A stochastic approach to optimize Maritime pine (Pinus pinaster Ait.) stand management scheduling under fire risk. An application in Portugal

The paper discusses research aiming at the development of a management scheduling model for even-aged stands that may take into consideration fuel treatments to address the risk of wildfires. A Stochastic dynamic programming (SDP) approach is proposed to determine the policy (e.g. the fuel treatment and thinning schedules and the rotation age) that produces the maximum expected discounted net revenue. Fuel treatment activities encompass shrub cleanings. Emphasis was on combining a deterministic stand-level growth and yield model with wildfire occurrence and damage models to design a SDP network. SDP stages are defined by age and state variables include both the stand basal area and the number of years since the last fuel treatment. Fire occurrence and damage scenarios are addressed at each stage. Results from an application to Maritime pine (Pinus pinaster Ait.) stand management scheduling in Leiria National Forest, Portugal, are presented. Results suggest that the modeling strategy may help assess the impact of wildfire risk on the optimal stand management schedule. They confirm that the maximum expected discounted net revenues decreases. Further, albeit some timber may be salvaged after the wildfire, rotation age also decreases when the risk of fire is considered. Finally, they provide interesting insights about the role of thinning and fuel treatment policies in mitigating risk.     

MODELING CATASTROPHIC RISK IN ECONOMIC ANALYSIS OF FOREST CARBON SEQUESTRATION

ABSTRACT. The effect of risk from catastrophic tree mortality, such as fire, insect outbreaks and hurricanes, on selling credits for carbon sequestration from a slash pine plantation is modeled. We achieve this task by developing a modified Hartman model and applying it to a slash pine plantation. It is found that risk decreases the land expectation value and the optimal rotation age on a forest stand producing timber and carbon sequestration benefits. This decrease is greater with higher prices of carbon. Furthermore, risk increases the amount of pulpwood produced from the stand and decreases the amount of sawtimber produced. Since pulpwood has a shorter life span than sawtimber this reduces the amount of carbon sequestered. This effect is greater for higher prices of carbon suggesting that risk dampens the effect that a carbon market would have in inducing landowners to sequester more carbon.     

Optimal harvest strategy for even‐aged stands with price uncertainty and risk of natural disturbances

We present a reservation price model to examine the joint impacts of natural disturbances and stumpage price uncertainty on the optimal harvesting decision for even‐aged forest stands. We consider a landowner who manages a loblolly pine stand to produce timber and amenities, under age‐dependent risk of wildfires and uncertainty in future timber prices. We show that the incorporation of risk of wildfires decreases the optimal reservation prices. The inclusion of risk of wildfires leads to lower land values and reduces the mean harvest age compared with the case of no‐risk of wildfires. Higher economic gains are obtained with the reservation price strategy compared with the deterministic rotation age model—a difference in the land value of $2,326 ha^?1 (21%) between the two approaches. Recommendations for Resource Managers

• Our adaptive harvest strategy shows that the incorporation of risk of wildfires decreases the optimal reservation prices compared with the case of no‐risk of wildfires.
• Low reservation prices—a price that makes the landowner indifferent between harvesting or waiting longer—result in lower economic benefits for landowners and potential conversions of lands to nonforest use.
• Forest management practices oriented to reduce the effects of catastrophic disturbances, for example, creating a more complex forest structure with different stand densities, become imperative to ensure the sustainability of forestlands in the US South.
• Our analysis also suggests that the valuation of forestry investments should consider not only the risk of catastrophic events but also uncertainty in future timber prices. Higher appraisals of land value are obtained when timber price uncertainty is explicitly recognized, providing financial incentives for landowners to invest in forestry.

