- Email: [email protected]
The use of heuristic optimization in risk management of wind damage in forest planning
Forest Ecology and Management 241 (2007) 189–199 www.elsevier.com/locate/foreco
The use of heuristic optimization in risk management of wind damage in forest planning Hongcheng Zeng *, Timo Pukkala, Heli Peltola Faculty of Forestry, University of Joensuu, P.O. Box 111, FI-80101 Joensuu, Finland Received 8 March 2006; received in revised form 7 December 2006; accepted 11 January 2007
Abstract In this work heuristic techniques were used with a forest growth model (SIMA), mechanistic wind damage model (HWIND) and GIS software (ArcGIS) in order to manage the risk of wind damage in forest planning. The study optimized clear-cut regimes taking into account the risk of wind damage and timber harvest over a 30-year simulation (planning) period in a forest located in central Finland. To demonstrate the effect of management goals related to wind damage, the amount of stand edges at risk was either minimized or maximized with or without even-flow targets of harvested timber. The three heuristic techniques included in the preliminary tests (simulated annealing, tabu search, and genetic algorithms) produced rather similar results for the planning problems. Tabu search performed slightly better than simulated annealing and genetic algorithms, and was therefore used in the subsequent analyses. The optimizations showed that the risk of wind damage could be decreased by aggregating clearcuts and avoiding clear-cuts at the edge of stands with a high possibility of being damaged. The even-flow timber harvesting objective limited the possibilities of minimizing the risk of wind damage. In addition, the optimization of clear-cut regimes was sensitive to the criterion of critical wind speed that bisected the stands into risky and non-risky ones. # 2007 Elsevier B.V. All rights reserved. Keywords: Clear-cut; Genetic algorithms; GIS; Integrated approach; Simulated annealing; Tabu search
1. Introduction Wind-induced damage is a continuous cause of economic loss in forests. For example, in Europe about 180 million m3 of timber was levelled by wind during storms in December 1999 (UNECE/ FAO, 2000). Recently in southern Sweden about 70 million m3 of timber was lost in a winter storm in 2004 (Nordstro¨m, 2005). Also in Finland, over 7 million m3 of timber was lost in November 2001 (Pellikka and Ja¨rvenpa¨a¨, 2003). The economic impact of wind damage is particularly severe in managed forests due to the reduction in the yield of recoverable timber, increased costs of unscheduled thinning and clear-cutting, and the necessity to deviate from the optimal cutting schedule. In principle, the susceptibility of a forest stand to wind damage is controlled by tree and stand characteristics, such as tree species, diameter, height and stand density (Coutts, 1986; Gardiner, 1995; Peltola et al., 1999). Since, these characteristics change dynamically along with forest growth, the risk of
* Corresponding author. Tel.: +358 13 251 4439; fax: +358 13 251 4444. E-mail address: [email protected] (H. Zeng). 0378-1127/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.foreco.2007.01.016
wind damage will also change (Slodicak, 1995; Zeng et al., 2006). Wind damage is most likely to be found where there are sudden changes in wind loading to which the trees are not acclimatized; such as in stands adjacent to newly clear-cut areas or in stands that have recently been heavily thinned (Neustein, 1965; Lohmander and Helles, 1987; Peltola, 1996a,b; Gardiner et al., 1997; Peltola et al., 1999). When planning the spatial patterns of clear-cuts and the management of forest edges, the fundamental issue is how clearcuts affect the local wind speed and direction of airflow at the downwind edges of the clearings, and consequently the level of risk in these conditions (Peltola, 1996a; Vena¨la¨inen et al., 2004). The risk of wind damage can be reduced at a regional scale, for example, by avoiding new edges especially in old stands and by cutting the most vulnerable stands (usually old ones, see Zeng et al., 2004). On the other hand, after the closure of regenerated gaps over time (as seedling stands grow), the risk of wind damage at the edges will decrease again (Zeng et al., 2006). Timber production objectives affect the temporal and spatial patterns of clear-cuts, which consequently affect the risk of wind damage. In recent years, statistical and process-based growth and yield models have been developed to simulate forest growth under
190
H. Zeng et al. / Forest Ecology and Management 241 (2007) 189–199
certain environmental and management conditions (e.g. Kelloma¨ki et al., 1992; Kelloma¨ki and Va¨isa¨nen, 1997; Matala et al., 2003). Mechanistic wind damage models based on tree and stand characteristics and environmental factors have been developed to predict the wind speeds needed for uprooting or breaking the stems of trees (e.g. Peltola et al., 1999; Gardiner et al., 2000; Ancelin et al., 2004). Recently, Zeng et al. (in press) embedded a forest growth model (SIMA, see Kelloma¨ki et al., 1992) and a mechanistic wind damage model (HWIND, see Peltola et al., 1999) into GIS software ArcGIS to build a decision support system (DSS). The DSS can assess the influence of certain forest management regimes (e.g. clear-cut) on the risk of wind damage at the stand and regional levels. However, it is not yet capable of optimizing the management regimes (timber harvesting) so as to minimize the risk of wind damage. On the other hand, heuristic optimization techniques are increasingly being used in forest planning (Borges et al., 2002). These techniques include simulated annealing (SA) (e.g. Dahlin ¨ hman, 2000), and Sallna¨s, 1993; Lockwood and Moore, 1993; O tabu search (TS) (e.g. Bettinger et al., 1997; Boston and Bettinger, 1999), and genetic algorithms (GA) (e.g. Lu and Eriksson, 2000; Falcao and Borges, 2001). Among others, different variations and combinations of these techniques have also been applied in forestry (Bettinger et al., 1999; Boston and Bettinger, 2002; Falcao and Borges, 2002; Heinonen and Pukkala, 2004). Unlike traditional mathematical programming, heuristic techniques have the potential to solve optimization problems with complicated spatial constraints, which are usually formulated as non-linear 0–1 integer programming problems (Boston and Bettinger, 2002). In the above context, geographical information system (GIS) can serve as a common data and analyses framework (Rao et al., 2000). It can be used to store forest data with spatial attributes, and couple models and techniques together. In addition, GIS defines the topology between polygons (e.g. forest stands) and polylines (e.g. forest edges) so that spatial calculation can be done within the software. We use, in this work, optimization methods to include the risk management of wind damage into forest planning, in addition to the objectives concerning timber harvest. For this purpose, heuristic optimization techniques were employed together with a forest growth model (SIMA), mechanistic wind damage model (HWIND) and GIS software (ArcGIS). The integrated approach was used to optimize the temporal and spatial patterns of clear-cuts in relation to objectives concerning the risk of wind damage and timber harvest over a 30-year simulation (planning) period in a forest located in central Finland. The risk of wind damage was either minimized or maximized with or without an even-flow target of harvested timber. These problems correspond to maximum and minimum impact of harvests on the risk of wind damage at forest edges. 2. Material and methods 2.1. Study site and forest database The forest area employed in this study represents a typical boreal forest in central Finland (638010 N; 278480 E). It was
mostly dominated by Scots pine (Pinus sylvestris) and Norway spruce (Picea abies) stands, but some birch (Betula spp.) and other broad-leaved stands were also present. The site was surveyed in 2001 and included 395 ha of forests and 46 ha of open terrain (i.e. lakes, fields and clear-cut areas). The 395 ha of forest consisted of 142 ha Scots pine (76 stands), 225 ha Norway spruce (158 stands), 26 ha of birch (27 stands) and 2.5 ha other broad-leaved species (5 stands). The area has an undulating terrain with some small hills and altitudes ranging between 90 and 170 m above sea level. In this work, GIS software ArcGIS 9 was used to store forest stands including their boundaries. Since trees located at forest edges were expected to have the highest risk of wind damage in Finnish conditions, only stands adjoining gaps were considered to have risk. The risk of wind damage was represented by the length of vulnerable edges (edges at risk). If a stand adjoined a gap and its critical wind speed was lower than the critical speed criterion (e.g. 20 m s1), the boundary between the stand and the gap was considered as a vulnerable edge. The relationship between forest stands and their boundaries were based on topology and created in ArcGIS. Each stand boundary segment was appended with its length, and left and right polygon identifiers. They were imported to the optimization algorithm in addition to the forest growth and harvest volume data. The optimal temporal schedule and spatial pattern of the clear-cuts, output by the optimization algorithm, was correspondingly imported to ArcGIS. In this way, all the clear-cut stands and the most vulnerable edges could be visualized on the maps. 2.2. Simulation of treatment alternatives 2.2.1. Simulation of stand dynamics with SIMA The growth and yield model SIMA (Kelloma¨ki et al., 1992) was used to simulate the growth and yield of treatment alternatives of stands. In the model, the mass growth (including foliage, branches, stem and roots) of each tree in a stand is calculated based on diameter growth, which is limited by temperature conditions and the availability of light, soil moisture and nitrogen (Kelloma¨ki et al., 1992). The mortality of the trees in a stand is controlled both by stand age and minimum allowable growth rate of trees (Kelloma¨ki et al., 1992). After clear-cut the stand was regenerated artificially by giving the initial seedling stand properties regarding tree species, stand density (number of trees per hectare) and diameter of seedlings. The properties of the SIMA model with its parameters and inputs and the validity of its outputs, have been described in detail by Kelloma¨ki et al. (1992), Kolstro¨m (1998) and Talkkari et al. (1999). In this work, we simulated the dynamics (forest growth with or without a clear-cut) of forest stands over a 30-year period. During the 30-year planning period, there may be no clear-cut, or a clear-cut alternatively took place at either the 5th, 15th or 25th year of the simulation. Therefore, each stand might have a maximum of four alternative schedules. The stands, which did not exceed clear-cut criteria at the 5th, 15th or 25th year, had number of alternative schedules less than 4. The criteria, which specified whether a clear-cut was allowed or not, were mean
H. Zeng et al. / Forest Ecology and Management 241 (2007) 189–199
diameter at breast height (DBH) and age. The clear-cut was simulated if the stand’s DBH exceeded the DBH criterion or its age exceeded the age criterion. The clear-cut criterion of DBH was set at 30 cm for Scots pine, and 28 cm for Norway spruce and birch; while the age criterion was 80 years for Scots pine and Norway spruce and 70 years for birch. After clear-cut, artificial regeneration was applied so that the stand was planted with seedlings of the same tree species which were previously growing there (2000 seedlings/ha for Scots pine and Norway spruce, and 1600 for birch). No other management practices took place during the simulation period. Because birth and death of trees are stochastic processes in SIMA, each schedule was simulated 50 times, and the average results (tree and stand variables) were used as inputs for the HWIND simulations and heuristic optimization. 2.2.2. Calculation of critical wind speeds for stands with HWIND The mechanistic wind damage model HWIND (Peltola et al., 1999) was used to describe the mechanistic behavior of Scots pine, Norway spruce and birch trees under wind loading. In the model, a tree is assumed to be uprooted if the maximum bending moment (due to forces by wind and gravity) exceeds the resistance of the root-soil plate (Peltola et al., 1999). Similarly, the stem is assumed to be broken if the breaking stress exceeds the critical value of the modulus of rupture (Petty and Worrell, 1981; Petty and Swain, 1985; Peltola et al., 1999). This makes it possible to calculate the minimum wind speed needed for uprooting or stem breakage (critical wind speed). The model outputs the mean critical wind speeds, lasting for 10 min at 10 m above the ground level, at which trees are uprooted and broken. The inputs of the model are tree species, average tree height and diameter at breast height (DBH), stand density (which were SIMA outputs in this work), in addition to distance from the forest edge and gap size (the length of gap in the direction of wind). The properties of the HWIND model, its parameters, inputs and the validity of its outputs for podzol soil conditions in Finland, have been discussed in detail by Peltola et al. (1999), Gardiner et al. (2000) and Talkkari et al. (2000). The gaps refer not only to clear-cut stands, but also water areas, open fields and seedling stands with an average tree height less than a defined criterion (2 m in this study). The gap size was assumed to be 10 times the average tree height at stand edge. This outputs the maximum risk (i.e. the lowest critical wind speed) in regard to gap size (Peltola et al., 1999). Furthermore, the critical wind speed of birch was simulated without leaves, to correspond to the time from late autumn to early spring, when most storms occur in Finland. The critical wind speed was calculated for each schedule and each stand with height 10 m in HWIND at the 5th, 15th and 25th year. These critical wind speeds were used to represent the risk of wind damage of the stand when it is located at the edges (adjoining a gap). The critical wind speeds were not calculated for young stands with height <10 m because these stands need very high wind speeds to be at risk. The critical wind speed of 20 m s1 was used as the baseline criterion for defining stands that were at risk since a typical range of wind speeds
