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Trade-off analysis of accuracy and spatial resolution in strategic forest planning models Otsu, Kaori 2008

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TRADE-OFF ANALYSIS OF ACCURACY AND SPATIAL RESOLUTION IN STRATEGIC FOREST PLANNING MODELS by KAORI OTSU B.Sc., The University of British Columbia, 2006  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in The Faculty of Graduate Studies (Forestry)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  July 2008 © Kaori Otsu, 2008  ABSTRACT When large areas of forest are modelled, spatial detail can create excessively large databases and adversely affect the processing time. Spatial generalization can be an efficient means of aggregating polygons into blocks in strategic forest planning models. In this study, a sensitivity analysis on spatial generalization was conducted to examine the trade-off between accuracy and spatial resolution to meet the objectives of strategic planning. Five scenarios were designed by generalizing forest cover polygons into the uniform hexagon block sizes of 5, 10, 20, 50 and 100 ha. To quantitatively assess accuracy, deviations caused by spatial generalization were calculated by criteria for hexagon scenarios relative to the base case. Criteria include model inputs (area of natural disturbance type and ungulate winter range) and outputs (harvest volume, growing stock and seral stage distribution). In general, deviations in all criteria increased with the block size. Spatial resolution was also evaluated by the database size and simulation runtime. A negative relationship was observed between spatial resolution and the block size. The trade-off analysis between accuracy and spatial resolution indicated that using the smallest block size of 5 ha creates more detail than necessary. Although scenarios with the block sizes of 50 and 100 ha reduced spatial resolution significantly, the maximum deviations relative to the base case were as high as 14% and 17% in growing stock, 12% and 12% in seral stage distribution, and 6% and 21% in ungulate winter range, respectively. For this study, the preferred block size is in the range of 10-20 ha, however, in general, the preferred block size will vary depending on the importance of each criterion used in the trade-off analysis.  ii  TABLE OF CONTENTS ABSTRACT ................................................................................................................................. ii TABLE OF CONTENTS ............................................................................................................. iii LIST OF TABLES....................................................................................................................... iv LIST OF FIGURES .................................................................................................................... v ACKNOWLEDGEMENTS .......................................................................................................... vi INTRODUCTION ....................................................................................................................... 1 Literature review ..................................................................................................................... 3 Objectives ............................................................................................................................... 7 METHODOLOGY....................................................................................................................... 8 Description of the study area .................................................................................................. 8 Generation of resultant polygons as model inputs – base case............................................. 11 Block-building procedures by spatial generalization – hexagon scenarios ............................ 11 Model simulations ................................................................................................................. 13 Evaluation criteria ................................................................................................................. 17 RESULTS AND DISCUSSION ................................................................................................. 18 Stand group .......................................................................................................................... 18 Age class .............................................................................................................................. 21 Natural disturbance type ....................................................................................................... 24 Ungulate winter range ........................................................................................................... 25 Harvest volume ..................................................................................................................... 29 Growing stock ....................................................................................................................... 31 Seral stage ........................................................................................................................... 32 Seral stage distribution in the total forested area ............................................................... 32 Seral stage distribution in the THLB................................................................................... 33 Seral stage representation by NDT .................................................................................... 36 General discussion ............................................................................................................... 39 Spatial resolution ............................................................................................................... 39 Trade-off analysis .............................................................................................................. 40 CONCLUSIONS....................................................................................................................... 43 AREAS FOR FUTURE RESEARCH ........................................................................................ 44 REFERENCES ........................................................................................................................ 45 APPENDICES .......................................................................................................................... 48 Appendix A: Example calculation of age by the area weighted average ................................ 48 Appendix B: Examples of generalized hexagon blocks ......................................................... 49 Appendix C: Spatial distribution of stand groups for the base case and hexagon scenarios . 53 Appendix D: Age class calculation ........................................................................................ 57  iii  LIST OF TABLES Table 1. Timber harvesting landbase determination for TFL 48 Block 4 ..................................... 8 Table 2. Distribution of biogeoclimatic zones in TFL48 Block 4 .................................................. 9 Table 3. Description of natural disturbance types and definition of seral stages ....................... 10 Table 4. Summary of the number, size and distribution of resultant polygons for the base case .......................................................................................................................................... 11 Table 5. Hexagon block configurations in the THLB ................................................................. 12 Table 6. Summary of stand groups in the THLB at t = 0 ........................................................... 15 Table 7. Constraints applied to the model ................................................................................ 16 Table 8. Recommended seral stage distribution for NDT 1-3 with the intermediate biodiversity emphasis option ................................................................................................................ 16 Table 9. Summary of the database size and simulation runtime............................................... 40 Table 10. Calculation of age by the area weighted average for scenario H5 (ID 39944)........... 48 Table 11. Calculation of age class by the area weighted average for scenario H100 (ID 3841) 57  iv  LIST OF FIGURES Figure 1. Initial age class distribution in the total forested area by non-THLB and THLB. ........... 9 Figure 2. Spatial distribution of natural disturbance types. ...................................................... 10 Figure 3. The left figure (a) shows overlaid THLB polygons with a hexagon grid (100 ha) for scenario H100. Shaded polygons are non-THLB polygons. The right figure (b) shows generalized hexagon blocks in THLB with non-THLB polygons. ........................................ 13 Figure 4. Initial stand group distribution in the THLB. ............................................................... 18 Figure 5. Area by stand group in the THLB for the base case and hexagon scenarios. ............ 19 Figure 6. Spatial distribution of stand groups 10 and 15 for a) the base case and b) scenario H100.................................................................................................................................. 