Multi-objective optimization to evaluate tradeoffs among forest ecosystem services following fire hazard reduction in the Deschutes National Forest, USA

Ecosystem Services ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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Multi-objective optimization to evaluate tradeoffs among forest ecosystem services following fire hazard reduction in the Deschutes National Forest, USA Svetlana A. (Kushch) Schroder a,n, Sándor F. Tóth a, Robert L. Deal b, Gregory J. Ettl a a b

School of Environmental and Forest Sciences, University of Washington, Box 352100, Seattle, WA, USA USDA Forest Service, Pacific Northwest Research Station, 620 SW Main Street, Portland, OR, USA

art ic l e i nf o

a b s t r a c t

Article history: Received 22 April 2015 Received in revised form 28 June 2016 Accepted 3 August 2016

Forest owners worldwide are increasingly interested in managing forests to provide a broad suite of ecosystem services, balancing multiple objectives and evaluating management activities in terms of potential tradeoffs. We describe a multi-objective mathematical programming model to quantify tradeoffs in expected sediment delivery and the preservation of Northern spotted owl (NSO) habitat following fuel treatments to reduce fire hazard in the Deschutes National forest in Central Oregon, USA. Our model integrates the management objective of fire hazard reduction and the provision of ecosystem services (water quality and NSO habitat protection) and helps evaluate tradeoffs among them. Our results suggest significant reductions in fire hazard can be achieved without compromising any NSO habitat by strategically placing the treatments; however, the treatments will lead to a short term increase in sediment delivery. An analysis of environmental risks showed that over the longer term, the increase in sediment delivery and NSO habitat loss caused by wildfires would be 30–50% greater in areas without fuel treatments. The use of the multi-objective optimization model described in this study can help managers quantify and assess potential tradeoffs among ecosystem services and provide data for more informed decision making. & 2016 Elsevier B.V. All rights reserved.

Keywords: Ecosystem services Multi-objective optimization models Tradeoffs Water quality Northern spotted owl habitat Environmental risk

1. Introduction An important goal of forest management is to ensure the sustainable provision of ecosystem services such as timber, clean water, recreation, wildlife habitat, and carbon sequestration (MEA, 2005). Wildfires can threaten these services; therefore, fuel treatments that remove woody material via thinning or prescribed burning to reduce fire hazard are often used in forest regions with high risk of catastrophic fire (Noss et al., 2006). The management goal is not to exclude fire from the ecosystem, but reduce its intensity and create conditions that would allow managers to use low-risk fire-fighting strategies in case wildfire extends to sensitive areas, such as watershed or wildlife habitat. Fuel treatments, however, can, in the short term, compromise ecosystem services such as wildlife habitat and/or clean water provision. We show how multi-objective optimization can be used for integrative ecosystem services assessment and quantitative analysis of these tradeoffs in a watershed in the Deschutes National Forest, USA, n

Corresponding author. E-mail address: [email protected] (S.A.(Schroder).

where the protection of water quality and northern spotted owl habitat (Strix occidentalis caurina; NSO) are both critical objectives. In the following, we summarize what we know about the positive and negative effects of fuel treatments on ecosystem services and discuss how optimization has been used in the past for tradeoff analysis in an attempt to find balanced compromises in forest and fire management. Strategically allocated fuel treatments not only modify fuel conditions to reduce fire severity and intensity to avoid significant loss of forest ecosystem services (Kalabokidis and Omi, 1998) such as wildlife habitat (Courtney et al., 2007), they can also have indirect effects on water quality. High-severity wildfires in mountainous watersheds can destabilize soils, leading to increased sedimentation (Meyer et al., 2001; Rieman and Clayton, 1997; Wondzella and King, 2003), and potentially erode stream channels, fish habitat and drinking water in the long term; thus, fire management's goal is to minimize these consequences. Fuel treatments can also have negative effects on forest ecosystem services. Prescribed burning removes ground cover, causing erosion and changes in soil carbon and nitrogen concentration (Neary et al., 2003), and increased sedimentation following fuel

http://dx.doi.org/10.1016/j.ecoser.2016.08.006 2212-0416/& 2016 Elsevier B.V. All rights reserved.

Please cite this article as: Schroder, S.A.(., et al., Multi-objective optimization to evaluate tradeoffs among forest ecosystem services following fire hazard reduction in the Deschutes National Forest, USA. Ecosystem Services (2016), http://dx.doi.org/10.1016/j. ecoser.2016.08.006i

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treatments are well documented (Elliot, 2005; Cram et al., 2007; Reid, 2010; Rhodes, 2007; USDA Forest Service, 2005 and Wright et al., 1976). The effects of fuel treatments, however, are not as adverse and long-lasting as the effects of severe wildfires (USDA Forest Service, 2005). A number of programs emphasize the importance of protecting watersheds, the source of much of the drinking water in the Western US, in fire prone forests because fuel treatments there help avoid costs associated with restoring water supply and quality post-fire (Carpe Diem West, 2015). Therefore, forest managers face the dilemma of how much area should be treated, and how, when and where treatments should occur to strike a balance between short-term costs and long-term benefits. As far as wildlife habitat is concerned, we know that fuel treatments reduce canopy closure, stem density and ground cover – by design. This, at least for the short term, may disrupt the habitat of sensitive species such as NSO that lives in old-growth forests in the Pacific Northwest, USA. Forests on the east side of the Cascade Range, where our study is located, provide habitat for NSO and its prey species (Hummel and Calkin, 2005; Buchanan et al., 1995; Everett et al., 1997); these forests, however, are prone to severe wildfires. For this reason, some researchers have suggested that habitat protection could be a limiting factor for fuel treatments (Gaines et al., 2010; Calkin et al., 2005). Others argue that modest treatments are unlikely to affect NSO habitat (Lee and Irwin, 2005). While there is uncertainty regarding the exact nature of these short term effects (Bond et al., 2002; Lee and Irwin, 2005), the long term benefits of fuel treatments are indisputable. High severity wildfires often destroy NSO habitat, which takes a long time to recover (Courtney et al., 2007), and fuel treatments, although their efficacy may vary, can significantly reduce the severity of wildfire effects (Murphy et al., 2010; Omi et al., 2010; Fernandes and Botelho, 2003; Pollet and Omi, 2002). Using forest vegetation and wildfire spread simulations, Ager et al. (2007) has previously shown that the expected loss of NSO habitat in late seral stage forests can be reduced substantially by strategically placing treatments outside the habitat areas because the treatments retarded the fire spread onto the habitat area. One of the benefits of the multi-objective optimization model proposed in this paper is that it can help us quantify the maximum reduction in fire hazard, defined as wildfire's resistance to control, both with and without treatments in NSO habitat (resistance to control is “the relative difficulty of constructing and holding a control line as affected by resistance to line construction and by fire behavior” (National Wildfire Coordinating Group, 2014)). The model not only finds the complete set of tradeoffs for fire hazard vs. NSO habitat but it also does so for water quality (as defined here by the expected amount of sediment delivery). Multi-objective mathematical programs comprise a set of functions that represent management objectives such as minimizing fire hazard or expected sediment delivery, and a set of inequalities that capture the constraints on management; e.g., budgetary, logistical or environmental restrictions. Both the objective functions and the inequalities are formulated as functions of the management decisions that are available on the ground. Thus, once solved, the model identifies the set of decisions that would need to be made to best achieve the objectives. Since forest management objectives are often in conflict, unique solutions that simultaneously optimize all objectives might not be attainable; hence the need for tradeoff analysis. Multi-objective mathematical programs quantify these tradeoffs by finding the set of solutions that are Pareto-optimal with respect to the objectives. A solution to the program (i.e., a management plan) is Pareto-optimal, i.e., none of the objectives can be further improved without compromising another objective. Such integration of ecosystem services and objectives is important in practice because land managers

