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Incorporating landscape pattern features in a spatial harvest model Kong, Xianhua 1999

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INCORPORATING LANDSCAPE PATTERN FEATURES IN A SPATIAL HARVEST MODEL by XIANHUA KONG B.Sc, Shandong Agricultural University of China, 1982 M.Sc, Lakehead University, 1993 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS'FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in \ THE FACULTY OF GRADUATE STUDIES Department of Forest Resources Management Faculty of Forestry We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May 1999 ©Xianhua Kong, 1999 In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Forest Resources Management Faculty of Forestry The University of British Columbia Vancouver, Canada 11 ABSTRACT The primary objective of this research is to solve area-based harvest scheduling problems which not only specify the timing and location of harvesting activities, but also predict the changes in landscape structure in terms of remnant patchiness. Remnant patches are considered to be ecologically important in maintaining biodiversity on the landscape. Based on existing knowledge and experience of spatially-constrained harvest scheduling and landscape pattern models, I developed the Landscape Harvesting Scheduling model (LHS) to meet the requirements of this research. LHS has four objectives related to timber harvesting: 1) opening size, 2) timber flow, 3) road construction cost, and 4) maximum disturbance rate (denoted by percentage of total planning area). It also has three objectives related to landscape pattern: 1) remnant patch size, 2) patch shape, and 3) inter-patch distance. Each objective is represented as an individual objective. All objectives are evaluated by penalty costs. A simulation annealing algorithm was used to randomly generate solutions and converge on those with minimum total penalty costs. A number of model runs were made under different management scenarios to: 1) determine the effects of adjacency constraints (opening size, green-up period) on timber production and landscape structure, 2) determine the effects of the remnant patch constraints on the changes in landscape structure, and 3) compare the simulation results to those from the harvest simulation model, ATLAS - A Tactical Landscape Analysis System. The simulation results show that the Relaxed Adjacency (RA) rule causes less timber reduction than the Strict Adjacency (SA) rule, and that timber reduction caused by exclusion period constraints can be offset by larger opening size limit constraints. The results also show that existing spatially-constrained harvest models cause forest landscapes to lose large remnant patches after about 60% of the total planning area is cut. It is concluded that without the remnant patch constraints, either changing the spatial constraint formulation or reducing the maximum harvest rate are not effective measures for achieving the objective of retaining large patches on the landscape. The simulation results under scenarios with and without the remnant patch (RP) objectives show that the RP constraints can control the dynamic changes in remnant patches on the forest landscape. The effects of reducing cutting rate on the landscape structure were significant only after the RP constraints were applied. The remnant patch Ill constraints can also affect the total edge length at a lower cutting rate. Applying the RP constraints did not cause significant timber reduction (from 0.5 - 2.4%) compared to the scenarios without the RP constraints. The simulation results under different priorities show that setting timber harvest as the top priority caused higher average periodic timber yield at the cost of high variation in periodic road construction cost, especially high investment in the first period. Setting even periodic road cost as the top priority resulted in relatively even road cost distribution among the planning periods, but this also caused a small reduction and some variation in periodic timber harvest. Setting opening size objectives as the top priority reduced both timber harvest, and initial road construction cost compared to scenarios with timber as top priority. The advantages under opening size scenarios are relatively larger remnant patches, and relatively less variation in periodic edge length. Comparison with the ATLAS model showed the harvest schedule generated by ATLAS had a lower timber harvest (about 5.4% reduction from the timber target), and higher initial road construction cost. However, it took much less computation effort to run ATLAS. The model developed in this study can solve operational planning problems with multiple objectives, including landscape structure. Its advantage over existing models is that it incorporates landscape structure simultaneously with other forest operational issues, such as timber harvest, and road construction. Its disadvantage is that it needs a longer time to run than other harvest scheduling models. Further studies are required in this research field. The important issues suggested for future study are: incorporating landscape heterogeneity in the model, linking landscape pattern with population dynamics of specific wildlife species, and allowing multiple rotation scheduling. iv TABLE OF CONTENTS A B S T R A C T II T A B L E O F C O N T E N T S IV LIST O F F I G U R E S VIII LIST O F T A B L E S X A C K N O W L E D G E M E N T XI C H A P T E R 1 I N T R O D U C T I O N 1 1.1. A n overview of biodiversity, conservation biology, and landscape ecology 2 1.2. The evolution of forest resource management 5 1.3. The problem definition 7 C H A P T E R 2 L I T E R A T U R E R E V I E W 10 2.1. Introduction 10 2.2. Spatially-constrianed scheduling models 11 2.3. Landscape pattern models 18 2.4. What needs to be done next 22 2.4.1. Objective '. 23 2.5. Summary 24 C H A P T E R 3 D E V E L O P M E N T O F T H E L A N D S C A P E H A R V E S T S C H E D U L I N G M O D E L . . . . 26 3.1. Introduction 26 3.2. LHS formulation 27 3.3. The procedure used in constructing the model 35 3.3.1. Model input 36 V 3.3.1.1. Spatial data and attributes 36 3.3.1.2. Model parameters 36 3.3.1.3. Penalty cost coefficients 38 3.3.1.4. Objective options 38 3.3.2. Solution algorithm 38 3.3.2.1. Initial solution 39 3.3.2.2. Transition process 41 3.3.3. Model output 43 3.4. Summary 44 C H A P T E R 4 T H E I M P A C T O F S P A T I A L C O N S T R A I N T S A N D L A N D W I T H D R A W A L O N T I M B E R H A R V E S T A N D L A N D S C A P E S T R U C T U R E 45 4.1. Introduction 45 4.2. Methods 46 4.2.1. The study area 46 4.2.2. Definition of the adjacency rule in the model 48 4.2.3. The problem formulations 49 4.2.4. Analysis of landscape pattern 52 4.3. Results and discussion 52 4.3.1. Timber production 52 4.3.2. Remnant patches 56 4.3.3. Edge 60 4.4. Conclusion 64 C H A P T E R 5 I N C O R P O R A T I N G L A N D S C A P E P A T T E R N S I N T O S P A T I A L H A R V E S T S C H E D U L I N G 67 5.1. Introduction 67 5.2. Methods 68 vi 5.2.1. Landscape Harvest Scheduling model (LHS) 68 5.2.2. Case study area and management scenario formulation 69 5.2.2.1. Study area 69 5.2.2.2. Management scenario formulation 71 5.2.2.3. Quantification of remnant patches and edge 75 5.2.2.4. Timber volume and road cost 76 5.3. Results and discussion •' 77 5.3.1. Spatial analysis 77 5.3.2. The analysis of timber production and road cost under different scenarios 83 5.4. Conclusion 88 C H A P T E R 6 O P E R A T I O N A L P L A N N I N G A N A L Y S I S U N D E R D I F F E R E N T M A N A G E M E N T S C E N A R I O S 89 6.1. Introduction 89 6.2. Methodology • 91 6.2.1. The models 91 6.2.2. Simulation procedure 92 6.2.3. Case study area 94 6.2.4. Analysis methods 95 6.3. Results and discussion 96 6.3.1. Timber production and road construction costs 96 6.3.2. The changes in landscape structures and edge length 102 6.4. Conclusion 106 C H A P T E R 7 G E N E R A L C O N C L U S I O N 108 7.1. Introduction 108 7.2. Why is this research important? 108 7.3. Achievements 110 V l l 7.4. Contribution to the forest resource management planning 113 7.5. Potential future studies? 113 7.6. Conclusion 115 L I T E R A T U R E C I T E D 116 V l l l LIST OF FIGURES Figure 3.1. Diagram of the LHS structure 28 Figure 4.1. Age class distribution of the timber production area in the Penfold watershed 47 Figure 4.2. Different opening configurations 49 Figure 4.3. Periodic timber harvest by The RA and SA rules. A. 10-year-exclusion period; B. 20-year-exclusion period, and C. 30 year exclusion period 55 Figure 4.4 The number of remnant patches in each decade of harvest by scenario 57 Figure 4.5. Changes in spatial landscape structure over time under scenarios O20-P10andO100-P10 59 Figure 4.6. The number of remnant patches under different disturbance rates from 70% (DR70) to 100% (DR100) in the planning horizon (10-year-eclusion period and 40-hectare-opening) 61 Figure 4.7. The total periodic edge length by scenario 63 Figure 4.8. Edge density for maximum disturbance rates from 70% (DR70) to 100%(DR100) under 40-ha opening size and 10-yr exclusion period objective 64 Figure 5.1. Age class distribution of Elphinstone watershed 70 Figure 5.2. Remnant patch distributions (100% cutting rate) throughout the planning horizon. (A) Scenario 1, without the RP objectives, and (B) Scenario 2, with the RP objectives 77 Figure 5.3. Remnant patch distributions (90% cutting rate) throughout the planning horizon. (C) Scenario 3, without the RP objectives, and (D) Scenario 4, with the RP objectives 78 Figure 5.4. Remnant patch distributions (80% cutting rate) throughout the planning horizon. (E) Scenario 5, without the RP objectives, and (F) Scenario 6, with the RP objectives 78 ix Figure 5.5. Mean remnant patch area by planning period and by management scenario.81 Figure 5.6. The total edge length of different period under different scenarios 83 Figure 5.7. Periodic timber yield under different scenarios 84 Figure 5.8. Periodic road costs by scenario 86 Figure 6.1. Age class distribution of all of stand groups in Elphinstone watershed 95 Figure 6.2. Periodic timber production under different scenarios 97 Figure 6.3. Periodic road cost under different scenarios 99 Figure 6.4. The opening size series and mean opening area (ha) under only maximum timber flow constraints 101 Figure 6.5. The changes in landscape structure over time under different scenarios. ... 103 Figure 6.6. The mean remnant patch and opening size under different scenarios 104 Figure 6.7. The periodic edge length under different scenarios 105 X LIST OF TABLES Table 3.1. The model parameters 37 Table 4.1. The scheduling scenarios based on the combination of opening size and exclusion periods used in RA scenarios 51 Table 5.1. Penalty coefficients for model objectives 72 Table 5.2. The model parameters 72 Table 5.3. The objective formulation for 6 management scenarios 74 Table 5.4. Selected percentages of the remnant area to total remnant area for different patch groups under different scenarios 80 Table 5.5. Computation time for model formulations and datasets 87 Table 6.1. The model parameters for all management scenarios 93 Table 6.2. Objective priorities of the 3 LHS scenarios 93 Table 6.3. Average periodic timber yield and road construction cost for each scenario .97 xi ACKNOWLEDGEMENT I would like to thank my major supervisor Dr. J. D. Nelson for his guidance, encouragement, and help while this study was conducted. I also want to thank Dr. P. Marshall and Dr. T. Sullivan who are my supervisory committee members for their helpful comments and suggestions in the development of my thesis. Additional thanks go to Dr. S. Glenn for her help in my understanding the concept of conservation biology and landscape ecology. As English is my second language, I want to thank Mr. T. Shannon and Mr. W. Vrzal for partially proofreading the draft of my thesis. Also, Dr. J. D. Nelson's extra time and energy on the English in my thesis is acknowledged. I would like to thank my wife, Li Zhang, and daughter, Chao Kong for their patience and spiritual support during my study in the University of British Columbia. Finally, I acknowledge financial support from the research grants of Dr. Nelson through NSERC and FRBC. 1 CHAPTER 1 INTRODUCTION Modern forest resource management problems are characterized by conflicting and competitive demands for use of forest resources. Scheduling forest harvests used to be relatively simple when forest resources seemed abundant, and timber production was the only objective. However, the picture has completely changed today, and forest resource management is in a difficult position. On the one hand, forest resources have become relatively scarce, and on the other, in response to changing environmental values and new information, the policies and objectives of forest management are continuously being modified to reflect public expectations. The situation challenges the capability of forest resource managers to develop and implement land use plans which consider both timber and non-timber uses under the principles of sustainability. Resource managers are responsible for managing forests not only to meet the demands of various users, but also to maintain ecological integrity and forest productivity. In the meantime, the continuous development of separate disciplines has introduced novel ideas and concepts to forest resource management. For example, terms, such as biodiversity, sustainability, landscape, and ecosystem management, have appeared (or re-appeared with new meaning) in forest resource management during the past 10 years. The growth of new knowledge has great potential for altering the basic principles and guidelines of forest resource management. 2 This chapter contains 3 main parts that integrate these new concepts with existing methods: 1. an overview of biodiversity, conservation biology, and landscape ecology, 2. an overview of the evolution of forest resource management planning, and 3. the problem definition. 1.1. An overview of biodiversity, conservation biology, and landscape ecology Forests play an important role in protecting the environment. People used to focus on the function of forests in protecting the physical environment, such as air, soil, and water. Today, while physical environmental protection is still important, more attention is paid to the role of forests in maintaining biological diversity, which has become a worldwide environmental issue. "Biodiversity is the diversity of life in all its forms and all levels of organization " (Hunter, 1990). The life forms refer to plants, animals and microorganisms, and all levels of diversity refer to genetic diversity, species diversity, and ecosystem diversity. The concept of biodiversity provides a scientific basis for such disciplines as conservation biology and landscape ecology. Conservation biology is a multiple disciplinary science that studies how to maintain biodiversity on earth (Hunter 1996, Primack 1993). There are two goals for conservation biology: 1) to investigate human impacts on biological diversity, and 2) to develop practical approaches to prevent the extinction of species. To conservation 3 biologists, a species has intrinsic value without reference to anything but its own existence, so they pay more attention to those species that are endangered, threatened, and rare. So called coarse and fine filters are used to prevent species from extinction (Shafer 1990). Coarse filters refer to setting aside lands to preserve species, and fine filters refer to preserving specific habitats for endangered, threatened, and rare species. Since loss of habitat, and habitat fragmentation and degradation are considered to be the main factors causing species extinction (Hunter 1996, Primack 1993), various models (such as island biogeography) are used to investigate human impact on biodiversity. Landscape ecology can be simply defined as the study of spatial patterns of ecosystems and interactions between ecosystems in a landscape. The landscape is defined as a heterogeneous area consisting of repeated interactive and interconnected ecosystems (Forman and Godron 1986). Landscape ecology involves large spatial and temporal scales. It seeks to understand the relationship between ecosystem structures and functions, and to understand landscape connectivity. The field of landscape ecology is very broad, and involves many interests, such as measurements of heterogeneity, the structure and function of patches, corridors, edges, landscape planning models, and many more. Landscape ecology provides an alternative approach to managing for biodiversity. The patch-matrix-corridor model provides tools for measuring landscape pattern or structure, hence evaluating biological and spatial relationship between landscape elements (Forman and Godron 1981, Forman and Godron 1986). By using the landscape approach, the problems of managing species habitats have become that of 4 managing landscape pattern, and maintaining landscape stability as a precondition for preserving biodiversity (Forman and Godron 1986). Forest landscape pattern is important for wildlife habitats, since wildlife have various home ranges, and make use of different habitats (Swanson et al. 1990). The idea has been generally accepted that wildlife ecology and behavior are strongly dependent on the nature and pattern of landscape elements (Siderits 1975, Forman and Godron 1986). Within a forest landscape, timber management causes the fragmentation of habitat, which is a primal threat to many wildlife species (Wilcove et al. 1986). Therefore, the viability of wildlife species is closely related to the alteration of their habitats. Conservation biology and landscape ecology, in turn, have shed light on natural resource management in terms of understanding the value of managing for biodiversity, and exploiting alternative approaches to solving the problem of resource management planning. The idea of preserving biodiversity has made forestry professionals change their view about resources, especially wildlife resources. Based on the principle of biodiversity, the definition of wildlife tends to be changed from "game animal species only" to "any living things wild, including the species of flora, fauna, and microorganisms" (Hunter 1990). Accordingly, the objective of wildlife management has been changed to maintain viable populations for all species (MacAuthur and Wilson 5 1967, Harris 1984, Shafer 1990). To conventional wildlife professionals who pay more attention to game species, clear-cutting is often beneficial because it creates forage habitats for game species. However, for today's wildlife managers, clear-cutting disturbs the habitats of some non-game species which require contiguous old growth forests, and preserving these habitats is more important than creating habitats for only game species. This is important because old growth forests could be easily lost or fragmented by human activities, which have already caused habitat loss, fragmentation, degradation, and hence mass extinction of species. Maintaining biodiversity has become a top priority in forest resource management. 