20 Figure 7. Initial age class distribution in the THLB for the base case. ....................................... 21 Figure 8. Area by age class in the THLB for the base case and hexagon scenarios. ............... 22 Figure 9. Spatial distribution of age classes 3 and 4 for a) the base case and b) scenario H100. See Appendix D for age class calculation of hexagon ID 3841. ......................................... 23 Figure 10. Initial distribution of NDT in the THLB...................................................................... 24 Figure 11. Percent deviation in area by NDT in the THLB relative to the base case. ................ 25 Figure 12. Percent deviation in area of UWR in the THLB relative to the base case. ............... 26 Figure 13. Distribution of UWR in TFL 48 Block 4 for the base case. ....................................... 27 Figure 14. Map showing the change in area and location of UWR for scenario H100 relative to the base case. ................................................................................................................... 28 Figure 15. Harvest flow in cubic metres per year for the base. ................................................. 29 Figure 16. % Deviation in harvest flow relative to the base case. ............................................. 30 Figure 17. Growing stock in the non-THLB, THLB and total landbase for the base case. ......... 31 Figure 18. Percent deviation in growing stock in the THLB relative to the base case. .............. 32 Figure 19. Seral stage distribution by NDT in the total forested area for the base case. ........... 34 Figure 20. Seral stage distribution by NDT in the THLB for the base case. .............................. 35 Figure 21. Deviation in early seral cover (%) by NDT in the total forested area relative to the base case. ......................................................................................................................... 37 Figure 22. Deviation in mature/old seral cover (%) by NDT in the total forested area relative to the base case. ................................................................................................................... 38 Figure 23. Linear relationship between the database size and simulation runtime. .................. 40 Figure 24. Trade-off between accuracy and spatial resolution by evaluation criteria. Spatial resolution is expressed in percentage by the number of blocks, database size and simulation runtime relative to the base case. The rest of criteria show maximum deviations relative to the base case. ................................................................................................... 41 Figure 25. The left figure shows overlaid THLB polygons with a hexagon grid (5 ha) for scenario H5. Shaded polygons are non-THLB polygons. The right figure shows generalized hexagon blocks in THLB. ................................................................................................... 49 Figure 26. The left figure shows overlaid THLB polygons with a hexagon grid (10 ha) for scenario H10. Shaded polygons are non-THLB polygons. The right figure shows generalized hexagon blocks in THLB................................................................................. 50 Figure 27. The left figure shows overlaid THLB polygons with a hexagon grid (20 ha) for scenario H20. Shaded polygons are non-THLB polygons. The right figure shows generalized hexagon blocks in THLB................................................................................. 51 Figure 28. The left figure shows overlaid THLB polygons with a hexagon grid (50 ha) for scenario H50. Shaded polygons are non-THLB polygons. The right figure shows generalized hexagon blocks in THLB................................................................................. 52 Figure 29. Spatial distribution of stand groups 10 and 15 for the base case and scenario H5. . 53 Figure 30. Spatial distribution of stand groups 10 and 15 for the base case and scenario H10. 54 Figure 31. Spatial distribution of stand groups 10 and 15 for the base case and scenario H20. 55 Figure 32. Spatial distribution of stand groups 10 and 15 for the base case and scenario H50. 56 v  ACKNOWLEDGEMENTS This research was funded by Genome Canada and Genome BC through Conifer Health project, and the Natural Sciences and Engineering Research Council of Canada (NSERC). I thank my committee members, Dr. Gary Bull, Dr. John Nelson, and Dr. Clive Welham for their significant contributions to this research. I owe special thanks to my supervisors Dr. Gary Bull and Dr. John Nelson for their thoughtful guidance, support and editorial time.  I feel very  fortunate that I was given this opportunity to work with such admirable supervisors. The growth and yield data were kindly provided by Dr. Brad Seely. The GIS data and technical assistance were provided by Arnold Moy. Columbia.  All are from the Faculty of Forestry, University of British  Lastly, I am deeply grateful that my family, friends and colleagues who have  encouraged me in many ways throughout my master’s program.  vi  INTRODUCTION In British Columbia, the majority of the province is publicly owned and it is mandatory for forest managers to maintain healthy and sustainable forests in order to meet a broad range of environmental, social and economic objectives.  To achieve these objectives, planning,  monitoring and assessing shifting forest values must be continuous for adjustment and improvement.  Forest planning is the first crucial step in forest management for projecting  harvest and growing stock levels, the timing and location of harvests, silviculture treatments, costs and profits, impacts on environmental and social values, and the risk of natural disturbance (Forestry Handbook for BC 2005).  Various models have been developed to  support landowners in making these decisions. The focus of early models was on economic objectives such as maximizing harvest volumes and maximizing the net present value (Forestry Handbook for BC 2005). However, as environmental and social objectives affecting the harvest have become more complex, forest planning models have increasingly used spatial data to help forecast both the timing and location of forest management activities (Baskent and Keles 2005). Today spatial forest planning is a commonly used method for modelling forest management scenarios and analyzing spatial aspects of watersheds, harvest blocks, visual quality, biodiversity, carbon content and wildlife habitat.  The ability to identify spatial  relationships and how these affect timber harvest schedules is critical. However, it becomes difficult to model changes over large forests areas when natural disturbances such as fire and disease occur unexpectedly.  For example, the mountain pine beetle (Dendroctonus  ponderosae) outbreak has had a significant impact on timber supply (Ministry of Forests and Range 2007) and adaptation of the spruce weevil (Pissodes strobi) to current and future climate change may also increase the extent and severity of spruce infestation (Spittlehouse and Stewart 2004). Therefore, changes in policy, markets, social demands, technology and climate require that strategic forest planning be revised frequently (e.g. Timber Supply Areas are analyzed every 5 years in British Columbia). 1  Strategic planning differs from tactical or operational planning in that it covers long time horizons and is applied to the entire forest estate to explore uncertainty and develop policy (Nelson 2001). A key issue in this increased planning effort is to determine the minimum level of spatial detail needed to model these forest estates and to answer strategic questions. Various techniques such as mathematical optimization, simulation and meta-heuristics are currently available for strategic forest planning (Baskent and Keles 2005). In spatial modelling the selection of extent and detail is critical. For example, when an enormous landbase such as a region or a province is modelled, spatial data are often aggregated into coarse resolution grids to reduce the database size and processing time. As a result, the associated data attributes are generalized into single values within grids by interpolating or averaging (Van Beurden and Douven 1999).  This is defined as spatial  generalization. When large areas of forest are modelled, it is important to match the level of spatial detail with the strategic objectives, such as estimating harvest levels and growing stock, identifying location and timing of habitat types, and mitigating recreation and visual impacts (Forestry Handbook for BC 2005). Some detailed attributes associated with the forest polygons are not necessary to meet these strategic objectives (Nelson and Davis 2002). Detail can create excessive large databases and adversely affect model processing time.  When the  polygons are merged, detailed forest cover attributes such as species composition, age, height, diameter and site index are generalized. As a result of reducing the number of polygons, database size and processing time can be reduced significantly.  