     

A SEQUENTIAL APPROACH TO DERIVATION OF STAND TREATMENT AND FOREST-WIDE HARVEST PRESCRIPTION OR SUPPLY

Current methods for optimization of stand treatment and forest-wide harvest scheduling use mathematical programming that presumes perfect information on production, costs, and revenues over long planning periods. These approaches simultaneously optimize harvest for all periods in the planning horizon. In contrast, the method presented here assumes that stand-level planning and harvest scheduling proceed sequentially rather than simultaneously over every period. A backward-recursion dynamic program is used to determine the discounted net value of a wide range of current harvest strategies for each stand class in the forest inventory on the basis of a projected set of optimal treatments for future harvest and regeneration of each stand. The most highly valued strategy is selected if there are no volume constraints. Otherwise, suboptimal harvest alternatives are ranked in order of increasing opportunity cost for increasing or decreasing harvest; constraints met only up to a maximum opportunity cost is also demonstrated.     

RANDOM ENTRY FORESTRY: TIMBER MANAGEMENT IN A TIME OF SPECIES CONSERVATION

In this paper we propose a timber management scheme which mimics the patchy stand structure of a fire climax forest and has the desirable characteristic of retaining stands of trees of very old ages. We go on to do a preliminary economic analysis and determine that if management is taking place under the restriction that a certain fraction of the forest must be of at least some given age then this approach may be far superior to standard single age rotation schemes.     

CLIMATE CHANGE AND OPTIMAL ROTATION IN A FLAMMABLE FOREST

ABSTRACT. This paper builds a Faustmann‐based model to study the effects of increased climate‐induced fire risk on the optimal forest rotation period. Simulations using species prevalent in North American forests indicate that both the commercial and socially optimal rotation ages decline as the risk increases. The reduced carbon absorbed by the standing timber can then create a positive feedback effect. This has potentially important policy implications. The Kyoto ratification agreement reached in the autumn of 2001 was dependent on allowing the ‘Umbrella Group’ of countries to use their forests' carbon‐absorbing ability to offset their need for fossil fuel emission reductions. This carbon‐absorbing ability will decline if rotation ages decrease with increased fire risk, weakening the force of the argument for allowing these countries to use their carbon ‘sinks’ to avoid reducing anthropomorphic emissions.     

MULTIPLE USE VALUES AND OPTIMAL STEADY STATE AGE DISTRIBUTIONS

Forest management today, generally, focuses not only on wood values but also on the many other amenities and services provided by growing forests. The significance of these multiple use values was recognized by Hartman [1976] who derived a formula for the optimal rotation for a single stand when the services provided by the stand throughout its life are considered in addition to the value of the final harvest. Some more recent work has focused on the case of multiple stands where the amenity values at a point in time depend on the age distribution of the stands at that time. One approach to harvesting multiple stands for wood values alone is the forestry maximum principle developed by Heaps [1984] and Wan [1985]. It will be shown here how the forestry maximum principle can be modified to incorporate the amenity services provided by the growing forest. The optimal steady state age distributions for the multiple stand forest can then be identified and described with the help of Hartman's rotation formula.     

THE FOREST ROTATION PROBLEM WITH STOCHASTIC HARVEST AND AMENITY VALUE

ABSTRACT. We present a general approach to study optimal rotation policy with amenity valuationunder stochastic forest stand value. We state a set of weak conditions under which a unique optimal harvesting threshold exists and derive the value of the optimal policy. We characterize the impact of forest stand value volatility on both the total and the marginal expected cumulative present value of the revenues accrued from amenities. We also illustrate our results numerically and find that depending on the precise characteristics of amenity valuation higher forest stand value volatility may accelerate the rotation policy by decreasing the optimal harvesting threshold.     