191
(e.g. 14–25 m s1 for 10 min) have been found to cause damage under Finnish conditions (Laiho, 1987; Talkkari et al., 2000; Pellikka and Ja¨rvenpa¨a¨, 2003; FMI, 2003). 2.3. Optimization of clear-cut regimes 2.3.1. Heuristic optimization methods Three different heuristics, i.e. simulated annealing, tabu search, and genetic algorithms, were used to find the optimal combination of the stand’s treatment schedules. These techniques have been previously described in detail by Heinonen and Pukkala (2004) and Pukkala and Kurttila (2005), and the parameters of the heuristics used in this work were also based on the experience gained in those studies. Simulated annealing and tabu search are local improvement methods. A change of the solution (forest plan) is called a move. In this work, a move was equal to making two simultaneous changes in the current solution, i.e. the treatment schedule was changed simultaneously in two stands. All solutions that can be obtained with one move form the neighborhood of the current solution. The neighborhood used in this study could be called a two-stand neighborhood because the solution differs in two stands from its neighbor solutions. The two-stand neighborhood has been found to be a better approach in spatial problems than the more commonly used one-stand neighborhood (Heinonen and Pukkala, 2004). Simulated annealing uses the best of a set of random combinations of stands’ treatment schedules as the initial solution. A candidate move consists of first selecting two random stands and then a random schedule per stand. The selected schedules replace the schedules that are currently in the solution. Moves that improve the objective function value are maintained. Non-improving moves are maintained with a probability of p ¼ expððU new U old Þ Ti1 Þ, where Ti is the current ‘‘temperature’’ and U is the objective function value. The ‘‘temperature’’ defines the probability of accepting a candidate solution poorer than the current solution. During the optimization process the temperature is gradually decreased so that at the end of the search the likelihood of accepting inferior moves is close to zero. The temperature cools according to a cooling schedule, which is implemented by multiplying the current temperature with a parameter less than one to get the next temperature. A certain number of candidate moves (iterations) are tested in every temperature. The number of tested moves in each temperature may change when the temperature decreases so that the search could be intensified as the process cools. In this study, the search was stopped when a user-specified stopping temperature was reached or a certain number of consecutive temperatures (5 in the analyses of this study) went without any change in the solution. The parameters of simulated annealing used were: number of random searches to produce an initial solution (we used 20, i.e. 0.1N, where N is the number of stands), starting temperature (0.00035, i.e. 0.1/ N), cooling multiplier (0.9), freezing (stopping) temperature (0.0000175, i.e. initial temperature/20), number of iterations (attempted moves) in the initial temperature (286, i.e. N), and
192
H. Zeng et al. / Forest Ecology and Management 241 (2007) 189–199
an iteration multiplier to get the number of iterations in the next temperature (1.05). Compared to simulated annealing, tabu search looks for the neighboring solution space before accepting one change in the solution. The production of a set of candidate moves and accepting one of them is repeated for many iterations. Typical of tabu search is also tabu lists. This study used only recency-based lists that memorize the most recent moves, and prevented them from being used again for some time (iterations). Schedules that participated in the move were kept in the tabu list for a certain number of iterations. This number was the initial tabu tenure of the schedule. An iteration reduced the tabu tenures of all schedules by one. A schedule could again participate in a move once its tabu tenure had decreased to 0. The best non-tabu move of the inspected candidates was accepted; or the one with the shortest tabu tenure if all candidates were in the tabu list. If a candidate move yielded a solution better than the previous best, it was accepted even if the move was tabu. The initial tabu tenure of a schedule that enters the solution may be different from the tabu tenure of a leaving schedule. Tabu search was stopped when a certain number of iterations were completed. The tabu search algorithm used in this study had four parameters: number of iterations (1440, i.e. 5N + 10), number of candidate moves per iteration, given as a percentage of the total number of treatment schedules of stands (54, i.e. 10% of the 545 schedules that were simulated for the stands), initial tabu tenure of a leaving schedule (exit tabu tenure) (14, i.e. N/30 + 5), and initial tabu tenure of a schedule that enters the solution (entry tabu tenure) (2, i.e. initial exit tabu tenure/5). Unlike simulated annealing and tabu search, the search process of genetic algorithms is not based on neighborhood search. Instead, genetic algorithms are based on an initial population of solution alternatives, their evaluation and their breeding. Each iteration (named as a generation) has a set of alternative solutions called parent chromosomes. Two of these parent chromosomes were selected to generate a new chromosome for the next generation. One chromosome was selected with a probability proportional to its ranking; the other was chosen randomly with an equal probability for all the remaining chromosomes. The two selected parent chromosomes were processed by crossing over (combining parts of two chromosomes) and mutation (random change in one or several genes, or stands) giving birth to a new chromosome (offspring). In the incremental genetic algorithm technique used in this study, the new chromosome replaced one chromosome of the current population. The removed chromosome was selected based on its ranking, the probability of removal being highest for chromosomes that had low objective function values. The parameters of genetic algorithms were: population size (50 solutions in this study), number of iterations, or generations (1072, i.e. 2N + 500), probability of mutation at first iteration (0.5), and probability of mutation at last iteration (2.0). The probability of a mutation for intermediate iterations was obtained with linear interpolation. A probability of 0.5 means that one random stand (gene) is mutated with a probability of 0.5. A probability of 2.0 means two random stands are mutated with a probability of 1.0.
2.3.2. Objective functions In our work, the purpose of optimization was to demonstrate the approach of integrating the management of the risk of wind damage into forest level optimization, and to illustrate the effect of risk considerations on optimal landscape configuration. For this purpose, five very different sets of management objectives were assumed, ignoring the possible irrelevance of some problem formulations in forestry practice: (1) the risk of wind damage was maximized as the only objective (Problem 1); (2) the risk of wind damage was minimized as the only objective (Problem 2); (3) the risk of wind damage was maximized with an even-flow target of harvested timber (Problem 3); (4) the risk of wind damage was minimized with an even-flow target of harvested timber (Problem 4); (5) even-flow of harvested timber was the only objective (Problem 5). The objective function was an additive utility function formulated as follows: U ¼ w11 u11 ðE1 Þ þ w12 u12 ðE2 Þ þ w13 u13 ðE3 Þ þ w21 u21 ðH 1 Þ þ w22 u22 ðH 2 Þ þ w23 u23 ðH 3 Þ (1) where U is total utility, wi j and uij are the importance and subutility function, respectively, of objective i in management period j (i = 1, 2; j = 1, 2, 3), Ej is the percentage of vulnerable edges (with critical wind speeds <20 m s1) in the middle of management period j, Hj is the total timber harvest during period j. In Problems 1 and 2, objective weights w21 , w22 , and w23 were 0 and weights w11 , w12 , and w13 were all 0.333 (1/3); while in Problem 5 weights w11 , w12 , and w13 were 0 and weights w21 , w22 , and w23 were all 0.333 (1/3). In Problems 3 and 4 all the weights were equal to 0.167 (1/6). In real-life simulation, the weights could be different according to the requirements of forest managers. In Problems 1 and 3, the sub-utility for risk of wind damage increased linearly as a function of the length of vulnerable edges (Fig. 1A), and decreased in Problems 2 and 4 (Fig. 1B) The sub-utility functions for harvesting had an ascending-descending shape with the sub-utility increasing until the target cut of 12,000 m3 was reached, after which the sub-utility started to decrease (Fig. 1C). There were no strict constrains. The risk of wind damage was defined as the percentage of the total length of vulnerable stand edges of the total length of all the stand boundaries of the forest (E). When a stand adjoined gaps and had a critical wind speed <20 m s1, part of its boundary, which adjoined the gaps, was considered as having a risk of damage (i.e. treated as vulnerable edges). Therefore, maximizing the risk of wind damage means trying to lengthen forest edges with critical wind speeds <20 m s1; while minimizing risk was trying to shorten forest edges with critical wind speeds <20 m s1. Moreover, fragmentation statistics were calculated for the forests to compare the difference of landscape configuration regarding tree height. The fragmentation metrics ContrastWeighted Edge Density (CWED, see FragStats, 2006) was applied in this work to represent the fragmentation at the
H. Zeng et al. / Forest Ecology and Management 241 (2007) 189–199
193
Fig. 2. The average percentage of the vulnerable edge of the 30-year planning period in the solutions of simulated annealing (SA), tabu search (TS) and genetic algorithms (GA). ( ) Maximize vulnerable edge; ( ) minimize vulnerable edge; ( ) maximize vulnerable edge, cut 12,000 m3/10 years; ( ) minimize vulnerable edge, cut 12,000 m3/10 years.
3. Results 3.1. Comparison of different heuristics All the three heuristic optimization methods compared in this study output logical and rather similar results (Fig. 2). The timber harvesting objectives (Problems 3–5) were almost fulfilled in each period. The difference observed between the actual harvest volume and target level (i.e. 12,000 m3/10 years) was very small in each period, ranging in Problems 3–5 from 16 to 13 m3/10 year in simulated annealing, from 80 to 34 and from 52 to 11 m3/10 years in tabu search and genetic algorithms, respectively. When Problem 4 was solved 10 times with each technique, tabu search performed slightly better than simulated annealing and genetic algorithms (Fig. 3). The further analysis of optimization results was therefore only based on the outputs of tabu search. Fig. 1. The shapes of sub-utility functions used in the study. ‘‘Min’’ and ‘‘Max’’ are, respectively, the minimum and maximum possible values of an objective variable (within the decision space), and ‘‘Target’’ is the target value (12,000 m3).
3.2. Effects of risk management and timber harvest objectives When minimizing the occurrence of vulnerable edges was the only objective (Problem 2), there were still some clear-cuts
landscape level. The CWED evaluated the fragmentation based on the contrast of the neighbor stands in terms of the tree height. 2.4. Sensitivity analysis As quite different speeds of winds were found to cause damage in Finnish forests, the optimizations were also done by changing the critical wind speed criterion by 25% (alternatively using speeds of 15 and 25 m s1). The different critical wind speed criteria corresponded to the storms with different speeds or different windy areas. Since, only minimizing vulnerable edges (Problems 2 and 4) were a realistic task in forest management, the sensitivity analyses were carried out with Problems 2 and 4. Similarly, the timber harvest objective was also changed by 25% (using 9000 and 15,000 m3/10 years) in Problem 4 to find out how a change in timber harvesting objective affected the results.
Fig. 3. The average percentage of vulnerable edges and its range of the 10 runs for Problem 4 (minimizing the length of edges at risk combined with even-flow harvest target of 12,000 m3/10 years) output by simulated annealing, tabu search and genetic algorithms.