want to achieve as much reduction in fire hazard as possible with as little short-term impact on water quality and wildlife habitat as possible. While this paper is the first attempt to map out the tradeoffs of fire hazard reduction and multiple ecosystem services for a real management problem, there are plenty of examples of other uses of multi-objective optimization in natural resources. Bare and Mendoza (1988) reported one of the first applications in forest management but instead of quantifying the entire set of tradeoffs, found solutions for competing timber and wildlife objectives via interactions with the decision makers who modified their preferences as new information became available. A significant advantage of our model is that it does not rely on interactions with the decision makers during optimization and identifies the entire set of Pareto-efficient solutions up front to let them make choices based on complete tradeoff information about chosen ecosystem services. In addition, our model's solutions, unlike Bare and Mendoza's (1988), are spatially explicit, due to the fact that integer, as opposed to linear, programming is used. Landscape-level fire management, along with its ecological consequences, has spatial implications that are best assessed with a spatial model, as presented in this study. Other studies have previously tested existing and proposed algorithms only on illustrative examples in the areas of harvest scheduling and optimal reserve selection (Tóth et al., 2006; Tóth and McDill, 2009; Burns et al., 2013; Tóth et al., 2010, 2013). The present paper is one of the first real applications. FuelSolve provided an important step in the development and application of multi-objective optimization techniques for wildfire management (Lehmkuhl et al., 2007; Kennedy et al., 2008). FuelSolve used an evolutionary algorithm to iteratively approximate the Pareto set of fuel treatment choices in the presence of wildlife objectives including NSO habitat, understory vegetation and the habitat of the NSO prey species. All of the wildlife objectives were formulated to support NSO, thus, the tradeoffs acquired in the authors’ analyses were limited to the interaction between treatment costs (area treated was used as a proxy) and treatment effects on NSO habitat. Our model incorporates an additional ecosystem service (water quality), to assist analysis of the impacts of fuel treatments, and both short and long term tradeoffs of the treatments. This is possible because our treatment allocation model is both spatially and temporally explicit. Our model, unlike FuelSolve, counts NSO habitat only if it occurs in large enough contiguous patches (c.f., Rebain and McDill, 2003). The contribution of patches of habitat that are smaller than a threshold size are discounted in the objective function, recognizing that contiguous interior habitat is more important for NSO than fragmented habitat. In addition, our approach allows capturing habitat connectivity using binary constraints (Rebain and McDill, 2003; Önal and Briers, 2006; Tóth et al., 2009; Conrad et al., 2012), which cannot be addressed with evolutionary programming (as in FuelSolve). Lastly, it is important to point out that there have been two fundamentally different ways to model fire behavior in optimization models. One focused on the projected effects of wildfires on particular values of interest such as ecosystem services or property values. For example, Ager et al. (2013) used the expected post-fire area of old-growth ponderosa pines as a proxy for the general health of a fire-adapted ecosystem. The authors then analyzed the tradeoffs using this metric as a function of the area treated – a proxy for cost. Another example is Chung et al. (2013) who simply deferred to the user to assign a value index for each treatment unit. They minimized the expected post-fire loss of the total of these indices as a function of the treated area using simulated annealing. An added benefit of their model was the capability to create treatment clusters for cost-efficiency. The second approach

Please cite this article as: Schroder, S.A.(., et al., Multi-objective optimization to evaluate tradeoffs among forest ecosystem services following fire hazard reduction in the Deschutes National Forest, USA. Ecosystem Services (2016), http://dx.doi.org/10.1016/j. ecoser.2016.08.006i

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is to treat fire threat independently from its effect on societal values. Hummel and Calkin (2005), for instance, studied the tradeoffs of alternative silvicultural treatments at the landscape level for both fire threat reduction and late seral stage forest structure. They too used simulated annealing as an optimization technique to approximate tradeoffs. The advantage of the first approach is that it directly captures the objectives of the decision makers, with regard to the particular problem being assessed. The second approach is more generally applicable with the caveat that it relies on the decision maker to interpret reductions in fire threat. Simulation models, Forest Vegetation Simulator (FVS; Dixon, 2013), its Fire and Fuels Extension (FVS-FFE; Rebain, 2014), and FlamMap were used in the cited studies to project vegetation and assess the effects of fuel treatments on potential fire behavior. Our model attempts to combine the benefits of both methods by formulating one objective function for general fire hazard reduction and the other ones for the particular ecosystem services of interest: in our case study expected sediment delivery and NSO habitat. In the next sections, we describe a multi-objective model to quantify tradeoffs in expected sedimentation and NSO habitat following fuel treatments to reduce fire hazard. This model is applied to a watershed in central Oregon: the Drink Planning Area in the Deschutes National Forest. The proposed model integrates ecosystem services and management goal of reducing fire hazard in order to lessen wildfire intensity, and assesses potential tradeoffs among them to guide decision making and planning. This methodology allows the analysis of tradeoffs among management objectives and evaluation of environmental risks associated with different management strategies; the results demonstrate the importance of the integrated valuation in practice.

2. Methods 2.1. Case study The data for this study are from the Drink Planning Area, a 7056 ha area located on the eastern slopes of the Cascade Range in the Deschutes National Forest (Fig. 1). The area provides a variety of important ecosystem services that might compromise each other and, thus, is an excellent study site for exploring the research

Legend Non-forested NSO habitat Watershed Neither habitat nor watershed Intersection f watershed and habitat Fig. 1. Bend municipal watershed and potential NSO habitat in the Drink Planning Area.

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questions of this paper. We analyzed the effects of fuel treatments designed to reduce fire hazard on ecosystem services that were identified as the most important values of this study area. The Drink area has a mixed fire severity regime with fire return interval ranging from 50 to 300 years, and wildfires have the potential to burn vast forested land area (Simpson, 2007; NelsonDean, 2012). In 2012, the Pole Creek Fire near our study area burned over 10,000 ha, severely destroying portions of the Three Sisters Wilderness (USDA FS, 2013). The Two Bulls Fire (InciWeb, 2014) burned approximately 2800 ha of private and public forest land a few miles east of our study area. The Drink area has never been harvested and no fuel treatments have been applied, and current forest stands have reached or are reaching the site's maximum stocking and density. Dense forest with high fuel loads in the study area creates an environment prone to severe fires (Hessburg et al., 2005), which are challenging to contain. The climate in the study area is hot and dry in the summer and cold in the winter, with slow decomposition of dead vegetation and high fuel accumulation. All of this contributes to high fire hazard. Therefore, one of the management goals in the Drink area is to reduce fire hazard to allow managers to plan effective and low-risk firefighting strategies. The Bend municipal watershed comprises one third of the Drink area. Water quality control is a key ecosystem service, because 50% of the water supplied to the city of Bend is drawn from the watershed in the area. The quality of the supplied water is very high and requires very little treatment before delivered to the users (City of Bend Utility Department, 2015). However, the soils in the watershed are sensitive to any disturbances, and removal of ground cover would cause an increase in sedimentation to streams and, potentially, significantly degrade water quality. Both wildfire and fuel treatments will affect water quality, although the magnitude and longevity of the impact may vary. Finally, 18% (1259 ha) of the Drink area has potential NSO habitat, and the USFS must prevent or mitigate the loss of such critical habitat according to the requirements of the Endangered Species Act (ESA, 1973). Fuel treatments in the area would reduce fire hazard, but also change vegetation parameters, and might disqualify the area from being viable NSO habitat. 2.2. The multi-objective mathematical programming model To analyze the tradeoffs among fire hazard reduction, sediment delivery and NSO habitat, we formulated a mixed integer linear programming model (MILP; Appendix A). The planning horizon of the model was 40 years, divided into two 20-year planning periods. The period length was chosen by the Deschutes National Forest staff to best match practical and theoretical assumptions regarding the longevity of the effects of fuel treatments as well as the growth of the vegetation in the study area (Agee and Skinner, 2005; Fernandes and Botelho, 2003). For simplicity, the potential fuel treatments were assumed to occur at the midpoint of the periods. For the model, the Drink Planning Area was divided into 303 treatment units, delineated based on manageability and ecological factors. The decision variables of the model were binary: whether a treatment assigned to a given unit in either or both of the two planning periods, or not. If the MILP found it optimal to assign the treatment to a unit in a given period, then the corresponding decision variable was set to one. Otherwise, its value remained zero. The fuel treatments themselves were designed by the Deschutes National Forest staff based on the vegetation characteristics and the plant association group of each treatment unit. Each treatment unit was prescribed exactly one potential treatment. The MILP only determined whether a unit was to be treated in a given planning period or not, but not how it was to be treated. The