Therefore, spatial  generalization can be an effective and efficient means to aggregate polygons into blocks in strategic planning models, provided the objectives are met. My thesis is organized as follow: First, a literature review relevant to my research is provided on planning hierarchies, heuristic techniques for spatial forest planning at the strategic level, robustness of solutions, and spatial generalization, followed by the objectives of my research. Next, the methodology describes the study area, generation of model inputs, the 2  block-building procedure by spatial generalization, model scenarios and simulations, and evaluation criteria.  Results of simulations are then presented and discussed according to  evaluation criteria for accuracy and spatial resolution. Literature review Forest planning consists of a three-level hierarchical structure: strategic, tactical and operational (Baskent and Keles 2005). At the highest level, strategic planning decisions are associated with land allocation over a long planning horizon for a large estate, and long-term objectives such as harvest volume targets are set.  Then, the tactical planning process  determines what to measure and how to measure it to achieve the strategic objectives for specific management units. Finally, at the operational level, detailed ground-level activities are planned (Baskent and Keles 2005). Traditionally, spatial relationships in forest planning (e.g. adjacency) were not considered at the strategic level due to the large number of binary decision variables involved (Baskent and Keles 2005).  However, with the introduction of modelling  techniques such as meta-heuristics and simulation, spatial forest planning problems can be solved at the strategic level (Baskent and Keles 2005). Monte Carlo integer programming (MCIP) is the simplest technique that has been used in spatial forest planning. Nelson et al. (1991) developed procedures for linking spatial shortterm plans to long-term strategic harvest goals. MCIP was used to generate 3-decade spatial plans that were then integrated into a 15-decade linear program (LP). Daust and Nelson (1993) also combined LP and MCIP to examine the impact of block size and exclusion period on sustained yield predictions and long-term harvest schedules. Simulated annealing (SA) and tabu search (TS) are common meta-heuristic techniques to solve spatial forest planning problems. Ohman and Eriksson (1998) used SA to generate aggregated reserves (i.e. core area) at the landscape level over a long-term planning period. Ohman and Eriksson (2002) solved a long-term forest planning problem with even-flow and inventory constraints using three approaches. One of them used only SA while the other two 3  were a combination of LP and SA. The results indicated that the combination of LP and SA produced more effective solutions. Ohman and Lamas (2003) used SA to develop a strategic model for aggregating harvests in time and space. Bettinger et al. (1997) used TS to derive a timber harvest schedule that achieves the maximum even-flow harvest level with harvest adjacency constraints and spatial wildlife habitat quality goals. Bettinger et al. (1998) developed a TS model to select feasible management activities with an even-flow harvest volume constraint and aquatic habitat quality goals. Results showed reasonable solutions that were within 10% of an estimated optimal solution. Caro et al. (2003) developed a multi-period forest planning model that maximizes the net present value with some spatial constraints, using a TS procedure with 2-opt moves.  2-opt moves can  simultaneously swap the harvest timing of two units while 1-opt moves change the harvest timing of a single unit (Bettinger et al. 2002). Other algorithms and hybrid algorithms have been examined by various researchers. Borgers and Hoganson (1999) developed a decomposition strategy combined with dynamic programming to solve an 80-year harvest scheduling problem with adjacency constraints. Bettinger et al. (2003) used a threshold accepting meta-heuristic technique to develop a spatial forest plan with wildlife habitat goals and silviculture management goals over a 100-year time horizon.  Using hybrid algorithms Boston and Bettinger (2001) examined two modelling  approaches to meet harvest volumes goals with wildlife habitat and green-up constraints over fifteen, 10-year periods. The first approach combined LP for assigning volume goals and TS for addressing spatial constraints. The second approach used only TS without the LP guidance for harvest volumes. Results showed that the first approach was superior in terms of net present value. Nalle et al. (2004) developed a method that combined an optimization model for timber production and a simulation model for species conservation to find cost-effective forest management alternatives over a 100-year planning horizon. Simulation models do not produce an optimal solution, however, they are simpler and faster than meta-heuristics in the solution procedure. They have the ability to run very large 4  problems and divide them into short time-steps, and to track detailed stand attributes (Forestry Handbook for BC 2005). Gustafson and Crow (1996) constructed a timber harvest allocation model HARVEST to predict the spatial pattern of forest openings with alternative harvest strategies over 150 years. HARVEST was able to assess the long-term spatial consequences of changes in landscape structure, commodity production, and other resource values that are spatially dependent.  Bettinger and Lennette (2004) developed a spatial simulation model  (LAMPS) to examine changes to landscape structure over 100 years, incorporating the management intentions of four major landowner groups and vegetation dynamics. Seely et al. (2004) used the simulation model FPS-ATLAS to examine a baseline natural disturbance scenario with no harvesting or fire suppression compared to two alternative landscape management scenarios with dispersed harvesting and aggregated harvesting. Each scenario was simulated for 300 years, and it was found that the aggregated scenario was more desirable than the dispersed scenario with respect to the amount of active road required, patch-size distributions and short-to-medium term impacts on backcountry recreation opportunities. Since a simulation technique does not optimize a solution, an optimization technique may appear more desirable in strategic forest planning. However, a simulation technique has the ability of relaxing the harvest level, which may react to changes over time better as uncertainty increases in the planning environment. Boyland et al. (2005) tested the robustness of optimization and simulation techniques by introducing random variation into solutions of harvest schedules and examining the ability of responding to changes under different levels of uncertainty. When uncertainty was low optimization produced a better solution than simulation. However, when uncertainty was high, flexibility becomes important in producing more robust schedules. In this case, simulation has more flexibility than optimization and is therefore more robust. A simulation model is used in my research because my intent is not to explore optimal solutions but rather to explore spatial generalization in strategic forest planning. Simulation models are commonly used to schedule harvesting in British Columbia and they have been used for various research projects on spatial forest planning at the strategic level. 5  Spatial generalization is a technique of aggregating spatial detail (e.g. polygons) and simplifying associated attributes in order to reduce the database size and processing time. This is a useful technique when large areas are modelled, however, spatial detail is often compromised. The research on spatial generalization in forest planning is relatively new and there have been few studies on this subject. Remsoft Inc. (1996) designed a blocking algorithm to aggregate polygons which corresponded to stand types that were to be selected for harvesting in a strategic harvest scheduling model.  The aggregated stands were then  subdivided into hexagons to form harvest blocks ranging from 20 to 120 hectares, with shape controls added to the algorithm to promote clustered blocks. Harvest flow from the schedule with shape controls was much higher than the schedule without shape controls. Nelson (2001) compared two blocking methods to split and aggregate polygons into three block size distributions, one method simply based on forest cover polygons and the other on detailed operational blocks that were designed manually. The results indicated that forest cover data provided a reasonable alternative to manual blocking in tactical and strategic plans. Nelson and Davis (2002) proposed a blocking method for generalizing GIS inventory data to a set of common polygons after defining the strategic questions to be answered. They generalized polygons into strata based on age, species, site productivity, and age relative to the minimum harvest age to compare the effectiveness of detailed and generalized polygons.  