint that ensures that the sum of the FPVs of the blocks harvested to produce timber volume exceeds some minimum (referred as to minimum fire protection level), which is designed to reduce the flammability of the landscape (Acuna et al. 2003). Our approach to FireSmart forest management We consider three types of strategies for managing flammable forests. Our first strategy, which we describe as our ‘‘base-case strategy,’’ is not a FireSmart strategy. Potential fire losses are incorporated into timber harvest schedule decision-making by assuming that some specified fraction of each harvest block (its BF) will burn during each period. A spatial burn probability model is used to predict the probability that each cell in the forest will burn next year given the current structure of the forest (e.g., the fuel type of each cell) and the anticipated fire ignition and suppression processes. Those cell-level burn probabilities are then used to estimate the harvest block burn fractions that are assumed to remain constant over the planning horizon. Given the structure of its objective function and constraints and assuming that all other attributes such as harvest block species and volumes are similar, the base-case model will attempt to harvest the higher burn probability harvest blocks earlier in the planning horizon before they are likely to burn. However, because the base-case BFs can and do vary by harvest block but do not vary over time, this strategy ignores the fact that harvesting may alter forest structure, landscape flammability, and the harvest block burn fractions over both time and space.4 4A deterministic forest succession model and a deterministic climate change scenario could be used to derive base-case burn probabilities that vary deterministically over time to reflect forest succession and (or) climate change process. We chose not to do so because how small changes in forest fuels (e.g., aging and succession) and their impact on fire behaviour currently are not well understood, and climate change was beyond the scope of our investigation. Note also that fire itself will, of course, alter forest composition and landscape flammability, but we cannot predict when and where fires will actually occur so we cannot include such information in our deterministic planning model. The extent to which probabilistic fire and weather information might be incorporated in a spatial stochastic programming model is a very challenging problem for future research. Published by NRC Research Press Acuna et al. 2373 Can. J. For. Res. Downloaded from cdnsciencepub.com by 3.236.70.69 on 09/28/22 For personal use only. Fig. 2. Schematic representation of integrated fire – forest management planning. Rectangles represent the components of the approach, and parallelograms represent data, intermediately derived information, and output data. FPV, fire protection value; BF, burn fraction; ignit. prob., ignition probability; Prop., propagation; constr., constraints. We describe our second strategy as our ‘‘phase I FireSmart strategy.’’ The harvests prescribed by the base-case strategy are used to predict which harvest blocks will be harvested during each period, how the forest fuel complex will change over time, and what it will be at the start of periods 2 through 8 assuming that it does not burn. Those seven ‘‘harvest-influenced’’ fuel complexes then serve as input to the burn probability model, which is then used to predict seven new sets of cell-level burn probabilities and harvest block burn fractions. The spatial harvest scheduling model is then used to develop a new harvest schedule based on these new, time-dependant burn fractions. Because harvested stands are assumed to be incapable of burning during the planning horizon, landscape flammability, cell burn probability, and harvest block burn fractions will be nonincreasing functions of time, and some harvest blocks, namely those influenced by harvesting, will likely ‘‘see’’ reduced burn fractions during subsequent periods. The reduction in landscape flammability will result in an increase in the harvest flow and PNW of the harvest. Phase I FireSmart forest management thus constitutes a relatively simple use of the principles of FireSmart forest management Published by NRC Research Press Can. J. For. Res. Downloaded from cdnsciencepub.com by 3.236.70.69 on 09/28/22 For personal use only. 2374 that has not, to our knowledge, been either recognized or exploited by others to date. Our third strategy, which we describe as ‘‘phase II FireSmart strategy’’, is a true FireSmart strategy sensu Hirsch et al. (2001). We use Palma et al.’s (2007) FPV model to identify crucial harvest stands, flammable stands that are positioned on the landscape such that their harvest has the potential to contribute to significant reductions in landscape flammability. In each period, harvest blocks are ranked by their FPV, and the harvest scheduling model is augmented by adding a level of protection (LOP) constraint that calls for some designated fraction of the forest’s FPV to be harvested when blocks are harvested to produce timber. This LOP constraint therefore forces the production of what we describe as fire protection by converting some high FPV stands to fuel breaks, thereby creating what Hirsch et al. (2001) describe as ‘‘fire doors.’’ The impact of the LOP constraint is to ensure that some high FPV stands that might not have been harvested to satisfy timber production needs will be harvested during periods when their FPV is high, contributing to a further reduction in landscape flammability beyond what would have been achieved by normal harvest scheduling (i.e., phase I FireSmart forest management). During the first iteration of phase II FireSmart forest management, the inclusion of the new LOP constraint will, of course, generate a harvest schedule, the PNW of which will be less than or equal to the PNW of the base-case harvest schedule. However, forcing the harvest of high FPV harvest blocks will reduce the flammability of the landscape, and the new burn fractions for periods 2 through 7 will be less than or equal to the burn fractions produced by phase I FireSmart forest management. Our assumption is that the reduced burn fractions resulting from the lower landscape flammability achieved by a low or moderate level of LOPinduced harvesting of high FPV stands will compensate for the addition of the new LOP constraint and result in an overall increase in the PNW of the forest. Eventually, as the LOP constraint is strengthened, we will reach a point at which the reduced flammability of the landscape does not compensate for the strengthened