Please cite this article as: Schroder, S.A.(., et al., Multi-objective optimization to evaluate tradeoffs among forest ecosystem services following fire hazard reduction in the Deschutes National Forest, USA. Ecosystem Services (2016), http://dx.doi.org/10.1016/j. ecoser.2016.08.006i

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prescribed treatments included manual thinning of trees less than 18 cm in diameter to reduce crown bulk density as well as surface fuels. The thinned woody material either stayed on site or was burned in piles. The detailed logic of the fuel treatment specifications is listed in Appendix B (Table B1). The treatments are admittedly very light due to management restrictions in this highly visible and sensitive municipal watershed, however, they were found to reduce fire hazard significantly if applied strategically. While higher intensity treatments would reduce fire hazard more efficiently (Johnson et al., 2011), in sites such as the Drink area, such treatments cannot be applied due to ecological and infrastructural constraints. Because our model is treatment-agnostic, however, it can be used to assess tradeoffs using whatever treatments are allowed. 2.2.1. Fire hazard minimization In the following, we describe the process that we followed to obtain the coefficients for the objective function. We used the SORNEC variant of FVS (Keyser, 2012), along with its Fire and Fuel Extension (FFE; Rebain, 2010) to project vegetation growth and fire characteristics given all treatment scenarios applicable to each treatment unit: “No treatment”, “Treatment in the first period”, “Treatment in the second period” and “Treatment in both periods”, using the corresponding treatment specifications for each unit (Appendix B, Table B1). SORNEC, like all FVS variants, accounts for local variations in vegetation and fuel types in the region. FVS simulates vegetation and fuel parameters in cycle-by-cycle tree lists, where each cycle represents a period of time for which tree growth and structural characteristics are predicted. For the simulations, each treatment unit was associated with one or more tree lists that were compiled with nearest neighbor imputation (GNN, Ohmann and Gregory, 2002) by the US Forest Service. We used the following settings to best represent local conditions. The decay rates in the simulations were adjusted using data provided by the Forest Management Service Center, USDA-FS (Rebain, 2012). Canopy closure was adjusted to approximate recent LiDAR data for the area (Yanez, 2013). Finally, crown base height projections were reduced by a factor of two to obtain best estimates of tree crown characteristics (Yanez, 2013). Estimates for the initial values of the surface fuels of different size classes came from fuel model data (Yanez, 2013). Fuel models are discrete sets of vegetation attributes designed to capture fire behavior for a forest stand or a management unit under the assumption of homogenous surface fuel distribution (Rothermel, 1972). Following Deschutes National Forest protocol and data availability, we used the original, limited set of 13 stylized fuel models (Anderson, 1982), and not the latest, extended 53 (Scott and Burgan, 2005). While Johnson et al. (2011) showed that the limited set of fuel models can lead to erroneous fire predictions for intense thinning scenarios (residual 125–250 tree/ha) in the absence of measured fuel loadings (Ottmar et al., 2007), such scenarios were not applicable in the Drink Planning Area due to its role as a municipal watershed. Using the treatment specifications provided by the USFS for our study site (Appendix B, Table B1), only 7.7% of the area is eligible for thinning to a residual density of 250 trees per ha or less. In fact, on 73.7% of the area, 80% or more of the basal area must be retained post-treatment. Again, while one could question the efficacy of such light treatments, our results suggest they can still have a great impact on fire hazard mitigation. Since one of standard FVS outputs for fire behavior is fuel models, which in turn are described by flame length, rate of spread and total fuel load, we created a proxy numerical ratings scheme for hazard based on these three metrics (Appendix B, Table B2). Higher ratings corresponded to higher, and lower ones to lower, fire hazard. The objective function coefficients were calculated as area-weighed reductions in these ratings compared to the no

treatment scenario. For example, a treatment schedule that is projected to change the fire characteristics of a 10 ha unit from fuel model 10 to 8, would contribute to the fire hazard minimizing objective function by 10 hazard
hectares (hazard
ha) because the assigned rating of fuel model 10 and 8 are 2 and 1, respectively. Taking the difference between 2 and 1 and multiplying it with the area of the unit (10 ha), we get 10 hazard
ha. The objective function maximized the sum of these area-weighed reductions in ratings. In other words, the objective is to minimize the area of the units where the fuel models have the higher rating assigned based on flame length, rate of spread, and fuel load. We chose this rating scheme based on its demonstrated superior performance relative to other proxy models (Schroder, 2013) in reducing fire hazard and burn probability as showed on maps acquired by FlamMap (a software for mapping and analyzing fire behavior characteristics; Finney, 2006). Weather conditions for FlamMap were defined to approximate weather during the fire season in the study area. The weather input for the simulations (fuel moisture, weather and wind files) was created in FireFamily Plus 4 (USDA Forest Service, 2002) using RAWS data from years 2002 to 2012 (KCPFast, 2013) for the nearby Tumalo Ridge station. According to the weather data, the predominant wind direction was from west to east. To evaluate the solution's robustness, we ran a few simulations with an easterly wind as well. FlamMap's azimuth parameter was set to 270 degrees to simulate a west wind, and to 90 degrees for an east wind. Wind speed in the simulations was set to 9 m/s, the gust speed taken from the records, because gust speed is more likely to affect fire growth, intensity and crown fire initiation than the average wind speed (Stratton, 2006). Foliar moisture content was set to 90%, as the literature recommends (Agee et al., 2002; Alexander, 2010; Keyes, 2006). FlamMap simulations were run for a few days, 8/12–8/17, chosen arbitrarily within the fire season. The input for the burn probability simulation included a list of 2000 random ignitions, compiled in RandIg (Missoula Fire Sciences Laboratory, 2011), a software package used to create lists of random ignitions based on spatial, vegetation and weather input. The goal was to simulate as many ignitions as computationally feasible. The maximum simulation time per ignition was arbitrarily set to 4200 min per simulated ignition. A longer simulation time would give more accurate results, but would take longer to run (at 4200 min, the simulation for each model took more than 8 h). The list of ignition locations was the same for each treatment plan. 2.2.2. Water quality Water quality was represented as the peak sediment caused by fuel treatments in the two planning periods, and higher sediment value corresponds to lower water quality. We minimized peak sediment in the planning horizon. The following procedure describes how sediment coefficients were estimated for each treatment unit in the watershed. 1. Average sediment rates were calculated using a simulator, USDA Agricultural Research Service's Online Water Erosion Prediction Project Model (WEPP; Flanagan and Nearing, 1995), using soil textures as input. Sediment rates in tons per ha were obtained for five different scenarios: no treatment, thinning, prescribed fire, low severity fire and high severity fire. 2. We used the Modified Soil Loss Equation (MSLE, Warrington, 1980) to extrapolate the average sediment rates given a set of forest specific factors such as rainfall (R), soil erodibility (K) in tons/pixel, slope length (L), slope (S), and the type of vegetation management (V M). For extrapolation, R was assumed to be constant because the study area is relatively small. Parameter K was set the same for each soil texture. Lastly, parameter V M was also constant across each management type (no treatment,