Their  generalized harvest schedules showed an average deviation of 0.2% over time relative to the detailed polygon schedules. Database size and run times were reduced by more than 80%. Boyland et al. (2004) used a simulated annealing (SA) approach to aggregate polygons from a GIS dataset into hexagon grids in order to lower the number of units and therefore reduce problem complexity and computing time. They explored seven problem sizes by increasing the number of units (decreasing hexagon size) and compared performance with an objective function that specified relative importance of 6 objectives. The SA algorithm found scores within 1.7% - 4.4% of theoretical optimum values from small to large size problems, respectively. The  6  best scores were found using smaller problems with a short computational time or larger problems with an increased computation time. Objectives Although there have been studies on deviations in model outputs caused by one level of spatial generalization and sensitivity analysis on objective functions by multiple levels of spatial generalization, no studies have been conducted that examine both at the same time. The focus of my research will be to incorporate increasing spatial generalization into strategic forest planning models and examine accuracy of model inputs and outputs. More specifically, I will explore generalizing forest cover polygons into progressively larger blocks and measure corresponding deviations from a non-generalized model in order to evaluate if these blocks are sufficient to achieve strategic objectives.  On Tree Farm Licence (TFL) 48 Block 4 I will  investigate the minimum spatial detail that is necessary to meet the objectives of strategic planning by analyzing a trade-off between accuracy and spatial resolution.  7  METHODOLOGY The methodology is presented in five sections: description of the study area, generation of resultant polygons as model inputs, block-building procedure by spatial generalization, model simulations, and evaluation criteria. Description of the study area TFL 48 Block 4 in the Dawson Creek Timber Supply Area was chosen as a case study. It is located in north-eastern British Columbia and managed by Canadian Forest Products Limited. The land cover is categorized into forest and non-forest types. The total area of Block 4 is 286 972 ha of which 87 % is productive forest and 57 % contributes to the timber harvesting landbase (THLB). Table 1 shows additional areas that are deducted from the total forested area to determine the THLB. Table 1. Timber harvesting landbase determination for TFL 48 Block 4 Category Total Area Non-Forest Total Forested Area Reduction: Inoperable Areas NDT5 Low Sites Problem Forest Parks Protected Areas Archaeological Sites Riparian Buffers Visual Preservation Wildlife Habitat Areas Rare Site Series Forested Islands Total Reduction Timber Harvest Landbase  Area (ha)  Total area (%)  Total forested area (%)  286 972 36 404 250 568  100% 13% 87%  100%  8 406 2 670 32 043 20 910 288 4 660 6 17 502 80 74 921 121 87 681 162 888  3% 1% 11% 7% 0.1% 2% 0.002% 6% 0.03% 0.03% 0.3% 0.04% 31% 57%  3% 1% 13% 8% 0.1% 2% 0.003% 7% 0.03% 0.03% 0.4% 0.05% 35% 65%  Block 4 is covered by four biogeoclimatic (BEC) zones: Engelmann Spruce-Subalpine Fir (ESSF), Boreal White and Black Spruce (BWBS), Sub-Boreal Spruce (SBS), and Alpine Tundra (AT).  The BEC zone distribution is summarized in Table 2.  The ESSF zone  encompasses more than half of Block 4 (57%) where the climate is severe with short, cool 8  growing seasons and long, cold winters (Klinka et al. 2000). The remainder of Block 4 is covered by BWBS zone (24%), SBS (23%) and AT (1%). The majority of commercial tree species are Engelmann spruce, white spruce, hybrid spruce, lodgepole pine, subalpine fir, trembling aspen and cottonwood (Ministry of Forests and Range 2007). The initial age of forest stands is categorized into age classes 1(0-20 years), 2(21-40 years), 3(41-60 years), 4(61-80 years), 5(81-100 years), 6(101-120 years), 7(121-140 years), 8(141-250 years) and 9(>250 years) and the age class distribution of the total forested area is presented in Figure 1. These age classes are used in the provincial forest cover inventory. The majority of stands in the THLB are old or mature, representing an old forest surplus. Table 2. Distribution of biogeoclimatic zones in TFL48 Block 4 BEC zone Area (ha) AT 3 464 BWBS 67 953 ESSF 150 939 SBS 64 616  Distribution 1% 24% 53% 23%  60,000  50,000  Area (ha)  40,000 Non-THLB  30,000  THLB  20,000  10,000  0 1 (0-20)  2 (21-40)  3 (41-60)  4 (61-80)  5 6 7 8 (81-100) (101-120) (121-140) (141-250)  9 (>250)  Age class  Figure 1. Initial age class distribution in the total forested area by non-THLB and THLB.  Four natural disturbance types (NDT) have been identified in Block 4: NDT 1, NDT 2, NDT 3, and NDT 5 (Ministry of Forests 1999). Stand-initiating events for each disturbance type 9  are described as rare (350-year interval) for NDT 1, infrequent (200-year interval) for NDT 2, and frequent (125-year interval) for NDT 3 (Ministry of Forests 1999). NDT 5 covers Alpine Tundra and Subalpine Parkland that occurs above the treeline (Ministry of Forests 1999). Therefore, polygons within NDT 5 are excluded from the THLB. NDTs tend to overlap with biogeoclimatic zones: NDT 1 with ESSF, NDT 2 with SBS, and NDT 3 with BWBS. Types of natural disturbance include wind, fire and landslides in NDT 1, drought and fire in NDT 2, and fire, outbreaks of defoliating insects and root diseases in NDT 3 (Ministry of Forests 1999). Definitions of seral stages within each NDT are shown in Table 3 (Ministry of Forests 1995) and their spatial distribution is presented in Figure 2. Table 3. Description of natural disturbance types and definition of seral stages Seral stage (age) NDT Forest area (ha) Distribution THLB (ha) Early Mature <40 >120 1 83 131 33% 45 454 <40 >100 2 104 684 42% 75 609 <40 >100 25% 41 799 3 61 844 Source: Biodiversity Guidebook 1995.  Old >250 >250 >140  Figure 2. Spatial distribution of natural disturbance types.  10  Generation of resultant polygons as model inputs – base case Forest cover polygons were defined by tree species composition, age class, site index and stocking class. Using GIS, the forest cover layer was overlaid with a set of other resource layers such as riparian areas, ecological reserves, visual zones and wildlife habitat areas (Seely et al. 2004). The inclusion of the other resource layers is important for representing other forest values to achieve environmental, social and economic objectives. As a result of overlaying various resource layers, a large number of ‘slivers’ were created consisting of polygons with a relatively small area. These small polygons are not practical to be used as harvest units and are problematic when adjacency constraints are applied. Slivers (i.e., polygons) in the THLB smaller than 0.01 hectare were therefore eliminated by merging them with the largest adjacent polygon. Non-THLB polygons <0.01 ha were not removed in order to maintain the detail of stream and road buffers. As a result of overlays, and following sliver removal 100 894 polygons were created for the base case. A summary of the number, size and distribution of resultant polygons for the base case is presented in Table 4. Table 4. Summary of the number, size and distribution of resultant polygons for the base case THLB Non-THLB Polygons Total polygons 41 909 58 985 Minimum size (ha) 0.01 < 0.01 Maximum size (ha) 110.49 121.71 Mean size (ha) 3.89 2.10 Polygons < 0.1 ha (%) 85 (0.2%) 5635 (9.6%) < 1 ha (%) 390 (0.9%) 21 452 (36.4%) < 5 ha (%) 32 049 (76.5%) 53 478 (90.7%) < 10 ha (%) 39 859 (95.1%) 58 106 (98.5%) < 100 ha (%) 41 908 (100.0%) 58 984 (100.0%)  Block-building procedures by spatial generalization – hexagon scenarios The block-building procedure aggregates THLB polygons into harvest blocks by spatial generalization using a hexagon grid system. GIS was used to overlay the THLB polygons with a hexagon grid. Once this was done, the resultant THLB polygons were aggregated into a single generalized unit within each hexagon. The non-THLB polygons were not aggregated to avoid compromising the detail of stream and road buffers, reserves and other significant resource zones. To spatially generalize polygon attributes, the dominant stand type by area 11  was selected and the age was determined by calculating the area weighted average of all THLB polygons within the hexagon (see Appendix A). This procedure was repeated using hexagon sizes of 5, 10, 20, 50 and 100 ha, and these were subsequently used in scenarios H5, H10, H20, H50 and H100. Hexagon block configurations in the THLB are summarized in Table 5. Scenario H5 generated more blocks than the number of polygons in the base case. This is because the polygons greater than 5 ha, which counts for 23.5% of the THLB polygons, were split by the 5 ha hexagon grid. Hexagons were chosen over squares or rectangles because they minimize corner point adjacency problems (Walters 1996). Figure 3 shows an example of generalized hexagon blocks for scenario H100. Examples for other scenarios H5, H10, H20 and H50 are presented in Appendix B. Table 5. Hexagon block configurations in the THLB Scenario Base H5 41 909 Number of blocks 47 852 (polygons) Number of blocks relative to the base 114% case (%)  H10  H20  H50  H100  24 915  12 944  5 466  2 838  59%  31%  13%  7%  12  (a) Before spatial generalization for scenario H100 (b) After spatial generalization for scenario H100 Figure 3. The left figure (a) shows overlaid THLB polygons with a hexagon grid (100 ha) for scenario H100. Shaded polygons are non-THLB polygons. The right figure (b) shows generalized hexagon blocks in THLB with non-THLB polygons.  