LOP constraint and the PNW of the forest will begin to decline. The burn probability model The fire (burn probability (BP)) model has both stochastic and deterministic components that are characteristic of the forest management unit’s fire regime. The BP model includes a fire occurrence module, an initial attack module, and a fire spread module. The fire occurrence module stochastically simulates the occurrence of fires during the next fire season. The predicted number of fire ignitions is based on the number of fires that have occurred on the landscape in the past, assuming recent spatial fire occurrence patterns (e.g., the probabilities that a fire will occur in a specific cell) can be used to model future ignition spatial patterns. The fire season is divided into three subseasons (spring, summer, and fall) to reflect the fact that fuel characteristics and fire occurrence patterns can vary throughout a fire season. Fires are partitioned into two fire cause groups (lightning- Can. J. For. Res. Vol. 40, 2010 caused fires and people-caused fires) to account for the fact that the number of fires and the spatial location patterns of fires can also differ by subseason and cause. We assume that the probability distribution of the number of fires (by subseason and cause) is Poisson with an average based on historical fire patterns for the area (Cunningham and Martell 1973). We developed and used fire ignition density maps to describe the historical spatial fire patterns. The input data consist of two ASCII files that contain the fire density for each cell — one for people-caused fire occurrences and the other for the lightning-caused fire occurrences. The initial attack component of the BP model models the effectiveness of fire suppression activities on the landscape by predicting the fraction of fires that escape initial attack and can grow across the landscape. The BP model assumes that the probability that a fire will escape initial attack is determined by its head fire intensity at the start of the initial attack action and the initial attack response time, the time interval between the time that the fire is reported and the initiation of suppression action by the initial attack crew. We assume that the probability that a fire will escape initial attack will increase as its head fire intensity increases. The escape index (EI, the product of the response time and the square root of the head fire intensity) is calibrated to reflect the historical performance of the initial attack system. All historical fires are ranked in increasing order of their EI, and the critical threshold value is the one that corresponds with the historically observed percentile of escaped fires since then. The historical fire data for our study area indicates that 5% of the fires escaped initial attack in that area, so the 95th percentile of the EI is the threshold beyond which all fires are assumed to escape initial attack. The growth of the fires that escape initial attack is modelled using J.B. Todd’s WILDFIRE deterministic spread model.5 WILDFIRE is an eight-point contagion cellular fire growth model first developed by Kourtz et al. (1977) that uses fuel data and the Canadian Forest Fire Behaviour Prediction System (FBP) calculations (Forestry Canada Fire Danger Group 1992) to project the growth of a fire’s perimeter. The time required for a fire to move from one cell to its neighbour was calculated using FBP equations based on fuel types, slope and aspect, and weather conditions in the cells. WILDFIRE grows fires that have escaped initial attack and records the total area burned, as well as the area burned by fuel type in each cell on the landscape. These fire models are used to predict the burn probability of each cell on the landscape. All of the cells burned by each simulated fire that occurs over a sample size of N iterations or simulated years are identified. Suppose that ni is the number of times that cell i burns during those N simulated years. Then Bi, the estimated probability that cell i will burn during the next fire season, is ni /N. We assume that the BF of a harvest block is the average BP of all cells in the block. Estimating the fire protection value of a harvest block The FPV of a harvest block is a measure of its potential 5 J.B. Todd, Fire Research Network, Canadian Forest Service, Edmonton, Alberta. User documentation for the wildland fire growth model and the wildfire display program. Unpublished, 1999. Published by NRC Research Press Acuna et al. 2375 Can. J. For. Res. Downloaded from cdnsciencepub.com by 3.236.70.69 on 09/28/22 For personal use only. impact on fire spread across the landscape. It is a measure of the marginal contribution that harvesting a block would make to the value of the forest by slowing fire spread and therefore reducing losses. A brief description of the FPV model is presented below, but for further details, readers are referred to Palma et al. (2007). The FPV model considers a landscape that is represented by a regular grid of cells, each of which can act as a fire ignition point (m), a fire destination point (n), or as part of a path along which forest fires can spread. For each ordered pair (m, n), the potential impact of a fire that is ignited in cell m on values at risk (in this case, timber volume) in cell n is ½1 FIm;n ¼ Pm  Vn  PLm;n where Pm is the probability that a fire ignites in cell m, Vn is the volume of timber in cell n (to be protected), and PLm,n is the probability that a fire that ignited in cell m will spread to cell n. Pm is obtained from the fire model described above, Vn comes from inventory data, and PLm,n is determined as follows. We first determined Lm,n, the time required for a fire to travel from cell m to cell n, by using the fire spread rates between adjacent cells provided by the fire model and a shortest path algorithm to identify the shortest route and corresponding shortest time required for a fire to travel from cell m to cell n. We then used the probability distribution function of fire duration (that we fitted using local data) to estimate the probability the fire would last more than Lm,n hours. If the probability distribution function of fire duration, F(x), represents the probability that the time that a fire burns freely is less than or equal to x, then PLm,n, or P(X > Lm,n), is 1 – P(X £ Lm,n) = 1 – F(Lm,n). To assess the effect of harvesting block k on the flammability of the land, we also estimated the probability that a fire that is ignited in cell m will reach cell n assuming that block k had been harvested, PLm,n(k). This was done as described above but assuming that fire cannot spread