1.2. The evolution of forest resource management A central part of forest management is the scheduling and planning of management activities, i.e., choosing among alternative courses of action (Davis and Johnson 1987, Leuschener 1990). The evolution of forest resource management could be described as a process that continuously solves problems by absorbing new knowledge and concepts. It has experienced three phases, namely, timber-only, multiple-use or integrated resource management, and landscape-level management, with the latter phase overlapping (not replacing) the former. Each phase has been associated with a set of mathematical models used to assist management planning. For timber-only management, the objective was to obtain sustainable timber yield while maintaining a desired normal state in terms of age-class distribution. The idea of a normal forest was put forward by European foresters in the 1800s, who emphasized even 6 flow as a means of maintaining the balance between harvest and growth. Since that time many different formulas and analytical techniques (e.g. linear programming and simulation models) have been used to schedule harvest activities. It is a desirable goal for foresters to obtain an equivalent amount of timber in a recurrent, predictable cycle. However, timber-only management ignores non-timber values of forests (i.e. wildlife, visual quality, hydrology), and forest practices often result in conflicts between timber and non-timber uses (Bowes and Krutilla 1989). Therefore, multiple-use management arose as a means of coordinating these various uses. Multiple-use management requires forest planning to extend beyond the timber-only objective into multiple goals. The focus of forest management evolved from simply making the harvest schedule to planning a variety of activities on the forest. Multiple-use management attempts to balance supply and demand of forest resources among different social groups. There are two different modeling approaches to solving multiple-use problems. One approach deals directly with multiple uses, such as timber, wildlife, and visual quality. Such an approach has been used in linear and goal programming models. Another approach deals indirectly with various uses. It employs spatial constraints to control the timing, size, and location of harvest blocks in order to maintain opportunities for non-timber uses (wildlife, visual quality etc.). Current studies which use this approach will be reviewed in detail in the next chapter. Compared with the above two phases, landscape management has its own characteristics. First, it embodies the concepts of conservation, and preservation of 7 biodiversity as one of its most important objectives. Second, it tries to interpret the structure and function of landscape patterns. Third, it considers both how to use forest resources, and the impact of using these resources on the landscape structure. Landscape management has moved from the paradigm of traditional forest resource management, and provided foresters, planners, and other related professionals with alternative approaches for managing forest resources. Although the notion of landscape management is relatively new, its application has generated a great interest in resource management, perhaps because landscape management is assumed to use more reasonable approaches to address resource issues, especially the preservation of biological diversity (Samson et al. 1991). Studies of landscape management as well as landscape pattern models will be reviewed in the next chapter. 1.3. The problem definition This research aims to develop a mathematical framework for solving resource management planning problems. As environmental issues, such as biodiversity, occupy a more important position in forest resource exploitation, landscape approaches seem to be in a position to replace traditional approaches. Hence a management plan should not only allocate forest resources in time and space, but also account for changes in landscape structure throughout the planning horizon. Landscape pattern can be used as either a criterion in evaluating management activities, or as a constraint in resource management planning. Few existing forest scheduling models, which will be reviewed in the next chapter, incorporate landscape patterns simultaneously with other forest 8 operational issues, such as timber, road cost, etc. The schedules generated from these models indicate where, and when to harvest each forest stand throughout the planning area, and how much can be gained from harvesting. However, these models do not indicate what happens to the structure of forested landscape following the harvest. Therefore, more effort should be made to incorporate the landscape pattern attributes in the spatial scheduling model. My thesis contains the following chapters: A. In Chapter 2,1 review the literature on area specific models and landscape pattern models, together with the concept of landscape pattern features. Following the literature review, I specify the objectives of this research. B. In Chapter 3,1 describe the model development. First, I describe the method of measuring landscape pattern features and incorporating them, together with timber harvest constraints, in the model. Second, I describe the simulated annealing algorithm used for obtaining optimized solutions. C. Real management problems in British Columbia are used as case studies in chapters 4, 5, and 6. There are two datasets used. One created for the Penfold watershed was used in chapter 4, and another created for the Elphinstone watershed was used in chapters 5 and 6. In Chapter 4,1 define two adjacency rules (strict and relaxed) and compare the impact of different adjacency constraints (opening size and green up period) on timber 9 production and landscape pattern. In Chapter 5,1 analyze the results of the model runs under different management scenarios. In Chapter 6,1 compare the results simulated under different priorities, and also compare the model performance with the discrete simulation model, ATLAS - A Tactical Landscape Analysis System (Nelson etal. 1995). D. In Chapter 7, general conclusions about this studies are made and suggestions for future research are presented. 10 CHAPTER 2 LITERATURE REVIEW 2.1. Introduction Mathematical models are important tools for aiding decision-making in forest resource management. They enable resource managers to view outcomes of different land use strategies implemented across large planning areas, and over long time periods. Hence, the models are regarded as "abstract representations of the real world " (Buongiorno and Gilless, 1987). Ideas on how to manage forest resources are changing. A timber-only policy is no longer accepted by policy makers, forest professionals, and the general public. Non-timber issues, such as biodiversity, wildlife, recreation, hydrology and environment, are closely related to forests, and these non-timber values have appreciated and gained prominence as much as timber (Bowes and Krutilla,1989). Even the term "multiple-use" received criticism for presumptively emphasizing timber volume over other uses (Barton 1994). The idea of biodiversity and landscape structure has gradually permeated the forest resource management domain, and become a popular topic among resource managers. The goal of management has switched from "sustained yield" to "maintaining ecological integrity". To catch up with this trend, model developers have tried to incorporate knowledge of ecosystem and landscape ecology into their models. 11 Geographic information systems (GISs) provide tools for model developers to spatially allocate forest resources, and analyze landscape structure. This chapter will: 1. review spatially-constrained scheduling models, 2. review landscape pattern models together with knowledge of landscape pattern attributes, and 3. specify the objective of this research based on current research on spatial harvest scheduling and landscape pattern models. 2.2. Spatially-constrained scheduling models. Forest land provides a basis for many uses beyond timber (wildlife, recreation, hydrology, etc.). The most effective means to manage these uses is to manage forest land. For example, wildlife managers usually do not do anything directly to wildlife (except for endangered species). Instead, they manage wildlife habitats in order to maintain viable populations of the species concerned (Mealy et al., 1982). Therefore, so called multiple-use or integrated resource management planning is essentially a decision-making problem about allocating forest lands to various timber and non-timber uses. Since timber harvesting is a major influence on all forest uses, a harvest schedule is a necessary part of a forest resource management plan. 12 To make a harvest schedule for a relatively large area, resource managers usually use models for assistance because of the problem's complexity (Davis and Johnson, 1987). Based on spatial detail, these models can be classified into strata-based and area-specific models (Nelson and Brodie 1990). Traditional forest management models, such as Timber Ram (Navon 1971), MUSYC (Johnson and Jones 1979), and FORPLAN (USDA 1988), were strata-based models which generate harvest schedules for a series of harvesting activities in each stratum in a time sequence. Since the strata are formed by aggregating forest stands with similar attributes (species, age, site class, etc.), strata-based models fail to account for spatial dimensions. Hence, they are unable to specify the geographical location of each harvesting activity (Hokans 1983, Nelson and Brodie 1990). Although different levels of stratification are possible in FORPLAN version 2, the model's capability for solving spatial problems is still limited (Shugart and Gilbert 1986). A strata-based model is suitable for strategic planning problems where the areas analyzed are large, but not adequate for operational planning problems where the location and timing of harvest needs to be clearly defined (Nelson and Brodie 1990, Jones et al. 1991a). An area-specific model is able to provide solutions for operational problems because solution variables are spatially defined, and a harvest schedule from the model can indicate when and where harvest activities to take place. Moreover, it is also able to analyze economic efficiency with regard to the location and timing of timber harvest, road construction and other operational alternatives, such as silvicultural systems, logging systems, and road standards (Jones et al. 1991a). 13 The concept of spatial constraints has been embodied in legislation for managing forest resources in the USA. For example, the US National Forest Management Act of 1976 and other policy statements sought to limit opening size in order to maintain the visual and ecological quality of public lands (Hokans 1983). In Canada, since the provinces have jurisdiction and powers in the field of planning and the administration of natural resources, each province has its own legislation for natural resources management. In British Columbia, maximum opening size and green-up period were not clearly specified until the enactment of the Forest Practices Code, where spatial constraints are regarded as the principles of integrated resource management (BCMOF 1995). Such legislative actions have encouraged the development of area-specific models to help comply with regulations on harvests and landscapes. The primary purpose of using area-specific models is to deal with multiple-use objectives in forest resource management planning. By spatially controlling harvest activities, opportunities for non-timber uses, such as visual quality and wildlife habitats, can be maintained or arranged temporally throughout the planning horizon. In the literature, spatial constraints are generally defined in two ways. One is called the exclusion rule, which states that once an individual unit is selected for harvesting, adjacent units (neighbours) are excluded from harvesting until the selected unit is greened-up (O'Hara et al. 1989). Another is called the opening size rule, which is different from the exclusion rule in that adjacent units can be harvested within an exclusion period as long as the total area of those units does not exceed a maximum opening size limit (Clements et al. 1990). Although no reports were found that compare 14 the effects of both rules on harvest scheduling, it seems that the opening size rule is less binding than the exclusion rule because there are more opportunities for the model to select harvest units. Various ways have been tried to formulate area-specific models and get optimal solutions. The pioneering work is attributed to Thompson et al. (1973), who incorporated spatial constraints into linear programming (LP) in order to obtain wildlife habitat objectives. Their work was followed by Mealey et al. (1982), who also used LP to solve habitat dispersion problems. Spatial constraints were stated explicitly by using a checkerboard model in the work of Mealey et al. (1982). However, those LP approaches were criticized for resulting in non-integer solutions, which are difficult to implement (O'Hara et al. 1989). To improve the situation, model developers turned to other approaches, including integer programming (IP) (Bare et al. 1984), and mixed integer programming (MIP) (Kirby et al. 1986, Nelson and Brodie 1990, Jones et al. 1991a). Roise (1990) used a penalty function in multicriteria nonlinear programming to find solutions under adjacency constraints. These approaches are limited by problem size since the number of constraints grow exponentially as the numbers of stands increase. When these methods are applied to operational problems, the problem size becomes impracticably large and complex (O'Hara et al. 1989). To overcome the limitation of problem size, researchers have tried two approaches. 15 The first approach is to reduce the number of adjacency constraints by using various techniques (Meneghin et al. 1988, Jones et al. 1991b, Torres and Brodie 1990, Yoshimoto and Brodie 1994b, Murray and Church 1995). A significant reduction of adjacency constraints from the conventional formulation was reported by Jones et al. (1991b), but they failed to test the constraints in solving practical problems (Snyder and ReVelle 1996). Murray and Church (1995) found a 73% reduction from the number of pairwise constraints by using constraint aggregation. Snyder and ReVelle (1996) formulated different integer programming models by using different types of adjacency constraints. They were able to solve grid packing problems which are relatively large (625 regular-shaped cells). Finding an optimal solution with certainty using existing computer software is the advantage of these approaches. However, these approaches for reducing constraints can not completely overcome the limitation of problem size for operational problems (extensive planning areas and multiple planning periods). The second approach to overcoming the limitation of problem size is to use heuristic approaches. O'Hara et al. (1989), Clements et al. (1990), and Nelson and Brodie (1990) used random search algorithms in heuristically finding good solutions in area-based planning problems. A random search technique was compared with the mixed integer program for solving the same harvest scheduling problem by Nelson and Brodie (1990), who found that the solutions by random search were as much as 4% lower than that of the mixed integer programming (MIP) method. Alternative algorithms were tried to obtain better solutions, such as, simulated annealing and Tabu search (Lockwood and Moore 1992, Dahlin and Salinas 1993, Murray and Church 1994). Although the 16 solutions from such algorithms are superior to that from the random search, they do not guarantee optimal solutions (Murray and Church 1994). However, heuristic approaches are easy to formulate, and need less computational efforts to solve problems (Nelson and Brodie 1990, Murray and Church 1994). Some simulation models (Baskent and Jordan 1991, Nelson et al. 1995) were developed to schedule timber harvest and road construction under adjacency constraints or called adjacency neighborhoods (Baskent and Jordan 1991). Although such models are capable of handling large problem sizes and quickly generate a solution, they are unable to optimize the problem solution. Applying adjacency constraints can result in some reduction of timber flow over the planning horizon. Jamnick and Walters (1992) used a spatial model to disaggregate strata-based timber harvest schedules into operational plans. As a result, they could only allocate about 80% of the area scheduled by their strata-based model into a schedule subject to adjacency restrictions. Daust and Nelson (1993) examined 27 hypothetical forests for evaluating the impact of block size and exclusion period on sustainable yield. Their results showed that the allowable harvest rate developed using adjacency constrained models may be 4% - 24% lower than those using strata-based models, and that the exclusion period was the factor accounting for the most reduction. A similar result was obtained by Yoshimoto and Brodie (1994b), when they found that the reduction caused by exclusion period constraints could be up to 40%. 