ENVIRONMENTAL AND FINANCIAL SUSTAINABILITY OF FOREST MANAGEMENT PRACTICES

One of the guiding themes for forest management policy throughout much of North America is sustained yield. The basic premise behind this theme is that a constant or nondeclining flow of services from the forest is socially desirable. Unfortunately, the act of capturing the benefits of this service (timber harvesting) often has detrimental effects on the timber-productive capacity of a forest site. This paper presents a dynamic program that is used to determine the optimal harvest system choice for a timber stand described by average piece size, stand density, a measure of site quality, and stumpage value. The harvest systems are defined by logging costs, reforestation and rehabilitation costs, and the impact of the system on the productivity of the site. An application of the model is presented for lodgepole pine in Alberta. We conclude that, at high discount rates, soil conservation is not economically rational. At lower discount rates, some degree of soil conservation is desirable on the more productive sites. At lower discount rates, there also appears to be an incentive for more intensive forest management. Limitations on acceptable harvest practices can have a large impact on optimal rotation age and the volume harvested. There is a large opportunity cost resulting from a requirement for sustainable volume production because of the impact of harvesting on soil productivity.     

Perspectives on experimental fires in Canadian forestry research

This paper offers some insights into the field approach to conducting experimental forest fires based on two decades of experience dealing with a wide variety of fuel types, burning conditions, and resultant fire behavior. The practical aspects involved in designing a study area for an experimental burning project and its successful execution are considered as well as the methods used in the measurement of physical fire characteristics, fuel properties, and fire weather elements. On the basis of this review, several impressions emerge about the possible future requirements and emphasis in outdoor forest fire behavior research involving naturally occurring fuel complexes. Finally, the conclusion is reached that there can be no substitute for actual “hands-on” experience in observing experimental fires as a basis for understanding the behavior of free-burning fires in the forest environment resulting from planned or accidental ignitions.     

Management of the risk of wind damage in forestry: a graph-based Markov decision process approach

This study deals with the problem of including the risk of wind damage in long-term forestry management. A model based on Graph-Based Markov Decision Processes (GMDP) is suggested for development of silvicultural management policies. The model can both take stochastic wind events into account and be applied to forest estates containing a large number of stands. The model is demonstrated for a forest estate in southern Sweden. Treatment of the stands according to the management policy specified by the GMDP model increased the expected net present value (NPV) of the whole forest only slightly, less than 2%, under different wind-risk assumptions. Most of the stands were managed in the same manner as when the risk of wind damage was not considered. For the stands that were treated differently, however, the expected NPV increased by 3% to 8%.     

Wildfire fuel management: Network-based models and optimization of prescribed burning

Wildfires are a common phenomenon on most continents. They have occurred for an estimated 60 million years and are part of a regular climatic cycle. Nevertheless, wildfires represent a real and continuing problem that can have a major impact on people, wildlife and the environment. The intensity and severity of wildfires can be reduced through fuel management activities. The most common and effective fuel management activity is prescribed burning. We propose a multi-period optimization framework based on mixed integer programming (MIP) techniques to determine the optimal spatial allocation of prescribed burning activities over a finite planning horizon. In contrast to the existing fuel management optimization literature, we model fuel accumulation with Olson’s equation. To capture potential fire spread along with irregular landscape connectivity considerations, we use a graph-theoretical approach that allows us to exploit graph connectivity measures (e.g., the number of connected components) as optimization objectives. The resulting mathematical programs can be tackled by general purpose MIP solvers, while for handling larger instances we propose a simple heuristic. Our computational experiments with test instances constructed based on real-life data reveal interesting insights and demonstrate the advantages and limitations of the proposed approaches.     

OPTIMAL HARVESTING OF FOREST AGE CLASSES UNDER PRICE UNCERTAINTY AND RISK AVERSION

ABSTRACT. . We analyze optimal forest harvesting under mean reverting and random walk timber price and include multiple age classes, forest owners' consumption‐savings decisions and risk aversion. This framework generalizes existing studies that assume a single stand and risk neutrality or include ad hoc risk aversion and obtain the result that uncertainty lengthens the optimal rotation. Including planting cost implies that price stochasticity may shorten the rotation period. Under the mean reverting price process, optimal harvesting becomes more sensitive to periodic price level, as compared to the random walk case. Including risk aversion completely changes the harvesting policy in the sense that, if the forest initially consists of just one age class, it is optimal to smooth the age class structure and have more frequent cuttings from younger age classes. With risk aversion, optimal cuttings depend on price level, even under a random walk price and zero replanting and harvesting costs. In addition, harvesting decisions become dependent on subjective time preference and forest owners' wealth.     