Model simulations The forest-level simulation model FPS-ATLAS (Nelson 2003) was used to model forest scenarios and forecast the long-term harvest sustained yield (LTSY). The LTSY is the steadystate harvest level following the conversion period (Forestry Handbook for BC 2005).  In this  study area the age class structure indicates an old forest surplus, therefore, I choose a harvest policy of maximizing harvests in the first 50 years by harvesting 20% higher than the LTSY. The model was run for a 250-year planning horizon using 10-year time steps. With an oldestfirst harvest priority, the model simulated timber harvest according to a combination of temporal and spatial objectives and a set of constraints (Nelson 2003). The silviculture system used is 13  clear-cutting with 5% retention of wildlife tree patches. Access to cutblocks is assumed to be available throughout the THLB, therefore, roads are not included in the model. Blocks and polygons are assigned to growth and yield curves based on the dominant stand group. Stand attributes such as species composition, site quality and harvest history are used as input data to generate growth and yield curves with the FORECAST simulation model.  FORECAST  (Kimmins et al. 1999) is a hybrid growth and yield model that combines the empirical modelling approach with the ecosystem process-based simulation modelling. Curve data provided by FORECAST were imported into FPS-ATLAS and used to create 13 natural and 13 managed stand groups (Table 6). Future stands are represented by the managed stand groups. Natural stands are converted to managed stand groups following harvest. The minimum harvest age for stand groups is based on a minimum merchantable volume of 140 m3 per hectare or the age that maximizes the mean annual increment (Ministry of Forests and Range 2007). Minimum harvest ages range from 70 to 200 years.  14  Table 6. Summary of stand groups in the THLB at t = 0 Stand Description (leading Stand Minimum group species-site quality) category harvest age 1 2 3 4 7 10 11 14 15 20 21 81 83 84 85 86 87 91 92 94 95 100 101 133  Pine-poor Spruce-poor Pine-medium Spruce-medium Deciduous-poor Deciduous-medium Spruce-good Mixed conifer-poor Mixed conifer-medium Mixed deciduous-poor Mixed deciduous-medium 1 Mixed conifer- ESSFw Pine-poor Pine-medium Spruce-poor Spruce-medium Spruce-good Deciduous-poor Deciduous-medium Mixed conifer-poor Mixed conifer-medium Mixed deciduous-poor Mixed deciduous-medium Mixed conifer-ESSFw  Natural  Managed  120 140 120 120 100 80 110 110 110 110 90 200 120 110 120 110 100 80 70 110 80 100 80 160  Post-harvest stand group 83 85 84 86 91 92 87 94 95 100 101 133 83 84 85 86 87 91 92 94 95 100 101 133  Area in THLB (ha) 23 222 41 872 24 117 9 445 2 198 8 141 556 1 676 8 001 1 164 2 672 25 095 0 1 535 2 328 4 913 82 0 436 316 512 0 70 4 537  Each hexagon scenario runs generalized blocks with a specific size of 5, 10, 20, 50 and 100 ha. Based on the current Rationale for AAC Determination (Ministry of Forest and Range 2007), constraints to maintain minimum levels of ungulate winter range (UWR), biodiversity and adjacency are applied in the model (Table 7). The adjacency constraint requires a minimum of 10 year green-up for adjacent blocks. UWR for the Sukunka Graveyard (elk and mule deer) covers 2637 ha and requires specific seral stage constraints (Ministry of Forest and Range 2007). The retention of wildlife tree patches (WTPs) is applied at 5% for each cutblock. WTPs are not spatially indentified; however, they are accounted for through harvest volume reductions as percent of block reserved. The seral stage distribution constraints are applied in each NDT and require a minimum level of mature and old stands, and a maximum level of early stands (see Table 8). These constraints are intended to modify harvesting by mimicking the frequency  1  ESSF subzone where it is very wet and very cold.  15  of stand initiating events.  Also, an old growth management constraint requires that at least  13% of the total area be kept older than 140 years. Blocks and polygons that belong to each of these categories are grouped into cliques in FPS-ATLAS so that specific constraints can be applied to each clique. When blocks and polygons belong to more than one clique, they must pass all constraints in order to be harvested. Table 7. Constraints applied to the model Category Area (ha) Description 162 888 Minimum 10 years between adjacent Green-up requirement (total THLB) polygons/blocks 2 637 Maximum 20% covered with trees < 3m and Ungulate winter range (THLB - 1506) Minimum 50% of stands > 100 years 250 568 Seral stage distribution by natural disturbance Landscape-level biodiversity (total forested area) type 1-3 (Table 8) 162 888 Retention 5% for wildlife tree patches within Stand-level biodiversity (total THLB) cutblock/polygon 250 568 Minimum 13% of the total forested area > 140 Old growth management (total forested area) years Source: Tree Farm Licence 48: Rationale for Allowable Annual Cut Determination 2007. Table 8. Recommended seral stage distribution for NDT 1-3 with the intermediate biodiversity emphasis option Seral stage NDT Early Mature/old (% of area) (% of area) 1 22 36 2 36 31 3 54 23 Source: Biodiversity Guidebook 1995.  Natural disturbances such as fires, insects and diseases are not simulated in the model. Therefore, the long-term timber supply and growing stock forecasts will likely be overestimated. While natural disturbance types according to fire frequencies are identified in the study area and seral constraints are applied, the FPS-ATLAS model requires an external disturbance module to explicitly simulate fire occurrences (Peter and Nelson 2005).  Adding another disturbance  module was not done because it complicates the process of isolating the effects of spatial generalization.  16  Evaluation criteria Model outputs include harvest volume, growing stock and seral stage distribution over time. Changes in area by model inputs such as NDT and UWR will also be calculated for evaluation. These inputs and outputs for hexagon scenarios will be compared to the base case for accuracy. To quantitatively assess accuracy of these criteria, the percent deviation caused by spatial generalization will be calculated as: [1]  % deviation = [(amount in scenario/amount in base case) - 1] x 100%  The model database size and simulation runtime for spatial resolution will also be compared for the base case and hexagon scenarios. Finally, a trade-off analysis between accuracy and spatial resolution by criteria will be used to evaluate which scenario is preferred.  17  RESULTS AND DISCUSSION This section presents changes in area of stand group and age class for hexagon scenarios relative to the base case, followed by deviations in evaluation criteria: natural disturbance type, ungulate winter range, harvest volume, growing stock and seral stage distribution. Stand group Figure 4 shows the initial stand group distribution in the THLB for the base case. Stand group 2 (spruce-poor) is notably dominant, covering 26% of the THLB, followed by stand group 81 (mixed conifer-ESSFw), stand group 3 (pine-medium) and stand group 1 (pine-poor). The majority of stands in the THLB are natural stands, with managed stands accounting for only 9% of the THLB. 50,000 45,000 40,000  Area (ha)  35,000 30,000 25,000 20,000 15,000 10,000 5,000 0 1  2  3  4  7  10 11 14 15 20 21 81 84 85 86 87 92 94 95 101 133 Stand group  Figure 4. Initial stand group distribution in the THLB.  Figure 5 shows differences in area by stand group between the base case and hexagon scenarios. Large differences in area were observed for stand groups 3, 4, 15 and 81. Areas were significantly overestimated for stand groups 3 and 81 and underestimated for stand groups 4 and 15. 18  45,000 40,000 35,000  Area (ha)  30,000  Base H5  25,000  H10 H20  20,000  H50 15,000  H100  10,000 5,000 0 1  2  3  4  7  10 11 14 15 20 21 81 84 85 86 87 92 94 95 101 133 Stand group  Figure 5. Area by stand group in the THLB for the base case and hexagon scenarios.  These differences are related to the spatial distribution of stand groups. Some stand groups have clustered polygons while others have dispersed polygons.  When areas are  underestimated for hexagon scenarios, small polygons within stand groups in the base case tend to be dispersed. On the other hand, when they are overestimated, polygons in the base case tend to form patchy clusters as observed in stand group 3 (pine-medium). These larger clusters of polygons tend to occupy more hexagon blocks than dispersed polygons. When there is little difference in area as observed in stand group 2 (spruce-poor), polygons in the base case tend to be in a small number of large clusters and these tend to be less dispersed. For example, stand group 10 (deciduous-medium) and stand group 15 (mixed conifer-medium) are almost equal in area, however, stand group 10 consists of more clustered deciduous stands (Figure 6). Areas in stand group 15 for hexagon scenarios are much smaller than the base case because the dispersed mixed conifer stands tend to get merged into more dominant stand groups at the time of spatial generalization. This trend becomes more apparent as the block size increases as shown for scenarios H5, H10, H20 and H50 in Appendix C.  19  a) Base Case  b) Scenario H100  Figure 6. Spatial distribution of stand groups 10 and 15 for a) the base case and b) scenario H100. 