17 The objectives of most spatial models are to optimize timber yield or timber related benefits. They account for wildlife and aesthetic opportunities simply by introducing spatial constraints. Therefore, those models are unable to identify optimal solutions for all of the uses (Hof and Joyce 1992). To overcome this, Hof and Joyce (1992) developed non-linear formulations to obtain spatial optimization for wildlife and timber in a single time period. Later on, similar approaches were proposed to optimize timber and wildlife (Hof and Joyce 1993), and to optimize wildlife populations (Hof et al. 1994). Those techniques focused on spatial optimization for wildlife habitats, but ignored adjacency restrictions (i.e. opening size and exclusion period) which are highly relevant to the problem. Moreover, the application of their models were limited to a small problem size with a specific cell-configuration (square, circle, etc.); the capability of their models for solving a real operation planning problem is limited by both cell configuration and problem size. The environmental consequences of applying spatial constraints in forestry have aroused the attention of many researchers in various fields. The concern is that spatially-constrained harvesting can create dispersed landscape patterns, thus causing serious wildlife habitat fragmentation problems as well as negative environmental consequences (Franklin and Forman, 1987, Swanson et al. 1990). In response to this problem, alternative approaches such as landscape models were developed and studied. 2.3. Landscape pattern models 18 After a forest is disturbed by natural factors or human activities, it progresses through a set of serai stages, involving one set of species at a younger stage replaced by others at older stages (Hunter 1990). Each serai stage provides habitats for a different set of wildlife species. Therefore, keeping a balance among serai stages in terms of their area and distribution is essential for maintaining biological diversity in the forest landscape (Hanson et al. 1991). Human disturbance (harvesting) tends to interrupt such a balance by depleting mature or old forest stands at a fast rate. Consequently, those species that are associated with mature or old growth forest would suffer from habitat loss or degradation, and would be threatened with local extinction (Rosenberg and Raphael 1986, Hunter 1996). A tremendous number of species have been extirpated directly or indirectly by human activities (Shafer 1990). Maintaining biodiversity has become an important objective of natural resource management. One of the means of preserving biodiversity is to develop reasonable landscape patterns (Harris 1984, Forman and Godron 1986). Forest landscape patterns are largely shaped by forest management practices and natural disturbances. Timber management, especially clear-cutting, is a major human activity causing forest ecosystem fragmentation. While dispersed habitats are appreciated by wildlife species that require multiple habitats, those habitats may be avoided by other species (usually non-game) that require non-fragmented ecosystems as habitats. The effects of changed landscapes on wildlife habitats have captured the 19 interests of wildlife researchers. Theories and tools are required to study and evaluate changes in the landscape structure. Landscape ecology is a new scientific discipline (Naveh and Lieberman, 1980, Forman and Godron 1986). Forest landscapes are studied based on the theory of "island" biogeography (MacArthur and Wilson 1967, Harris 1984). Remnant patches left by timber management are considered as habitat "islands" in the landscape. The relationship between wildlife populations and attributes of remnant patches has been intensively studied (Fahrig and Merriam 1993, Kattan and Giraldo 1994, Yahner 1988, Temple and Cary 1988). Just like an oceanic island, habitat island size (area) is an important factor for predicting wildlife species dynamics. A large patch tends to contain more species than a small patch (Harris 1984, Forman and Godron 1981). In the case of species that require interior habitats, species extinction is closely related to the patch size (Shafer 1991, Kattan and Giraldo 1994, Bissonette at al. 1991). In a small patch, ecosystem dynamics are affected significantly by the environmental and biotic changes associated with edges. Consequently, little or no core area is left to support interior species. Rosenberg and Raphael (1986) suggested that the definition of an old-growth stand should include stand area as a criterion. However, researchers are not certain about the minimum ecosystem size for retaining characteristics of species diversity and species composition (Saunders et al. 1991, Forman and Godron 1986). There are debates about whether a larger patch could accommodate more species than a collection of smaller patches equal in total area (Saunders et al. 1991, Hunter 20 1990). Large remnant patches are important in maintaining viable species populations, and serve as source areas for recolonization of surrounding patches. Small remnant patches are equally important in providing both source and sink as well as "stepping-stones" for species dispersal (Shafer 1990, Forman and Godron 1986, and Forman 1995). However, a fragmented landscape caused by logging tends to have few large remnant patches. A number of models that predict landscape changes with forest harvesting have been created and supported by knowledge of landscape ecology. Wallin et al. (1994) compared two clear-cutting patterns (dispersed and aggregated) in changing landscape structure. They found that the dispersed pattern created more edges and smaller remnant patches than the aggregated pattern. Moreover, their study also showed that "once established, the landscape pattern created by dispersed disturbance is difficult to erase...". Li et al. (1993), who examined five cutting patterns, found the aggregated pattern was an effective way to reduce forest fragmentation. Baskent and Jordan (1996) developed a landscape management model which was later used in a case study to examine the impact of different harvest patterns on landscape fragmentation by Baskent (1997). He showed that the scattered (dispersed) harvest pattern caused more fragmentation than the aggregated pattern. Gustafson and Crow (1994) developed a model for examining the effects of logging on landscape structure and the spatial distribution of cowbird brood parasitism. Their results suggested that forest opening sizes needed to be over 10 ha in order to reduce 21 fragmentation, and parasitism rates. Another model developed by Gustafson and Crow (1996) to evaluate the impact of different harvesting intensity on habitat fragmentation showed that even though timber production was reduced by 60%, spatial components of habitat for interior species were not improved significantly. They suggested that some area be withdrawn from the timber base in order to create habitats for interior species. Their opinion was supported by Li et al. (1993) and Cox and Sullivan (1995). Using a checkerboard model, Franklin and Forman (1987) examined the ecological consequences of a dispersed cutting pattern. Their results showed that a fragmented landscape developed by a dispersed cutting pattern will rapidly lose large remnant patches which are habitats for interior species. The landscape is also more susceptible to natural damage (such as windthrow, fire) because more edges between forested and clear-cut area are created by the cutting pattern. Besides remnant patch size, patch shape is a variable to be considered in the context of edge. Different shapes of a patch have different amount of edges, hence different amount of patch interior. Two patches of the same size but with different shapes may have different wildlife dynamics (Fahrig and Merriam 1993). However, the shape factor can be ignored if the patch size is large (Saunders et al. 1991). Distance between patches and connectivity between patches are measures of potential interaction and dispersion of the wildlife population. Finally, wildlife dynamics depend partly on the habitat quality in a fragmented landscape. Since forest management activities have great potential for altering landscape 22 patterns, and wildlife habitat, production of wildlife can be regarded as a forest landscape issue (Swanson et al. 1990) 2.4. What needs to be done next Guidelines and policies of natural forest resource management have to be revised frequently as our knowledge about natural systems evolves. For example, wildlife management used to concentrate mainly on game-species, and a great many publications are found regarding habitats of ungulate species (i.e., deer, moose and elk). Numerous guidelines for timber harvesting have been developed at different administration levels for creating habitats of game species in logging operations. Such guidelines led resource managers to consider the use of spatial scheduling models for integrated resource planning because spatial harvesting can create dispersed habitats for wildlife game species (Thompson et al. 1973, Mealy et al. 1982), and spatial harvesting can maintain visual quality of the forest land (Hokans 1983). As new knowledge, such as biodiversity, landscape ecology, and ecosystem management, is introduced into the resource management domain, guidelines and policies have to be modified in order to embody this knowledge. Under such circumstances, resource managers have to pay attention to all the species in order to reach the goal of maintaining biological diversity. Hunter (1990) classified wildlife species into three categories based on their habitat needs, namely, common-habitat species, multihabitat species, and special-habitat species. Common-habitat species, such 23 as openland birds, can use a variety of habitats. Multihabitat species, such as game species, require different habitats for food, cover, etc. Special-habitat species use relatively uniform habitats, which often means mature or old-growth forest. To meet the habitat requirement of all species, resource managers should be able to predict the changes in landscape patterns caused by timber harvesting (Swanson et al. 1990). Therefore, landscape pattern is another objective which should be considered in management planning, and another constraint (objective) for formulating harvesting scheduling models. More efforts are required in the development of such models since existing models either do not deal with the landscape pattern issue, like spatially-constrained timber models, or only handle the landscape pattern issue, and overlook others (timber, transportation costs, etc.), like the landscape pattern models. 2.4.1. Objective The primary objective of this research is to solve area-based harvest scheduling problems which not only specify the timing and location of harvesting activities, but also predict the changes in landscape structure in terms of remnant patchiness. Since no existing models met the requirement of my research, I developed my own model. The model is able to handle landscape spatial pattern objectives simultaneously with other objectives. To accomplish the primary objective, I will use case studies to: 1) investigate the impact of different management policies, such as opening size, green-up period, and disturbance rates on changes of landscape pattern. 24 2) schedule timber harvest, road construction under multiple objectives, to investigate the impact of the remnant patch objective on timber production, road costs, and landscape pattern. 3) formulate management scenarios by using different planning priorities to observe economic trade-offs among management objectives. 4) compare results with those obtained by using another simulation method that does not consider landscape pattern (i.e., ATLAS), and identify the relative advantages and disadvantages. 2.5. Summary Models are important tools to assist in resource management planning. The growth of natural science knowledge and experience forces model developers to modify models. Strata-based models are still useful in long term strategic planning for large areas. Spatially-constrained scheduling models were developed to deal with operational planning, which is area specific in terms of geographic location and timing of timber harvesting (Jones 1991a, Nelson and Brodie 1990). The aim of using adjacency constraints (opening size, exclusion period) in formulating spatial models is to integrate non-timber uses (visual quality and wildlife habitat, etc.) with timber production (Hokans 1983). Harvesting according to dispersed patterns suggested by spatial 25 scheduling models is effective in creating habitats for those wildlife species which require multiple habitats, but it causes a quick loss of habitats for some interior species because of accelerated habitat fragmentation. The dispersed patterns created by following the suggested schedules have negative environmental consequences. Current spatial harvesting models have not fully incorporated knowledge of landscape ecology. As a result, their solutions are insensitive to changes in landscape pattern. Landscape models can help resource managers or policy makers in formulating management strategies. However, these models are not sufficient for all factors (social, ecological, economical, and environmental) required for real operational problems. For modern forest resource management, an optimal solution requires not only maximizing timber volume but also controlling the rate of fragmentation. These are conflicting phenomena. The problem can be solved only by compromising between these management objectives. The formulation of a model which can simultaneously deal with both landscape pattern and harvest scheduling is the topic of this research. 26 CHAPTER3 DEVELOPMENT OF THE LANDSCAPE HARVEST SCHEDULING MODEL 3.1. Introduction In chapter 2, it was observed that current models for solving spatial harvest scheduling problems do not account for the impact of timber harvesting on the landscape pattern, and therefore do not meet the requirements of landscape management. In this chapter, I will describe how to develop a model which incorporates landscape pattern in spatial harvest scheduling. I call this model the Landscape Harvest Scheduling (LHS) model. I will concentrate on patches caused by timber harvesting. A patch is defined as "a relatively homogeneous nonlinear area that differs from its surroundings" (Forman and Godron 1981). Two terms will be used to describe the status of patches in a landscape; 1) disturbance patch, and 2) remnant patch. A disturbance patch refers to a recently clear-cut area, and a remnant patch refers to either original old growth or second-growth which is older than a specified age. Through timber harvesting and forest growth, the patchiness of a landscape will undergo a series of changes in terms of number, area, and status of patches. At the beginning of fragmentation, the whole landscape can be regarded as one remnant patch, thereafter, disturbed patches will be introduced (harvest), and a landscape mosaic will be formed with disturbed, and remnant patches. In developing LHS, I make the following assumptions: 27 1. clear-cutting is the only disturbance factor. Other factors, such as different silvicultural systems (patch cutting, and selection cutting) and natural disturbance regimes (fire, insect, disease, and windthrow, etc.) are not considered, 2. regeneration starts immediately following harvesting, 3. edge effect is assumed to be greatest when two adjacent patches are in striking contrast in their structure (Harris 1988). Therefore, the model only calculates the amount of edge between remnant patches and recently harvested patches (<20 years), 4. every point in a forest landscape is equal to one another with respect to providing habitat for wildlife regardless of tree species and site class. Thus, the aggregation of remnant patches is only based on stand age, and is not affected by tree species and site class, and 5. remnant patches are more important in enhancing biodiversity than other patches. Although other patches are also important to biodiversity, remnant patches are critical for species population development (Hunter 1990). Therefore, the most attention is given to the alteration of remnant patches. 