Please cite this article as: Schroder, S.A.(., et al., Multi-objective optimization to evaluate tradeoffs among forest ecosystem services following fire hazard reduction in the Deschutes National Forest, USA. Ecosystem Services (2016), http://dx.doi.org/10.1016/j. ecoser.2016.08.006i

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prescribed burn, etc.):

A = C · LS,

(1)

where C¼ R
K
V M was estimated from the rates calculated in the WEPP model using the average combined slope-length factor(LS); A is the sediment rate. The constant C was particular to each combination of soil texture K and management V M. 3. The portion of sediment delivered to the stream was adjusted by a pixel-specific sediment delivery ratio (SDR) calculated using Spatially Explicit Delivery MODel (SEDMOD, Fraser, 1999), an ArcGIS module. Sediment yield was then calculated as a product of estimated erosion and SDR

Ad = A · SDR

(2)

where Ad is the delivered sediment rate, and A the sediment estimated using MSLE. 4. The per-pixel sediment delivery data were aggregated to obtain sediment rates for each treatment unit in the watershed. 5. The sediment delivery rate in (2) is the rate in the first year after a disturbance (fuel treatments or fire). Following a disturbance, sedimentation will decrease over time, returning to the predisturbance level in 3–5 years (Reneau et al., 2007). To calculate the post-disturbance decrease of sediment rates, we used the following procedure to approximate sediment dynamics previously reported (e.g, Reneau et al., 2007; Ryan and Elliot, 2005). (a) Sediment rates were estimated based on the sediment delivery in the first year after disturbance; (b) Sediment rates in the first year were discounted at 70% to obtain the second year rate; (c) Sediment rates in the third and every subsequent year were calculated by discounting the sediment rate in the previous year by 50% until the value is the same as pre-disturbance sediment rate. 2.2.3. NSO habitat We expressed the protection of NSO habitat in terms of total area of treatment units meeting the following three criteria at the end of the planning horizon: the elevation of the unit is less than 1830 m; canopy cover is at least 60%, and finally, large trees, at least 76 cm in diameter, should be present. Units that met all of these criteria qualified as potential NSO habitat, provided that they formed clusters with contiguous areas of at least 200 ha (Webb, 2013). If a unit met the three criteria for NSO habitat but was not a part of a cluster it was still considered as potential NSO habitat, but discounted at 50%. We accounted for the units that have the potential of becoming NSO habitat, i.e. units that can qualify as viable NSO habitat under certain treatment scenarios at the end of the planning horizon even if they did not satisfy the criteria at the beginning. The FVS output was used to evaluate whether the treatments changed the vegetation structure and characteristics that would disqualify areas from providing potential NSO habitat. Once we populated the three objective functions representing fire hazard mitigation, water quality and NSO habitat with the coefficients described above, we solved the resulting multi-objective MILP under two scenarios. The first scenario, model L, assumed that only 17% of the landscape could be treated in each planning period. In the second scenario, model H, a maximum of 34% could be treated in each period. These baseline areas were chosen based on the conclusions of Collins et al. (2010) and Finney (2007) regarding the effects of treatment extent on fire behavior parameters. Collins et al. (2010) concluded that treating approximately 20% of area will result in a noticeable effect in fire behavior, whereas treatment of more than 40% of the landscape neglects the importance of any particular criteria for treatment allocation

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(Finney, 2007). Either level of treatment would be feasible for the Deschutes National Forest. The solutions of the models are spatially and temporally explicit management plans that allocate treatments on the landscape. The solutions are Pareto optimal, meaning that an improvement in the value of one objective cannot be achieved without compromising the other(s). Each management plan is associated with specific values of ecosystem services: an estimate of the sediment delivered to the stream and the area of protected NSO habitat as a result of treatments. These values were used to build tradeoff curves. The output of the model represented shortterm loss of ecosystem services as a result of fuel treatments. To get an idea of how the absence of treatments can affect the landscape, we performed post-optimization analysis of a wildfire scenario in the Drink area. We assess these risks at the end of the planning horizon, considering it as long term effects, because it is the latest time for which simulated vegetation data was obtained. For a set of management plans, we obtained fire hazard and burn probability maps using FlamMap (Finney, 2006) to further analyze the solutions. While fire hazard maps are used for delineating the areas that are potentially the most risky and challenging for firefighting, burn probability maps show the chance of fire in each pixel of the landscape independent of ignition. We estimated the environmental risks of fuel treatments using the approach described by O'Laughlin (2005). The term environmental risk as used throughout this paper represents adverse effects on ecosystem and ecosystem services. Any loss of ecosystem services either natural or human-caused is referred as environmental risk. To estimate environmental risk, first, we separated the treated and non-treated stands. Fires in treated areas are typically low severity (Pollet and Omi, 2002; Safford et al., 2009; Skinner et al., 2004); therefore, for the estimation of sedimentation in the treated areas we applied low severity fire rates. Sedimentation rates after a high severity fire were applied to the non-treated units: assuming that the wildfire starts in the Drink area, it is likely to be a high severity fire given the vegetation characteristics and fire regimes in the study area (Simpson, 2007). Then, we obtained burn probability for each stand based on the FlamMap output. We assume the fire strikes the area at the end of the planning horizon, when all treatments are completed. Finally, to calculate the sediment in case of fire in the watershed, we compute the sediment from each stand as a product of the stand area, probability that the fire burns the stand, and the sediment rate depending on fire intensity. We accounted for fire severity in our estimation of habitat loss: treated units were accounted as intact habitat in case of wildfire (Gaines et al., 2010), whereas non-treated units were considered to be lost NSO habitat. We calculated habitat loss in terms of hectares burned, applying burn probabilities spatially. In other words, lost habitat is calculated as a product of stand areas and burn probability. Such calculations provided a very conservative estimation, because wildfires can break the spatial continuity of the habitat, resulting in collections of unburned units that do not form clusters and therefore have lower quality habitat. Because of the unpredictable character of wildfire and wind direction, however, it would be difficult to predict the actual spatial configuration of burned areas and the disruption of the spatial continuity of the areas that qualify as potential post-fire NSO habitat.