194
H. Zeng et al. / Forest Ecology and Management 241 (2007) 189–199 Table 2 Number of gaps and average gap area of different 10-year periods in each planning problem Planning problems
Fig. 4. The percentage of vulnerable edge (A), and fragmentation of the forest landscape (B) for maximizing or minimizing the length of edges at risk with or without even-flow harvest target of 12,000 m3/10 years (Problems 1–4), and the planning with only even-flow harvest target (Problem 5). ( ) 1st period; ( ) 2nd period; ( ) 3rd period.
(Table 1 and Fig. 4A). Those clear-cut stands were clustered to avoid the increment of edges. The forest had therefore few gaps with generally a large mean area (Table 2). The landscape gradually became smooth (Fig. 4B), because new gaps were placed next to young stands (Fig. 5). Some old stands were not cut due to their small risks (critical wind speeds 20 m s1), even though they adjoined the gaps (Fig. 5). If the minimization of vulnerable edges was combined with the even-flow of timber production (Problem 4), there were more vulnerable edges (Fig. 4A). The clear-cut stands in Problem 4 were not as well clustered as in Problem 2 so that more gaps appeared (Table 2). Compared to Problem 2 over the 30-year planning period, the forest in Problem 4 had on average nearly four times more vulnerable edges and 132% more total harvested timber. Therefore, the even-flow clear-cuts limited the minimization of the length of vulnerable edges.
1
2
3
4
5
1st period Number of gaps Mean area (ha)
17 2.4
10 2.0
26 2.3
20 2.9
20 3.2
2nd period Number of gaps Mean area (ha)
27 1.9
12 3.6
33 1.7
19 3.1
27 2.0
3rd period Number of gaps Mean area (ha)
45 1.4
9 2.8
24 2.3
25 2.1
23 2.3
The forest in Problem 4 had generally fewer gaps with larger mean areas than when the risk of wind damage was maximized with the even-flow harvesting target (Problem 3) or when evenflow of timber harvesting was the only objective (Problem 5, see Table 2). Although the landscape was more fragmented in Problem 4 than in Problem 2, it was smoother than the landscapes in Problems 3 and 5 (Fig. 4B). On the other hand, if maximizing the occurrence of vulnerable edges was the only objective (Problem 1), the clear-cuts were distributed uniformly and often next to old stands and more gaps were created (Table 2). As a result, the landscape developed towards a fragmented landscape regarding tree height (Fig. 5). Furthermore, fewer clear-cuts occurred compared to the optimization with the even-flow target (Problems 3 and 4; see Table 1). There were less vulnerable edges (28%) in Problem 3 than in Problem 1, although the length of vulnerable edge was also maximized in Problem 3. Thus, the even-flow target limited the possibility to maximize the length of vulnerable edges. When the risk of wind damage was not a management objective (Problem 5), the length of vulnerable edges was quite variable. The even-flow harvesting target, however, reduced the number of old stands in the study area. Thus, the length of vulnerable edges decreased towards the end of the 30-year planning period (Fig. 4A). It may be noted that for all the problems that maximized the length of vulnerable edges, some edges adjoining gaps (height <2 m) were not susceptible for the risk of wind damage. Edge stands with tree height less than 10 m or
Table 1 The optimal harvest and final volume in tabu search solutions Planning problem
Problem 1
Problem 3
Problem 4
Problem 5
1st period (m3) 2nd period (m3) 3rd period (m3)
6,964 9,307 15,561
2,989 8,752 3,698
12,015 12,006 12,007
11,958 11,932 11,999
11,998 11,999 12,003
31,832
15,439
36,028
35,889
36,000
67,536
81,929
64,087
64,606
Total harvest (m3) 3
Final volume (m )
Problem 2
64,874 3
Note: Problem 1: maximize vulnerable edges; Problem 2: minimize vulnerable edges; Problem 3: maximize vulnerable edges, with cut of 12,000 m /10 years; Problem 4: minimize vulnerable edges, with cut of 12,000 m3/10 years; Problem 5: cut of 12,000 m3/10 years as the only objective.
H. Zeng et al. / Forest Ecology and Management 241 (2007) 189–199
195
Fig. 5. The landscape configuration regarding stand height in the middle of the first (A(1), B(1), C(1)) or the third (A(3), B(3), C(3)) 10-year period when maximizing (A) or minimizing (B) vulnerable edges without harvest target (Problems 1 and 2) or aiming at harvesting of 12,000 m3/10 years (C) (Problem 5).
critical wind speed greater than 20 m s1 were not expected to have any risk of wind damage although they were also located at edges. Young stands could therefore be located at edges without increasing the risk of wind damage of the landscape.
3.3. Effect of critical wind speed criterion and harvesting target When the critical wind speed criterion was decreased by 25% (to 15 m s1), fewer stands were expected to have a
196
H. Zeng et al. / Forest Ecology and Management 241 (2007) 189–199
significant risk compared to the baseline wind speed of 20 m s1. Therefore, the total length of vulnerable edges was significantly decreased (on average 96 and 93% in Problems 2 and 4, respectively), while the timber harvests were increased (94%) over the 30-year period in Problem 2 (Table 3), which means that the clear-cut patterns changed accordingly. On the other hand, when the critical wind speed criterion was increased by 25% (to 25 m s1), more stands were expected to have a significant risk compared to the baseline wind speed of 20 m s1. Thus, the total length of vulnerable edges increased in both Problems 2 and 4 (66 and 119%); whilst the timber harvest decreased (34%) in Problem 2 (Table 3) compared to critical wind speed 20 m s1.
The harvested stands in Problem 4, over the 30-year simulation, were almost the same for all the three critical wind speed criteria when the problems had the same timber harvesting target (Fig. 6). With the critical wind speed criterion of 15 m s1, 91% of the harvested stands in Problem 4 were the same as with criterion of 20 m s1. The percentage of the same clear-cuts was 88% for critical wind speed criterion of 25 m s1. The high similarity is because there were many young stands, and most stands fulfilling the cutting criteria had to be cut during the 30 years to satisfy the harvesting objective. However, the clear-cut stands in Problem 4 often differed in the timing of cutting within the 30-year simulation (Fig. 6). In cases of 15 and 25 m s1, at most 50% of the clear-cut stands of
Fig. 6. The effect of 25% change in critical wind speed criterion on the spatial pattern of clear-cut when aiming at minimizing vulnerable edges with harvest of 12,000 m3/10 years (Problem 4, B and C), as compared to 20 m s1 critical wind speed criterion (A).
H. Zeng et al. / Forest Ecology and Management 241 (2007) 189–199
197
Table 3 Percentage change in objective variables as affected by a 25% change of critical wind speed criterion compared to baseline of 20 m s1 Wind speed 15 m s1
Variables
Wind speed 25 m s1
Problem 2
Problem 4
Problem 2
Problem 4
93 96 100
93 100 86
148 7 44
34 209 113
Average vulnerable edges
96
93
66
119
Harvest, 1st period Harvest, 2nd period Harvest, 3rd period
66 33 183
<1 <1 <1
11 25 88
<1 <1 <1
94
<1
34
<1
Vulnerable edge, 1st period Vulnerable edge, 2nd period Vulnerable edge, 3rd period
Total harvest
Table 4 Percentage change vulnerable edges as affected by a 25% change in harvested timber compared to baseline of 12,000 m3/10 years in Problem 4 Variables
Harvest 9000 m3/10 years
Harvest 15,000 m3/10 years
Vulnerable edge, 1st period Vulnerable edge, 2nd period Vulnerable edge, 3rd period
30 37 65
17 85 1
24
23
Average vulnerable edges
a 10-year period were the same as the clear-cut stands with critical wind speed criterion of 20 m s1. When the timber production objective was decreased to 9000 or increased up to 15,000 m3/10 years compared to the baseline harvest of 12,000 m3/10 years, there were small increments in the total length of vulnerable edges of the whole optimization period (Table 4). Therefore, changing the harvest level alone is not a sufficient way to reduce the risk. It should be noted, however, that the harvest objective of 15,000 m3/10 years could not be fulfilled since there were not enough old stands satisfying the clear-cut criteria. 4. Discussion and conclusions In today’s forest planning, management problems are diverse and complex (Pukkala and Kurttila, 2005). An example of this complexity is the effects of management on the risk of wind damage over time, which should be taken into account in careful planning (e.g. clear-cut regimes; see Zeng et al., 2006). It is not simple to assess the impacts of clear-cuts on the risk of wind damage and find an optimal clear-cut regime related to simultaneous timber harvesting objectives based on traditional methods. This study presented a first attempt to employ heuristic optimization techniques together with a forest growth model (SIMA), mechanistic wind damage model (HWIND) and GIS software (ArcGIS) to solve this type of planning problems. We compared three different heuristic techniques, namely simulated annealing (SA), tabu search (TS) and genetic algorithms (GA) when optimizing clear-cut schedules and patterns for minimal or maximal wind damage with or without an even flow of harvested timber.
The heuristics utilized in this work are commonly used in forest planning problems (Borges et al., 2002; Pukkala and Kurttila, 2005). GIS software, such as ArcGIS, which was used in this study, offers tools to define the neighborhood between forest stands (polygons) and link the forest boundary (arc) to its left and right forest stands based on topology. The vector data of the forest could, therefore, be directly processed in the integrated approach. The output results were more approximate to actual situations. The three heuristic techniques output rather similar results for all the planning problems. However, tabu search was found, on the average, to perform better than simulated annealing and genetic algorithms in Problem 4, which most resembles the reallife forest management problems (minimizing the risk of wind damage combined with timber production). On the other hand, Bettinger et al. (2002) found that simulated annealing performed better than the other two heuristics in wildlife planning problems; and Palahi et al. (2004), Pukkala and Kurttila (2005) suggested that genetic algorithms were the best methods for solving the most difficult spatial problems. However, the optimization problems and implementations of the algorithms differed between these studies. In general, an overall performance ranking of different heuristic techniques is impossible (Crowe and Nelson, 2002). In addition, parameter settings can greatly affect the performance of different algorithms. It should be kept in mind that the development of forest stands is variable since some processes are stochastic (e.g. the uncertainty of environmental factors). Only the averaged stand development from the SIMA simulation was used in order to simplify optimization. More complicated methods may be needed in the future to study both the uncertainty of timber production and the risk of wind damage. In our case, the planning problems that focused solely on either minimizing the length of edges at risk (Problem 2), or maintaining an even flow of harvested timber (Problem 5), or combined both objectives (Problem 4), were realistic planning problems unlike those in which the length of vulnerable edges was maximized (Problems 1 and 3). However, Problems 1 and 3 represented the maximum impacts of forest harvesting on the risk of wind damage at forest edges. As demonstrated in Problems 1 and 3, improper clear-cut regimes would significantly increase the risk of wind damage.