through any cell in the harvested block k. As this forces fires to use alternative and possibly longer paths, Lm,n(k), the fire’s shortest path from cell m to cell n (expressed in hours) if all the cells in block k had been harvested, will be greater than or equal to Lm,n. Consequently, PLm,n(k) will be less than or equal to PLm,n. Thus, the fire protection of block k with respect to the cell pair (m, n), FPm,n(k), is defined as the difference in the fire effect of cell m on cell n with and without block k: ½2 FPm;n ðkÞ ¼ Pm  Vn  ðPLm;n  PLm;n ðkÞÞ For each block, we repeated the process for all pairs (m, n) for which there was a non-zero probability that a fire would ignite the source cell and spread to the destination cell. The fire protection value of block k, FPV(k), is then the sum of the protection values associated with all of the fire paths between pairs (m, n) that pass through block k: X ½3 FPVðkÞ ¼ FPm;n ðkÞ m;n We assessed FPV(k) in isolation from the harvest of other blocks on the landscape. Although some interaction may ex- ist when multiple blocks are harvested simultaneously, considering all possible interactions would be computationally intractable. We address the potential implication of this assumption in our Discussion. Spatial timber harvest scheduling model We extended Reed and Errico’s (1986) model III (timber harvesting scheduling linear programming model) to develop a mixed integer linear programming model that incorporates fire protection values in harvest schedule decision-making. Reed and Errico’s model III assumes that some known fraction of the forest burns each year to account for probabilistic fire losses, and it constitutes a more general form of Johnson and Scheurman’s (1977) model II. We assumed that within a time period, harvesting takes place after burning. Initially, we also assume that this proportion, which we refer to as the burn fraction, does not vary over time. Our model’s objective function was the net present value produced by harvesting timber, which was to be maximized over an 80-year planning horizon. We partitioned the 80 years into eight 10year periods; fifteen 10-year age classes were used in our model. Our model is based on the assumption that all stands are accessible by road at the start of the planning horizon, harvest flows are constrained to vary by no more than ±5% between periods, and harvested and burned areas regenerate naturally at no cost. We incorporated both harvesting costs and stumpage rates into our model, but we ignored postfire salvage. We also assumed that if some part of a harvest block was to be harvested during a period, then all of that block was harvested during that period. Input data The input for our model is a description of the initial state of the forest, which includes the attributes of the cutting blocks: species and the commercial volume by species and age class. Cutting block We used a digital landscape map using the ArcInfo geographic information system (ESRI, Redlands, California) to define the cutting blocks. Individual cells were subjectively aggregated into 464 cutting blocks ranging in size from 13 to 46 ha, averaging 27.9 ha. Wood volumes, ages, and species Species and age class were associated with each cutting block. Table 1 describes the number and area of the harvest blocks in each of the cover types we used. Merchantable wood volumes and yield tables (by species and age class) were provided by Millar Western Forest Products Ltd. (2000). Network representation of the spatial harvest scheduling model The model can be represented as a network of subnetworks, one for each cutting block, similar to that presented and described in Boychuk and Martell (1996) and depicted in Fig. 3, which shows how forest area within a harvest block flows through time. The structure of the forest at the beginning of each period is characterized by the area in each age class in each cutting block. The nodes represent Published by NRC Research Press 2376 Can. J. For. Res. Vol. 40, 2010 Table 1. Description of the forest cover types and harvest blocks in the study area. No. of blocks 162 170 10 14 33 75 464 Forest cover type White spruce Black spruce Trembling aspen Pine–aspen Spruce–aspen Lodgepole pine Total Area (ha) 4 692 4 740 268 355 894 2 012 12 964 % of total area 36.2 36.6 2.1 2.7 6.9 15.5 100.0 Can. J. For. Res. Downloaded from cdnsciencepub.com by 3.236.70.69 on 09/28/22 For personal use only. Note: White spruce, Picea glauca; black spruce, Picea mariana; trembling aspen, Populus tremuloides; lodgepole pine, Pinus contorta the existing area of each age class at the beginning of each period. The arcs represent the flow of area between pairs of nodes. Thus, if the decision is made to harvest a cutting block during a particular period (Fig. 3a), then the entire area harvested from all of the age classes within the block is brought together into a harvesting node, which will then flow (along with any burned area) into the regeneration age class (age class 1) at the start of the next period. Similarly, if a cutting block is not harvested (Fig. 3b), all of the area in each age class that is not burned flows (grows) up into the next age class (except for the top or upper collecting class) at the start of the following period. Mathematical formulation of the model The spatial harvest scheduling model can be expressed mathematically as follows. Sets, parameters, and variables are presented in Table 2. Objective function Equation 4 is used to maximize the PNW over an 80-year planning horizon: X at ðNET REVENUEt Þ ½4 Max Z ¼ t where at is the discount factor for period t, assuming that the harvesting is carried out at the midpoint of the period, and NET REVENUEt represents the total net revenue (stumpage rate of wood minus logging costs) of harvesting the blocks in period t. Stumpage rates and logging costs for single blocks (dollars per cubic metre) were obtained by using representative values depending on the species and the harvesting systems used in the study area. Constraints Equations 5, 6, and 7 are used for computing the area harvested, volume harvested, and total volume harvested, respectively. ½5 AHi;j;t ¼ ðXi;j;t  ð1  BFi;t ÞÞ  ATi;j;t 8 i 2 I; j 2 J; t 2 T ½6 VHi;j;t ¼ AHi;j;t  VOLi;j ½7 TVHt ¼ XX i j VHi;j;t 8 i 2 I; j 2 J; t 2 T 8t 2 T The constraints of area and volume burned are calculated by eqs. 8 and 9, respectively. ½8 ABi;j;t ¼ Xi;j;t  BFi;t ½9 VBi;j;t ¼ ABi;j;t  VOLi;j 8 i 2 I; j 2 J; t 2 T 8 i 2 I; j 2 J; t 2 T The level of protection (LOP) constraint that ensures some minimum level of fire protection value is ‘‘produced.’’ XX Hi;t  FPVi;t  MPL ½10 i t In phase II, we ran the model with the level of protection constraint (eq. 10) where MPL represented a level of protection of 15% (phase II-A) and 30% (phase II-B) of the sum of the FPVs of all of the harvest blocks in the forest management unit. These runs produced FireSmart harvest schedules that were used to produce revised BPs that compensated for the addition of the new LOP constraint and resulted in an overall improvement in the PNW of the forest. Initial age class distribution of the forest is calculated as ½11 Xi;j;P1 ¼ IAi;j 8 i 2 I; j 2 J Conservation of area flow into the youngest age class (AC1; regeneration) is determined by X ðAHi;j;t1 þ ABi;j;t1 Þ ½12 Xi;AC1;t ¼ j 8 i 2 I; t 2 fT n P1g where {T \ P1} denotes the elements of the set T other than P1. Conservation of area flow into the intermediate age classes is determined by ½13 Xi;j;t ¼ ATi;j1;t1 8 i 2 I; j 2 fJ n AC1; AC15g; t 2 fT n P1g Conservation of area flow into the upper collecting age class is determined by ½14 Xi;AC15;t ¼ ATi;AC14;t1 þ ATi;AC15;t1 8 i 2 I; j 2 J; t 2 fT n P1g Harvest flow is constrained to vary by no more than 5% per period: ½15 TVHt  ð1  0:05ÞTVHt1 8 t 2 fT n P1g ½16 TVHt  ð1 þ 0:05ÞTVHt1 8 t 2 fT n P1g Equations 15 and 16 were used during the first four periods, whereas for the last four periods, the volume harvested was controlled by a non-declining flow constraint. Constraints ensuring that only entire harvest blocks are harvested are as follows: X AHi;j;t 8 i 2 I; t 2 T ½17 TAHi;t ¼ j Published by NRC Research Press Acuna et al. 2377 Can. J. For. Res. Downloaded from cdnsciencepub.com by 3.236.70.69 on 09/28/22 For personal use only. Fig. 3. Network representation of the spatial harvest scheduling model: (a) a block is harvested and (b) a block is not harvested. Table 2. List of sets, parameters, and variables used in the mathematical formulation of the model. Term Definition Sets i cutting blocks j age classes t periods i [ I = {S1, S2, . . ., S464} j [ J = {AC1, AC2, . . ., AC15} t [ T = {P1, P2, . . ., P8} Parameters Ai IAi,j VOLi,j FPVi,t BFi,t MPL Area of block i (ha) Initial area of age class j in block i (ha) Gross merchantable volume of timber in age class j in block i (m3ha–1) Fire protection value of block i in period t, calculated according to eq. 3 Burn fraction (probability) of block i in period t Minimum fire protection level Variables Hit Xi,j,t AHi,j,t VHi,j,t ABi,j,t VBi,j,t ATi,j,t Binary, 1 if block i is harvested in period t, 0 otherwise Area of age class j in block i at the start of period t (ha) Area harvested from age class j in block i in period t (ha) Volume harvested from age class j in block i in period t (m3) Area of age class j in block i burned in period t (ha) Volume burned of age class j in block i in period t (m3) Area transferred from age class j in block i in period t to age class j + 1 in block i in period t + 1 (ha); the area transferred is the area that moves from one age class to the next, and from one period to the next, when the block is not harvested Total area harvested from block i in period t (ha) Total area transferred from block i in period t (ha) Total volume harvested in period t (m3) TAHi,t TATi,t TVHt ½18 TATi;t ¼ X ATi;j;t 8 i 2 I; t 2 T j ½19 TAHi;t  Ai  Hi;t 8 i 2 I; t 2 T ½20 TATi;t  Ai  ð1  Hi;t Þ 8 i 2 I; t 2 T Equations 17 to 20 ensure that if a block is harvested during any period, no area is transferred to older age classes in the next period and the area harvested is bounded by the area of this block. The model was implemented using the GAMS IDE modelling language (version 19.6; GAMS Development Corporation, Washington, DC, USA ) and the CPLEX solver (version 7.1; IBM Corporation, Armonk, New York, USA). The model was run on a Centrino Duo computer with a 1.66 GHz processor and 1.0 Mb of RAM memory. Results Fire protection values (FPV) The FPVs of the harvest blocks are shown in Fig. 4 in which darker colors indicate higher fire protection values. Published by NRC Research Press 2378 Can. J. For. Res. Vol. 40, 2010 Can. J. For. Res. Downloaded from cdnsciencepub.com by 3.236.70.69 on 09/28/22 For personal use only. Fig. 4. Estimated fire protection values (FPV) in the study area (reproduced from Palma et al. 2007). Although we generated them and they were used as input for our spatial harvest planning model, they could be used on a stand-alone basis by forest managers charged with the responsibility of subjectively deciding when and where to harvest to ‘‘beat’’ fire and when and where to establish fuel breaks. The harvesting of large blocks removes more flammable vegetation and therefore reduces the spread of fires starting and spreading more than the harvest of smaller blocks in the same area. Fuel type or species should contribute to variation in protection values from block to block. These results are consistent with the fact that spruce (primarily white spruce, or what fire specialists refer to as the C-2 fuel type) is more flammable than any of the other species (e.g., aspen), so their harvest should cool the landscape more than the harvest of less flammable stands. Also, higher protection values are associated with blocks that are located in the vicinity of the most valuable areas, that is, where there is more timber volume. Conversely, blocks with the lowest protection values are in areas of sparse forest or close to natural fire spread barriers such as rivers or roads around the area that would envelope the study area, in which fires could occur and spread. Spatial planning model A summary with the characteristics of the model that we used for assessing the effect of fire protection on the harvest schedule is presented in Table 3. Of the total number of constraints, 111 361 (31.9%) are related to the inclusion of fire losses and to the protection of harvest blocks from fire. Both non-FireSmart (base-case) and FireSmart (phases I, II-A, and II-B) forest management strategies were evaluated to compare the area and volume harvested in each period, as well as the economic effects of different fire protection strategies. In comparison with the base-case, there was a decrease in the mean burn fraction values in phases I and II, with a consequent larger area available to be cut. Mean burn fraction values were 6% (base-case), 4.9% (phase I), Table 3. Dimensions of the optimization problem. Characteristic Value General characteristics Number of harvest blocks Number of periods Number of age classes 464 8 15 Decision variables Number of continuous variables Number of binary variables Total 345 260 3 712 348 973 Constraints Blocks of equations Number of equations 36 349 443 Fig. 5. Total area harvested by period and fire protection strategy. 