3.2. LHS formulation As shown in Figure 3.1, there are seven objectives in LHS: timber flow, adjacency, transportation cost, maximum disturbance rate, patch size, patch shape, and inter-patch 28 Start In put Timber flow cH Adjacency Road cost CM Maximum disturbance rate CH Landscape pattern Patch size Patch shape Inter-patch distance c 1 H C H C H Solution Algorithm Ou tput > < End Figure 3.1. Diagram of the LHS structure. distance. The 'switch' sign ( + ) means that an individual objective can be switched on or off to meet the requirements of different planning problems. Three attributes (i.e. patch size, shape, and inter-patch distance) form the components of the landscape pattern objective. This section will describe how the objectives are introduced into the model. LHS was to be formulated to solve area-based planning problems which have multiple objectives. Since no common unit could be found to evaluate all the objectives, 29 penalty functions were defined for each objective. Therefore, whether or not an objective is satisfied depends on the evaluation of its penalty cost. The optimal solution of LHS is the one that minimizes the total penalty cost. LHS is formulated as follows: Z is the objective function value (total penalty cost) N is the number of objectives Xj is the total penalty cost of objective i Since there are 7 objectives in the model, N is equal to seven. The total penalty costs of each objective were determined as follows: 1. Total timber flow penalty cost (TFPC). TFPC values a solution in terms of meeting the desired volume flow for all planning periods. The penalty will be given to deviations from the periodic timber target. It is evaluated by the following formula: N Minimize Z = £ X (3.1) i=l where, T F P C = E G * |(V. - TGT.) * 100%/TGTi (3.2) where, 30 C; is the penalty cost coefficient for deviation from the timber target in each period T is the number of planning periods Vj is the timber volume in period i (m3) TGTj is the timber target in period i (m3) 2. Total opening size penalty cost (OSPC). In the model, two or more adjacent polygons can be harvested within a green-up period so as to form a disturbance patch. The desired opening size is predetermined as an area range. An opening that falls into this range has no penalty cost, otherwise, it results in a penalty. OSPC is calculated as: T NP T MP OSPC = X Z C 2 l A A* + E Z C 2 S ^ (3-3) p=\ j=l p=l i=\ where, C21 is the coefficient for an opening size larger than the desired area range C2S is the penalty coefficient for a harvest block smaller than the desired area range T is the number of planning periods N p is the number of harvest blocks for which the size is larger than the desired range in period p M p is the number of harvest blocks for which the size is smaller than the desired range in period p AApj is the area deviation of jth patch from the upper bound of the desired area range in period p 31 AApi is the area deviation of ith patch from the lower bound of the desired area range in period p 3. Total transportation penalty cost (TPC). TPC is used to evaluate the ability of a solution to minimize cost for road construction. A penalty cost is given to those planning periods in which the road construction cost is higher than a maximum cost limit (MAXCOST). This penalty can be described as: T TPC = X G(B - MAXCOST) (3.4) where, Q is the coefficient for high transportation cost, which = 0 if E; < MAXCOST MAXCOST is the transportation cost limit in each planning period ($) Ej is the total transportation cost in period i ($) T is the number of periods in the planning horizon For evaluating road construction cost, a road network is required. The network consists of all road links in the planning area. A table is attached to the network for storing attributes of road links, such as road class, length, and built status (built or unbuilt). Within each forest stand road links are connected to the main transportation 32 road. When a forest stand is selected for harvesting in a certain period, the corresponding unbuilt road links are triggered, the construction costs are calculated, and the construction status of the road is updated. 4. Total patch size penalty cost (PSPC). The penalty for size of remnant patches is evaluated using equation 3.5. It is assumed that the patch size for interior wildlife species has a minimum size bound. A penalty cost is given to a patch if its size is less than this bound. PSPC is the sum of penalty costs related to the size of remnant patches. PSPC= J f i C i C S - A O (3.5) i=i j=i where, Ay is the area of patch j in period i (ha) Q is the patch size penalty cost coefficient in period i, which = 0 if Ay >S N; is the number of patches in period i S is the lower patch size bound (ha) T is the number of periods A patch will never have a negative penalty cost in formula (3.5), because if a patch is larger than the minimum limit (A y >S), the patch size penalty is always zero. 33 5. Total patch shape penalty cost'(PSPC). PSPC is the sum of the penalty costs associated with the shape of remnant patches. Since a small patch contains no interior area due to edge effects (Forman and Godron 1981, Fahrig and Merriam 1994), its shape will make no difference in considering biological effects; small remnant patches were excluded from the patch shape factor. On the other hand, if a patch is very large, its shape is unimportant in providing habitats for interior species (Saunders et al. 1991). Therefore, penalty shape cost is only applied to patches within a specified range. A patch whose area is outside this range will receive no shape penalty. A simple formula is used to estimate the shape index: SI= (3.6) 0 . 2 5TID 2 where, SI is the shape index of a patch. A is the area of a patch (ha) D is the longest diameter of a patch (m) The shape index is the result of comparing the size of a patch with the area of a standard circle determined by the widest diameter of the patch. A patch will result in a penalty cost if its shape index is lower than a desired index value. PSPC is calculated as follows: 34 T Ni p s p c = £ Z C i ( D I - S L ) (3.7) i=i j=i where, Sly is the shape index of patch j in period i C; is the shape penalty cost coefficient, which equals 0 if Sly > DI; DI is the desired index value. N; is the number of patches in period i T is the number of periods 6. Total inter-patch distance penalty cost (IDPC). The inter-patch distance is measured by the distance between the centroid of a patch and the centroid of its nearest neighbour. The area range for evaluating this penalty is the same as that for evaluating the shape penalty. A maximum distance is set as a limit, and any distance between a patch and its nearest neighbor beyond this limit is penalized: T Ni TCPC = EZC.(D,-MD) i=ij=i (3.8) where, Q is the distance penalty cost coefficient, which equals 0 if MD > D y MD is maximum distance for which there is no penalty cost (m) Dy is distance between patch j and its nearest neighbor patch in period i (m) Nj is number of patches in period i T is number of periods 35 Using distance between the centroids of two patches as inter-patch distance can create problems if the patches are very large. Since I was unable to find the minimum distance between two patch edge points, the centroid had to be used. 7. Total disturbance penalty cost (TDPC). In each period, total clear-cut area is controlled by a maximum disturbance limit. There will be a penalty if the total harvested area exceeds the limit, as shown in the following formula: TDPC = X G(Ai - AL) (3.9) i=l where, Q is the penalty coefficient for disturbance in period i, which equals 0 if Alj > Aj A; is the total harvested area at period i (ha) Al; is the maximum disturbance limit in period i (ha) T is the number of periods 3.3. The procedure used in constructing the model The model was coded in Visual C++ and runs on a Pentium-90 PC computer. As shown in Figure 3.1, the model contains three major components: input, the solution algorithm, and output. These components are described next. 3.3.1. Model input 36 The model was developed with an interface to enable users to input data, policy, penalty coefficients, and objective options for solving specific scheduling problems. 3.3.1.1. Spatial data and attributes Since the basic solution variables in the model are polygons and road-links, both attribute and spatial data are required for these variables. The attributes of polygons and road-links are: - polygon attributes. Polygon-id, stand group, area, age, site class, - road link attribute. Link-id, class, length. The spatial data specify geographic coordinates of both polygons and road-links. Besides these data, other data, such as volume curves by stand group, and road construction unit cost ($/m) by road class, are needed. All the data are stored in a Microsoft Access database. Different datasets for planning areas in British Columbia have been created by the UBC Forest Operations Group, and these datasets are available for case studies. 3.3.1.2. Model parameters Table 3.1 shows the parameters required by the model to represent management planning policies. Periodic road cost limits are calculated at the beginning of the 37 Table 3.1. The model parameters Categories Parameters General number of planning periods period length (years) number of exclusion periods exclusion period length (years) minimum harvest age (years) maximum disturbance limit (ha/period) Timber timber volume flow target (m /period) Opening size maximum opening size (ha) Landscape pattern minimum patch size without penalty (ha) patch size range for evaluating shape and inter-patch distance maximum distance without penalty (m) desired patch shape index without penalty Road transportation cost limit ($/period) simulation by computing the total cost of unbuilt road links, and then dividing the total cost by the number of periods. 38 3.3.1.3. Penalty cost coefficients The penalty cost coefficients for each objective can be altered based on the priority of management objectives. 3.3.1.4. Objective options All seven objectives can be switched on or off in order to solve different planning problems. For example, if landscape pattern is not considered to be important for harvest scheduling, the objectives of landscape pattern (i.e. patch size, shape, and inter-patch distance) can be excluded, and the model is no longer penalized for not meeting landscape pattern objectives (an ordinary area-based problem). 3.3.2. Solution algorithm A Simulated Annealing (SA) algorithm was used for solving the problems. As discussed by Aarts and Korst (1989), the SA algorithm comes from the idea of annealing a metal, which is the process of moving matter from a high-energy state to a low-energy state. In the high energy state, particles move about freely, or rearrange themselves, hence forming different configurations. As the temperature cools down, the mobility of particles gradually decreases until the metal becomes a solid. The SA method has been previously applied to forest planning problems (Lockwood and Moore 1993, Dahlin and Salinas 1993, Murray and Church 1994). Murray and Church (1994) used different heuristic algorithms to solve the same 39 problem, and their results show that solutions obtained by using SA were superior to those found with random searches. In this study, the simulation process starts with an initial solution, followed by a transition process. 3.3.2.1. Initial solution The following procedure is used to generate an initial solution: (1) Define the following: • N is the number of planning periods • i is the period counter • Parray is the polygon array • PSarray is the solution array for polygon variables • RSarray is the solution array for road-link variables. Initialize PSarray, and RSarray, and set the period counter i = 1; (2) initialize Parray, and queue the polygons that are eligible to be cut based on polygon age; (3) randomly choose a polygon, denoted by X, from the queue; 40 (4) remove X from the eligible queue, and use X as a seed. Recursively search the polygons adjacent to X whose age is less than the green-up age to form a disturbance patch. If the area of the patch is larger than a certain area limit, go to (3), else go to (5); (5) put polygon X into Parray. Check the total harvest area and timber volume of the period, if either of them exceeds their corresponding limits, go to (6), otherwise, go to (3), (6) transfer the contents of Parray into PSarray, and conduct the following calculations: • road construction. Search the unbuilt road-links which are linked to the polygons to be harvested in the ith period. Set the state of these road-links to be built, calculate the construction cost, and put these links into the road solution array, RSarray; • patches. Create a dynamic data structure for storing the attributes of remnant patches (i.e., patch-id, area, period, shape, the coordinates of its centroid, and the id of its nearest neighbor patch). Search the remnant patches throughout the planning area, and calculate each patch's corresponding attributes and store them in the data structure. (7) If the period counter i is less than N, set i = i+1, update the age of all the polygons by period length, and go to (2), otherwise stop and go to the transition process. 41 3.3.2.2. Transition process In the transition process: (1) Find the initial penalty cost. Based on the initial solution, determine the initial objective function value, Z, by summing each penalty function. (2) Mark polygons. Those polygons that fall into the initial solution array are marked by their period index, and those not in the initial solution array are marked by N+l, where N is the total number of planning periods. (3) Begin the annealing process procedure: a) Define the following: • T is the initial temperature, • COUNT is iteration counter, • TLimit is the iteration limit for each temperature, • Crate is the cooling rate, • TV is the terminating value. Set COUNT = 1; b) generate a new solution, by randomly trading a pair of polygons between two periods; 42 c) calculate the new Z by summing all penalty functions; d) accept the new solution immediately if the objective function value is improved. To determine whether or not to accept a solution which is inferior to the old one, the Metropolis criterion (Aarts and Korst 1989) was used: P is the probability of the acceptance, Z0id is the objective value of the old solution, Z n e w is the objective value of the new solution, and T is the control temperature. If p is larger than a test value which is randomly drawn from the interval [0,1], the new solution is accepted as the current solution. Otherwise the old solution is retained. e) if the solution is accepted, update both polygon and road link solution arrays, and the remnant patch data structure; (3.10) where: f) if COUNT is less than TLimit, set COUNT = COUNT +1, go to b, otherwise, go tog); 43 g) if the temperature T is less than TV, decease T by Crate, set COUNT = 1, and go to b), otherwise, stop. At the beginning of the process, T is large, hence the accepting probability is high. As T is gradually decreased at a fixed cooling rate, the possibility of accepting a new solution gradually decreases, until finally a point is reached where only those solutions that improve the objective value are accepted. The simulated annealing process continues until T reaches a terminal value, TV. 3.3.3. Model output Model output includes; - harvest and road construction schedule, - timber volume, harvested area, and road construction cost by period, and - the number of disturbance and remnant patches plus their attributes. Landscape pattern is a component of the model's output, whether the landscape pattern objectives are applied or not. If they are applied, landscape pattern attributes from the model run are stored in a dynamic data structure. If they are not applied, the model will calculate the pattern following the final result of the harvest schedule. In this way, changes in landscape can be analyzed for the simulation results with or without applying landscape objectives. 44 Output also sums the edge between different patches. There are many edge types between combinations of different succession stages, but edges between newly disturbed and remnant patches are an important indicator of forest fragmentation. The model will calculate the total length of these edges for each planning period. The results can be used to analyze effects of different management strategies on landscape fragmentation. 3.4. Summary The model's performance is controlled by seven objectives which are represented in the model's objective function. Since different objectives are typically evaluated in different units, penalty cost functions are used to make all the objectives commensurate. The optimal solution is the one that minimizes the total penalty costs. By using the simulated annealing approach, solutions are expected to be optimized (or near optimal), and the model can be used for realistic sized problems. As LHS was developed with an interface feature, the model's input can be altered to meet the requirement of various operational planning problems under different management policies and guidelines. 45 CHAPTER 4 THE IMPACT OF SPATIAL CONSTRAINTS AND LAND WITHDRAWAL ON TIMBER HARVEST AND LANDSCAPE STRUCTURE 4.1. Introduction In this chapter, I investigate the changes in landscape related to spatial harvest constraints and maximum disturbance rates. The objectives of this chapter are to determine: • the impact of relaxed and strict adjacency rules on timber flows, • the impact of opening size and exclusion period on landscape pattern and landscape fragmentation, and • the impact of different disturbance rates on the landscape. Combinations of spatial constraints (opening size and exclusion periods) and maximum disturbance rates are used to formulate different management scenarios. In the methods section, I first describe the data set for the study area, and how the spatial constraints are developed. Then I describe problem formulations, and how the problems are solved as objectives in the LHS model. Finally, I describe how the landscape pattern is analyzed. In the results section, simulations for the different problem formulations are analyzed and discussed relative to the objectives of this chapter. 46 4.2. Methods 4.2.1. The study area The Penfold watershed, located near Williams Lake, British Columbia, was selected as the case study. A vector-based data set containing both attribute and spatial data of the watershed was created by the UBC Forest Operations Group. The total area of the watershed is 21196 ha, of which only 9764 ha are considered as available for timber harvest. The remainder is delineated as reserve areas (alpine, riparian, rock, and non-timber uses such as wildlife habitat or visual quality). Western hemlock (Tsuga heterophylla (Engl.) carr.), interior spruce (Picea engelmanii x glauca A. Dietr.), Douglas fir (Pseudotsuga menziesii (Mirb.) Franco), and western red cedar (Thuja plicata L.) are the dominant species in the area. Only about 3% of the area has been disturbed in the last 50 years by harvesting and/or natural fire, and about 90% of the operable forest stands is older than 120 years of age, thereafter referred to as old growth (Figure 4.1). The timber production area has been divided into 526 harvest polygons, ranging from 1 to 63 ha. There are also 197 polygons for the reserve area, which were ignored during harvest scheduling. Timber yield curves for the stand groups were also included in the dataset. 