3. Results 3.1. Tradeoffs between fire hazard reduction, NSO habitat and water quality We first analyzed the results coming directly from the multiobjective optimization model (Figs. 2–4). The results suggested

Please cite this article as: Schroder, S.A.(., et al., Multi-objective optimization to evaluate tradeoffs among forest ecosystem services following fire hazard reduction in the Deschutes National Forest, USA. Ecosystem Services (2016), http://dx.doi.org/10.1016/j. ecoser.2016.08.006i

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350

Model H Model L

300

Sediment, ton

250 200 150 100 50 0 0

1000

2000

3000

4000

5000

6000

7000

8000

Fire hazard reduction, hazard-ha

Fig. 2. Tradeoffs between fire hazard reduction and sediment delivery following fuel treatments. High values of fire hazard reduction represented an improvement in fire behavior, whereas high values of sediment represented a decrease in water quality. Model H allows treatment of 34% and Model L treatment of 17% of the Drink area.

Protected NSO habitat, ha

1400

Model H

1200 1000 800

Fig. 4. Tradeoffs between sediment delivery and NSO habitat protection. Model H allows treatment of 34% and Model L treatment of 17% of the Drink area. The contour lines are the levels of fire hazard reduction, which is lowest in the lower right corners of the plots.

600 400 200 0

Protected NSO habitat, ha

0

2000 4000 6000 Fire hazard reduction, hazard-ha

1400

8000

Model L

1200 1000 800 600 400 200 0 0

1000

2000 3000 4000 5000 6000 Fire hazard reduction, hazard-ha

7000

8000

Fig. 3. Tradeoffs between fire hazard reduction and NSO habitat protection. Model H allows treatment of 34% and Model L treatment of 17% of the Drink area.

that fire hazard reduction compromised the provision of both ecosystem services (water quality and NSO habitat). Tradeoffs between water quality control and fire hazard reduction were clearly visible in model H, where higher fire hazard reduction was associated with higher sediment (Fig. 2; Appendix C Figs. C4 and C5). The tradeoff curves for both models showed that an increase in fire hazard reduction would cause a decrease in water quality in the short term. Similarly, fire hazard reduction compromised NSO habitat protection when treatments were placed within the existing habitat area (Figs. 1 and 3; Appendix C Figs. C4 and C5). Plotted solutions of both models showed similar “elbow”-shaped curves, where the group of solutions to the left of the dividing line corresponded to management plans with no tradeoffs between the objectives. Values plotted to the right of the dividers, however, formed steep slopes showing that objectives significantly compromised each other in the presence of the fuel treatments. Overall, there was a negative correlation between water quality

(sedimentation) and NSO habitat protection for each increasing level of fire hazard reduction. These tradeoffs were most visible in the solutions of model H (Fig. 4; Appendix C Figs. C2 and C3). Similar to the tradeoff curves for fire hazard reduction and NSO habitat protection, the vertical part of the “elbow” corresponded to the solutions where fuel treatments were allocated outside of the NSO habitat; therefore, there were no tradeoffs between the provision of these two ecosystem services. The horizontal part of the curve showed that, for greater area of NSO habitat protection, fewer treatments were allocated in the potential habitat area but more in the watershed, and vice versa. The tight (model L) and relaxed (model H) constraints on the area that can be treated in each period highlight the extent of tradeoffs between fire hazard reduction and water quality (Fig. 2). Because of the relaxed constraints on area treated, model H allowed more extensive treatments than model L, and both fire hazard reduction and sedimentation were higher. In model L, better fire hazard reduction was achieved only at a higher cost in water quality; indicated by steeper slope of the curve as the values of fire hazard reduction increased. The tight constraints on area treated prevented treatment outside the watershed because treatments in the watershed were more effective at reducing fire hazard. In model L both fire hazard reduction and post-treatment sediment were lower; however, the decrease in the values was not proportional to the decrease in area treated. The tradeoffs between the other two objectives, fire hazard reduction and the protection of the NSO habitat, were most visible on the curves to the right of the dividers (Fig. 3). The tradeoffs between these objectives exist only if a certain fire hazard reduction threshold was reached. These two objectives compromised each other because the solutions represent management plans in which treatments were allocated on the east side of the Drink area, where NSO habitat is concentrated. The slope of the curve indicated that even a marginal increase in fire hazard reduction would cause a significant decrease in protected NSO habitat. The horizontal part of the curve, to the left of the divider, represents the solutions where the areas treated in either of the

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Table 1 Post-treatment and post-fire sediment and habitat loss. Solution

Fire hazard reduction, hazard-ha

Short term sediment increase, ton Post-treatment

Expected post-fire

Area of habitat not affected by treatments, ha

Habitat loss, ha Post-treatment (short Expected post-fire term)

0

0

853.59

1258.96

0

1054.62

6274.47 6180.87 6124.64 5938.09 5897.81 5068.42

262.76 224.83 236.84 193.30 193.26 108.74

195.74 224.03 237.64 268.80 265.67 363.69

1182.43 1183.74 1240.83 1211.23 1235.75 1248.87

76.53 75.22 18.12 47.73 23.20 10.08

170.05 182.82 199.10 205.59 211.61 250.96

Model L 7 8 9 10 11 12 13 14

4762.76 4719.58 4701.20 4678.22 4657.67 4655.76 4630.03 4570.10

210.31 215.78 200.96 158.80 152.24 165.43 152.34 145.26

283.13 296.77 320.18 370.37 381.57 355.84 375.26 384.10

1135.73 1201.76 1235.75 1182.43 1198.61 1248.87 1211.73 1258.96

123.22 57.20 23.21 76.53 60.35 10.08 47.23 0

217.63 231.18 246.47 250.12 269.12 264.56 268.57 284.23

500 Expected post-fire habitat loss, ha

Expected post-firesediment, ton

No-Treat Model H 1 2 3 4 5 6

400 300 200 100 0 4500

Model H Model L 5000

5500

6000

6500

300 250 200 150 100 50

0 4500

Model H Model L 5000

450 400 350 300 250 200 150 100 50 0

Model H Model L

0

100

200

6000

6500

Fire hazard reduction Expected post-fire habitat loss, ha

Expected post-fire sedimant, ton

Fire hazard reduction

5500

300

Post-treatment sediment, ton

300 250 200 150 100

Model H

50 0

Model L 0

50

100

150

Post-treatment habitat loss, ha

Fig. 5. Correlation between fire hazard reduction and post-treatment and post-fire sediment and habitat loss. Correlation between fire hazard reduction and post-fire loss of ecosystem services was strong (p-value o 0.05). While correlation between post-treatment and expected post-fire sediment delivery was strong (p-value o 0.05), the correlation between post-treatment and post-fire habitat loss was weak (p-value Z 0.05).

planning period did not intersect with the NSO habitat. Therefore, these two objectives and solutions were compatible. Tradeoffs between water quality and NSO habitat occurred only if fuel treatments were planned in the Drink area. The point with the lowest fire hazard reduction (Fig. 4) represented a management plan where no treatments were planned; thus, both services are protected. In the rest of the management plans, for better water quality control, treatments were “pushed” out of the watershed onto the potential habitat, disqualifying units from remaining viable NSO habitat. To protect larger areas of NSO habitat, treatments were driven onto the watershed, increasing sedimentation and decreasing water quality. The tradeoffs between water quality and NSO habitat protection were less severe in

model L because less area could be treated in each period, and there were more possibilities for treatments outside both the watershed and the NSO habitat area. The area that was both potential habitat and watershed was relatively small (Fig. 1); nevertheless, solutions where treatments were allocated in the intersection of the watershed and NSO habitat represented scenarios where the provision of both ecosystem services decreased. 3.2. Comparison of the environmental risks of fuel treatments An important result was that both post-fire sediment and NSO habitat loss in treated areas were significantly lower compared to the corresponding values for the No Treatment scenario (Table 1,