4.5% (phase II-A), and 3.9% (phase II-B) for all blocks and periods. Assessment of FireSmart forest management strategies A comparison of the total area harvested in each period for the fire protection strategies that we investigated is prePublished by NRC Research Press Can. J. For. Res. Downloaded from cdnsciencepub.com by 3.236.70.69 on 09/28/22 For personal use only. Acuna et al. 2379 Fig. 6. Total volume harvested by period and fire protection strategy. Fig. 7. Net present value achieved by fire protection strategy. MM, million. sented in Fig. 5, which illustrates an increase in the total area harvested as the level of harvesting of fire protection blocks increases. Considering all four strategies investigated, the average area harvested in the last four periods was approximately 1000 ha greater (6688 ha) than in the first four periods (5636 ha). The largest difference was obtained with the base-case for which 5442 ha were harvested during the first four periods and 6744 ha were harvested during the last four periods. These results in part are due to the burn fraction values and FPVs of the blocks harvested through the planning horizon, as well as the nature of the objective function (maximization of PNW) used, all of which affect the area harvested. Because net revenue is discounted using an interest rate of 5%, the model attempts to schedule the harvest of larger volumes in the early periods to maximize the PNW. Thus, despite the fact that smaller areas were harvested during the first four periods, the total volume harvested during those periods is considerably larger than during the last four periods. Figure 6 illustrates the breakdown of the volume harvested by period and fire protection strategy. There is a reduction in the volume harvested from the first period to the fourth period, which is followed by a slight increase during the last four periods. Considering all of the protection strategies and periods, the harvested volume remains within a band that varies between 197 000 and 235 000 m3. This is due to the constraint on the variation in volume harvested between consecutive periods (5% of variation) and the nondeclining flow constraint that were used to control the volume harvested during the last four periods. Independent of the protection strategy, the largest timber volume (over 205 000 m3) is harvested during the three first periods of the planning horizon to maximize the PNW. The net present values that can be achieved by using integrated fire protection strategies are presented in Fig. 7. When comparing the best FireSmart forest management strategy (phase II-B) with the base-case strategy, an increase of 8.1% in PNW ($980 417) is obtained for the entire planning horizon. The greatest marginal increase (an increase of $381 762 or 3.14%) in PNW is obtained when phase I is compared with the base-case. Within the FireSmart forest management strategies, there is an increase of $245 686 (2.02%) when phase II-A is compared with phase I and a further increase of $352 969 (2.90%) when phase II-B is compared with phase II-A. These results are a consequence of the reduced burn probabilities obtained when using FireSmart forest management strategies (phases I and II) as described earlier. Thus, the revised burn probabilities computed in phase I are less than those computed in the base-case, because the new burn probabilities vary over both time and space, and because harvested blocks do not support fire spread, the burn probability of blocks are a non-increasing function of time, which results in an increase in the NPW computed in phase I. The same reduction in the revised burn probabilities occurs when the impact that harvesting a block will have on fire spread is included in the model (inclusion of FPVs and LOP constraint in phases II-A and II-B). The FPVs provide a measure of that impact, so an increase in the level of protection causes a reduction of the revised burn probabilities, which compensates for the addition of the new LOP constraint and results in an overall improvement in the PNW of the forest. The annual allowable cut, the net present value by area, and the value of the forest for different protection levels are summarized in Table 4. The results presented in Table 4 indicate that the annual allowable cut increases with higher protection levels. The best FireSmart forest management strategy (phase II-B) produces an 8.1% increase in the annual harvest volume compared with the base-case harvest volume. It is important to note, however, that these results are specific to our study area. Discussion and conclusions We have developed and implemented a FireSmart forest management planning methodology that integrates fire and forest management and accounts for and exploits the interactions between those two important aspects of forest management. Our methodology is iterative and based on fire ignition, suppression, and spread models, a heuristic procedure that identifies crucial stands that can influence the spread of fires across a landscape, and a spatially explicit timber harvest scheduling model that can be used to assess the economic impact of alternative FireSmart forest management strategies. Our approach to estimating fire protection values is based Published by NRC Research Press 2380 Can. J. For. Res. Vol. 40, 2010 Table 4. Annual allowable cut and net present value of the protection strategies considered. Level of protection strategy Base-case using the BPs computed at the start of the planning horizon Phase I, FireSmart forest management with BPs that vary by period Phase II-A, FireSmart forest management with 15% protection Phase II-B, FireSmart forest management with 30% protection Annual allowable cut (m3ha–1year–1) 1.66 Present net worth by area ($ha–1) 937 Increase in the value of the forest* (%) — 1.70 967 3.1 1.74 986 5.2 1.75 1013 8.1 Can. J. For. Res. Downloaded from cdnsciencepub.com by 3.236.70.69 on 09/28/22 For personal use only. *Increment in PNV per unit area (based on the 12 964 ha forested portion of the 20 790 ha study area) relative to the base-case. on evaluations of harvest blocks on the assumption that when a block is harvested, all of the paths that fire might use in that block are interrupted and fire is forced to use alternate paths. We assume that fire may travel between any two points over multiple paths, so the harvesting of that block may not stop the fire, but rather force it to travel over a less flammable (i.e., slower) route, thereby slowing its advance. We define the protection value of a harvest block as the sum of the impacts of all possible fire paths