198
H. Zeng et al. / Forest Ecology and Management 241 (2007) 189–199
With a proper intensity, interval and placement of cuttings, it is possible to reduce the risk of wind damage in a forest. As suggested in this study, the total length of vulnerable edges could be reduced by: (i) aggregating clear-cuts (i.e. decrease the total length of edges); (ii) locating clear-cuts at the edges of young stands (i.e. tree height <10 m) or at the edges of stands with high critical wind speeds; (iii) making the landscape smooth in terms of stand height. In addition, clustering the clear-cut stands of the same period will decrease the costs of logging operations (Pukkala and Kurttila, 2005). However, the requirement for an even-flow of harvesting may limit the possibilities to decrease the risk of wind damage (measured as the total length of vulnerable edges) as was demonstrated in this work (see Problem 4 compared to Problem 2). The optimal solution was found to be quite sensitive to the criterion of critical wind speed. Therefore, it is useful to know how a change in this criterion affects the optimization solution. This information will help forest managers to predict the impacts of different storms on the stands in a region. It should also be noted that when minimizing the risk of wind damage without setting any specific harvest objectives (Problem 2), the amount of harvested timber does not always increase when the critical wind speed criterion is decreased and vice versa. At the forest unit level, the optimized clear-cut regimes also depend on the age structure and spatial distributions of permanent gaps and old stands. The harvesting criteria and even-flow harvesting target controlled the flexibility of selecting clear-cut stands. Since, the study area used in this work had a large proportion of young stands, most of the harvested stands were the same in the whole 30-year period even when the critical wind speed criterion was changed by 25%. More flexibility in rotation length and periodical cutting target may be needed when optimizing the harvesting patterns in more windy areas in order to avoid the risks. Moreover, the results of optimization are sensitive to the weights of different criteria in the objective function which depend on the preferences of forest owners. The optimal clear-cut pattern is also affected by topography, which has an influence on the local wind climate (Zeng et al., 2004, 2006). However, it is complicated to calculate the local wind climate and difficult to embed it into the optimization program. Fortunately, topography is not a significant factor in Finnish conditions as Finland is generally a flat country. Thus, this study focused on the impact of forest structures on the risk of wind damage at forest edges. Simplifications were also made regarding the effect of gap sizes. In reality the gap sizes differ in different directions of the same gap and even in different locations of the same edge (Zeng et al., 2006). However, a constant gap size (10 times the tree heights) was used to simplify the calculations. This might overestimate the risk of edge stands adjoining small gaps. Furthermore, the total length of vulnerable edges used in this work as an indicator of the risk of wind damage represents the first occurrence of wind damage. If a storm lasts long enough, the trees located inside the forest may also be uprooted or broken. Moreover, the framework built in this work should also be expanded in the future so that commercial thinning will be
applied in addition to final harvest when assessing the risk of wind damage related to forest planning. Acknowledgements This work is related to the research carried out under the Finnish Centre of Excellence Program (2000–2005) at the Centre of Excellence for Forest Ecology and Management (Project No. 64308), led by Academy Prof. Seppo Kelloma¨ki, University of Joensuu, Faculty of Forestry. It was also partly funded through the SUNARE Research Program promoted by the Academy of Finland (2001–2004), under the project ‘‘Silvicultural strategies for managing wind and snow-induced risks in forestry’’ (SilviRisks, Project No. 52724). The support from the Academy of Finland, the National Technology Agency (Tekes) and the University of Joensuu is gratefully acknowledged. The authors would also like to thank Mr. Juha Hiltunen, Forest Centre Pohjois-Savo, for providing the forest stand data (X-forest-data) for the area. Mr. David Gritten is acknowledged for checking the English of the manuscript. References Ancelin, P., Courbaud, B., Fourcaud, T., 2004. Development of an individual tree-based mechanical model to predict wind damage within forest stands. For. Ecol. Manage. 203, 101–121. Bettinger, P., Sessions, J., Boston, K., 1997. Using tabu search to schedule timber harvest subject to spatial wildlife goals for big game. Ecol. Model. 94, 111–123. Bettinger, P., Boston, K., Sessions, J., 1999. Combinatorial optimization of elk habitat effectiveness and timber harvest volume. Environ. Model. Assess. 4, 143–153. Bettinger, P., Graetz, D., Boston, K., Sessions, J., Chung, W., 2002. Eight heuristic planning techniques applied to three increasing difficult wildlife planning problems. Silva Fenn. 36 (2), 561–584. Borges, J.G., Hoganson, H.M., Falcao, A.O., 2002. Heuristics in multi-objective forest planning. In: Pukkala, T. (Ed.), Multi-objective Forest Planning. Kluwer Academic Publishers, Dordrecht, pp. 119–151. Boston, K., Bettinger, P., 1999. An analysis of Monte Carlo integer programming, simulated annealing and tabu search for solving spatial harvest scheduling problems. For. Sci. 45, 292–301. Boston, K., Bettinger, P., 2002. Combining tabu search and genetic algorithm heuristic techniques to solve spatial harvest schedule problems. For. Sci. 48 (1), 35–46. Coutts, M.P., 1986. Components of tree stability in Sitka spruce on peaty gley soil. Forestry 59 (2), 173–197. Crowe, K., Nelson, J., 2002. An indirect search algorithm for harvest scheduling under adjacency constraints. For. Sci. 49 (1), 1–11. Dahlin, B., Sallna¨s, O., 1993. Harvest scheduling under adjacency constraints— a planning problem study from the Swedish sub-alpine region. Scand. J. For. Res. 8, 281–290. Falcao, A.O., Borges, J.G., 2001. Designing an evolution program for solving integer forest management scheduling models: an application in Portugal. For. Sci. 47 (2), 158–168. Falcao, A.O., Borges, J., 2002. Combining random and systematic search heuristic procedures for solving spatially constrained forest management scheduling models. For. Sci. 48 (3), 608–621. FMI (Finnish Meteorological Institute), 2003. Weather statistics of the storms in Finland (online). Available from http://www.ilmatieteenlaitos.fi/saa/tilastot_21.html (cited March 16, 2003). FragStats, 2006. FragStats documentation (online). Available from http:// www.umass.edu/landeco/research/fragstats/documents/fragstats_documents.html (cited November 14, 2006).
H. Zeng et al. / Forest Ecology and Management 241 (2007) 189–199 Gardiner, B.A., 1995. The interactions of wind and tree movement in forest canopies. In: Coutts, M.P., Grace, J. (Eds.), Wind and Trees. Cambridge University Press, U.K, pp. 41–59. Gardiner, B.A., Stacey, G.R., Belcher, R.E., Wood, C.J., 1997. Field and wind tunnel assessments of the implications of respacing and thinning for tree stability. Forestry 70 (3), 233–252. Gardiner, B.A., Peltola, H., Kelloma¨ki, S., 2000. Comparison of two models for predicting the critical wind speeds required to damage coniferous trees. Ecol. Model. 129, 1–23. Heinonen, T., Pukkala, T., 2004. A comparison of one- and two-compartment neighborhoods in heuristic search with spatial forest management goals. Silva Fenn. 38 (3), 319–332. Kelloma¨ki, S., Va¨isa¨nen, H., 1997. Modelling the dynamics of the forest ecosystem for climate change studies in the boreal conditions. Ecol. Model. 97, 121–140. Kelloma¨ki, S., Va¨isa¨nen, H., Ha¨nninen, H., Kolstro¨m, T., Lauhanen, R., Mattila, U., Pajari, B., 1992. Sima: a model for forest succession based on the carbon and nitrogen cycles with application to silvicultural management of the forest ecosystem. Silva Carelica 22, 1–91. Kolstro¨m, M., 1998. Ecological simulation model for studying diversity of stand structure in boreal forests. Ecol. Model. 111, 17–36. Laiho, O., 1987. Metsiko¨iden alttius tuulituhoille Etela¨-Suomessa. (Susceptibility of forest stands to wind throw in southern Finland). Folia For. 706, 1– 24 (In Finnish with English summary). Lockwood, C., Moore, T., 1993. Harvest scheduling with spatial constraints, a simulated annealing approach. Can. J. For. Res. 23, 468–478. Lohmander, P., Helles, F., 1987. Windthrow probability as a function of stand characteristics and shelter. Scand. J. For. Res. 2 (2), 227–238. Lu, F., Eriksson, L.O., 2000. Formation of harvest units with genetic algorithms. For. Ecol. Manage. 130, 57–67. Matala, J., Hynynen, J., Miina, J., Ojansuu, R., Peltola, H., Sieva¨nen, R., Va¨isa¨nen, H., Kelloma¨ki, S., 2003. Comparison of a physiological model and a statistical model for prediction of growth and yield in boreal forests. Ecol. Model. 161, 95–116. Neustein, S.A., 1965. Windthrow on the margins of various sizes of felling area. Report on forest research for the year ended March 1964. Forestry Commission, pp. 166–171. Nordstro¨m, M., 2005. Estimation of gusty winds in RCA. Examensarbete vid Institutionen fo¨r Geovetenskaper. ISSN 1650-6553 Nr 101, p. 4. ¨ hman, K., 2000. Creating continuous areas of old forest in long-term forest O planning. Can. J. For. Res. 19, 715–724. Palahi, M., Pukkala, T., Pascual, L., Trasobares, A., 2004. Examining alternative landscape metrics in ecological forest landscape planning: a case for capercaillie in Catalonia. Invest. Agrar. Sist. Recur. For. 13, 527–538. Pellikka, P., Ja¨rvenpa¨a¨, E., 2003. Forest stand characteristics and wind and snow induced forest damage in boreal forest. In: Proceedings of the International
199
Conference on Wind Effects on Trees, University of Karlsruhe, Germany, September 16–18, 2003, p. 8. Peltola, H., 1996a. Swaying of trees in a response to wind and thinning in a stand of Scots pine. Boundary-Lay. Meteorol. 77, 285–304. Peltola, H., 1996b. Model computations on wind flow and turning moment by wind for Scots pines along the margins of clear-cut areas. For. Ecol. Manage. 83, 203–215. Peltola, H., Kelloma¨ki, S., Va¨isa¨nen, H., Ikonen, V.P., 1999. A mechanistic model for assessing the risk of wind and snow damage to single trees and stands of Scots pine, Norway spruce, and birch. Can. J. For. Res. 29, 647– 661. Petty, J.A., Swain, C., 1985. Factors influencing stem breakage of conifers in high winds. Forestry 58, 75–84. Petty, J.A., Worrell, R., 1981. Stability of coniferous tree stems in relation to damage by snow. Forestry 54 (2), 115–128. Pukkala, T., Kurttila, M., 2005. Examining the performance of six heuristic optimisation techniques in different forest planning problems. Silva Fenn. 39 (1), 67–80. Rao, M.N., Waits, D.A., Neilsen, M.L., 2000. A GIS-based modelling approach for implementation of sustainable farm management practices. Environ. Model. Softw. 15, 745–753. Slodicak, M., 1995. Thinning regime in stands of Norway spruce subjected to snow and wind damage. In: Coutts, M.P., Grace, J. (Eds.), Wind and Trees. Cambridge University Press, pp. 436–447. Talkkari, A., Kelloma¨ki, S., Peltola, H., 1999. Bridging a gap between a gap model and a physiological model for calculating the effect of temperature on forest growth under boreal conditions. For. Ecol. Manage. 119, 137–150. Talkkari, A., Peltola, H., Kelloma¨ki, S., Strandman, H., 2000. Integration of component models from the tree, stand and regional levels to assess the risk of wind damage at forest margins. For. Ecol. Manage. 135, 303–313. UNECE/FAO, 2000. Forest Products Annual Market Review. United Nations Economic Commission for Europe (Geneva), Food and Agriculture Organization of the United Nations (Roma). Vena¨la¨inen, A., Zeng, H., Peltola, H., Talkkari, A., Strandman, H., Kelloma¨ki, S., 2004. Simulations of the influence of forest management on wind climate on a regional scale. Agric. For. Meteorol. 123, 149–158. Zeng, H., Peltola, H., Talkkari, A., Vena¨la¨inen, A., Strandman, H., Kelloma¨ki, S., Wang, K., 2004. Influence of clear-cutting on the risk of wind damage at forest edges. For. Ecol. Manage. 203, 77–88. Zeng, H., Peltola, H., Talkkari, A., Vena¨la¨inen, A., Strandman, H., Wang, K., Kelloma¨ki, S., 2006. Simulations of the influence of clear-cuttings on the risk of wind damage on a regional scale over a 20-year period. Can. J. For. Res. 36, 2247–2258. Zeng, H., Talkkari, A., Peltola, H., Kelloma¨ki, S., in press. A GIS-based decision support system for risk assessment of wind damage in forest management. Environ. Model. Softw.