47 10000 7000 to 5000 " CU 2000 + 1000 -H i l l <20 30 70 Age class Figure 4.1. Age class distribution of the timber production area in the Penfold watershed. The edge length between a polygon and each of its neighbours was added to the dataset. In this study, adjacency is defined as any two polygons sharing a common boundary, with length > 0. Because I chose to use an undisturbed landscape for examining the effects of management scenarios on the changes in landscape structure, polygons younger than the minimum harvest age were set to the minimum harvest age at the beginning of simulation, 48 4.2.2. Definition of the adjacency rule in the model Spatial harvest scheduling models are characterized by adjacency constraints. In the literature, there are two methods of using adjacency constraints. One method follows a strict adjacency (SA) rule in selecting harvest units. With this method, after a polygon is selected, all of the adjacent units are excluded from harvesting for a period of time. The other method uses a relaxed adjacency (RA) rule. Here, the adjacent polygon can be harvested as long as the total area of the selected polygons does not exceed a maximum opening size. If the SA rule is used, harvest units cannot be aggregated into an opening, or in other words, any opening always consists of only one polygon. Therefore, to formulate problems with different opening sizes requires that the data set be redesigned for each case, which involves capturing, storing, and processing attributes and spatial features of polygons and road links. In this study, the work of redesigning the data sets was avoided by using the RA rule, which allows the harvest of adjacent units subject to the opening size limit. The RA rule allows the computer to automatically aggregate polygons into an opening, and therefore increases the problem complexity by expanding the solution space. The differences between the SA and the RA rules are demonstrated in Figure 4.2. The sample problem set in Figure 4.2 contains three 0-1 integer variables, denoted by xl, x2, and x3, each of which can take a value of 1 if selected for harvesting, and 0 if not. If the SA rule is used, the adjacency constraint can be expressed as: 49 Figure 4.2. Different opening configurations xl+x2 + x3<=l (4.1) Under the SA rule, there are three possible solutions for this problem, that is, si(l,0,0), s2(0,l,0), and S3(0,0,l). Figure 4.2A shows the solution S\. If the RA rule is used, the right hand-side value in equation (4.1) can vary from 1 to 3. Besides Si, s 2 and s3, four more possible solutions, denoted by s4(l,0,l), s5(l,l,0), s6(0,l,l), and s 7(l,l,l) could be added to the solution space if the total area of the three polygons is below the opening size limit (Figure 4.2B, C, D and E). By using the RA rule, only one data set is needed for exploring different opening size configurations. 4.2.3. The problem formulations In Chapter Three, the development of the LHS model was described in detail. The model has four objectives related to timber harvesting; 1) opening size, 2) timber even flow, 3) maximum disturbance rate (denoted by percentage of total planning area), and 4) transportation cost. There are three remnant patch objectives: 1) size, 2) shape and 3) inter-patch distance. The problem formulations in this chapter required only three 50 objectives (opening size, timber even flow and maximum disturbance rates). Here, the remnant patches are only measured, and not used to constrain the model. In the model, penalty costs are used to evaluate any violations of the objectives. A desired range is set for a particular opening size. An opening either smaller or larger than the range results in a penalty, but a larger opening consisting of only one polygon is not penalized because the basic harvest units may not be split into smaller ones (a limitation of the data set). A deviation greater than 5% from the timber target is penalized. The objective of the model is to minimize the total penalty costs. Using penalty costs to evaluate a solution assumes that all the solutions during the simulation are feasible; the best solution has the minimum penalty cost. Under the RA rule, different scheduling scenarios were formulated by using combinations of three opening sizes, and three exclusion periods (Table 4.1). In order to examine the impact of harvest intensity on landscape pattern, four other scenarios were formulated and denoted by DR70, DR80, DR90, and DR100, which respectively refer to 70%, 80%, 90%, and 100% maximum disturbance rates. A maximum disturbance fate is defined as the percent of the total area eligible for harvest. On a 1000-ha landscape, a 90% maximum disturbance rate allows 90 ha to be harvested per period throughout a 10-period horizon. A 40-hectare-opening size and ten-year-exclusion period were used as spatial constraints for the scenarios with different maximum disturbance rates. 51 Table 4.1. The scheduling scenarios based on the combination of opening size and exclusion periods used in RA scenarios Opening size (ha) Exclusion period (yr) 10 20 30 20 O20-P10* O20-P20 O20-P30 40 O40-P10 O40-P20 O40-P30 100 O100-P10 O100-P20 O100-P30 * O20-P10 - 'O20' denotes maximum opening size limit is 20 ha, and 'P10' denotes 10-year exclusion. The same rule is applied to the other scenarios. A function of the C++ program was added to the model for scheduling timber harvest under the SA rule. The simulated annealing algorithm (described in Chapter 3) was used to maximize timber volume. Three timber harvest scheduling scenarios under the SA rule were generated using different exclusion periods, i.e., 10 (SA10), 20(SA20), and 30 (SA30) years. Under the SA rule, a harvest block consists of only one polygon. The periodic timber target was set by running the model several times under only timber flow constraints. With each run, the timber target was adjusted until it reached maximum even flow. 52 4.2.4. Analysis of landscape pattern Remnant patches were used to evaluate the landscape pattern resulting from different harvest constraints. This analysis was only done for the final solution of each scenario. The following procedures were used: • Remnant patches. For each period, the total number of remnant patches were determined. Remnant polygons sharing a common boundary were aggregated into one patch. The patches were classified into five groups based on their size (i.e., <20, 20-200, 201-500, 501 - 1000, and > 1000 ha). • Edge length. Edge was defined as the common boundary between harvest openings (<20 yr) and remnant patches (>100 yr). For each period, total edge length (km) was calculated. 4.3. Results and discussion 4.3.1. Timber production One of the objectives is to examine how the spatial constraints of opening size and exclusion period affect timber flow. Although there are some studies on this topic (e.g., Yoshimoto and Brodie 1994a, Daust and Nelson 1993, Nelson and Finn 1991), the problem formulations in this study were different from others in that both the RA and SA rules were applied. The timber flows resulting from scheduling at a 100% maximum 53 disturbance rate were analyzed because spatial constraints were expected to have the most binding effects when 100 % of the total planning area was allowed to be harvested. The periodic timber target at a 100% disturbance rate was 378000 m3, which was obtained by running the model with only the timber even flow objective. Table 4.3 shows, by scenario, the mean periodic volume and the percent reduction from the timber target. When the exclusion period was less than 20 years, there were only minor differences in timber harvest among scenarios. However, when the exclusion period was increased to 30 years, various reductions were found in scenarios with small opening sizes. As the opening size increased, the reduction decreased until there was little difference at the 100-ha opening size and 30-year exclusion (O100-P30). Scenario O20-P30 resulted in the highest reduction (about 12% from the timber target) among the scenarios under the RA rule. However, the 30-year-exclusion period under the SA rule (SA30) resulted in an even higher timber reduction than scenario O20-P30. The timber harvest flow for each scenario is shown in Figure 4.3. All the scenarios except O20-P30 under the RA rule met the timber even flow objective within ±10% variation. The spatial constraint of a 20-hectare-opening size and 30-year-exclusion period resulted in more severe conflicts with the timber even flow constraint. A higher penalty was required to obtain an even flow for scenario O20-P30; however, doing this comes at the cost of larger openings. 54 More periodic timber yield variations were observed under the S A rule than under the RA rule (Figure 4.3), because less attention was given to the timber even flow under the SA constraint, and moreover, the SA constraint allows less scheduling flexibility. Figure 4.3C shows that with a 30-year-excfusion period, the SA rule leads to less periodic timber production than the RA rule. Table 4.3. Average periodic timber volume and deviations by scenario Scenarios Timber % of reduction from (1000 m3) the timber target O20-P10 372.2 1.5 O40-P10 371.4 1.7 O100-P10 371.8 1.6 O20-P20 366.3 3.1 O40-P20 371.6 1.7 O100-P20 372.0 1.6 O20-P30 331.6 12.3 O40-P30 356.4 5.7 O100-P30 371.4 1.7 SA101 373.3 1.2 SA202 369.4 2.3 SA303 307.9 18.5 1. 10-year-exclusion period under the SA rule. 2. 20-year-exclusion period under the SA rule. 3. 30-year-exclusion period under the SA rule. 55 100 1 2 3 4 5 6 7 8 9 10 Decade 450 t SA20 O20-P20 O40-P20 O100-P20 —i 1 10 400 Figure 4.3. Periodic timber harvest by The RA and SA rules. A. 10-year-exclusion period; B. 20-year-exclusion period, and C. 30 year exclusion period. 56 Exclusion period is considered to be a more important factor than opening size in causing timber reductions (Yoshimoto and Brodie 1994a, Daust and Nelson 1993, Nelson and Finn 1991). The reason for the lower timber reduction with the 30-year-exclusion period under the RA rule than under the SA rule is obvious. Under the RA rule, the model allows the basic harvest units to be dynamically aggregated into openings, and hence it will produce harvest blocks diverse in size and composition. The larger the opening size limit was, the more diversified the openings tended to be. For example, under a 30-year exclusion period, a 40-ha harvest block in decade 3 may contain two or more harvest units from decades 1, 2, and 3, thus the aggregation may allow more opportunities to harvest "desired" units. Under the SA rule, the model was forced to select less desirable units (i.e., few scheduling choices) at inappropriate times (Daust and Nelson, 1993). The biogeophysical conditions of the planning area will effect the timber flow reductions. For example, smaller reductions would be expected in homogeneous areas (species, age, and site), because less scheduling flexibility is needed to harvest stands at the optimal rotation age. 4.3.2. Remnant patches Results for the number of remnant patches by scenario (without maximum disturbance-rate constraints) are shown in Figure 4.4. The changes in the number of 57 1 2 3 4 5 6 7 8 9 10 Decade Figure 4.4 The number of remnant patches in each decade of harvest by scenario. patches in response to different opening and exclusion period constraints follow a similar pattern throughout the planning horizon. At the beginning of the harvest, the effects of these constraints were not distinct. In most cases, the greatest number of remnant patches were observed between 70 to 80 years, when approximately 70 - 80% of the total planning area was harvested. The scenarios with small opening sizes and longer exclusion periods had more remnant patches than the scenarios with larger opening sizes and shorter exclusion periods. At the peak points, scenario O100-P10 was the lowest and scenario O20-P20 was the highest (about 3 times as many remnant 58 patches as that of scenario OIOO-PIO). Although longer exclusion periods tended to create more patches, these impacts on the landscape patchiness were limited to times when the exclusion periods were the least restrictive. Figure 4.4 shows that the 20-ha opening and 20-year exclusion constraints (O20-P20) resulted in more remnant patches than O20-P30. This is because the harvested area was reduced by the longer exclusion period, and remnant area increased. Following periodic harvesting, harvest blocks are distributed over the landscape, and gradually carve large remnant patches into small ones. Since the large patches are important components of the landscape in providing habitats for interior species, it is desirable to retain the large patches as long as possible over the planning horizon. Therefore, the time at which the large patches are lost across the planning horizon is an important threshold to be identified. Figure 4.5 shows images of landscape structure at different periods under scenarios O20-P20 and O100-P10. These scenarios had, respectively, the greatest and smallest number of remnant patches, at the peak points (Figure 4.4). The distinct contrast in landscape structure can be seen between the two scenarios. With O20-P20, the remnant patches were more fragmented (porous) relative to O100-P10. However, even scenario O100-P10 could not retain large patches (>500 ha) at Year 60, when about 60% of the planning area was cut (Figure 4.5). The results show that there are still large patches (>1000 ha) when 50% of the area was cut over, regardless of the scenario. 59 YearO Year 40 Year 60 Year 80 Year 100 H I Reserve Disturbed Remnant Figure 4.5. Changes in spatial landscape structure over time under scenarios O20-P10 andOlOO-PlO. This is not consistent with the findings of Franklin and Forman (1987), who used checkerboard model to demonstrate that the dispersed harvest pattern would cause the landscape to lose large patches when about 30% of the forest was cut-over. There are two factors that account for this difference. First, the basic harvest polygons were irregularly structured in terms of shape, size, and the number of adjacent polygons, therefore, there may be more opportunities for these polygons to be aggregated into patches. Second, the harvest pattern created by LHS is different from that of Franklin 60 and Forman (1987) because the harvest blocks are not evenly distributed over the landscape. I now turn to the effects of reduced maximum disturbance rates. Results show that the scenarios resulted in different numbers of remnant patches (Figure 4.6). All curves peaked in different planning periods. Reducing the disturbance rate tended to delay the period when the maximum number of patches occurred. Figure 4.6 also shows that the maximum number of remnant patches were higher with lower disturbance rates than with higher rates. It is interesting that no patches larger than 500 ha were left on the landscape in later periods even when the disturbance rate was reduced to 70% (Table 4.3). The simulation results showed that current harvest schedules with spatial constraints were not able to retain large remnant patches simply by reducing disturbance rates. In Chapter 5, patch constraints are used to control the changes in landscape pattern. 4.3.3. Edge Edge is an indicator of landscape fragmentation. Periodic edge lengths (km) by scenario (100% maximum disturbance rate) are shown in Figure 4.7. The greatest edge length for all scenarios occurred in period 2, when approximately 20% of the land was cut. At the peak points, the scenarios can be roughly classified into three groups by opening size (20, 40, and 100 ha). With the exception of scenario O20-P10, each group 61 70 n Decade Figure 4.6. The number of remnant patches under different disturbance rates from 70% (DR70) to 100% (DR100) in the planning horizon (10-year-eclusion period and 40-hectare-opening). contains scenarios with the same opening size, but with different exclusion periods. The differences within a group can be considered as the effects of exclusion periods on the amount of, and differences between groups as the effects of opening size on the amount of edge. Obviously, exclusion periods had less effect on edge than the opening size limits. 62 Table 4.3. The remnant patch area (ha) in each patch group by scenario Scenarios Period Patch group (ha) Total <20 21-200 201-500 501-1000 >1000 (ha) DR100 7 69 2521 215 0 0 2805 8 75 1777 0 0 0 1852 9 24 934 0 0 0 958 10 0 0 0 0 0 0 DR90 7 85 1882 1610 0 0 3577 8 99 2164 427 0 0 2690 9 74 1725 0 0 0 1799 10 199 719 0 0 0 918 DR80 7 166 1442 755 1720 0 4083 8 190 2110 996 0 0 3296 9 259 1624 730 0 0 2613 10 293 1527 0 0 0 1820 DR70 7 134 1141 619 2955 0 4879 8 140 1507 1158 1355 0 4160 9 228 1971 1274 0 0 3473 10 308 2475 0 0 0 2783 63 200 180 160 140 120 100 i J 80 6X * - O 60 40 20 0 /fc-////• V 1. • A T -" l b . —•—O20-P10 • C40-P10 O100-P10 Q20-P20 • O40-P20 --A---O100-P20 o Q20-P30 -B--O40-P30 & O100-P30 I' 5 6 Decade 10 Figure 4.7. The total periodic edge length by scenario. The impact of maximum disturbance rates on edge density is shown in Figure 4.8, where each edge curve represents one disturbance rate which controls harvest scheduling under a 40-ha opening and 10-yr exclusion period constraint. The peak of all edge curves occurred after 20 years of harvesting (Figure 4.8), where the largest differences were found between the 70% (DR70) and 100% (DR100) maximum disturbance rates. 64 1 2 3 4 5 6 7 8 9 10 Decade Figure 4.8. Edge density for maximum disturbance rates from 70% (DR70) to 100%(DR100) under 40-ha opening size and 10-yr exclusion period objective. It can be seen from Figure 4.8 that reducing disturbance rates also reduced the amount of edge at peak points. However, in the later periods, the scenarios with lower disturbance rates (DR70) have more edges because there is relatively more remnant area left on the landscape. 