20  Age class The initial age class distribution in the THLB for the base case is shown in Figure 7. The most dominant age class 8 (141-250 years) covers 23% of the THLB, followed by age class 5 (81-100 years) at 20%. It is apparent that there is a surplus of mature and old stands within the THLB.  50,000 45,000 40,000  Area (ha)  35,000 30,000 25,000 20,000 15,000 10,000 5,000 0 1 (0-20)  2 (21-40)  3 (41-60)  4 (61-80)  5 6 7 8 (81-100) (101-120) (121-140) (141-250)  9 (>250)  Age class  Figure 7. Initial age class distribution in the THLB for the base case.  Figure 8 shows differences in area by age class between the base case and hexagon scenarios.  Similar to stand groups, the differences become greater as the hexagon size  increases. There are little differences in age classes 2, 3 and 5 for all hexagon scenarios. Notably, while areas of age class 1 for all hexagon scenarios were significantly underestimated from the base case, areas of age class 6 were significantly overestimated.  21  45,000 40,000 35,000  Area (ha)  30,000  Base H5  25,000  H10 H20  20,000  H50 H100  15,000 10,000 5,000 0 1  2  3  4  5  6  7  8  9  Age class  Figure 8. Area by age class in the THLB for the base case and hexagon scenarios.  As described for stand groups, these differences in area are related to the spatial distribution of age classes. For example, areas of age class 1 were significantly underestimated for all hexagon scenarios because calculating the weighted average age by area at the time of spatial generalization decreased the area of age class 1.  This can be explained by the  dispersed distribution of many small polygons in age class 1, resulting from dispersed harvesting over the past 20 years. Initial areas of age classes 3 and 4 are almost equal, however, differences for hexagon scenarios in age class 4 are much larger than age class 3. As a result of calculating the weighted average ages by area, generalized blocks with new values happened to be concentrated in age class 4 and the area of age class 4 increased as shown in Figure 9. Appendix D provides an example of age calculation by the area weighted average and shows how hexagon ID 3841 in Figure 9 became age class 4.  22  a) Base Case  b) Scenario H100  Figure 9. Spatial distribution of age classes 3 and 4 for a) the base case and b) scenario H100. See Appendix D for age class calculation of hexagon ID 3841. 23  Natural disturbance type Figure 10 shows the distribution of natural disturbance types (NDT) 1-3 in the THLB for the base case. NDT 2 is most dominant covering almost a half of the THLB. 100,000  80,000  Area (ha)  60,000  40,000  20,000  0 NDT 1  NDT 2  NDT 3  Figure 10. Initial distribution of NDT in the THLB.  Figure 11 shows deviations in area by NDT for hexagon scenarios relative to the base case. Deviations for all hexagon scenarios are relatively small since each NDT is large in area. These range from 0.1% to 1.5% in NDT 1, -1.0% to 0.0% in NDT 2, and -0.3% to 0.2% in NDT 3. There is little difference in deviations among all scenarios.  24  2.0% 1.5%  Deviation (%)  1.0% 0.5%  H5 H10  0.0%  H20 H50 H100  -0.5% -1.0% -1.5% -2.0% NDT1  NDT2  NDT3  Figure 11. Percent deviation in area by NDT in the THLB relative to the base case.  Ungulate winter range Figure 12 shows deviations in area of ungulate winter range (UWR) for hexagon scenarios relative to the base case. The area of UWR in the THLB for the base case is 1506 hectares and this was used to calculate deviations. Deviations for hexagon scenarios range from -20.9% to 2.2% and tend to increase with the block size.  25  25% 20% 15%  Deviation (%)  10% 5% 0% -5% -10% -15% -20% -25% H5  H10  H20  H50  H100  Scenario Block Size (ha)  Figure 12. Percent deviation in area of UWR in the THLB relative to the base case.  There is little change in area of UWR for scenarios H5, H10 and H20 while deviations become negatively large for scenarios H50 and H100. Notably, scenario H20 represents the base case well. This is because the hexagon size of scenario H20 more closely matches to the average patch size of UWR in the THLB, calculated as 21.5 ha. When THLB polygons are aggregated into a larger block such as scenarios H50 and H100, some polygons that used to be within UWR disappear. Underestimating the area of UWR is an example of problems caused by spatial generalization. For example, the distribution of UWR is shown in Figure 13 and there are 7 UWRs in the north-eastern part of Block 4. Since each UWR is small in area and they are dispersed, the edge polygons of UWR easily lose the UWR attribute when they are merged into a large block.  26  Figure 13. Distribution of UWR in TFL 48 Block 4 for the base case.  Figure 14 shows original UWR clusters for the base case and illustrates the change in area and location of UWR for scenario H100. Non-THLB polygons which belong to UWR always remain within original UWR boundaries for all hexagon scenarios. However, spatial generalization tends to change the location of THLB polygons beyond those boundaries. Spatial generalization not only underestimating the area of UWR but also caused clusters of UWR to be more fragmented. One way to avoid this problem in the future is to treat important habitat similar to non-THLB polygons that are not aggregated.  27  Figure 14. Map showing the change in area and location of UWR for scenario H100 relative to the base case.  28  Harvest volume The harvest flow for the base case is shown in Figure 15. Given that the THLB starts with an old forest surplus, harvest scheduling is designed to maximize the harvest volume during the first 50 years before dropping to the long term sustained yield (LTSY). The harvest level for the base case is 434,000m3/year during the first 50 years and 362,000m3/year in the long term.  500,000  Volume (m3) / year  400,000  300,000  200,000  100,000  0 10  30  50  70  90  110  130  150  170  190  210  230  250  Year Figure 15. Harvest flow in cubic metres per year for the base.  Deviations for harvest flow from hexagon scenarios relative to the base case are shown in Figure 16. Overall, deviations for all hexagon scenarios are not large. There is an increasing trend from 0.5% to 3.9% as the block size increases from 5 ha to 100 ha. While scenarios H5 and H10 show little change in the harvest volume, scenarios H20, H50 and H100 overestimate the harvest volume by approximately 3-4%.  This is because  spatial generalization changed the areas by stand group and age class. One reason is that overestimating the area of stand groups on good sites increased the LTSY. As seen in Figure 5, scenario H100 overestimated the area in stand group 3 (pine-medium) by 8 000 hectares.  29  5% 4% 3%  Deviation (%)  2% 1% 0% -1% -2% -3% -4% -5% H5  H10  H20  H50  H100  Scenario Block size (ha)  Figure 16. % Deviation in harvest flow relative to the base case.  Stand group 3, in fact, is most productive site with 465m3 per hectare at the maximum mean annual increment. Another reason is that overestimating the generalized age increased the area of mature forests available for harvesting (Figure 8). This was confirmed by estimating the LTSY using the Hanzlik formula (Davis et al. 2000). As a result, the harvest volume was overestimated for all hexagon scenarios. In general, larger blocks tend to ease the adjacency constraint and allow more volume to be harvested. However, in this model 10-year adjacency constraint did not affect the harvest flow for any scenario when the constraint was applied. This means that 10-year adjacency constraint is not strict enough to cause reduction in harvest flow.  When the adjacency  constraint increased the green-up age to a minimum of 20-30 years, reduction in harvest flow was observed. Therefore, the adjacency constraint was likely not a contributing factor to the deviations in harvest flow.  30  Growing stock Figure 17 shows growing stock over time in the non-THLB, THLB and total landbase for the base case. During intensive harvesting in the first 50 years, growing stock in the THLB continues to decrease because regenerating stands cannot produce more volume than the volume being lost to harvest. However, it starts to recover by the end of the first rotation period and stabilizes in the second rotation period. Growing stock in the non-THLB increases because reserved stands continue to grow in the absence of disturbance.  60,000,000  50,000,000  Volume (m3)  40,000,000  Non-THLB THLB Total  30,000,000  20,000,000  10,000,000  0 0  20  40  60  80  100 120 140 160 180 200 220 240 Year  Figure 17. Growing stock in the non-THLB, THLB and total landbase for the base case.  Deviations in growing stock in the THLB for hexagon scenarios relative to the base case are shown in Figure 18.  In general growing stock in the THLB for hexagon scenarios is  overestimated more as the hexagon size increases. Up to year 100, significant deviations are observed for all hexagon scenarios. Between years 100 and 150, deviations become smaller and closer to 0% for all scenarios. After year 150, deviations for scenarios H5 and H10 become stable around 0%. In contrast, scenarios H20, H50 and H100 then start to underestimate growing stock significantly.  