The use of heuristic optimization in risk management of wind damage in forest planning Hongcheng Zeng *, Timo Pukkala, Heli Peltola Faculty of Forestry, University of Joensuu, P.O. Box 111, FI-80101 Joensuu, Finland Received 8 March 2006; received in revised form 7 December 2006; accepted 11 January 2007
Abstract In this work heuristic techniques were used with a forest growth model (SIMA), mechanistic wind damage model (HWIND) and GIS software (ArcGIS) in order to manage the risk of wind damage in forest planning. The study optimized clear-cut regimes taking into account the risk of wind damage and timber harvest over a 30-year simulation (planning) period in a forest located in central Finland. To demonstrate the effect of management goals related to wind damage, the amount of stand edges at risk was either minimized or maximized with or without even-flow targets of harvested timber. The three heuristic techniques included in the preliminary tests (simulated annealing, tabu search, and genetic algorithms) produced rather similar results for the planning problems. Tabu search performed slightly better than simulated annealing and genetic algorithms, and was therefore used in the subsequent analyses. The optimizations showed that the risk of wind damage could be decreased by aggregating clearcuts and avoiding clear-cuts at the edge of stands with a high possibility of being damaged. The even-flow timber harvesting objective limited the possibilities of minimizing the risk of wind damage. In addition, the optimization of clear-cut regimes was sensitive to the criterion of critical wind speed that bisected the stands into risky and non-risky ones. # 2007 Elsevier B.V. All rights reserved. Keywords: Clear-cut; Genetic algorithms; GIS; Integrated approach; Simulated annealing; Tabu search
1. Introduction Wind-induced damage is a continuous cause of economic loss in forests. For example, in Europe about 180 million m3 of timber was levelled by wind during storms in December 1999 (UNECE/ FAO, 2000). Recently in southern Sweden about 70 million m3 of timber was lost in a winter storm in 2004 (Nordstro¨m, 2005). Also in Finland, over 7 million m3 of timber was lost in November 2001 (Pellikka and Ja¨rvenpa¨a¨, 2003). The economic impact of wind damage is particularly severe in managed forests due to the reduction in the yield of recoverable timber, increased costs of unscheduled thinning and clear-cutting, and the necessity to deviate from the optimal cutting schedule. In principle, the susceptibility of a forest stand to wind damage is controlled by tree and stand characteristics, such as tree species, diameter, height and stand density (Coutts, 1986; Gardiner, 1995; Peltola et al., 1999). Since, these characteristics change dynamically along with forest growth, the risk of
* Corresponding author. Tel.: +358 13 251 4439; fax: +358 13 251 4444. E-mail address: [email protected] (H. Zeng). 0378-1127/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.foreco.2007.01.016
wind damage will also change (Slodicak, 1995; Zeng et al., 2006). Wind damage is most likely to be found where there are sudden changes in wind loading to which the trees are not acclimatized; such as in stands adjacent to newly clear-cut areas or in stands that have recently been heavily thinned (Neustein, 1965; Lohmander and Helles, 1987; Peltola, 1996a,b; Gardiner et al., 1997; Peltola et al., 1999). When planning the spatial patterns of clear-cuts and the management of forest edges, the fundamental issue is how clearcuts affect the local wind speed and direction of airflow at the downwind edges of the clearings, and consequently the level of risk in these conditions (Peltola, 1996a; Vena¨la¨inen et al., 2004). The risk of wind damage can be reduced at a regional scale, for example, by avoiding new edges especially in old stands and by cutting the most vulnerable stands (usually old ones, see Zeng et al., 2004). On the other hand, after the closure of regenerated gaps over time (as seedling stands grow), the risk of wind damage at the edges will decrease again (Zeng et al., 2006). Timber production objectives affect the temporal and spatial patterns of clear-cuts, which consequently affect the risk of wind damage. In recent years, statistical and process-based growth and yield models have been developed to simulate forest growth under
190
H. Zeng et al. / Forest Ecology and Management 241 (2007) 189–199
certain environmental and management conditions (e.g. Kelloma¨ki et al., 1992; Kelloma¨ki and Va¨isa¨nen, 1997; Matala et al., 2003). Mechanistic wind damage models based on tree and stand characteristics and environmental factors have been developed to predict the wind speeds needed for uprooting or breaking the stems of trees (e.g. Peltola et al., 1999; Gardiner et al., 2000; Ancelin et al., 2004). Recently, Zeng et al. (in press) embedded a forest growth model (SIMA, see Kelloma¨ki et al., 1992) and a mechanistic wind damage model (HWIND, see Peltola et al., 1999) into GIS software ArcGIS to build a decision support system (DSS). The DSS can assess the influence of certain forest management regimes (e.g. clear-cut) on the risk of wind damage at the stand and regional levels. However, it is not yet capable of optimizing the management regimes (timber harvesting) so as to minimize the risk of wind damage. On the other hand, heuristic optimization techniques are increasingly being used in forest planning (Borges et al., 2002). These techniques include simulated annealing (SA) (e.g. Dahlin ¨ hman, 2000), and Sallna¨s, 1993; Lockwood and Moore, 1993; O tabu search (TS) (e.g. Bettinger et al., 1997; Boston and Bettinger, 1999), and genetic algorithms (GA) (e.g. Lu and Eriksson, 2000; Falcao and Borges, 2001). Among others, different variations and combinations of these techniques have also been applied in forestry (Bettinger et al., 1999; Boston and Bettinger, 2002; Falcao and Borges, 2002; Heinonen and Pukkala, 2004). Unlike traditional mathematical programming, heuristic techniques have the potential to solve optimization problems with complicated spatial constraints, which are usually formulated as non-linear 0–1 integer programming problems (Boston and Bettinger, 2002). In the above context, geographical information system (GIS) can serve as a common data and analyses framework (Rao et al., 2000). It can be used to store forest data with spatial attributes, and couple models and techniques together. In addition, GIS defines the topology between polygons (e.g. forest stands) and polylines (e.g. forest edges) so that spatial calculation can be done within the software. We use, in this work, optimization methods to include the risk management of wind damage into forest planning, in addition to the objectives concerning timber harvest. For this purpose, heuristic optimization techniques were employed together with a forest growth model (SIMA), mechanistic wind damage model (HWIND) and GIS software (ArcGIS). The integrated approach was used to optimize the temporal and spatial patterns of clear-cuts in relation to objectives concerning the risk of wind damage and timber harvest over a 30-year simulation (planning) period in a forest located in central Finland. The risk of wind damage was either minimized or maximized with or without an even-flow target of harvested timber. These problems correspond to maximum and minimum impact of harvests on the risk of wind damage at forest edges. 2. Material and methods 2.1. Study site and forest database The forest area employed in this study represents a typical boreal forest in central Finland (638010 N; 278480 E). It was
mostly dominated by Scots pine (Pinus sylvestris) and Norway spruce (Picea abies) stands, but some birch (Betula spp.) and other broad-leaved stands were also present. The site was surveyed in 2001 and included 395 ha of forests and 46 ha of open terrain (i.e. lakes, fields and clear-cut areas). The 395 ha of forest consisted of 142 ha Scots pine (76 stands), 225 ha Norway spruce (158 stands), 26 ha of birch (27 stands) and 2.5 ha other broad-leaved species (5 stands). The area has an undulating terrain with some small hills and altitudes ranging between 90 and 170 m above sea level. In this work, GIS software ArcGIS 9 was used to store forest stands including their boundaries. Since trees located at forest edges were expected to have the highest risk of wind damage in Finnish conditions, only stands adjoining gaps were considered to have risk. The risk of wind damage was represented by the length of vulnerable edges (edges at risk). If a stand adjoined a gap and its critical wind speed was lower than the critical speed criterion (e.g. 20 m s1), the boundary between the stand and the gap was considered as a vulnerable edge. The relationship between forest stands and their boundaries were based on topology and created in ArcGIS. Each stand boundary segment was appended with its length, and left and right polygon identifiers. They were imported to the optimization algorithm in addition to the forest growth and harvest volume data. The optimal temporal schedule and spatial pattern of the clear-cuts, output by the optimization algorithm, was correspondingly imported to ArcGIS. In this way, all the clear-cut stands and the most vulnerable edges could be visualized on the maps. 2.2. Simulation of treatment alternatives 2.2.1. Simulation of stand dynamics with SIMA The growth and yield model SIMA (Kelloma¨ki et al., 1992) was used to simulate the growth and yield of treatment alternatives of stands. In the model, the mass growth (including foliage, branches, stem and roots) of each tree in a stand is calculated based on diameter growth, which is limited by temperature conditions and the availability of light, soil moisture and nitrogen (Kelloma¨ki et al., 1992). The mortality of the trees in a stand is controlled both by stand age and minimum allowable growth rate of trees (Kelloma¨ki et al., 1992). After clear-cut the stand was regenerated artificially by giving the initial seedling stand properties regarding tree species, stand density (number of trees per hectare) and diameter of seedlings. The properties of the SIMA model with its parameters and inputs and the validity of its outputs, have been described in detail by Kelloma¨ki et al. (1992), Kolstro¨m (1998) and Talkkari et al. (1999). In this work, we simulated the dynamics (forest growth with or without a clear-cut) of forest stands over a 30-year period. During the 30-year planning period, there may be no clear-cut, or a clear-cut alternatively took place at either the 5th, 15th or 25th year of the simulation. Therefore, each stand might have a maximum of four alternative schedules. The stands, which did not exceed clear-cut criteria at the 5th, 15th or 25th year, had number of alternative schedules less than 4. The criteria, which specified whether a clear-cut was allowed or not, were mean
H. Zeng et al. / Forest Ecology and Management 241 (2007) 189–199
diameter at breast height (DBH) and age. The clear-cut was simulated if the stand’s DBH exceeded the DBH criterion or its age exceeded the age criterion. The clear-cut criterion of DBH was set at 30 cm for Scots pine, and 28 cm for Norway spruce and birch; while the age criterion was 80 years for Scots pine and Norway spruce and 70 years for birch. After clear-cut, artificial regeneration was applied so that the stand was planted with seedlings of the same tree species which were previously growing there (2000 seedlings/ha for Scots pine and Norway spruce, and 1600 for birch). No other management practices took place during the simulation period. Because birth and death of trees are stochastic processes in SIMA, each schedule was simulated 50 times, and the average results (tree and stand variables) were used as inputs for the HWIND simulations and heuristic optimization. 2.2.2. Calculation of critical wind speeds for stands with HWIND The mechanistic wind damage model HWIND (Peltola et al., 1999) was used to describe the mechanistic behavior of Scots pine, Norway spruce and birch trees under wind loading. In the model, a tree is assumed to be uprooted if the maximum bending moment (due to forces by wind and gravity) exceeds the resistance of the root-soil plate (Peltola et al., 1999). Similarly, the stem is assumed to be broken if the breaking stress exceeds the critical value of the modulus of rupture (Petty and Worrell, 1981; Petty and Swain, 1985; Peltola et al., 1999). This makes it possible to calculate the minimum wind speed needed for uprooting or stem breakage (critical wind speed). The model outputs the mean critical wind speeds, lasting for 10 min at 10 m above the ground level, at which trees are uprooted and broken. The inputs of the model are tree species, average tree height and diameter at breast height (DBH), stand density (which were SIMA outputs in this work), in addition to distance from the forest edge and gap size (the length of gap in the direction of wind). The properties of the HWIND model, its parameters, inputs and the validity of its outputs for podzol soil conditions in Finland, have been discussed in detail by Peltola et al. (1999), Gardiner et al. (2000) and Talkkari et al. (2000). The gaps refer not only to clear-cut stands, but also water areas, open fields and seedling stands with an average tree height less than a defined criterion (2 m in this study). The gap size was assumed to be 10 times the average tree height at stand edge. This outputs the maximum risk (i.e. the lowest critical wind speed) in regard to gap size (Peltola et al., 1999). Furthermore, the critical wind speed of birch was simulated without leaves, to correspond to the time from late autumn to early spring, when most storms occur in Finland. The critical wind speed was calculated for each schedule and each stand with height 10 m in HWIND at the 5th, 15th and 25th year. These critical wind speeds were used to represent the risk of wind damage of the stand when it is located at the edges (adjoining a gap). The critical wind speeds were not calculated for young stands with height <10 m because these stands need very high wind speeds to be at risk. The critical wind speed of 20 m s1 was used as the baseline criterion for defining stands that were at risk since a typical range of wind speeds