4.4. Conclusion The exclusion period showed less effect in restricting timber flow under the RA rule than under the SA rule, and, in fact, differences of timber flow were not detected until the exclusion period increased to 3 decades. The largest reduction in timber flow was 65 12% under the RA rule with 3 0-year-exclusion period and 20-hectare-opening constraints and 18% under the SA rule with the 30-year-exclusion period. Increasing maximum opening size constraints compensated for the average timber reduction caused by exclusion periods. Allowing the computer to automatically aggregate harvest blocks provided more opportunities to select harvest units in each planning period than predesigning the data set with a certain block size configuration. The maximum number of remnant patches occurred when approximately 70% of the land was harvested. Extending the exclusion period increased the number of remnant patches, and thereby caused more habitat fragmentation; however, this effect is only visible when the exclusion periods do not restrict the periodic harvest area. Remnant patches larger than 500 ha disappeared when about 60% of the total planning area was harvested. Longer exclusion periods caused the landscape to lose large patches earlier, but the relationship between the length of exclusion period and the time at which large patches were lost was not distinct. Reducing the disturbance rates postponed the time when the greatest number of remnant patches appeared; however, reducing the amount of area did not significantly reduce fragmentation in terms of patchiness in the landscape. At the peak point on patch number curves, a lower disturbance rate created more patches than a higher rate. Furthermore, reducing harvest by as much as 30% still did not guarantee that large patches (>500ha) were retained throughout the planning horizon. Therefore, if large remnant patches are required for providing habitat for some wildlife species, either 66 changing the spatial constraint formulation or reducing the maximum disturbance rates are not effective measures for achieving this objective. Small openings created more edges than large openings, but the differences were visible only during the first few decades in the planning horizon. In most cases, only minor differences in the total periodic edge length (km) were detected among different exclusion periods. Lower maximum disturbance rates resulted in smaller amount of edge at the peak points than did higher rates, but had more edge in the later periods. 67 CHAPTER 5 INCORPORATING LANDSCAPE PATTERNS INTO SPATIAL HARVEST SCHEDULING 5.1. Introduction Although spatially-constrained harvest models are criticized for ignoring ecological and environmental consequences (e.g., Wallin et al. 1994, Spies et al. 1994, and Franklin and Forman 1987), these models are still applied in British Columbia. Several reasons possibly account for this. First, spatial harvest is demanded by law, such as the Forest Practices Code of British Columbia (BCMOF 1995), in which adjacency constraints in terms of harvest block size and green-up periods are clearly specified. Second, spatial harvest models under adjacency constraints may achieve some goals of integrated resource management, such as timber, visual quality, hydrology, and wildlife (Hof et al. 1994, Nelson and Brodie 1990). Third, dispersing harvest blocks over a forest landscape can be arranged to mimic a natural disturbance regime, such as fire (Bunnell 1995, Delong and Tanner 1996). Therefore, it seems that spatially-constrained harvest models are necessary for handling integrated management planning problems. However, these models have to be improved in order to address landscape pattern changes following harvesting disturbance. In Chapter 4, the impacts of spatial constraints and area withdrawal oh the structure of landscape patterns were investigated. The results showed that smaller opening sizes 68 with long exclusion periods could create a greater number of remnant patches, hence more fragmentation than larger opening sizes with short exclusion periods. Moreover, even reducing the disturbance rate by 30% could not guarantee that large remnant patches will be retained throughout the planning horizon when dispersed harvest pattern was applied. In this chapter, LHS is used to solve resource management planning problems. Based on existing spatially-constrained models, remnant patch constraints were added to LHS to evaluate landscape structure. A harvest schedule from the model simulation not only specifies where, and when to harvest, but also indicates the changes in the size and spatial configuration of remnant patches in the landscape. The objectives are to characterize the differences in timber flow, road cost, and landscape structure over time resulting from the different management strategies. 5.2. Methods 5.2.1. Landscape Harvest Scheduling model (LHS) LHS was constructed to incorporate landscape pattern as objectives in the harvest scheduling simulation. Because remnant patches are biologically important elements in forming landscape patterns, and they are sensitive to timber harvesting, LHS uses remnant patch objectives to control the changes in landscape structure. Here, the selection of harvest units may be directed by both timber management (opening size, green-up period, timber target, and road cost) and remnant patch criteria (remnant patch 69 size, shape, and inter-patch distance). Landscape patterns produced by the model are affected by the initial landscape conditions and the proposed management activities. The model is complicated in that it tries to meet the timber target and maintain timber even flow among the planning periods, to distribute road costs among the planning periods, and to retain large remnant patches as long as possible. The model uses penalty costs to evaluate target violations. In this study, clear-cutting was considered to be the only means of creating openings in the forest, and natural disturbance factors and other silviculture systems (such as partial cutting) were not modeled. 5.2.2. Case study area and management scenario formulation 5.2.2.1. Study area The Elphinstone watershed was selected as the case study area. The total area of the watershed is 8926 ha, of which 7791 ha were considered to be available for timber production. The remainder was designed as reserve areas for riparian, and non-timber uses (wildlife habitat or visual quality). The timber production area was delineated into 704 polygons, which ranged from 0.22 to 78 ha. Western hemlock, interior spruce, Douglas-fir, and western red cedar were the main species in the area. The area has been highly disturbed by both nature and harvesting. Stands younger than 80 years constitute about 50 percent (3700 ha) of the total timber production area (Figure 5.1). 70 Figure 5.1. Age class distribution of Elphinstone watershed. 71 5.2.2.2. Management scenario formulation The objectives for all scenarios have the same priorities. The penalty cost coefficient for each objective can be found in Table 5.1. The general model parameters are shown in Table 5.2. The penalty cost coefficient for each objective in Table 5.1 was determined after a number of test runs to assess how sensitive this parameter was in affecting the outcome. Generally, the more sensitive objectives were given lower penalty coefficients. High coefficients should not be interpreted as meaning that the objective has a high priority. For example, even though timber is given a high penalty cost coefficient, it does not mean that this objective is given a higher priority than one with a lower coefficient (e.g. Opening size). If the penalty cost coefficients are changed by the same amount, a more sensitive objective will cause more significant change in the results than a less sensitive objective. For the simulation, six management scenarios were formulated by using different cutting rates and model objectives (Table 5.3). An "X" in the table means that the objective was selected. The three cutting rates are denoted by 100%, 90%, and 80%. A 72 Table 5.1. Penalty coefficients for model objectives Objective Coefficient Timber even flow 20 Maximum disturbance rate 30 Opening size 2 Road cost even flow 20 Remnant patch size 2 Remnant patch shape 4 Inter-patch distance 5 Table 5.2. The model parameters Parameters Value Planning horizon (yr) 100 Period interval (yr) 10 Green-up period (yr) 10 Minimum harvest age (yr) 100 Maximum opening size (ha) 40 Maximum disturbance limit (ha/period) 780 Minimum path size without penalty (ha) 200 Patch size range for evaluating patch shape and inter- 20 -200 patch distance (ha) Maximum inter-patch distance without penalty (m) 500 Desired patch shape index without penalty 0.6 73 cutting rate is equivalent to the maximum disturbance rate, which is the ratio of allowable cut area to the mean area available for harvest per period. Under each cutting rate, a pairwise comparison was made to examine the effects of applying the RP objectives on landscape structure, timber yield, and road cost. The maximum opening size was considered as a "hard" objective in order to ensure that all the openings had a strict upper bound. As opening size is increased, fewer blocks are created, and hence the landscape was less fragmented (i.e. it would have larger remnant patches). The analysis of landscape pattern would be biased if the maximum opening size was not kept constant across management scenarios. The remaining objectives were considered as "soft" objectives; each objective had the same penalty coefficient across all scenarios. The periodic timber target was determined by running the model several times with only the timber flow objective. With each model 73 penalty cost coefficient was given to an objective based on its sensitivity for binding the model. Generally, a more sensitive objective was given a lower coefficient. If the penalty cost coefficients are changed by the same amount, a more sensitive objective will cause more significant change in the result of model run than a less sensitive objective. For the simulation, six management scenarios were formulated by using different cutting rates and model objectives (Table 5.3). An "X" in the table means that the objective was selected. The three cutting rates are denoted by 100%, 90%, and 80%. A cutting rate is equivalent to the maximum disturbance rate, which is the ratio of allowable cut area to the mean area available for harvest per period. Under each cutting rate, a pairwise comparison was made to examine the effects of applying the RP objectives on landscape structure, timber yield, and road cost. The maximum opening size was considered as a "hard" objective in order to ensure that all the openings had a strict upper bound. As opening size is increased, fewer blocks are created, and hence the landscape was less fragmented (i.e. it would have larger remnant patches). The analysis of landscape pattern would be biased if the maximum opening size was not kept constant across management scenarios. The remaining objectives were considered as "soft" objectives; each objective had the same penalty coefficient across all scenarios. The periodic timber target was determined by running the model several times with only the timber flow objective. With each model 74 Table 5.3. The objective formulation for 6 management scenarios. Model objectives* Scenario Cutting rate Timber flow Opening size Road Disturbance cost limit Remnant patch 1 100% X** X X 2 100% X X X X 3 90% X X X X 4 90% X X X X X 5 80% X X X X 6 80% X X X X X See table 5.1 for objective priorities An "X" indicates the objective was selected run, the periodic timber production was adjusted to reach the point of maximum even flow, which was subsequently used as the timber target. Each road link could be constructed only once during the harvest simulation. The model only calculated road construction cost and ignored other costs, such as timber hauling, and road maintenance costs. At the beginning of the simulation, the model searched all the road links which were required to be built for timber transportation, and calculated the total road construction cost based on individual road link class, length, and 75 unit cost ($/m). In this way, the periodic road construction cost target was determined by dividing the total road cost by the number of periods. 5.2.2.3. Quantification of remnant patches and edge Remnant patches were defined as continuous areas in which the age of trees was above the minimum harvest age (>100 yrs). Stands which were young initially could age to become remnant patches during simulations. Aggregation of remnant patches was not affected by other biophysical factors, such as species, topography, and site class. Because the model randomly selected harvesting units in each planning period, every unit had an equal possibility of being selected. Timber harvests resulted in a landscape mosaic with forest stands at different serai stages. Remnant patches following each period of harvest were assumed to have two characteristics: 1) individual remnant patches were dynamically distributed across the landscape, and 2) the patches were perforated. It was hard to retain large patches of contiguous old growth without perforation when spatial harvest objectives were applied. In this study, large perforated patches were assumed to be more important than small ones in providing habitat for interior species. The landscape pattern analysis focused on the changes in remnant patches in terms of number, size, and spatial configuration in each planning period. The remnant patches were arbitrarily classified into five groups based on size: very small (< 20ha), small (21 to 200 ha), medium (201 - 500 ha), large (501 - 1000 ha), and very large (>1000 ha). The ratios of the area of each group to the 76 total remnant area were computed in each period. In addition, the mean patch size was also used as an index for quantifying landscape structure. Remnant patch shape and inter-patch distance were used only as objectives, and they were not examined in detail. Since the calculation of patch shape and inter-patch distance depends on the size of remnant patches between 20 to 200 ha, it does not make sense to compare different landscapes using remnant patch shape and inter-patch distance if the number and individual sizes of remnant patches vary from one landscape to another. In this study, edge was defined as the common boundary between harvest openings (<20 year) and remnant patches (>100 year). In each period, total length was calculated to examine the effects of harvest cutting rates and the RP objectives. 5.2.2.4. Timber volume and road cost The periodic timber production and road construction cost were compared, in order to examine the impact of remnant patch objectives on timber production and road construction cost. 77 5.3. Results and discussion 5.3.1. Spatial analysis The spatial distribution of remnant patches for the 6 scenarios are shown in Figures 5.2, 5.3, and 5.4. For each scenario, there are 5 images which show the changes in landscape structure from the beginning (Year 0) to the end of the harvest schedule (Year 100). Under the scenarios that applied the RP objectives, timber harvesting resulted in fewer remnant patches, especially after 60 years of the harvest cycle (Figures 5.2B, 5.3D, and 5.4F). Furthermore, the spatial distribution of remnant patches tended to be YearO Year 40 Year 60 Year 80 Year 100 | Res eve d Disturbed H§ Remnant Figure 5.2. Remnant patch distributions (100% cutting rate) throughout the planning horizon. (A) Scenario 1, without the RP objectives, and (B) Scenario 2, with the RP objectives. 78 YearO Year 40 Year 60 Year 80 Year 100 Figure 5.3. Remnant patch distributions (90% cutting rate) throughout the planning horizon. (C) Scenario 3, without the RP objectives, and (D) Scenario 4, with the RP objectives YearO Year 40 Year 60 Year 80 Year 100 | Res eve d Disturbed Hf Remnant Figure 5.4. Remnant patch distributions (80% cutting rate) throughout the planning horizon. (E) Scenario 5, without the RP objectives, and (F) Scenario 6, with the RP objectives. 79 aggregated, which was a distinct contrast with the spatial distribution of the remnant patches under scenarios without the RP objectives. The results also indicate the time when the large patches are lost. Without the RP objectives (scenarios 1,3, and 5), both very large patches (>1000 ha) and large patches (> 500 and < 1000 ha) were lost before year 80, but with the RP objectives, scenario 6 retained very large patches, and scenario 4 retained large patches until Year 100. More detailed observations about the impact of applying the RP objectives on landscape structure are shown in Table 5.4. With a 100% disturbance rate, the large remnant patch group (501 - 1000 ha) constituted about 37% the total remnant area in period 8 with the RP objective (scenario 2), and 0% in the same period without the RP objectives (scenario 1). In Figure 5.5, three observations about the mean patch size can be made based on different cutting rates and the effect of the RP objectives: 1. application of the RP objectives caused a significant increase in the mean remnant patch size for all three cutting rates, 2 reduced cutting rates had no effect on the mean remnant patch size when the RP objectives were not applied, and 3. reducing harvest intensities increased the mean remnant patch size for scenarios with the RP objectives. 