Influence of temporal aggregation on strategic forest management under risk of wind damage

A key aspect when optimizing strategic and long-term forest management policies is the temporal aggregation utilizing time periods of a specific length. As the length of the time periods influence both the problem size and the possible interaction of the management policy with the state of the forest, it implicitly has a major influence on the feasibility of computing the optimal management policy and the quality of the resulting management policy. The objective of this study was twofold: (i) to evaluate the value of considering the risk of wind damage in large-scale strategic forestry management policies, (ii) to investigate the influence of the length of the time periods on the value of considering the risk of wind damage in the management policy. The analysis was executed utilizing a graph-based Markov decision process model capable of considering stochastic wind damage event, and a case study utilizing a forest estate consisting of 1200 ha of forestry, divided into 623 stands. Twenty-, ten-, and five-year-long time periods were utilized to evaluate the influence of the length of the time periods, while the value of considering the risk of wind damage in the management of the estate was evaluated by optimizing and evaluating long-term management policies recognizing and not recognizing the risk of wind damage. Results show that the value of considering the risk of wind damage was small for the whole estate. The expected net present value of the estate increased by ≤2% by managing the estate according to the risk of wind damage. Furthermore, while the length of the time periods had a small influence on the scale of the entire estate, it had a larger influence on the scale of a smaller subset of stands in the estate. For the whole estate, the value of considering the risk of wind damage varied with ≤1.5% depending on the length of the time periods. While for a selected subset of stands, the value of considering the risk of wind damage varied with ≤6.5% depending on the length of the time periods.     

A spatial optimisation model for multi-period landscape level fuel management to mitigate wildfire impacts

Elevated fuel loads are contributing to an increase in the occurrence of, and area burned by, severe wildfires in many regions across the globe. In an attempt to reverse this trend, fire and land management agencies are investing in extensive fuel management programs. However, the planning of fuel treatment activities poses complicated decision-making problems with spatial and temporal dimensions. Here, we present a mixed integer programming model for spatially explicit multi-period scheduling of fuel treatments. The model provides a flexible framework that allows for landscape heterogeneity and a range of ecological and operational considerations and constraints. The model’s functionality is demonstrated on a series of hypothetical test landscapes and a number of implementation issues are discussed.     

MODELING IMPACTS OF BIOENERGY MARKETS ON NONINDUSTRIAL PRIVATE FOREST MANAGEMENT IN THE SOUTHEASTERN UNITED STATES

Abstract The potential impacts of bioenergy markets on slash pine plantation management on nonindustrial private forestlands in the southeastern United States were analyzed. We developed an integrated Black–Scholes and modified Hartman model to achieve this task. The risk of damage from catastrophic natural disturbances such as wildfires and pest outbreaks associated with the exclusion/incorporation of thinnings and variation in timber salvage rates was also included. Three scenario sets were considered: status quo or no thinning scenario, thinning scenario for pulpwood, and thinning scenario for bioenergy at differing levels of risk and salvage. The results indicated that the incorporation of thinnings either for pulpwood or bioenergy increases the forestland value regardless of the risk when the salvage value of the stand is 0.8. When the two thinning scenarios were compared, the land expectation value for the thinning scenario for bioenergy was greater at any level of risk compared with the thinning scenario for pulpwood, averaging a difference of 11.5% and 11.7% for salvageable portions of 0.8 and 0, respectively.     

Modelling forest fire spread using hexagonal cellular automata

In this paper a new mathematical model for predicting the spread of a fire front in homogeneous and inhomogeneous environments is presented. It is based on a bidimensional cellular automata model, whose cells stand for regular hexagonal areas of the forest. The results obtained are in agreement with the fire spreading in real forests.