191
(e.g. 14–25 m s1 for 10 min) have been found to cause damage under Finnish conditions (Laiho, 1987; Talkkari et al., 2000; Pellikka and Ja¨rvenpa¨a¨, 2003; FMI, 2003). 2.3. Optimization of clear-cut regimes 2.3.1. Heuristic optimization methods Three different heuristics, i.e. simulated annealing, tabu search, and genetic algorithms, were used to find the optimal combination of the stand’s treatment schedules. These techniques have been previously described in detail by Heinonen and Pukkala (2004) and Pukkala and Kurttila (2005), and the parameters of the heuristics used in this work were also based on the experience gained in those studies. Simulated annealing and tabu search are local improvement methods. A change of the solution (forest plan) is called a move. In this work, a move was equal to making two simultaneous changes in the current solution, i.e. the treatment schedule was changed simultaneously in two stands. All solutions that can be obtained with one move form the neighborhood of the current solution. The neighborhood used in this study could be called a two-stand neighborhood because the solution differs in two stands from its neighbor solutions. The two-stand neighborhood has been found to be a better approach in spatial problems than the more commonly used one-stand neighborhood (Heinonen and Pukkala, 2004). Simulated annealing uses the best of a set of random combinations of stands’ treatment schedules as the initial solution. A candidate move consists of first selecting two random stands and then a random schedule per stand. The selected schedules replace the schedules that are currently in the solution. Moves that improve the objective function value are maintained. Non-improving moves are maintained with a probability of p ¼ expððU new U old Þ Ti1 Þ, where Ti is the current ‘‘temperature’’ and U is the objective function value. The ‘‘temperature’’ defines the probability of accepting a candidate solution poorer than the current solution. During the optimization process the temperature is gradually decreased so that at the end of the search the likelihood of accepting inferior moves is close to zero. The temperature cools according to a cooling schedule, which is implemented by multiplying the current temperature with a parameter less than one to get the next temperature. A certain number of candidate moves (iterations) are tested in every temperature. The number of tested moves in each temperature may change when the temperature decreases so that the search could be intensified as the process cools. In this study, the search was stopped when a user-specified stopping temperature was reached or a certain number of consecutive temperatures (5 in the analyses of this study) went without any change in the solution. The parameters of simulated annealing used were: number of random searches to produce an initial solution (we used 20, i.e. 0.1N, where N is the number of stands), starting temperature (0.00035, i.e. 0.1/ N), cooling multiplier (0.9), freezing (stopping) temperature (0.0000175, i.e. initial temperature/20), number of iterations (attempted moves) in the initial temperature (286, i.e. N), and
192
H. Zeng et al. / Forest Ecology and Management 241 (2007) 189–199
an iteration multiplier to get the number of iterations in the next temperature (1.05). Compared to simulated annealing, tabu search looks for the neighboring solution space before accepting one change in the solution. The production of a set of candidate moves and accepting one of them is repeated for many iterations. Typical of tabu search is also tabu lists. This study used only recency-based lists that memorize the most recent moves, and prevented them from being used again for some time (iterations). Schedules that participated in the move were kept in the tabu list for a certain number of iterations. This number was the initial tabu tenure of the schedule. An iteration reduced the tabu tenures of all schedules by one. A schedule could again participate in a move once its tabu tenure had decreased to 0. The best non-tabu move of the inspected candidates was accepted; or the one with the shortest tabu tenure if all candidates were in the tabu list. If a candidate move yielded a solution better than the previous best, it was accepted even if the move was tabu. The initial tabu tenure of a schedule that enters the solution may be different from the tabu tenure of a leaving schedule. Tabu search was stopped when a certain number of iterations were completed. The tabu search algorithm used in this study had four parameters: number of iterations (1440, i.e. 5N + 10), number of candidate moves per iteration, given as a percentage of the total number of treatment schedules of stands (54, i.e. 10% of the 545 schedules that were simulated for the stands), initial tabu tenure of a leaving schedule (exit tabu tenure) (14, i.e. N/30 + 5), and initial tabu tenure of a schedule that enters the solution (entry tabu tenure) (2, i.e. initial exit tabu tenure/5). Unlike simulated annealing and tabu search, the search process of genetic algorithms is not based on neighborhood search. Instead, genetic algorithms are based on an initial population of solution alternatives, their evaluation and their breeding. Each iteration (named as a generation) has a set of alternative solutions called parent chromosomes. Two of these parent chromosomes were selected to generate a new chromosome for the next generation. One chromosome was selected with a probability proportional to its ranking; the other was chosen randomly with an equal probability for all the remaining chromosomes. The two selected parent chromosomes were processed by crossing over (combining parts of two chromosomes) and mutation (random change in one or several genes, or stands) giving birth to a new chromosome (offspring). In the incremental genetic algorithm technique used in this study, the new chromosome replaced one chromosome of the current population. The removed chromosome was selected based on its ranking, the probability of removal being highest for chromosomes that had low objective function values. The parameters of genetic algorithms were: population size (50 solutions in this study), number of iterations, or generations (1072, i.e. 2N + 500), probability of mutation at first iteration (0.5), and probability of mutation at last iteration (2.0). The probability of a mutation for intermediate iterations was obtained with linear interpolation. A probability of 0.5 means that one random stand (gene) is mutated with a probability of 0.5. A probability of 2.0 means two random stands are mutated with a probability of 1.0.
2.3.2. Objective functions In our work, the purpose of optimization was to demonstrate the approach of integrating the management of the risk of wind damage into forest level optimization, and to illustrate the effect of risk considerations on optimal landscape configuration. For this purpose, five very different sets of management objectives were assumed, ignoring the possible irrelevance of some problem formulations in forestry practice: (1) the risk of wind damage was maximized as the only objective (Problem 1); (2) the risk of wind damage was minimized as the only objective (Problem 2); (3) the risk of wind damage was maximized with an even-flow target of harvested timber (Problem 3); (4) the risk of wind damage was minimized with an even-flow target of harvested timber (Problem 4); (5) even-flow of harvested timber was the only objective (Problem 5). The objective function was an additive utility function formulated as follows: U ¼ w11 u11 ðE1 Þ þ w12 u12 ðE2 Þ þ w13 u13 ðE3 Þ þ w21 u21 ðH 1 Þ þ w22 u22 ðH 2 Þ þ w23 u23 ðH 3 Þ (1) where U is total utility, wi j and uij are the importance and subutility function, respectively, of objective i in management period j (i = 1, 2; j = 1, 2, 3), Ej is the percentage of vulnerable edges (with critical wind speeds <20 m s1) in the middle of management period j, Hj is the total timber harvest during period j. In Problems 1 and 2, objective weights w21 , w22 , and w23 were 0 and weights w11 , w12 , and w13 were all 0.333 (1/3); while in Problem 5 weights w11 , w12 , and w13 were 0 and weights w21 , w22 , and w23 were all 0.333 (1/3). In Problems 3 and 4 all the weights were equal to 0.167 (1/6). In real-life simulation, the weights could be different according to the requirements of forest managers. In Problems 1 and 3, the sub-utility for risk of wind damage increased linearly as a function of the length of vulnerable edges (Fig. 1A), and decreased in Problems 2 and 4 (Fig. 1B) The sub-utility functions for harvesting had an ascending-descending shape with the sub-utility increasing until the target cut of 12,000 m3 was reached, after which the sub-utility started to decrease (Fig. 1C). There were no strict constrains. The risk of wind damage was defined as the percentage of the total length of vulnerable stand edges of the total length of all the stand boundaries of the forest (E). When a stand adjoined gaps and had a critical wind speed <20 m s1, part of its boundary, which adjoined the gaps, was considered as having a risk of damage (i.e. treated as vulnerable edges). Therefore, maximizing the risk of wind damage means trying to lengthen forest edges with critical wind speeds <20 m s1; while minimizing risk was trying to shorten forest edges with critical wind speeds <20 m s1. Moreover, fragmentation statistics were calculated for the forests to compare the difference of landscape configuration regarding tree height. The fragmentation metrics ContrastWeighted Edge Density (CWED, see FragStats, 2006) was applied in this work to represent the fragmentation at the
H. Zeng et al. / Forest Ecology and Management 241 (2007) 189–199
193
Fig. 2. The average percentage of the vulnerable edge of the 30-year planning period in the solutions of simulated annealing (SA), tabu search (TS) and genetic algorithms (GA). ( ) Maximize vulnerable edge; ( ) minimize vulnerable edge; ( ) maximize vulnerable edge, cut 12,000 m3/10 years; ( ) minimize vulnerable edge, cut 12,000 m3/10 years.
3. Results 3.1. Comparison of different heuristics All the three heuristic optimization methods compared in this study output logical and rather similar results (Fig. 2). The timber harvesting objectives (Problems 3–5) were almost fulfilled in each period. The difference observed between the actual harvest volume and target level (i.e. 12,000 m3/10 years) was very small in each period, ranging in Problems 3–5 from 16 to 13 m3/10 year in simulated annealing, from 80 to 34 and from 52 to 11 m3/10 years in tabu search and genetic algorithms, respectively. When Problem 4 was solved 10 times with each technique, tabu search performed slightly better than simulated annealing and genetic algorithms (Fig. 3). The further analysis of optimization results was therefore only based on the outputs of tabu search. Fig. 1. The shapes of sub-utility functions used in the study. ‘‘Min’’ and ‘‘Max’’ are, respectively, the minimum and maximum possible values of an objective variable (within the decision space), and ‘‘Target’’ is the target value (12,000 m3).
3.2. Effects of risk management and timber harvest objectives When minimizing the occurrence of vulnerable edges was the only objective (Problem 2), there were still some clear-cuts
landscape level. The CWED evaluated the fragmentation based on the contrast of the neighbor stands in terms of the tree height. 2.4. Sensitivity analysis As quite different speeds of winds were found to cause damage in Finnish forests, the optimizations were also done by changing the critical wind speed criterion by 25% (alternatively using speeds of 15 and 25 m s1). The different critical wind speed criteria corresponded to the storms with different speeds or different windy areas. Since, only minimizing vulnerable edges (Problems 2 and 4) were a realistic task in forest management, the sensitivity analyses were carried out with Problems 2 and 4. Similarly, the timber harvest objective was also changed by 25% (using 9000 and 15,000 m3/10 years) in Problem 4 to find out how a change in timber harvesting objective affected the results.
Fig. 3. The average percentage of vulnerable edges and its range of the 10 runs for Problem 4 (minimizing the length of edges at risk combined with even-flow harvest target of 12,000 m3/10 years) output by simulated annealing, tabu search and genetic algorithms.