80 Table 5.4. Selected percentages of the remnant area to total remnant area for different patch groups under different scenarios Patch group (ha) Scenarios Period <20 21 - 200 201 - 500 501 - 1000 >1000 1 8 8 78 14 9 11 89 2 8 2 23 38 37 9 7 93 3 8 15 74 11 9 26 74 10 52 48 4 8 0 16 37 47 9 4 20 18 58 10 8 17 75 5 8 17 66 17 9 23 65 12 10 39 61 6 8 1 23 13 63 9 4 20 10 66 10 4 20 76 Remnant patch size is an indicator used to quantify landscape fragmentation. It is generally recognized that dispersed harvesting models cause the landscape to quickly lose large patches, especially when the harvest block size is small (Gustafson and Crow 1994). The results of this study show that by adding the RP objectives to the dispersed model, the model was able to effectively control the changes in landscape patchwork over time, especially when cutting rate was reduced (e.g., Scenarios 4 and 6). This ability was not affected by harvest block size because the maximum opening size limit 81 Decade Figure 5.5. Mean remnant patch area by planning period and by management scenario. was kept constant for all scenarios. At the same time, the simulation results show that there was little variation in the mean periodic harvest block size between the scenarios with and without the remnant patch objectives. The effects of applying the RP objectives on the mean remnant patch size could be attributed to the harvest block distribution. Since smaller remnant patches result in higher penalty costs than larger ones, these smaller patches were either entirely cut or aggregated to large patches in order to reduce the penalty. 82 The total edge length after each period by scenario are shown in Figure 5.6. At the 100% cutting rate, applying the RP objectives (Scenario 2) had an insignificant impact on the amount of edge relative to Scenario 1. However, when the harvest rate was reduced, the RP objectives had some impact on the periodic edge length (Scenarios 4, and 6 in Figure 5.6). First, the amount of edge at the peak points on the curves were less under Scenarios 4 and 6 than that under Scenarios 3 and 5. Second, the amount of edge changed more smoothly from the peak points to the lowest points along the edge curves. Therefore, there was less variation in the amount of edge between planning periods under Scenarios 4 and 6 than under Scenarios 3 and 5. The simulation results also show that simply reducing the harvest rate without applying the RP objectives does not significantly reduce the amount of edge. Spies et al. (1994) stated that "cutting rate can have a greater effect on the amount of edge and interior forests in a landscape than cutting p a t t e r n T h e results from this study contradict this statement. Reducing the harvest rate did not effectively increase the mean remnant patch size, or decrease the amount of edge relative to the scenarios with the RP objectives. A similar result was reported by Gustafson and Crow (1996), who found that under the same dispersed pattern, reducing the cutting rate by 60% and using small cut blocks could produce as much edge as a scenario with 100% cutting rate. The simulation results for the scenarios without the RP objectives seem to support Gustafson and Crow (1996). 83 ••— Scenario 1 Decade Figure 5.6. The total edge length of different period under different scenarios. 5.3.2. The analysis of timber production and road cost under different scenarios If the timber flow policy was set within ±10 % of the timber target, the periodic timber yield of all scenarios met the timber flow objective (Figure 5.7 A, B, and C). The timber volume curves in Figure 5.7 show that the scenarios which applied the RP objectives (Scenarios 2, 4, and 6) affected timber production in two ways. First, there was slightly higher variation among the periodic timber flows, and second, there was slightly lower total timber production. The total timber volume relative to no RP objectives was reduced by 0.5%, 2.4%, and 1.8 % respectively, under scenarios 2, 4, and 84 A 600.0 T <P 500.0 § 400.0 w 300.0 + p g 200.0 "3 > 100.0 + 0.0 f_» P n H 1 1 r-i * i H 1 9 10 • SCENARIO! • SCENARIO 2 Tinier Target B 500.0 m £ 400.0 o o 2 300.0 B 200.0 > 100.0 0.0 • —i 1 1 1 1 1 1 1 3 4 5 6 7 8 9 10 • SCENARIO 3 • SCENARIO 4 Timber Target 450.0 400.0 <^  350.0 J 300.0 O 250.0 C k 200.0 -150.0 O 100.0 > 50.0 0.0 H 1 h 3 4 5 6 7 Planing period ( 1 0 years) H h 9 10 • SCENARIO 5 • SCENARIO 6 Timber Target Figure 5.7. Periodic timber yield under different scenarios 85 6. Since timber production is closely related to species, stand age, and site, the impact of applying the RP objectives on timber production depends on the heterogeneity of the forest landscape (e.g., abundance and spatial arrangement of forest stands). In a heterogeneous forest landscape, the RP objectives (remnant patch size, shape, and inter-patch distance) might force the model to select less desirable harvest units, and thereby negatively affect timber production. Little difference was found among road costs associated with the RP objectives under all scenarios (Figure 5.8). The changes in road costs over time followed a similar pattern under all scenarios. All the scenarios failed to meet the objective of even flow road costs, because road costs were not given a higher priority (Table 5.1). These results show the RP objectives had little or no effect on road construction costs. The problem of how to achieve even periodic road costs will be dealt with in the next chapter. The RP objectives influenced timber production by changing the configuration of harvest blocks. This case study showed that the model could meet the timber even flow objective at 10% deviation from the target with the RP objectives; however, the total 86 0.0 -1 1 1 1 1 1 1 1 1 1 1 2 3 4 5 6 7 8 9 10 D e c a d e Figure 5.8. Periodic road costs by scenario. timber production was reduced by 0.5% - 2.4 % compared to scenarios without the RP objectives. The amount of reduction is expected to vary in different landscapes because the timber yield is closely related to the distribution of forest stands, species, ages, and site classes. 5.3.3 Simulation time for model formulations with different datasets Simulation with the RP objectives required large number of calculations of the size, shape, and inter-patch distance of remnant patches on a periodic basis. Table 5.5 shows 87 the processing time of simulations on a Pentium/90 computer for the case study area and other areas under different objective formulations. Generally, a simulation that included Table 5.5. Computation time for model formulations and datasets Dataset Number of polygons Number of road links Obiective formulation* flY 1 (2) (3) 1 ime (mm Squamish 292 581 3.8 7.0 30 Penfold 526 292 5.5 50 140 Elphinstone 704 2118 6.4 39 110 Lakes 1001 1278 8.4 40 154 The objective formulation: (1) Timber even flow and opening size; (2) Timber even flow, opening size, and road cost even flow; (3) Timber even flow, opening size, road cost even flow, and landscape pattern. the RP objectives took much longer time to run than those without such objectives. Applying the road cost objectives also increased the computation time. The simulation time was closely related to the number of polygons and road links. 5.4. Conclusion 88 Pairwise comparisons of different cutting rates showed that the RP objectives can have major impacts on the changes in landscape structure. Although remnant patches were dynamically distributed over the landscape, the RP objectives could control the dynamic changes in terms of patch size, shape, and inter-patch distance. As a result, large remnant patches could be kept much longer compared to scenarios without the RP objectives. Although the remnant patches created by the LHS model were highly fragmented or porous (Figures 5.2, 5.3, and 5.4), I believe they are more important than small patches for providing habitat for a variety of biological species. To meet the habitat requirements for species, such as the spotted owl, that may require large and contiguous old growth patches, different strategies, such as preservation, could be used. The results also show that the effects of reducing the cutting rate on landscape structure were important only if the RP objectives were applied. The RP objectives also affected the total edge length when lower cutting rates were used. 89 CHAPTER 6 OPERATIONAL PLANNING ANALYSIS UNDER DIFFERENT MANAGEMENT SCENARIOS 6.1. Introduction Forest planning in British Columbia consists of three hierarchical levels. The top level is strategic planning which involves implementing forest-wide objectives. Here problems on a large scale are dealt with to determine management strategies, like long term sustainability goals, wilderness or natural park preservation, and special wildlife species habitat delineation. The second level is tactical planning, which translates the activities specified in the strategic level to large geographic units. The third level is operational planning (e.g., a landscape or a watershed), which involves scheduling management activities, such as stand harvesting, road building and maintenance, etc. From the top level to the operational level, spatial detail is increased to make management activities more specific. Each level has been the subject of mathematical optimization research. In the past decade, more attention has been given to operational planning research, because of several factors. First, the development of Geographic Information Systems (GIS) facilitated obtaining spatial data for planning. Second, spatially distributing harvest units across the forest land was believed to be an effective approach to managing forests for multiple objectives, like timber, wildlife, aesthetics. Third, the growing 90 awareness of the importance of landscape management, ecosystem management, and biodiversity has influenced the need for more spatial detail. Operational planning problems are characterized by a large number of objectives, making them very difficult to formulate and solve. Although there have been many approaches to these problems, no one particular approach has been generally accepted. The incentive for doing this study came from an assumption that resource managers may have different priorities within their operational plans. Their top priorities may be maximum even flow of timber, uniform investment in road construction during each planning period, or maintaining the mean opening size as close to maximum as possible. These three priorities can be translated into management alternatives, or scenarios. With Landscape Harvest Scheduling models (LHS), these management scenarios can be formulated by adjusting the penalty coefficient based on the priority of each objective. Another alternative is to use the ATLAS model (Nelson et al. 1995) to solve the same operational planning problem. There are several objectives to this chapter: 1) to investigate the impact of different planning priorities on timber flow and road cost over the planning horizon, (predict economic tradeoffs among different scenarios); 2) to examine the effects of different planning priorities on landscape structure in terms of mean remnant patch size and periodic total edge length; and 3) to compare the simulation results from the LHS model and ATLAS. 91 6.2. Methodology 6.2.1. The models ATLAS (Nelson et al. 1995) is a spatial, landscape level planning model. It is a time-step simulation model designed to schedule harvest units according to a wide range of spatial and temporal objectives. With its interface feature, users are able to: 1. set model parameters, like period length, planning horizon, harvest priority; 2. set constraints, such as adjacency, serai stage, reserve, and maximum disturbance rate; 3. make queries of the database and then view the results on a map; and 4. create new objects, like yield curves, super blocks1, and cliques, and add them to the database. The'solution provided by ATLAS is unique under a certain set of objectives. The model generates feasible solutions, but does not optimize the solution. Even so, it has already been recognized and applied in some forest resource planning problems (Thibodeau 1994), and has been used in education. 1 Super block - A block containing more than one polygon which is harvested at one time 92 The capabilities of LHS were described in Chapter 3. 6.2.2. Simulation procedure Four management scenarios were used. For the Atlas Scenario, the solution was obtained with the ATLAS model. The other three scenarios were identified based on the top priority, namely, Timber Scenario (TS) for maximum timber even flow, Road Scenario (RS) for even road construction cost among different planning periods, and Opening size Scenario (OS) for keeping opening size as close to maximum as possible. The general model parameters for both models are listed in Table 6.1. Table 6.2 shows the priorities of the objectives and the penalty cost weights for each objective. The penalty cost coefficients for these objectives can be found in Table 5.1. In Chapter 5,1 described how to set the penalty cost coefficient for each objective. The same rule was applied to setting penalty cost weights here (i.e., within the same priority the more sensitive objective was given a lower weight). For example, in the first priority, opening size (OS) is given a weight of 5, which is much lower than the timber objective (TS), which was given a weight of 25 (Table 6.2). For the Atlas Scenario, the simulation was performed under the strict adjacency rule, and the model was set up to select polygons by age (oldest first). ATLAS was run several times, and after each run, the timber target was adjusted until the timber production reached the maximum even flow. The harvest schedule was then input into LHS for calculating road cost, remnant patches, and edge. 93 LHS was used for the TS, RS, and OS scenarios. The maximum opening size was 20 ha, which was based on two factors. First, ATLAS cannot aggregate polygons into an opening during the simulation (i.e., any opening consists of only one polygon). Table 6.1. The model parameters for all management scenarios Parameters Value Planning horizon 100 yr Period interval lOyr Minimum harvest stand age 100 yr Green-up period lOyr Maximum opening size 20 ha Table 6.2. Objective priorities of the 3 LHS scenarios Priority Scenarios a 1 2 3 TS Timber Opening Road (25)b (2.5) (1) RS Road Timber Opening (25) (2.5) (1) OS Opening Timber Road (5) (1.5) (1) a. TS - Timber scenario; RS - Road scenario; and OS - Opening size scenario b. The penalty cost weight. 94 Second, the mean polygon area is about 11 ha in the case study area, so in order to make comparisons with ATLAS, 20 ha was picked as a reasonable maximum opening size for LHS. All openings under the TS, RS, and OS scenarios were restricted to the 20-ha maximum opening size, but an opening larger than 20 ha was allowed if it consisted of only one polygon. The timber target was determined by running the model several times under only the timber flow objective, and with each run, the timber target was adjusted until the timber production reach the maximum even flow. The road cost target was determined at the beginning of the simulation based on the total cost of unbuilt road links. 6.2.3. Case study area The Elphinstone watershed was selected as the case study area. A detailed description of this dataset can be found in Chapter 5. Stands younger than 80 years old constitute about 50 percent (or 3700 ha) of the total timber production area (Figure 6.1). 95 6.2.4. Analysis methods For all scenarios, comparisons were made on total timber production and road construction cost, and on their variation across the planning periods. Mean remnant patch size was used as an index for evaluating changes in landscape structure under the different scenarios. Total edge length was calculated in each period 96 for all 4 scenarios. Edge is defined as the common boundary between harvest openings (<20 years) and remnant patches (>100 years). 6.3. Results and discussion 6.3.1. Timber production and road construction costs The periodic timber target was 445000 m3, which was obtained by running the model with only the timber even flow objective. The average periodic timber yield and road construction cost under each scenario are summarized in Table 6.3. Also reported are the percent reduction from the Timber Scenario (TS) and the percent reduction from the timber target. Figures 6.2 and 6.3 show the timber harvest and the road construction cost for each scenario over time, respectively. On a Pentium/90 computer, ATLAS took less than a minute to generate a solution. LHS took about 40 minutes because it had to go through more than 20000 iterations to find the best solution. Figure 6.2 shows that the timber yield curves for scenarios TS, RS, and OS descend abruptly in decade 10, and for the Atlas Scenario, in decade 9. This is because about 20% of the stands in landscape were initially in the regeneration stage (<20 years) (Figure 6.1), and they only reached a mature age in decade 10, when they produced relatively less timber than the older stands. 97 Table 6.3. Average periodic timber yield and road construction cost for each scenario Scenarios Timber yield % of reduction % of reduction Road cost Ratio of road (1000mA3) fromTS from Timber Target (1000$) cost / timber TS 437 0.0 1.8 819 1.87 Atlas 421 3.7 5.4 803 1.90 RS 431 1.4 3.1 819 1.90 OS 422 3.4 5.2 818 1.93 480 " 460 1 2 3 4 5 6 7 8 9 10 Decade Figure 6.2. Periodic timber production under different scenarios Timber reduction from the timber target was observed in all scenarios, with the TS having the lowest reduction (1.8%) and the Atlas Scenario the highest (5.4%). 