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Table B1 Fuel treatment specifications for the Drink Planning Areaa. Stand density indexb

Crown bulk density, kg/mc

Lodgepole pine plant association o87 NA Z87

40.037

Number of trees o 18 cm dbh per ha

Fuel modelc

Treatment Combined basal area of mountain hemlock and white fir 446 cm dbh, (m2)

NA

NA

NA

Prescribed burningd

449

10, 11, 12, 13 o 10

NA NA

Thin & Pile and burn slash and fuelse Thin & Pile and burn slash

NA

Prescribed burning

47.5

Mixed conifer wet or Mountain Hemlock plant associations o87 NA NA NA Z87

40.037

r 0.037 NA

449

¼10

r 49 NA NA

r7.5 11,12,13 NA o 10 NA ¼10 Z7.5 ¼10 Z7.5 ¼6,8,9 or 10 NA

Thin & Pile and burn slash and fuels & Prescribed burning Thin & Pile and burn slash and fuels Thin & Pile and burn slash and fuels Thin & Pile and burn slash Prescribed burning Prescribed burning Prescribed burning (if prescribed burning occurred in period 1; the treatment applies to second period only)

Mixed Conifer dry plant association o87 NA NA Z87

40.037

r 0.037 NA

NA

NA

Prescribed burning

449

10, 11

NA

r 49 NA NA

12,13 o 10 10,11 10,11 6,8,9 or 10

NA NA NA NA NA

Thin & Pile and burn slash and fuels & Prescribed burning Thin & Pile and burn slash and fuels Thin & Pile and burn slash Prescribed burning Prescribed burning Prescribed burning (if prescribed burning occurred in period 1; the treatment applies to second period only)

a Unless otherwise specified, vegetation conditions are assessed at the beginning of each planning period. If the conditions are met a corresponding combination of treatments is scheduled. No treatment is applied if none of the criteria is met. b The stand density index, a measurement of relative density of forested stands, is in metric units; conversion to imperial units is need for simulations using Forest Vegetation Simulator. c Fuel models are standard combinations of fuel characteristics that is often used to estimate the fire behavior in forests (Anderson, 1982). d Prescribed burning is an application of prescribed fire, a fire ignited by management actions to meet specific objectives (Glossary of Wildland Fire Terminology, 2012). e Pile and burn slash assumes removal of the cut trees only, while pile and burn slash and fuels involves removal of the materials that were on the ground before thin (Wall, Powers, 2012; personal communication).

Table B2 Fuel model ratings. Fuel model

Hazard rating

Group

Flame length (m)

Rate of spread (m/hour)

Total fuel Total area in 2011, ha load (tons/ha)

5 8 10 12

4 1 2 4

1.22 0.30 1.46 2.44

362.10 32.19 158.92 261.52

8.65 12.36 29.65 85.50

135.19 2650.94 3810.24 459.13

13

5

Shrub Timber Timber Logging Slash Logging Slash

3.20

271.58

143.57

–

Each fuel model was assigned an ad hoc numerical hazard rating based on its associated flame length, spread rate and total fuel load. Lower ratings indicate lower, while higher ones indicate higher fire hazard

Fig. 5). Projected post-fire sediment under the No Treatment scenario was twice as high as the largest post-fire sediment in the solutions. Similarly, habitat loss was at least 25% greater under the No Treatment scenario compared to the scenarios where treatments were scheduled to reduce fire hazard. In both models, the post-fire sediment was lower for solutions where fire hazard reduction and treated watershed area were high (Table 1). For the same level of fire hazard reduction, the post-fire sediment was higher in those solutions where less watershed area was treated. Similarly, for the same area of watershed treated, a higher post-fire

Fig. C1. A point cloud that represents the solution surface for the model with MAT ¼ 1214.06 ha. Each point corresponds to a management plan that is associated with the values of fire hazard reduction and provision of the ecosystem services of water quality and NSO habitat protection.

sediment level corresponded to a lower level of fire hazard reduction. Fuel treatments decreased fire hazard and burn probability in the Drink area and consequently, lowered the projected loss of water quality and NSO habitat in case of wildfire. The treatments, however, caused a short term sediment increase and loss of NSO habitat. In summary, treatments had a negative environmental impact, specifically, increased sedimentation and loss of habitat, in

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Fig. C2. Treatment allocation for Solution 54 (MAT ¼ 1214.06 ha). The corresponding management plan provides high fire hazard reduction. NSO habitat is affected by the treatments (habitat protected ¼ 1135.73 ha) and water quality is low (sediment ¼ 210.31 t).

the short term, the first two years immediately after the treatments. The risk of a much greater impact was reduced following the treatments at the end of the planning horizon, what we consider the long term. Because model H more effectively reduced hazard and burn probability across the landscape (Figs. 2 and 4), the post-fire loss of the water quality and NSO habitat were lower,

even when approximately the same area of potential habitat or watershed was treated. Model H more effectively reduced fire hazard because more area was allowed to be treated, i.e. fuels were removed on a larger area. Because of the fuel removal, the fire intensity would be lower and fuel conditions would not support fires that reached the watershed and habitat. Thus, the

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Fig. C3. Treatment allocation for Solution 141 (MAT ¼ 1214.06 ha). Fire hazard reduction achieved in this management plan is relatively high. Water quality is moderately affected by the treatments (sediment ¼ 145.07 t), whereas treatments in the NSO habitat disqualifies its significant part: habitat protected is 786.7 ha.

projected burn probability was lower in the watershed and habitat, and consequently, the post-fire sediment and habitat loss were lower for the management plans in model H. Habitat loss was correlated with fire hazard reduction in the Drink area, but the total treated area of the NSO habitat did not significantly affect its post-fire loss of habitat. Less habitat area was affected by fire in the scenarios with maximum overall fire

hazard reduction. However, the results do not suggest that treatments in NSO habitat would prevent loss of habitat in case of wildfire. The treatments defined for the Drink area did not effectively reduce fire hazard on the east side of the Drink area, where most potential habitat was located. The ineffectiveness of the treatments in the NSO habitat area reduced the value of treatments for protecting NSO habitat. The inclusion of additional

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Fig. C4. Treatment allocation for Solution 175 (MAT ¼ 1214.06 ha). The management plan achieves relatively good fire hazard reduction. Both water quality and NSO habitat are moderately affected: sediment load is 152.24 t and NSO habitat protected is 1198.6 ha.

treatments, such as mowing and slash removal, might help reduce small fuel loading and catastrophic flame length potential, and thus reduce overall fire hazard. Our results, however, did not show a significant correlation between area of habitat treated and decrease in potential habitat loss due to fire. Treatments allocated outside the habitat area reduced fire hazard and burn probability and, thus, prevented additional loss of habitat from fire.