31  20% 15%  Deviation (%)  10% H5  5%  H10 0%  H20 H50  -5%  H100  -10% -15% -20% 0  20  40  60  80  100  120  140  160  180  200  220  240  Year  Figure 18. Percent deviation in growing stock in the THLB relative to the base case.  It takes almost one rotation period to resolve significant deviations for all hexagon scenarios. This can be explained by deviations in estimating initial areas by age class as shown in Figure 8. Areas of early seral (age class 1) and old seral (age class 8-9) were underestimated for all hexagon scenarios.  These age classes typically have lower annual  growth rates relative to age classes 2-7. On the other hand, areas of mature stands (age class 6-7) were overestimated for all hexagon scenarios where the growth is much higher. Therefore, deviations in growing stock in the THLB continue to increase positively up to year 50. At year 50 deviations for scenarios H5 and H10 decrease and remain very small after year 100 because the harvest flow is very close to the base case (Figure 16). However, the harvest levels for scenarios H20, H50 and H100 are higher than the base case, consequently, growing stock keeps decreasing from years 50 to 220 and becomes much lower than the base case. Seral stage Seral stage distribution in the total forested area Figure 19 shows the seral stage distribution over time by NDT in the total forested area for the 32  base case. The seral stage definitions (Table 3) and the seral stage constraints (Table 8) applied to the total forested area vary by NDT. Firstly, the distribution in NDT 1 is more stable relative to those in NDTs 2 and 3. Mature/old seral cover is much higher in NDT 1 than early seral cover over the entire planning horizon. In NDTs 2 and 3, on the other hand, the difference between seral covers becomes very small in the second rotation period. This is explained by the way seral stage constraints were applied in NDT 1 where the maximum percent of the early seral cover (22%) is lower and the minimum percent of the mature/old seral cover (36%) is higher than other NDTs. In NDT 1 binding points of the early seral cover are observed at years 10-50, 80-90, and 170 while the mature/seral constraint is not binding. In NDT 2, constraints are binding at years 40-50 for the early seral cover (36%) and at year 100 for the mature/old seral cover (31%). Both early and mature/old seral constraints are never binding in NDT 3. In NDTs 2 and 3 early seral cover continues to increase while mature/old seral cover continues to decrease in the first 100 years. It appears that relaxed constraints of the maximum percentage of the early seral cover and the minimum percentage of the mature/old seral cover allowed more harvesting in NDTs 2 and 3.  In the second rotation period those seral distributions  become relatively stable as harvesting and regeneration become regulated by the seral constraints. Seral stage distribution in the THLB Figure 20 shows the seral stage distribution over time by NDT exclusively for the THLB for the base case. More extremes are observed here because the constraints were applied to the total forested area. Early seral cover continues to increase in the first 50 years in all NDTs as new stands are quickly created during intensive harvesting. Then, early seral cover exceeds mature/old seral cover. Mature/old seral cover in all NDTs continues to drop significantly in the first 100-120 years (one rotation period) while the THLB (initially old forest surplus) is being harvested. They then fluctuate in the second rotation period but remain lower than 20%. Large portions of mature/old seral cover are maintained within the non-THLB. 33  a) NDT 1 – high seral constraint 80%  Early  70%  Mature/old  early 22% mature/old 36%  Area cover (%)  60% 50% 40% 30% 20% 10% 0% 0  20  40  60  80 100 120 140 160 180 200 220 240  Year  b) NDT 2 – intermediate seral constraint 80%  Early  70%  Mature/old  Area cover (%)  60%  early 36% mature/old 31%  50% 40% 30% 20% 10% 0% 0  20  40  60  80 100 120 140 160 180 200 220 240  Year  c) NDT 3 – low seral constraint 80%  Early Mature/old  Area cover (%)  70%  early 54% mature/old 23%  60% 50% 40% 30% 20% 10% 0% 0  20  40  60  80 100 120 140 160 180 200 220 240  Year  Figure 19. Seral stage distribution by NDT in the total forested area for the base case. 34  a) NDT 1 – high seral constraint 80%  Early  Area cover (%)  70%  Mature/old  early 22% mature/old 36%  60% 50% 40% 30% 20% 10% 0% 0  20  40  60  80 100 120 140 160 180 200 220 240  Year  b) NDT 2 – intermediate seral constraint 80%  Early Mature/old  70%  Area cover (%)  60%  early 36% mature/old 31%  50% 40% 30% 20% 10% 0% 0  20  40  60  80 100 120 140 160 180 200 220 240  Year  c) NDT 3 – low seral constraint 80%  Early Mature/old  70%  early 54% mature/old 23%  Area cover (%)  60% 50% 40% 30% 20% 10% 0% 0  20  40  60  80 100 120 140 160 180 200 220 240  Year  Figure 20. Seral stage distribution by NDT in the THLB for the base case. 35  Seral stage representation by NDT Figure 21 shows early seral cover deviations by NDT in the total forest area for hexagon scenarios relative to the base case. Deviations for all hexagon scenarios are significantly large and fluctuate over time differently in each NDT. Initially, deviations are negatively large in all NDTs. This is because areas of the initial age class 1 for hexagon scenarios were significantly underestimated. However, those deviations become small within the first 40 years in NDTs 1 and 2 as the underestimated stands within age class 1 leave the early seral stage, and uniform levels of early seral cover are created within 40 years. Figure 22 shows mature/old seral cover deviations by NDT in the total forest area for hexagon scenarios relative to the base case. As observed in Figure 21, deviations for hexagon scenarios fluctuate depending on the NDT and whether initial age classes were overestimated or underestimated. In general, up to year 80 deviations tend to increase positively as initially overestimated age classes from 2 to 5 shift to the mature seral stage. Then after year 100, they drop and become negatively large when the underestimated age class 1 at year 0 turns into mature seral. Overall, the prominent deviations and fluctuation were observed in NDT 3. deviations expressed as percentages reflect the smaller area of NDT 3.  Large  Also, deviations  fluctuate more in NDT 3 where the seral constraints are less binding. On the other hand, NDT 2 occupies the largest area with the intermediate seral constraint. Therefore, the deviations tend to smooth out over time. Similar trends were observed within the THLB for all NDTs.  36  a) NDT 1 – high seral constraint  15%  early 22%  Deviation (%)  10% 5%  H5 H10 H20 H50 H100  0% -5% -10% -15% 0  20 40 60 80 100 120 140 160 180 200 220 240  Deviation (%)  Year  15%  b) NDT 2 – intermediate seral constraint  10%  early 36%  5%  H5 H10 H20 H50 H100  0% -5% -10% -15% 0  20 40 60 80 100 120 140 160 180 200 220 240  Year  c) NDT 3 – low seral constraint  15%  early 54%  Deviation (%)  10% 5%  H5 H10 H20 H50 H100  0% -5% -10% -15% 0  20 40 60 80 100 120 140 160 180 200 220 240  Year  Figure 21. Deviation in early seral cover (%) by NDT in the total forested area relative to the base case. 37  a) NDT 1 – high seral constraint  15%  mature/old 36%  Deviation (%)  10% 5%  H5 H10 H20 H50 H100  0% -5% -10% -15% 0  20 40 60 80 100 120 140 160 180 200 220 240  Deviation (%)  Year  15%  b) NDT 2 – intermediate seral constraint  10%  mature/old 31%  5%  H5 H10 H20 H50 H100  0% -5% -10% -15% 0  20 40 60 80 100 120 140 160 180 200 220 240  Year  c) NDT 3 – low seral constraint  15%  mature/old 23%  Deviation (%)  10% 5%  H5 H10 H20 H50 H100  0% -5% -10% -15% 0  20 40 60 80 100 120 140 160 180 200 220 240  Year  Figure 22. Deviation in mature/old seral cover (%) by NDT in the total forested area relative to the base case. 38  General discussion In this section I discuss consequences of the deviations caused by spatial generalization for each criterion. Harvest volume shows that scenarios H20, H50 and H100 overestimated the harvest volume available for the next 250 years by 3-4%. Overestimating the harvest volume is more problematic than underestimating. If we continue harvesting more than the actual volume available, a deficit will happen in the long run and the LTSY objective will not be satisfied. Growing stock was overestimated for all hexagon scenarios by 7-17% at the peak of the first rotation period while it was underestimated for scenarios H20, H50 and H100 by 4-7% at the end of the second rotation period.  Significantly overestimating or underestimating growing  stock can be a critical problem in the both short and long run when it comes to estimating timber inventories and carbon storage. For example, as the Kyoto Protocol and Montreal Process address sustainable forest carbon management, underestimating carbon storage may fail to achieve the target required by certification. The prominent deviations were observed for both early and mature/old seral stages in NDT 3.  