194
H. Zeng et al. / Forest Ecology and Management 241 (2007) 189–199 Table 2 Number of gaps and average gap area of different 10-year periods in each planning problem Planning problems
Fig. 4. The percentage of vulnerable edge (A), and fragmentation of the forest landscape (B) for maximizing or minimizing the length of edges at risk with or without even-flow harvest target of 12,000 m3/10 years (Problems 1–4), and the planning with only even-flow harvest target (Problem 5). ( ) 1st period; ( ) 2nd period; ( ) 3rd period.
(Table 1 and Fig. 4A). Those clear-cut stands were clustered to avoid the increment of edges. The forest had therefore few gaps with generally a large mean area (Table 2). The landscape gradually became smooth (Fig. 4B), because new gaps were placed next to young stands (Fig. 5). Some old stands were not cut due to their small risks (critical wind speeds 20 m s1), even though they adjoined the gaps (Fig. 5). If the minimization of vulnerable edges was combined with the even-flow of timber production (Problem 4), there were more vulnerable edges (Fig. 4A). The clear-cut stands in Problem 4 were not as well clustered as in Problem 2 so that more gaps appeared (Table 2). Compared to Problem 2 over the 30-year planning period, the forest in Problem 4 had on average nearly four times more vulnerable edges and 132% more total harvested timber. Therefore, the even-flow clear-cuts limited the minimization of the length of vulnerable edges.
1
2
3
4
5
1st period Number of gaps Mean area (ha)
17 2.4
10 2.0
26 2.3
20 2.9
20 3.2
2nd period Number of gaps Mean area (ha)
27 1.9
12 3.6
33 1.7
19 3.1
27 2.0
3rd period Number of gaps Mean area (ha)
45 1.4
9 2.8
24 2.3
25 2.1
23 2.3
The forest in Problem 4 had generally fewer gaps with larger mean areas than when the risk of wind damage was maximized with the even-flow harvesting target (Problem 3) or when evenflow of timber harvesting was the only objective (Problem 5, see Table 2). Although the landscape was more fragmented in Problem 4 than in Problem 2, it was smoother than the landscapes in Problems 3 and 5 (Fig. 4B). On the other hand, if maximizing the occurrence of vulnerable edges was the only objective (Problem 1), the clear-cuts were distributed uniformly and often next to old stands and more gaps were created (Table 2). As a result, the landscape developed towards a fragmented landscape regarding tree height (Fig. 5). Furthermore, fewer clear-cuts occurred compared to the optimization with the even-flow target (Problems 3 and 4; see Table 1). There were less vulnerable edges (28%) in Problem 3 than in Problem 1, although the length of vulnerable edge was also maximized in Problem 3. Thus, the even-flow target limited the possibility to maximize the length of vulnerable edges. When the risk of wind damage was not a management objective (Problem 5), the length of vulnerable edges was quite variable. The even-flow harvesting target, however, reduced the number of old stands in the study area. Thus, the length of vulnerable edges decreased towards the end of the 30-year planning period (Fig. 4A). It may be noted that for all the problems that maximized the length of vulnerable edges, some edges adjoining gaps (height <2 m) were not susceptible for the risk of wind damage. Edge stands with tree height less than 10 m or
Table 1 The optimal harvest and final volume in tabu search solutions Planning problem
Problem 1
Problem 3
Problem 4
Problem 5
1st period (m3) 2nd period (m3) 3rd period (m3)
6,964 9,307 15,561
2,989 8,752 3,698
12,015 12,006 12,007
11,958 11,932 11,999
11,998 11,999 12,003
31,832
15,439
36,028
35,889
36,000
67,536
81,929
64,087
64,606
Total harvest (m3) 3
Final volume (m )
Problem 2
64,874 3
Note: Problem 1: maximize vulnerable edges; Problem 2: minimize vulnerable edges; Problem 3: maximize vulnerable edges, with cut of 12,000 m /10 years; Problem 4: minimize vulnerable edges, with cut of 12,000 m3/10 years; Problem 5: cut of 12,000 m3/10 years as the only objective.
H. Zeng et al. / Forest Ecology and Management 241 (2007) 189–199
195
Fig. 5. The landscape configuration regarding stand height in the middle of the first (A(1), B(1), C(1)) or the third (A(3), B(3), C(3)) 10-year period when maximizing (A) or minimizing (B) vulnerable edges without harvest target (Problems 1 and 2) or aiming at harvesting of 12,000 m3/10 years (C) (Problem 5).
critical wind speed greater than 20 m s1 were not expected to have any risk of wind damage although they were also located at edges. Young stands could therefore be located at edges without increasing the risk of wind damage of the landscape.
3.3. Effect of critical wind speed criterion and harvesting target When the critical wind speed criterion was decreased by 25% (to 15 m s1), fewer stands were expected to have a
196
H. Zeng et al. / Forest Ecology and Management 241 (2007) 189–199
significant risk compared to the baseline wind speed of 20 m s1. Therefore, the total length of vulnerable edges was significantly decreased (on average 96 and 93% in Problems 2 and 4, respectively), while the timber harvests were increased (94%) over the 30-year period in Problem 2 (Table 3), which means that the clear-cut patterns changed accordingly. On the other hand, when the critical wind speed criterion was increased by 25% (to 25 m s1), more stands were expected to have a significant risk compared to the baseline wind speed of 20 m s1. Thus, the total length of vulnerable edges increased in both Problems 2 and 4 (66 and 119%); whilst the timber harvest decreased (34%) in Problem 2 (Table 3) compared to critical wind speed 20 m s1.
The harvested stands in Problem 4, over the 30-year simulation, were almost the same for all the three critical wind speed criteria when the problems had the same timber harvesting target (Fig. 6). With the critical wind speed criterion of 15 m s1, 91% of the harvested stands in Problem 4 were the same as with criterion of 20 m s1. The percentage of the same clear-cuts was 88% for critical wind speed criterion of 25 m s1. The high similarity is because there were many young stands, and most stands fulfilling the cutting criteria had to be cut during the 30 years to satisfy the harvesting objective. However, the clear-cut stands in Problem 4 often differed in the timing of cutting within the 30-year simulation (Fig. 6). In cases of 15 and 25 m s1, at most 50% of the clear-cut stands of
Fig. 6. The effect of 25% change in critical wind speed criterion on the spatial pattern of clear-cut when aiming at minimizing vulnerable edges with harvest of 12,000 m3/10 years (Problem 4, B and C), as compared to 20 m s1 critical wind speed criterion (A).
H. Zeng et al. / Forest Ecology and Management 241 (2007) 189–199
197
Table 3 Percentage change in objective variables as affected by a 25% change of critical wind speed criterion compared to baseline of 20 m s1 Wind speed 15 m s1
Variables
Wind speed 25 m s1
Problem 2
Problem 4
Problem 2
Problem 4
93 96 100
93 100 86
148 7 44
34 209 113
Average vulnerable edges
96
93
66
119
Harvest, 1st period Harvest, 2nd period Harvest, 3rd period
66 33 183
<1 <1 <1
11 25 88
<1 <1 <1
94
<1
34
<1
Vulnerable edge, 1st period Vulnerable edge, 2nd period Vulnerable edge, 3rd period
Total harvest
Table 4 Percentage change vulnerable edges as affected by a 25% change in harvested timber compared to baseline of 12,000 m3/10 years in Problem 4 Variables
Harvest 9000 m3/10 years
Harvest 15,000 m3/10 years
Vulnerable edge, 1st period Vulnerable edge, 2nd period Vulnerable edge, 3rd period
30 37 65
17 85 1
24
23
Average vulnerable edges
a 10-year period were the same as the clear-cut stands with critical wind speed criterion of 20 m s1. When the timber production objective was decreased to 9000 or increased up to 15,000 m3/10 years compared to the baseline harvest of 12,000 m3/10 years, there were small increments in the total length of vulnerable edges of the whole optimization period (Table 4). Therefore, changing the harvest level alone is not a sufficient way to reduce the risk. It should be noted, however, that the harvest objective of 15,000 m3/10 years could not be fulfilled since there were not enough old stands satisfying the clear-cut criteria. 4. Discussion and conclusions In today’s forest planning, management problems are diverse and complex (Pukkala and Kurttila, 2005). An example of this complexity is the effects of management on the risk of wind damage over time, which should be taken into account in careful planning (e.g. clear-cut regimes; see Zeng et al., 2006). It is not simple to assess the impacts of clear-cuts on the risk of wind damage and find an optimal clear-cut regime related to simultaneous timber harvesting objectives based on traditional methods. This study presented a first attempt to employ heuristic optimization techniques together with a forest growth model (SIMA), mechanistic wind damage model (HWIND) and GIS software (ArcGIS) to solve this type of planning problems. We compared three different heuristic techniques, namely simulated annealing (SA), tabu search (TS) and genetic algorithms (GA) when optimizing clear-cut schedules and patterns for minimal or maximal wind damage with or without an even flow of harvested timber.
The heuristics utilized in this work are commonly used in forest planning problems (Borges et al., 2002; Pukkala and Kurttila, 2005). GIS software, such as ArcGIS, which was used in this study, offers tools to define the neighborhood between forest stands (polygons) and link the forest boundary (arc) to its left and right forest stands based on topology. The vector data of the forest could, therefore, be directly processed in the integrated approach. The output results were more approximate to actual situations. The three heuristic techniques output rather similar results for all the planning problems. However, tabu search was found, on the average, to perform better than simulated annealing and genetic algorithms in Problem 4, which most resembles the reallife forest management problems (minimizing the risk of wind damage combined with timber production). On the other hand, Bettinger et al. (2002) found that simulated annealing performed better than the other two heuristics in wildlife planning problems; and Palahi et al. (2004), Pukkala and Kurttila (2005) suggested that genetic algorithms were the best methods for solving the most difficult spatial problems. However, the optimization problems and implementations of the algorithms differed between these studies. In general, an overall performance ranking of different heuristic techniques is impossible (Crowe and Nelson, 2002). In addition, parameter settings can greatly affect the performance of different algorithms. It should be kept in mind that the development of forest stands is variable since some processes are stochastic (e.g. the uncertainty of environmental factors). Only the averaged stand development from the SIMA simulation was used in order to simplify optimization. More complicated methods may be needed in the future to study both the uncertainty of timber production and the risk of wind damage. In our case, the planning problems that focused solely on either minimizing the length of edges at risk (Problem 2), or maintaining an even flow of harvested timber (Problem 5), or combined both objectives (Problem 4), were realistic planning problems unlike those in which the length of vulnerable edges was maximized (Problems 1 and 3). However, Problems 1 and 3 represented the maximum impacts of forest harvesting on the risk of wind damage at forest edges. As demonstrated in Problems 1 and 3, improper clear-cut regimes would significantly increase the risk of wind damage.