4. Discussion 4.1. Synthesis of research In this study, we analyzed tradeoffs between the provision of the ecosystem services of water quality, NSO habitat protection and fire hazard reduction by solving mathematical programs that

Please cite this article as: Schroder, S.A.(., et al., Multi-objective optimization to evaluate tradeoffs among forest ecosystem services following fire hazard reduction in the Deschutes National Forest, USA. Ecosystem Services (2016), http://dx.doi.org/10.1016/j. ecoser.2016.08.006i

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Fig. C5. Treatment allocation for Solution 211 (MAT ¼ 1214.06 ha). Treatments according to this management plan do not affect NSO habitat and only marginally decrease water quality (sediment ¼ 40.65 t). However, the level of fire hazard reduction in this management plan is low.

integrate all these values. We present the estimates of the potential environmental risk, i.e. increase in sedimentation and lost NSO habitat in case of wildfire given the projections of the vegetation parameters at the end of the planning horizon. We do not account for the uncertainty of fire's occurrence but rather analyze the potential losses given the fire happens. There were short term effects on expected sediment delivery and NSO habitat caused by fuel treatments, but these effects were more than compensated for

by an overall reduction in fire hazard at the end of the planning horizon. Our study results agree with previously published reports regarding the tradeoffs between fire hazard reduction and its effects on habitat protection (Kennedy et al., 2008; Lee and Irwin, 2005). Previous studies showed that treatment of potential habitat might not be necessary to prevent large-scale habitat loss following wildfire (Ager et al., 2007). Fuel treatments placed strategically around sensitive areas, such as habitat or watershed, will

Please cite this article as: Schroder, S.A.(., et al., Multi-objective optimization to evaluate tradeoffs among forest ecosystem services following fire hazard reduction in the Deschutes National Forest, USA. Ecosystem Services (2016), http://dx.doi.org/10.1016/j. ecoser.2016.08.006i

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Fig. C6. A point cloud that represents solution surface for the model with MAT ¼ 2428.12 ha. Each point represents a management plan that provides a certain level of fire hazard reduction, water quality control, and NSO habitat protection.

either retard the spread of wildfire or reduce the fire's severity to allow timely and low risk firefighting strategies, provided that the treatments are designed to reduce these fire characteristics under the extreme weather and fuel moisture conditions that are likely to occur. However, as Lee and Irwin (2005) suggested, moderate treatments might be compatible with both conservation and fire management goals. Fuel treatments themselves can affect the habitat, but their effects are not as severe as those of wildfires. Large wildfires pose significant challenges to fire management agencies charged with protecting human life, property and natural resources; and since 1990, areas burned by large wildfires, suppression costs and property damage have increased significantly (National Interagency Fire Center, 2015; Gorte, 2013). Strategies for reducing fire hazard will provide a number of potential benefits, especially in areas with high likelihood of very severe wildfires. Locating fuel treatments strategically to reduce the likelihood of high intensity fires will be important to maintain the sustainable provision of ecosystem services (Schoennagel et al., 2009). 4.2. Management applications of multi-objective optimization The methodology we developed in this study could be used to assess potential tradeoffs between other services. For example, the Deschutes National Forest is a popular recreational destination, and fuel treatments might affect several aesthetic values. Tumalo Falls and the surrounding areas contain numerous hiking trails, bike paths and recreational areas that attract thousands of tourists every year (Smith et al., 2011). Fuel treatments might help protect these recreational values from wildfires, but thinning may reduce the attractiveness of the area. Similarly, the effects of treatments are short-term, whereas high severity wildfires could significantly degrade many important ecosystem services for several decades. The results can inform planning efforts and decision making in forest management, because the models operate on objective data with explicit objectives and assumptions. The results could be used to justify proposed management actions for the NEPA process. Our model applications are not limited to a project or a small area, and the same method can be used for a broader analysis of larger areas and forests. However, a model's solution times and solution optimality might be affected by increasing the size of the model, e.g. modeling a larger forest, or adding more objectives and/or constraints. Other applications of this model include analysis of current ecosystem services projects in the Pacific Northwest. The Deschutes National Forest in central Oregon is applying an ecosystem services concept in the Marsh project (Foley et al., 2014), one of the largest high elevation wetland/marsh complexes in the continental United States. The USFS staff has identified several important ecosystem services in the 12,200 ha Marsh project area, including mushroom harvesting, water quality,

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cultural values, dispersed recreation and forest products. These services and values have already been delineated; our model could be used to quantify and evaluate potential tradeoffs among these services. Another ecosystem services project, the Cool Soda project (Smith, 2014) on the Willamette National Forest in western Oregon, uses an all-lands approach. Following the recent Forest Service Planning Rule (USFS, 2012) the all-lands approach intends to feature collaboration among diverse landowner groups to build common understanding of the rules, values and contributions of public lands within the broader landscape (Deal et al., 2012). This project includes the provision of forest products and timber, aquatic and fish habitat, and community and cultural values including tribal cultural values and recreation opportunities. The 4000 ha Cool Soda planning area includes both private and public lands. Our model could be used to quantify and assess tradeoffs among some of these ecosystem services to evaluate different management options for several of these services. Carbon sequestration, another important function for mitigating climate change, is currently attracting significant attention (Sundquist et al., 2008). Vaillant et al. (2013) showed that fuel treatments can affect carbon stocks in the short term, while in the long term these treatments can benefit both carbon pools and the protection of forest resources. The model described here can be adjusted to account for this ecosystem service and assess whether there are tradeoffs between carbon sequestration and other management objectives. Incorporation of the proposed method would assist planning and decision making options for forest managers and outline a range of potential tradeoffs among different services following management, providing forest managers a number of alternative strategies. Recently, a case was considered in the court of the city of Bozeman, MT, where the reduction of fuels in the forested watershed was proposed as a way to avoid catastrophic post-fire sediment increase in the streams that provide 80% of the source water for the city. Although these treatments would cause moderate water quality degradation in the short term, without the treatments the city's water treatment facilities would not be able to continue supplying water in case of fire (NEF, 2012). Another example is the collaboration between Denver Water and the Rocky Mountain region of the US FS in Colorado (USDA, 2012). Denver Water provides clean water for 1.3 million people in the metropolitan area of Denver, CO, USA. A partnership was established between Denver Water and the U.S. Forest Service to reduce the risk of catastrophic fire and sedimentation these fires cause for water utilities. Through this partnership, Denver Water plans to match the U.S. Forest Service's $16.5 million investment, for a total of $33 million toward forest treatment and watershed protection projects over a five-year period in priority watersheds critical to Denver Water's water supply. Denver Water and the US FS have a shared interest in improving forest and watershed conditions to protect water supplies and water quality, as well as to continue providing other public benefits, such as wildlife habitat and recreation opportunities. The city of Bend might face a similar dilemma, and the results of this study could be used to estimate the risks and benefits of different management strategies, inform decision making and the design of long term forest management plans, advocate the potential benefits of forest management and communicate the prospective outcomes of the chosen strategies to stakeholders. Similarly, the method and the results of this study can be used for the realization of the ecosystem services framework being applied by some National Forests and Ranger Districts (Smith et al., 2011), one of whose components involves the valuation of ecosystem services and the effects of forest management on their provision.

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Fig. C7. Treatment allocation for Solution 210 (MAT ¼ 2428.12 ha). This management plan achieves a high level of fire hazard reduction; however, water quality decrease is significant (sediment ¼ 262.76 t) and NSO habitat is moderately affected (NSO habitat protected ¼ 1182.43 ha).