that are slowed when that block is harvested. We used timber volume as our value at risk, but our methodology could be used to assess the impact of such activities on any measurable values at risk (Palma et al. 2007). Our methodology could be used to assess the impact of other stochastic contagious processes that percolate across forest landscapes such as, for example, insect outbreaks. The FPV model that produces a surrogate measure of the value of making a harvest block incapable of supporting fire spread is based on an assumption that fires are independent events, and we did not consider the fact that destination cells can be burned by multiple fires. This modelling simplification may produce overestimates of the FPVs, an issue that should be investigated in future studies. When we assessed the FPVs, we assessed the effect of harvesting each block in isolation from all other blocks on the landscape and thereby did not account for the effect that groups (multiple blocks) could have on the protection of the entire forest. There may be some interactions when multiple blocks are harvested, with protection values of individual blocks being affected by those of their adjacent blocks. Both of these modelling assumptions should be investigated in future studies. We developed a spatial mixed integer programming model to generate and evaluate FireSmart forest management strategies. Our model is an enhancement of the spatial model III developed by Reed and Errico (1986) and its variant used by Martell (1994). We maximize the net present value over an 80-year planning horizon that was partitioned into eight 10-year periods. We did not impose terminal constraints on the merchantable volume growing in our forest or its age-class distribution at the end of the planning horizon, but we did impose harvest flow constraints that not only stabilized the harvest flow, but also ensured that there would be a reasonably balanced age-class structure in our forest at the end of the planning horizon. The effect of those con- straints was that with both the non-FireSmart and our FireSmart forest management strategies, the volume growing in our forest at the end of the 80-year planning horizon was greater than 50% of the volume available at the beginning of the planning horizon. These results are very similar to those obtained by other authors on much larger areas and over much longer planning horizons (Martell 1994; Khajuria et al. 2008) and are consistent with the fact that, in general, forest management planners typically impose terminal constraints at the larger FMA scale rather than on smaller scale areas such as our study area. Our model prescribed that 12 186 ha or 94% of the 12 964 ha forested portion of our study area should be harvested over our 80-year planning horizon, and because the prescribed harvesting activity was reasonably balanced over all eight periods by the harvest flow constraint (see Fig. 5), it had a reasonably balanced age-class structure at the end of the planning horizon without the inclusion of terminal state constraints.6 Because our primary objective was to investigate the extent to which FireSmart management can mitigate fire losses and because the impact of a rigid terminal volume constraint, depending on its magnitude, is likely to have reduced the present net worths of all three strategies, it is reasonable to assume that the percentage differences between the base-case and phase I and phase II Firesmart forest management would not have been significantly impacted by such a constraint. Our FireSmart forest management planning methodology is based on a computationally intractable optimization problem that cannot be solved to optimality. It is therefore important to note that our methodology does not necessarily produce an optimal solution but that it does produce improved solutions. We found that the implementation of our FireSmart forest management planning methodology (phase II-B) would increase the volume harvested by 5.7% and the net present value by 8.1% when compared with the nonFireSmart forest management strategy (base-case) for our study area. These results demonstrate that the FireSmart harvesting of blocks based on their fire protection values can reduce the negative impact of fire on forests and increase both the annual allowable cut and the economic value of a forest. We focussed on the economics of timber production, but given the landscape fragmentation that can result from FireSmart forest management, there is an obvious need to investigate the potential impact of such practices on wildlife and 6 Note that the mixed integer form of our model with binary harvest decision variables and harvest flow constraints prevented the harvesting of the entire study area as would be the case had we used continuous decision variables. Published by NRC Research Press Can. J. For. Res. Downloaded from cdnsciencepub.com by 3.236.70.69 on 09/28/22 For personal use only. Acuna et al. other ecosystem values. Such values could be included in an expanded version of our spatial model. There are, of course, limitations to our approach. For example, we assumed that fire cannot spread through harvested blocks, but this limitation could easily be addressed by modelling and allowing slower spread rates through treated blocks, thereby facilitating the evaluation of a rich array of fuel management measures. We assumed that there was only one tree species growing in each harvest block, and it was assumed that after a fire or cut, a new block will re-establish immediately and grow according to the same volume–age relation as in the existing stands. We also assumed that the only constraints on harvesting were related to harvest flow and did not include accessibility, postfire salvage, and other factors. In addition, we ignored uncertainties in the demand for timber and the resulting stumpage values. Such issues could and should be addressed in a more comprehensive model before our methodology is actually used by forest managers. When Reed and Errico (1986) published their ‘‘mean value approach,’’ they showed that it was reasonable to use it for strategic forest management planning under uncertainty due to fire. They pointed out that ‘‘The relation between optimal stochastic and deterministic feedback harvesting policies has been studied in the related field of animal resource management (Ludwig and Varah 1979; Reed 1979). Results seem to indicate little difference between the two.’’ They concluded by stating ‘‘In consequence, in any period given the state x, the use of the deterministic optimum policy [which we and others in the forest management planning community now refer to as the solution to the mean value problem] should be only slightly suboptimal.’’ Boychuk and Martell (1996) subsequently followed up on Reed and Errico’s (1986) use of the phrase ‘‘should be only slightly suboptimal’’ and carried out a detailed investigation of the validity of using the mean value approach to planning under uncertainty due to fire and found that Reed and Errico’s (1986) belief was in fact valid for fire regimes characteristic of those observed in forest management units in the province of Ontario. The mean value approach to strategic forest management planning is now widely accepted as being valid throughout both the forest management planning research and forest management planning communities. From the methodological point of view, it is clear that the benefits of FireSmart forest management strategies are higher on landscapes strongly affected by fire and where the ‘‘smart’’ harvest of blocks according to protection values has the potential to reduce the annual burn fraction significantly. Future research should be directed at the effects of different species, forest structures, and age-class distributions and their impact on flammability and on the potential timber volume to be harvested. Additional effects of harvesting such as fragmentation of the landscape, impact on wildlife, and environmental consequences of harvest decisions should also be investigated. It is important to note that our FPV model produces what is essentially a surrogate measure of the fire protection value of a harvest block because it is based on the assumption that it and only it is harvested. We first identify the shortest paths between all pairs of cells in which fires can ignite and 2381 cells that contain values that can be destroyed by fire. We then determine which of those shortest paths pass through each harvest block. The FPV of a harvest block is the net impact of harvesting that block on all of the shortest paths that pass through that block. The lengths of all of the shortest paths between all pairs of ignition cells and value cells depend on the structure of the entire forest fuel complex before any harvesting takes place, but each harvest block’s FPV is assessed on the assumption that none of the other harvest blocks are harvested. As we pointed out in Palma et al. (2007), if FPV(k) and FPV(k’) are the fire protection values of two different harvest blocks k and k’ that may or may not be spatially adjacent to each other and k k’ represents the aggregation of those two harvest blocks into a aggregate block, all of which will be harvested at the same time, then FPV(k k’) will not necessarily equal FPV(k) + FPV(k’). Our method of estimating the FPV of a harvest block is myopic inasmuch as when we estimate a harvest block’s FPV, it is based on the assumption that no other harvest blocks are to be cut. Of course, it would be preferable to determine the true FPV of harvesting each of the many possible sets of harvest blocks or patterns that could be harvested, but it is not possible to do so. Consider, for example, creating aggregate harvest blocks comprised of 2, 3, 4, . . . individual harvest blocks and evaluating their FPVs. Unfortunately, even if one could do so, one would then be left with the problem of deciding how to use such information as our decision variables are stand-specific. One could, in principle, expand our harvest scheduling model and define corresponding aggregate decision variables that called, for example, for stand 1, or stand 2, or stands 1 and 2 and so on to be harvested in period t. Unfortunately, the expansion of our model to include aggregate harvest blocks comprised of 2, 3, 4, . . . individual harvest blocks would make an already computationally challenging model totally intractable and contribute little towards enhanced management of the landscape. Our intuition is that using our FPV to force the harvest scheduling model to cut some of the higher FPV stands should reduce the flammability of the landscape and produce improved harvest schedules, and our results are consistent with our intuition. If and when better FPVs are available, we expect that they will produce even better solutions. We also recognize that our use of the Palma et al. (2007) FPV methodology to identify crucial stands is very computationally intensive and there may well be other, less computationally challenging methods for identifying crucial harvest blocks. One might, for example, designate as crucial any harvest block that has a burn fraction that exceeds some designated threshold and is at the centre of a circle of some designated radius that contains some minimum volume of merchantable wood. The development and evaluation of strategies for identifying crucial harvest blocks that can be incorporated into phase II FireSmart forest management thus appears to be a fruitful avenue for future research. Throughout this paper, we have focussed on the detrimental impact of fire because we are addressing the management of a portion of a real forest management unit that is used for industrial timber production and the FireSmart approach that we are testing was developed to minimize the impact of fire on timber production. It is, however, imporPublished by NRC Research Press Can. J. For. Res. Downloaded from cdnsciencepub.com by 3.236.70.69 on 09/28/22 For personal use only. 2382 tant to remember that although it poses real threats to public safety, property, and timber production, fire is a natural ecosystem process that produces beneficial ecological impacts that should not be totally eliminated from fire-dependant forest ecosystems. FireSmarting was first developed and is most often applied to address community protection needs, but it will no doubt be considered for application at broader landscape levels as fuel management methods are applied to more extensively managed forest landscapes in the future, and our model could be modified to address such needs. One could, for example, impose goals that call for the average annual burn fraction to fall within designated upper and lower bounds that might vary by age class and forest type. One could also constrain the average annual area harvested or burned to vary within designated limits that could also vary by age class and forest type. Acknowledgements This research was supported in part by the Sustainable Forest Management Network. We thank the late Bernie Todd of the Canadian Forest Service (CFS), who provided us with a copy of his WILDFIRE model, and Kelvin Hirsch (also CFS), who encouraged us to study this problem and shared many of his ideas concerning FireSmart forest management with us. Special thanks are due to Jonathan Russell of Millar Western Forest Products Ltd., who provided us with valuable advice and the Millar Western data that we required to carry out this study. We also thank an anonymous Associate Editor and two anonymous referees whose comments and suggestions helped improve earlier versions of this manuscript. References Acuna, M., Palma, C., Weintraub, A., Martell, D., and Cui, W. 2003. Integrated timber harvest and fire management planning. In Proceedings of the 2003 Systems Analysis in Forest Resources Symposium. Compiled by M. Bevers and T.M. Barrett. General Technical Report PNW-GTR-656, USDA Forest Service, Pacific Northwest Research Station, Portland, Oregon. Agee, J., Bahro, B., Finney, M., Omi, P., Sapsis, D., Skinner, C., Van Wagtendonk, J., and Weatherspoon, C. 2000. The use of shaded fuelbreaks in landscape fire management. For. Ecol. Manage. 