98 Obviously, the reduction in harvest was caused by applying opening size and road cost objectives in the LHS model, and by the adjacency constraint in the Atlas model. Average road construction costs in each period are similar under TS, RS, and OS, but there are variations between periods for all scenarios. Under the TS, the highest periodic harvest was observed at the lowest road cost ratio ($/m3) compared with other scenarios (Table 6.3). However, the TS also resulted in high initial costs, followed by a rapid decline (Figure 6.3). This means the cut was dispersed rapidly across landscape in order to maximize timber production. This trend was also observed in the Atlas and OS scenarios. Compared with the TS, when road cost was set as the top priority (RS), only a 1.4% of reduction in timber harvest was detected (Table 6.3). However, a large variation in timber harvest among periods was observed - the highest periodic volume was 462000 m3, and the lowest, 344000 m3 (Figure 6.2). The RS compensated for its negative effects on timber by the relatively even road construction costs in each period (Figure 6.3). It may be attractive to resource managers for reducing as much as 50% of the initial road construction costs compared with that of the TS. The reduction of initial road costs means that higher revenue may be realized in the early periods. Figure 6.3 shows that the objective of even periodic road construction cost is not exactly met under 99 the RS. The model can meet this objective by using a stricter penalty on road cost, and by simultaneously relaxing opening size and timber even flow constraints. However, it would also have more negative effects on timber production, because there would be relatively fewer candidate stands under strict road constraints. When opening size is set as the top priority (OS), it caused an even larger reduction, but less periodic variation in timber harvest than the RS. Compared with the other scenarios, the ratio of periodic road cost / timber harvest ($/m3) was the highest under the OS (Table 6.3), but the road cost in the first period of the OS was about 25% lower 100 than that of the TS. The opening size constraint can force small polygons to be aggregated into a large opening, so some reduction in early road construction costs is possible. Compared with the other three scenarios, the average timber production was the lowest, and the average road costs were also the lowest under the Atlas Scenario (Table 6.3). Because ATLAS cannot optimize the solution, its solution is not expected to be better than that of LHS. Low average periodic road construction cost under the Atlas Scenario was due to the reduced harvest. It can be seen that even with the low average timber harvest and the low average road cost, the initial road construction cost was still as high as that under TS (Figure 6.3). The simulation results with LHS under only even timber flow constraints showed that a solution for maximum even timber flow was characterized by a range of opening sizes in each period (Figure 6.4). Without adjacency constraints, maximizing timber production will result in a wide size range of openings. These openings can be regarded as an optimal opening series for the timber production objective. Any attempt to change this size series will result in a reduction in timber harvest. The optimal series will differ in other landscapes, depending on the spatial distribution of stands. The results from this study support the finding that spatial harvesting causes high initial road construction cost (Nelson and Finn 1991). However, with LHS, initial construction cost was greatly reduced under the RS at the cost of 1.4% of the timber 101 S <16 ha CT116-20 ha ^ >20 ha Mean opening size 1 2 3 4 5 6 7 8 9 10 Decade Figure 6.4. The opening size series and mean opening area (ha) under only maximum timber flow constraints. harvest and some variation in the average periodic timber harvest. It should be noted that some major road links are already built in the landscape, hence making the problem less binding under the road cost constraints. The RS would have higher timber reduction and greater periodic variation if all the road links in the landscape were unbuilt. 102 6.3.2. The changes in landscape structures and edge length Changes in landscape structure in terms of the distribution of remnant and disturbed patches under each scenario are shown in Figure 6.5. Also reported are changes in the mean remnant patch size and opening size (Figure 6.6), and the periodic edge length (Figure 6.7). The map images in Figure 6.5 show that the landscape was highly fragmented in Year 0. The landscape structure under the Atlas Scenario was closely related to the serai stage distribution. The remnant patch distribution depended on the distribution of these serai stages because the oldest stage had the highest priority for harvest. Since the serai stages were distributed in an aggregated manner in the study area, the landscape under the Atlas Scenario was relatively less fragmented in terms of mean remnant patch size from decade 3 to decade 9. It also had the least amount of edge before decade 6, compared to the other scenarios (Figures 6.6 and 6.7). It can be seen that under the OS, mean opening size was the largest of all the scenarios, the mean patch size was larger than those of the TS and RS in the first 5 decades (Figure 6.6), and the periodic edge length did not change so abruptly as it did under the TS (Figure 6.7). These effects can be regarded as trade offs for reduced timber production as previously discussed. 103 r YearO Year 40 Year 60 Year 80 Year 100 Figure 6.5. The changes in landscape structure over time under different scenarios. 104 Remnant patch Opening TS Atlas • Figure 6.6. The mean remnant patch and opening RS OS A size under different scenarios. 105 o -i 1 1 1 1 1 1 1 1 1 1 2 3 4 5 6 7 8 9 10 Decade Figure 6.7. The periodic edge length under different scenarios. Mean remnant patch size under the RS is larger than under the TS and OS after the 5th decade (Figure 6.6), but the RS did not result in much change in mean opening size, and edge length compared with the TS (Figures 6.6, and 6.7). 106 6.4. Conclusion I explored formulating and solving operational planning problems with different priorities. The results of this study provide resource managers with an indication of how timber supply, road costs, and landscape structure change according to objectives. Setting timber harvest as the top priority resulted in a higher average timber yield; however, this was accompanied by high periodic road construction costs during the early periods. When road cost was set as the top priority, the road costs were relatively evenly distributed in each decade with a small reduction and some variation in periodic timber harvest relative to the TS. From an economic perspective, postponing investment on road construction will increase the present net worth of the timber harvest. From this perspective, the RS is more attractive than the TS. Strict opening size resulted in less timber harvest, and the initial road construction cost was reduced relative to the TS. The advantages of setting opening size as the top priority are related to the landscape structure, such as larger remnant patches. ATLAS produced lower timber harvests, but higher variation in periodic road cost than the LHS scenarios. Since it is a simulation model, it can quickly explore solution space, carry lots of data (less limited by the problem size), and it can be a good learning tool to understand operational problems. However, it should not be used to get the "best" solution. LHS is an "optimization" model. It gives the "best" solution after 107 thousands of iterations that explore the solution space. With LHS, users can highlight solution strategies, and simultaneously deal with many objectives. It should be pointed out that the results from this study are specific to the set of constraints and the initial landscape. Alternative solutions can be obtained by adjusting the combination of objectives, priorities, and their penalty costs. 108 CHAPTER 7 GENERAL CONCLUSION 7.1. Introduction In this research, I have presented techniques for incorporating remnant patch features into a spatial harvest model, LHS. This model is different from other harvest scheduling models in that it is able to account for changes in landscape structure over the planning horizon. Simulation using LHS allows prediction of not only the timing and location of timber harvest or road building, but also what happens to the landscape after timber harvest. 7.2. Why is this research important? Studies of forest resource management through mathematical models can be roughly classified into two groups. Researchers whose studies fall into the first group concentrate on scheduling timber harvest to obtain maximum revenue from forest lands. They are interested in finding optimal solutions in terms of timber harvest and road cost. Non-timber uses (visual quality, wildlife, and hydrology) are dealt with either by using reserves (e.g. environmentally sensitive area, riparian, and special wildlife habitat), or by spatial arrangement of harvest blocks. The researchers whose studies fall into the second group pay more attention to the impact of harvesting on biodiversity and the remnant landscape pattern following harvest 109 activities. Timber harvest is given a lower priority in this group. In British Columbia, the timber industry plays such an important role in the provincial economy that maintaining timber yield is closely related to employment and income, which, in turn, is related to the stability of communities. Therefore, forest management planning should take all the factors (economical, social, biological, environmental) into account. Under these circumstances, studies of the first group seem to be consistent with the goals of forest resource management. On the other hand, the work of the second group is also important because the landscape structure disturbed by forest harvesting has significant impacts on biodiversity. My work makes the ideas of both groups complementary. I have developed the LHS model based on the knowledge of both groups; LHS can be used as a tool to simultaneously schedule timber harvest and analyze the changing landscape structure. With LHS, dispersed harvesting pattern can be improved to meet the requirement of area-based planning with multiple criteria. Since large temporary remnant patches on the landscape are considered as "coarse" filters for maintaining biodiversity (Shafer 1990), this concept has been given more emphasis in LHS than in existing spatial harvest models. By using LHS, the trade-offs were quantified, as a result, resource managers are able to understand long-term consequences of management strategies. 110 7.3. Achievements The achievements of this study fall into two areas. One is the development of the model, and the other is the findings based on model simulations under different scenarios. The development of LHS overcame some difficulties. First, it was difficult to introduce the remnant patch objectives into the model. The remnant patch objective consisted of three remnant patch features, i.e. size, shape, and inter-patch distance. Quantifying these features is not difficult, but the number of calculations is limiting. In a multiperiod planning environment, the simulation involves finding, calculating, and recording remnant patches for each period. The scheduling process involves selecting or de-selecting harvest units, which changes the status of a harvest unit from remnant to harvested and vice versa. Such changes make it very difficult to find a new configuration of remnant patches across the landscape in the periods concerned. Second, it was difficult to meet the objective of even periodic road construction cost. Since each harvest unit has a list of unbuilt road links and, in most cases, a road link is shared by a number of units, the difficulty lies in frequently changing link status (built or unbuilt) following the change of harvest unit status in order to update the periodic road construction costs. Overcoming these difficulties was certainly one of the achievements of this research, since introducing remnant patches and road cost as constraints is highly relevant to operational planning problems. I l l The results of using LHS for different management scenarios may be summarized as follows: 1. The simulation results under different spatial objectives, expressed in terms of opening size and exclusion periods, showed that the exclusion periods caused less reduction in timber harvest under the Relaxed Adjacency rule than under the Strict Adjacency rule. Reduction in timber volume caused by exclusion period constraints could be offset by a larger opening size constraint. In terms of landscape structure, longer exclusion periods tended to increase the number of remnant patches, and thereby caused more habitat fragmentation. However, this effect was only detectable when the exclusion periods did not restrict the periodic harvest area. Remnant patches larger than 500 ha disappeared when about 60% of the total planning area was cut over. Reducing the disturbance rate postponed the time when the greatest number of remnant patches appeared, but doing this did not significantly reduce fragmentation in terms of the patchiness in the landscape. Even reducing the harvest rate by as much as 30% did not guarantee that the large patches (>500 ha) were retained across the planning horizon. Therefore, it is concluded that either changing the spatial constraint formulation or reducing the maximum harvest rate is not effective measure for retaining large patches on the landscape. 2. The simulation results under scenarios with and without the remnant patch (RP) constraints showed that the RP constraints could significantly impact on the changes in landscape structure. The RP constraints controlled dynamic changes in terms of 112 the number, size, and distribution of remnant patches on the landscape. As a result, large remnant patches could be kept much longer compared to scenarios without remnant patch constraints. The results also showed that the effects of reducing the cutting rates on landscape structure were significant only after the RP constraints were applied. The RP constraints also affected the total edge length at a lower cutting rate. Applying the RP constraints did not cause significant timber reduction (from 0.5 - 2.4%) compared with the scenarios without such constraints. However, the effects will vary depending on the landscape's heterogeneity in terms of the composition (species, age, and site class), and on the spatial arrangement of forest stands. The simulation results under different priorities show that setting timber harvest as the top priority caused higher average periodic timber yield at the cost of high variation of periodic road construction cost, with especially high investment in the first period. Setting even periodic road cost as the top priority resulted in relatively even road cost distribution among the planning periods, but this also caused some reduction in timber volume and some variation in periodic timber harvest. The results also showed that strict opening size constraints resulted in less timber harvest, while the initial timber road construction cost was reduced compared to the timber scenarios. However, the advantages of the opening size scenarios were that it resulted in larger remnant patches and relatively less variation in periodic edge length. The results of the comparison with the ATLAS model showed that the harvest schedule generated by ATLAS had a lower timber harvest, and higher 113 variation in periodic road construction cost, compared to the solution produced by LHS. However, ATLAS is fast, more than 50 times faster than LHS, and it is less limited by problem size than LHS. 7.4. Contribution to the forest resource management planning This research has made the following contributions to forest resource management planning: 1. a decision support framework for addressing complicated and conflicting resource scheduling/allocation problems, 2. an approach for introducing the landscape pattern into the spatially constrained model in order to predict and control the dynamics of landscape pattern caused by forest harvesting, 3. techniques to optimize solutions under multiple objectives, especially even-flow road costs remnant patches, which took considerable effort to develop, and 4. a means to explore and understand timber supply and landscape pattern under adjacency constraints, landscape pattern constraints, and objective priorities. 7.5. Potential future studies? For future studies, I offer the following suggestions: 114 1. With the development of landscape ecology, alternative measures could be used to quantify landscape patterns. For example, landscape heterogeneity could be added to the model. There are three dimensions of this feature, namely evenness, abundance, and the spatial arrangement of each serai stage in the landscape. A heterogeneity index can be used as a more meaningful approach to interpreting landscape structure since it takes all serai stages into consideration. Currently it is difficult to quantify the spatial arrangement of serai stages on the landscape. This is the reason that spatial heterogeneity was not used in the model. 2. More factors could be used in aggregating remnant patches, instead of only age as used in this research. Possible factors include tree species, stockings, terrain, site class, and so on. These factors can be used as criteria for evaluating various wildlife habitats; however, this will increase the model's complexity. 3. Habitat suitability indices for various wildlife species could be linked to the changes in landscape pattern in the model, and hence could be evaluated during a simulation. However, much more work in establishing the relationship between species habits and the landscape structure is needed. It was impossible for this research to deal with this issue. 4. In this study, the planning horizon with LHS was limited to one rotation. In other words, each unit is harvested only one time. The model could be improved for solving long term planning problems with multiple rotations. In that case, the model 115 will be much more complicated. For the interim, run it, and then using final solution as beginning inventory, run it again. 7 . 6 . Conclusion The LHS model is basically a timber harvesting scheduling model with the added consideration of landscape structure. It has been developed based on the knowledge of both spatial timber harvest scheduling models and landscape pattern models. 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