5. Conclusion Our study provides an example of how an optimization-based approach can be used in practice to design management strategies that integrate diverse management objectives and quantify and evaluate tradeoffs among different ecosystem services. The results showed that management activities planned in areas of high

ecological importance, such as NSO habitat and municipal watersheds, affect the important ecosystem services these areas provide. In the short term, fire hazard reduction led to increases in sedimentation and reduced water quality and some loss of potential NSO habitat. However, analysis of the environmental risks showed that over the longer term the loss of water quality and NSO habitat caused by wildfire would be 30–50% less than without any

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Fig. C8. Treatment allocation for Solution 211 (MAT ¼ 2428.12 ha). Treatments according to this management plan would reduce fire hazard significantly but decrease water quality (sediment ¼ 211.83 t) and destroy more than a half of the NSO habitat (NSO habitat protected ¼ 587.94 ha).

treatments to reduce wildfire hazard. The key advantage that our method provides is that it incorporates different management objectives and allows the analysis of tradeoffs among these objectives and evaluation of environmental risks associated with different management strategies. These results can inform planning efforts in forest management, because the models operate on objective data with explicit objectives and assumptions. The spatially and temporally explicit management plans produced in this

study are ready to use in planning and decision making as well as at stakeholder meetings for presenting different options for the Drink area management. These plans provide alternative strategies where different objectives are prioritized differently; thus they present a wide range of choices to meet different requirements and public demands. The expertize of forest managers will further refine the suggested management plans, creating well-informed and effective management strategies.

Please cite this article as: Schroder, S.A.(., et al., Multi-objective optimization to evaluate tradeoffs among forest ecosystem services following fire hazard reduction in the Deschutes National Forest, USA. Ecosystem Services (2016), http://dx.doi.org/10.1016/j. ecoser.2016.08.006i

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Fig. C9. Treatment allocation for Solution 396 (MAT ¼ 2428.12 ha). This management plan would provide relatively high level of fire hazard reduction while moderately affecting the ecosystem services: sediment load is 193.24 t and NSO habitat protected is 1235.75 ha.

Acknowledgments Our project was funded by the US Forest Service, Pacific Northwest Research Station (Grant number PNW 10-JV-11261975086 MOD02). We thank the Deschutes National Forest Staff Leo Yanez, Deana Wall, Peter Powers, Barbara Webb and Todd Reinwald for providing GIS data for the project as well as valuable comments and suggestions regarding the results during the course

of the project. We thank two reviewers for their helpful comments to improve the manuscript.

Appendix A The multi-objective model formulation is the following: Objectives:

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Fig. C10. Treatment allocation for Solution 399 (MAT ¼ 2428.12 ha). The provision of ecosystem services is not affected in this management plan: water quality decrease is insignificant and sediment level is close to natural. The NSO habitat is protected in its entirety. However, the level of fire hazard reduction is low.

max

∑

Cirxir

i ∈ I , r ∈ R /0

max

∑ i ∈ Iw, j ∈ Jr

⎛ ⎛ ⎞⎞ ⎜ a p + ea ⎜ ∑ x − p ⎟⎟ i i ij i ⎟⎟ ⎜ ⎜ i ⎝ j∈J ⎠⎠ ⎝

(A1)

⎛ ⎧ ⎪ ⎨ min⎜⎜ max⎪ ∑ sir xir , ⎩ i ∈ I, r ∈{1,12} ⎝

⎫⎞ ⎪ ⎬⎟ sir xir ⎪ ⎟ ⎭⎠ i ∈ I , r ∈{2,12}

∑

(A3)

Subject to:

(A2)

∑ i∈I/U

bi xir ≤ B, r ∈ { 1, 2, 12}

(A4)

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∑ ∑

x rj − Sc qc ≥ 0, for all c ∈ C

d ∈ Dc j ∈ R d

∑

qc − pd ≥ 0, for all d ∈ Iw

c ∈ Cd

∑ xir = 1,

(A6)

for all i ∈ I /U (A7)

r∈R

∑

(A5)

ai(xir + xi12) = Hr , for all r ∈ { 1, 2}

i∈I/U

(A8)

Hr ≤ A, forall r ∈ { 1, 2}

(A9)

lH1 − H2 ≤ 0

(A10)

−uH1 + H2 ≤ 0

(A11)

xir , pi , qc ∈

{ 0, 1},

for all i ∈ I , r ∈ R, c ∈ C , d ∈ D

(A12)

Variables in the multi-objective model are the following: xir ¼ one if unit i is assigned a prescription r and zero, otherwise. pd ¼ one if unit d belongs to a cluster that satisfies the NSO habitat criteria; qc ¼ one if cluster c meets the NSO habitat criteria at the end of the planning horizon; Hr ¼ an accounting variable for the total area treated in period r. The model parameters are the following: I ¼ the set of treatment units (indexed by i); R ¼ {1, 2, 12, 0}, indicating treatment in period 1, 2, both or none, respectively; indexed by r; Iw ¼ the set of units that potentially satisfy the NSO habitat criteria (Iw ⊂ I). U ¼ the set of treatment units that are non-forested; Dc ¼ the set of units that form cluster c (Dc ⊂ I), indexed by d; Rd ¼ the set of prescriptions where unit d satisfies the habitat criteria, indexed by j; C ¼ the set of all clusters, indexed by c; Cd ¼ the set of clusters that contain management unit d (Cd ⊂ C); B ¼ the budget limit allocated for fuel treatments in each planning period, in US dollars; Cir ¼ fire hazard reduction coefficient in stand i if prescription r applied; bi ¼ the cost of treatment in unit i in US dollars, discounted at 4% (Kourantidou and Christodoulou, 2012; Row et al., 1981; Rambaud and Torrecillas, 2005); sir ¼ the sediment coefficient from unit i if prescription r was applied; ai ¼ the area of unit i; A ¼ the maximum total area that can be treated in each planning period (MAT); e ¼ the discounting coefficient to account for habitat fragmentation; e ¼ 50%; l,u ¼ the lower and upper bounds on area fluctuations treated in periods 1 and 2. Function (A1) expresses the fire hazard minimization. Function (A2) maximizes the area that satisfies the NSO habitat criteria at the end of the planning horizon. Function (A3) minimizes the peak sediment that fuel treatments cause. Inequality (A4) does not allow the total cost of fuel treatments exceed budget B. Constraint (A5) determines whether the entire

cluster c satisfies the NSO habitat criteria and constraint (A6) defines whether unit d belongs to such a cluster at the end of the planning horizon (adopted from Rebain and McDill (2003)). Constraint (A7) ensures that only one prescription is assigned to a unit in the planning horizon. Constraints (A8)–(A11) work together to balance the area treated in the two planning periods. Accounting constraint (A8) calculates the area treated in each period. Inequality (A9) constrains the total area treated in each period. The last two inequalities (A10) and (A11) ensure that the area treated in the second period does not decrease (increase) by more than a factor of l (u). Finally, the last constraint set (A12) defines variables xir, pi, and qc as binary. The models were solved using CPLEX 12.4 on a Dell PE2950 with a 3 GHz Intel 5160 dual-core CPU and 16 GB RAM. Each model was solved to optimality in approximately 8 h. We used AlphaDelta algorithm (Tóth et al., 2009; Tóth et al., 2006) to solve the models. The algorithm starts by finding the optimal solution, i.e., the set of optimal prescriptions for each management unit, with respect to each of the three objective functions, one at a time without regard to another objective. Pareto-efficient solutions, solutions where none of the associated objective function values can be improved without compromising another objective value, were found iteratively using a slightly sloped composite objective function. For further algorithmic details, see Tóth et al. (2009).

Appendix B. Treatment specification for the drink planning area See Appendix Tables.

Appendix C See Appendix Figs. C1–C10.

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