127(1–3): 55–66. doi:10.1016/S0378-1127(99)00116-4. Boychuk, D.B., and Martell, D.L. 1996. A multistage stochastic programming model for sustainable forest-level timber supply under risk of fire. For. Sci. 42(1): 11–26. Cunningham, A., and Martell, D.L. 1973. A stochastic model for the occurrence of man-caused forest fires. Can. J. For. Res. 3(2): 282–287. doi:10.1139/x73-038. Finney, M. 2001. Design of regular landscape fuel treatment patterns for modifying fire growth and behavior. For. Sci. 47: 219–228. Finney, M., and Cohen, J. 2003. Expectation and evaluation of fuel management objectives. In Fire, Fuel Treatments, and Ecological Restoration: Conference Proceedings, 16–18 April 2002, Fort Collins, Colorado. RMRS-P 29, USDA Forest Service, Rocky Mountain Research Station, Fort Collins, Colorado. pp. 353–366. Forestry Canada Fire Danger Group. 1992. Development and structure of the Canadian forest fire behaviour prediction system. Information Report ST-X-3, Forestry Canada and Science and Sustainable Development Directorate, Ottawa, Ontario. González, J.R., Palahi, M., and Pukkala, T. 2005. Integrating fire Can. J. For. Res. Vol. 40, 2010 risk considerations in forest management planning in Spain — a landscape-level perspective. Landsc. Ecol. 20(8): 957–970. doi:10.1007/s10980-005-5388-8. Graham, R., Harvey, A., Jain, T., and Tonn, J. 1999. The effects of thinning and similar stand treatments on fire behavior in western forests. General Technical Report PNW-GTR-463, USDA Forest Service, Pacific Northwest Research Station, Portland, Oregon. Gustafson, E., Zollner, P., Sturtevant, B., He, H., and Mladenoff, D. 2004. Influence of forest management alternatives and land type on susceptibility to fire in northern Wisconsin, USA. Landsc. Ecol. 19(3): 327–341. doi:10.1023/B:LAND. 0000030431.12912.7f. Hirsch, K., and Pengelly, I. 1997. Forest fuels management in theory and practice. In Proceedings of Symposium on Stand Density Management: Planning and Implementation, Alberta Environmental Protection, Edmonton, Alberta, 6 and 7 November 1997. Edited by C.R. Bamsey. Clear Lake Ltd., Edmonton, Alberta, Canada. ISBN 0-9695385-4-5. pp. 112–116. Hirsch, K., Kafka, V., Tymstra, C., McAlpine, R., Hawkes, B., Stegehuis, H., Quintilio, S., Gauthier, S., and Peck, K. 2001. Firesmart forest management: a pragmatic approach to sustainable forest management in fire-dominated ecosystems. For. Chron. 77: 357–363. Johnson, K., and Scheurman, H. 1977. Techniques for prescribing optimal timber harvest and investment under different objectives — discussion and synthesis. For. Sci. Monogr. 18. Johnson, K., Sessions, J., and Gabriel, J. 1998. Integrating wildfire into strategic planning for Sierra Nevada forests. J. For. 96: 42–49. Khajuria, R.P., Laaksonen-Craig, S., and Kant, S. 2008. A marginal cost analysis of trade-offs in old-growth preservation in Ontario. For. Policy Econ. 10: 326–335. Kourtz, P., Nozaki, P, and O’Regan, W. 1977. Forest fires in the computer. A model to predict the perimeter location of a forest fire. Fisheries and Environment Canada Inf. Rep. FF-X-65. Ludwig, D., and Varah, J.M. 1979. Optimal harvesting of a randomly fluctuating resource II: numerical methods and results. SIAM J. Appl. Math. 37(1): 185–205. doi:10.1137/0137012. Martell, D.L. 1994. The impact of fire on timber supply in Ontario. For. Chron. 70(2): 164–173. Martell, D., Hirsch, K., Malcolm, J., McAlpine, R., Weintraub, A., Acuna, M., Cui, W., Espinoza, A., Johnson, J., and Palma, C. 2004. A FireSmart approach to integrated fire and forest management in the boreal forest region of Canada. Sustainable Forest Management Network Projects Reports 2003/2004. Millar Western Forest Products Ltd. 2000. Detailed forest management plan 1997–2000. Vol. 1, Ch. 1. Millar Western Forest Products Ltd., Edmonton, Alberta. Natural Regions Committee. 2006. Natural regions and subregions of Alberta. Edited by D.J. Downing and W.W. Pettapiece. Government of Alberta Publication No. T/852, Edmonton, Altberta. Palma, C., Cui, W., Martell, D., Robak, D., and Weintraub, A. 2007. Assessing the impact of stand-level harvests on the flammability of forest landscapes. Int. J. Wildland Fire, 16(5): 584–592. doi:10.1071/WF06116. Pollet, J., and Omi, P. 2002. Effect of thinning and prescribed burning on crown fire severity in ponderosa pine forests. Int. J. Wildland Fire, 11(1): 1–10. doi:10.1071/WF01045. Reed, W.J. 1979. Optimal escapement levels in stochastic and deterministic harvesting models. J. Environ. Econ. Manage. 6(4): 350–363. doi:10.1016/0095-0696(79)90014-7. Reed, W., and Errico, D. 1986. Optimal harvest scheduling at the forest level in the presence of the risk of fire. Can. J. For. Res. 16(2): 266–278. doi:10.1139/x86-047. Sanchez-Guisandez, M., Cui, W., and Martell, D. 2007. A decision Published by NRC Research Press Acuna et al. Van Wagner, C.E. 1979. The economic impact of individual fires on the whole forest. For. Chron. 55(2): 47–50. Wei, Y., Rideout, D., and Kirsch, A. 2008. An optimization model for locating fuel treatments across a landscape to reduce expected fire losses. Can. J. For. Res. 38(4): 868–877. doi:10. 1139/X07-162. Can. J. For. Res. Downloaded from cdnsciencepub.com by 3.236.70.69 on 09/28/22 For personal use only. support system for evaluating fuel management strategies for wildland urban interfaces areas. In Proceedings of the 4th International Wildland Fire Conference, Sevilla, Spain, 13–17 May 2007. Spanish Ministry of Environment, Madrid, Spain. Stephens, S. 1998. Evaluation of the effects of silvicultural and fuels treatments on potential fire behaviour in Sierra Nevada mixed-conifer forests. For. Ecol. Manage. 105(1–3): 21–35. doi:10.1016/S0378-1127(97)00293-4. 2383 Published by NRC Research Press