198
H. Zeng et al. / Forest Ecology and Management 241 (2007) 189–199
With a proper intensity, interval and placement of cuttings, it is possible to reduce the risk of wind damage in a forest. As suggested in this study, the total length of vulnerable edges could be reduced by: (i) aggregating clear-cuts (i.e. decrease the total length of edges); (ii) locating clear-cuts at the edges of young stands (i.e. tree height <10 m) or at the edges of stands with high critical wind speeds; (iii) making the landscape smooth in terms of stand height. In addition, clustering the clear-cut stands of the same period will decrease the costs of logging operations (Pukkala and Kurttila, 2005). However, the requirement for an even-flow of harvesting may limit the possibilities to decrease the risk of wind damage (measured as the total length of vulnerable edges) as was demonstrated in this work (see Problem 4 compared to Problem 2). The optimal solution was found to be quite sensitive to the criterion of critical wind speed. Therefore, it is useful to know how a change in this criterion affects the optimization solution. This information will help forest managers to predict the impacts of different storms on the stands in a region. It should also be noted that when minimizing the risk of wind damage without setting any specific harvest objectives (Problem 2), the amount of harvested timber does not always increase when the critical wind speed criterion is decreased and vice versa. At the forest unit level, the optimized clear-cut regimes also depend on the age structure and spatial distributions of permanent gaps and old stands. The harvesting criteria and even-flow harvesting target controlled the flexibility of selecting clear-cut stands. Since, the study area used in this work had a large proportion of young stands, most of the harvested stands were the same in the whole 30-year period even when the critical wind speed criterion was changed by 25%. More flexibility in rotation length and periodical cutting target may be needed when optimizing the harvesting patterns in more windy areas in order to avoid the risks. Moreover, the results of optimization are sensitive to the weights of different criteria in the objective function which depend on the preferences of forest owners. The optimal clear-cut pattern is also affected by topography, which has an influence on the local wind climate (Zeng et al., 2004, 2006). However, it is complicated to calculate the local wind climate and difficult to embed it into the optimization program. Fortunately, topography is not a significant factor in Finnish conditions as Finland is generally a flat country. Thus, this study focused on the impact of forest structures on the risk of wind damage at forest edges. Simplifications were also made regarding the effect of gap sizes. In reality the gap sizes differ in different directions of the same gap and even in different locations of the same edge (Zeng et al., 2006). However, a constant gap size (10 times the tree heights) was used to simplify the calculations. This might overestimate the risk of edge stands adjoining small gaps. Furthermore, the total length of vulnerable edges used in this work as an indicator of the risk of wind damage represents the first occurrence of wind damage. If a storm lasts long enough, the trees located inside the forest may also be uprooted or broken. Moreover, the framework built in this work should also be expanded in the future so that commercial thinning will be
applied in addition to final harvest when assessing the risk of wind damage related to forest planning. Acknowledgements This work is related to the research carried out under the Finnish Centre of Excellence Program (2000–2005) at the Centre of Excellence for Forest Ecology and Management (Project No. 64308), led by Academy Prof. Seppo Kelloma¨ki, University of Joensuu, Faculty of Forestry. It was also partly funded through the SUNARE Research Program promoted by the Academy of Finland (2001–2004), under the project ‘‘Silvicultural strategies for managing wind and snow-induced risks in forestry’’ (SilviRisks, Project No. 52724). The support from the Academy of Finland, the National Technology Agency (Tekes) and the University of Joensuu is gratefully acknowledged. The authors would also like to thank Mr. Juha Hiltunen, Forest Centre Pohjois-Savo, for providing the forest stand data (X-forest-data) for the area. Mr. David Gritten is acknowledged for checking the English of the manuscript. References Ancelin, P., Courbaud, B., Fourcaud, T., 2004. Development of an individual tree-based mechanical model to predict wind damage within forest stands. For. Ecol. Manage. 203, 101–121. Bettinger, P., Sessions, J., Boston, K., 1997. Using tabu search to schedule timber harvest subject to spatial wildlife goals for big game. Ecol. Model. 94, 111–123. Bettinger, P., Boston, K., Sessions, J., 1999. Combinatorial optimization of elk habitat effectiveness and timber harvest volume. Environ. Model. Assess. 4, 143–153. Bettinger, P., Graetz, D., Boston, K., Sessions, J., Chung, W., 2002. Eight heuristic planning techniques applied to three increasing difficult wildlife planning problems. Silva Fenn. 36 (2), 561–584. Borges, J.G., Hoganson, H.M., Falcao, A.O., 2002. Heuristics in multi-objective forest planning. In: Pukkala, T. (Ed.), Multi-objective Forest Planning. Kluwer Academic Publishers, Dordrecht, pp. 119–151. Boston, K., Bettinger, P., 1999. An analysis of Monte Carlo integer programming, simulated annealing and tabu search for solving spatial harvest scheduling problems. For. Sci. 45, 292–301. Boston, K., Bettinger, P., 2002. Combining tabu search and genetic algorithm heuristic techniques to solve spatial harvest schedule problems. For. Sci. 48 (1), 35–46. Coutts, M.P., 1986. Components of tree stability in Sitka spruce on peaty gley soil. Forestry 59 (2), 173–197. Crowe, K., Nelson, J., 2002. An indirect search algorithm for harvest scheduling under adjacency constraints. For. Sci. 49 (1), 1–11. Dahlin, B., Sallna¨s, O., 1993. Harvest scheduling under adjacency constraints— a planning problem study from the Swedish sub-alpine region. Scand. J. For. Res. 8, 281–290. Falcao, A.O., Borges, J.G., 2001. Designing an evolution program for solving integer forest management scheduling models: an application in Portugal. For. Sci. 47 (2), 158–168. Falcao, A.O., Borges, J., 2002. Combining random and systematic search heuristic procedures for solving spatially constrained forest management scheduling models. For. Sci. 48 (3), 608–621. FMI (Finnish Meteorological Institute), 2003. Weather statistics of the storms in Finland (online). Available from http://www.ilmatieteenlaitos.fi/saa/tilastot_21.html (cited March 16, 2003). FragStats, 2006. FragStats documentation (online). Available from http:// www.umass.edu/landeco/research/fragstats/documents/fragstats_documents.html (cited November 14, 2006).
H. Zeng et al. / Forest Ecology and Management 241 (2007) 189–199 Gardiner, B.A., 1995. The interactions of wind and tree movement in forest canopies. In: Coutts, M.P., Grace, J. (Eds.), Wind and Trees. Cambridge University Press, U.K, pp. 41–59. Gardiner, B.A., Stacey, G.R., Belcher, R.E., Wood, C.J., 1997. Field and wind tunnel assessments of the implications of respacing and thinning for tree stability. Forestry 70 (3), 233–252. Gardiner, B.A., Peltola, H., Kelloma¨ki, S., 2000. Comparison of two models for predicting the critical wind speeds required to damage coniferous trees. Ecol. Model. 129, 1–23. Heinonen, T., Pukkala, T., 2004. A comparison of one- and two-compartment neighborhoods in heuristic search with spatial forest management goals. Silva Fenn. 38 (3), 319–332. Kelloma¨ki, S., Va¨isa¨nen, H., 1997. Modelling the dynamics of the forest ecosystem for climate change studies in the boreal conditions. Ecol. Model. 97, 121–140. Kelloma¨ki, S., Va¨isa¨nen, H., Ha¨nninen, H., Kolstro¨m, T., Lauhanen, R., Mattila, U., Pajari, B., 1992. Sima: a model for forest succession based on the carbon and nitrogen cycles with application to silvicultural management of the forest ecosystem. Silva Carelica 22, 1–91. Kolstro¨m, M., 1998. Ecological simulation model for studying diversity of stand structure in boreal forests. Ecol. Model. 111, 17–36. Laiho, O., 1987. Metsiko¨iden alttius tuulituhoille Etela¨-Suomessa. (Susceptibility of forest stands to wind throw in southern Finland). Folia For. 706, 1– 24 (In Finnish with English summary). Lockwood, C., Moore, T., 1993. Harvest scheduling with spatial constraints, a simulated annealing approach. Can. J. For. Res. 23, 468–478. Lohmander, P., Helles, F., 1987. Windthrow probability as a function of stand characteristics and shelter. Scand. J. For. Res. 2 (2), 227–238. Lu, F., Eriksson, L.O., 2000. Formation of harvest units with genetic algorithms. For. Ecol. Manage. 130, 57–67. Matala, J., Hynynen, J., Miina, J., Ojansuu, R., Peltola, H., Sieva¨nen, R., Va¨isa¨nen, H., Kelloma¨ki, S., 2003. Comparison of a physiological model and a statistical model for prediction of growth and yield in boreal forests. Ecol. Model. 161, 95–116. Neustein, S.A., 1965. Windthrow on the margins of various sizes of felling area. Report on forest research for the year ended March 1964. Forestry Commission, pp. 166–171. Nordstro¨m, M., 2005. Estimation of gusty winds in RCA. Examensarbete vid Institutionen fo¨r Geovetenskaper. ISSN 1650-6553 Nr 101, p. 4. ¨ hman, K., 2000. Creating continuous areas of old forest in long-term forest O planning. Can. J. For. Res. 19, 715–724. Palahi, M., Pukkala, T., Pascual, L., Trasobares, A., 2004. Examining alternative landscape metrics in ecological forest landscape planning: a case for capercaillie in Catalonia. Invest. Agrar. Sist. Recur. For. 13, 527–538. Pellikka, P., Ja¨rvenpa¨a¨, E., 2003. Forest stand characteristics and wind and snow induced forest damage in boreal forest. In: Proceedings of the International
199
Conference on Wind Effects on Trees, University of Karlsruhe, Germany, September 16–18, 2003, p. 8. Peltola, H., 1996a. Swaying of trees in a response to wind and thinning in a stand of Scots pine. Boundary-Lay. Meteorol. 77, 285–304. Peltola, H., 1996b. Model computations on wind flow and turning moment by wind for Scots pines along the margins of clear-cut areas. For. Ecol. Manage. 83, 203–215. Peltola, H., Kelloma¨ki, S., Va¨isa¨nen, H., Ikonen, V.P., 1999. A mechanistic model for assessing the risk of wind and snow damage to single trees and stands of Scots pine, Norway spruce, and birch. Can. J. For. Res. 29, 647– 661. Petty, J.A., Swain, C., 1985. Factors influencing stem breakage of conifers in high winds. Forestry 58, 75–84. Petty, J.A., Worrell, R., 1981. Stability of coniferous tree stems in relation to damage by snow. Forestry 54 (2), 115–128. Pukkala, T., Kurttila, M., 2005. Examining the performance of six heuristic optimisation techniques in different forest planning problems. Silva Fenn. 39 (1), 67–80. Rao, M.N., Waits, D.A., Neilsen, M.L., 2000. A GIS-based modelling approach for implementation of sustainable farm management practices. Environ. Model. Softw. 15, 745–753. Slodicak, M., 1995. Thinning regime in stands of Norway spruce subjected to snow and wind damage. In: Coutts, M.P., Grace, J. (Eds.), Wind and Trees. Cambridge University Press, pp. 436–447. Talkkari, A., Kelloma¨ki, S., Peltola, H., 1999. Bridging a gap between a gap model and a physiological model for calculating the effect of temperature on forest growth under boreal conditions. For. Ecol. Manage. 119, 137–150. Talkkari, A., Peltola, H., Kelloma¨ki, S., Strandman, H., 2000. Integration of component models from the tree, stand and regional levels to assess the risk of wind damage at forest margins. For. Ecol. Manage. 135, 303–313. UNECE/FAO, 2000. Forest Products Annual Market Review. United Nations Economic Commission for Europe (Geneva), Food and Agriculture Organization of the United Nations (Roma). Vena¨la¨inen, A., Zeng, H., Peltola, H., Talkkari, A., Strandman, H., Kelloma¨ki, S., 2004. Simulations of the influence of forest management on wind climate on a regional scale. Agric. For. Meteorol. 123, 149–158. Zeng, H., Peltola, H., Talkkari, A., Vena¨la¨inen, A., Strandman, H., Kelloma¨ki, S., Wang, K., 2004. Influence of clear-cutting on the risk of wind damage at forest edges. For. Ecol. Manage. 203, 77–88. Zeng, H., Peltola, H., Talkkari, A., Vena¨la¨inen, A., Strandman, H., Wang, K., Kelloma¨ki, S., 2006. Simulations of the influence of clear-cuttings on the risk of wind damage on a regional scale over a 20-year period. Can. J. For. Res. 36, 2247–2258. Zeng, H., Talkkari, A., Peltola, H., Kelloma¨ki, S., in press. A GIS-based decision support system for risk assessment of wind damage in forest management. Environ. Model. Softw.