Good representation of each seral stage is  expected to help maintain landscape-level biodiversity, and conservation of old seral forest is key to achieving this objective (Ministry of Forests and Range 2007). Wildlife habitat also requires a specific seral stage distribution as described for UWR. All these problems in model outputs stem from errors in area estimates for stand group and age class during spatial generalization.  Although all hexagon scenarios represented the distribution of NDT well,  underestimating UWR for scenarios H50 and H100, by 6% and 21% respectively, is problematic for habitat sustainability. The same issue can be addressed for wildlife habitat areas that have been identified by the BC Conservation Data Centre for red- and blue-listed species in TFL 48 (Ministry of Forests and Range 2007). Spatial resolution Spatial resolution is represented by the block size, database size and simulation runtime. Table 9 summarizes and compares the database size and simulation runtime for the 39  base case and hexagon scenarios. A linear relationship observed in Figure 23 indicates that it takes more time to run a simulation as the database size increases. Although the database size in this study was relatively small, a database from a large forest area and with more detail will generate significant differences between the base case and hexagon scenarios. Table 9. Summary of the database size and simulation runtime Scenario Base H5 H10 18.4 19.3 15.6 Database size (MB) Database size relative to the base 105% 85% 100% case (%) 21 16 20 Simulation runtime (sec) Simulation runtime relative to the base case (%)  100%  105%  H20 13.6  H50 12.3  H100 11.9  74%  67%  65%  13  12  11  65%  60%  55%  80%  Simulation runtime (second)  25  20 Base H5  15  H10 H20 10  H50 H100  5  0 0  5  10  15  20  25  Database size (MB)  Figure 23. Linear relationship between the database size and simulation runtime.  Trade-off analysis A trade-off between accuracy and spatial resolution is key to determining which hexagon scenario is preferred. In general, the more homogeneous the forest, the larger the grids can be, while still meeting acceptable accuracy. On the other hand, more heterogeneous forests may require smaller grids to adequately represent variation in stand group and age. How much detail or accuracy is required depends on the objective for a specific forest. When some detail 40  is not necessary to achieve the objective, larger grids can be used to reduce the database size and speed up the simulation runtime. When there is little difference in accuracy, a database with larger grids is preferred to smaller grids because of these efficiencies. Figure 24 illustrates a trade-off between accuracy and spatial resolution by evaluation criteria using maximum deviations observed for hexagon scenarios relative to the base case.  120%  22% Number of blocks  20% 18%  Database size  16% 80%  14% 12%  60%  10% 8%  40%  Simulation runtime  Deviation (%)  Spatial resolution (%)  100%  Harvest volume Growing stock Seral stage  6% 20% 0%  4%  NDT  2%  UWR  0% 5  10  20  50  100  Block size (ha)  Figure 24. Trade-off between accuracy and spatial resolution by evaluation criteria. Spatial resolution is expressed in percentage by the number of blocks, database size and simulation runtime relative to the base case. The rest of criteria show maximum deviations relative to the base case.  Although scenario H5 shows the smallest deviations, the trade-off between accuracy and spatial resolution may not be optimal. This is because there were noticeable deviations in outputs relative to the base case while spatial resolution increased. This is a result of using the artificial grid system that generalizes polygons, and I would argue that the resolution of the 5 hectare-grid is more detailed than necessary. Scenario H10 reduced the database size by 15% and simulation runtime by 20% from the base case, and yet the deviations were as small as scenario H5.  Scenario H20 reduced the database size and simulation runtime further but  slightly compromised accuracy in some outputs. However, the deviations for scenario H20 were as small as scenarios H5 or H10 in criteria such as seral stage distribution, NDT and 41  UWR. Although scenarios H50 and H100 reduced the database size and simulation runtime significantly, acceptability of the deviations is doubtful.  For this study area, the trade-off  between all evaluation criteria seems to be most balanced with the block size in the range of 1020 ha. Trade-off analysis helps decision makers to see what their priorities are.  Some  landowners may not consider deviations for scenarios H50 and H100 as serious as others may. In that case, they would rather simplify the database and minimize the simulation runtime. Different landowners may emphasize different criteria in terms of accuracy.  For example,  accuracy of estimating the area of UWR may be more or less important than other criteria. Therefore, the preferred scenario observed from the trade-off analysis will vary depending on a specific criterion.  42  CONCLUSIONS In this study, the sensitivity analysis on spatial generalization was conducted to determine the trade-off between accuracy and spatial resolution to meet the objectives of strategic planning such as harvest volume, growing stock and seral stage distribution. artificial hexagon grid system was used for block-building by spatial generalization.  An Five  hexagon scenarios were designed by generalizing forest cover polygons into the uniform block sizes of 5, 10, 20, 50 and 100 ha. All the scenarios were compared to the base case in terms of accuracy of the results and spatial resolution.  For evaluating accuracy, deviations were  calculated for input criteria: NDT and UWR, and output criteria: harvest volume, growing stock and seral stage distribution. In general, deviations in all criteria increased with the block size, and deviations in outputs were derived from errors in estimating stand group and age class that are related to the spatial distribution in the base case. Spatial resolution was also evaluated by the database size and simulation runtime.  A negative relationship was observed between  spatial resolution and the block size. Lastly, a trade-off between accuracy and spatial resolution was evaluated by criteria. The trade-off analysis helps landowners to prioritize their objectives. The preferred hexagon scenario for strategic forest planning will vary according to the specific objectives of the forest.  43  AREAS FOR FUTURE RESEARCH There are opportunities for further research related to this study.  Those include  conducting the same analysis on different types of forests as the results presented in this study are site-specific. A wider range of homogenous to heterogeneous forest should be explored. In terms of the block-building procedure for hexagon scenarios, better ways of interpolating or averaging model inputs such as stand group and age class should be investigated to minimize deviations in output criteria. Additionally, the block-building procedure used in this study was time-consuming since the databases were manually processed. A program to automate the procedure should be developed. In this study a hexagon grid system was used as one method to aggregate polygons.  There are other types of block-building procedures by spatial  generalization that aggregate adjacent polygons by homogenous forest cover attributes such as stand type and age (Nelson and Davis 2002). Sensitivity analysis on the block size of spatial aggregation using these methods could be conducted for this study area and compared to the results of the hexagon scenarios. Lastly, for validation of the results generated by the FPSATLAS, it would be useful to compare the results from different simulation or optimization models for this study area.  Developing procedures for spatial generalization using different  approaches could generate valuable results and help determine the minimum spatial detail necessary for strategic forest planning.  44  REFERENCES Baskent, E.Z. and Keles, S. 2005. Spatial forest planning: A review. Ecological Modelling 188: 145-173. Bettinger, P., Johnson, D.L., Johnson, K.N., 2003. Spatial forest plan development with ecological and economic goals. Ecol. Model. 169 (2–3), 215–236. Bettinger, P., Graetz, D., Boston, K., Sessions, J. & Chung, W. 2002. Eight heuristic planning techniques applied to three increasingly difficult wildlife planning problems. Silva Fennica 36(2): 561–584. Bettinger, P and Lennette, M. 2004. Landscape Management Policy Simulator (LAMPS), Version 1.1. USER GUIDE. Research Contribution 43, Forest Research Laboratory, Oregon State University, Corvallis, OR. Bettinger, P., Sessions, J., 2003. Spatial forest planning: to adopt, or not to adopt? J. Forestry 101 (2003) (2), pp. 24–29. Bettinger, P., Sessions, J., Boston, K., 1997. Using tabu search to schedule timber harvests subject to spatial wildlife goals for big game. Ecol. Model. 94, 111–123. Bettinger, P., Sessions, J., Johnson, K.N., 1998. Ensuring the compatibility of aquatic habitat and commodity production goals in eastern Oregon with a tabu search procedure. Forest Sci. 44 (1), 96–112. Borges, J.G., Hoganson, H.M., Rose, D.W., 1999. Combining a decomposition strategy with dynamic programming to solve spatially constrained forest management scheduling problems. Forest Sci. 45, 201–212. Boston, K., Bettinger, P., 2001. Development of spatially feasible forest plans: a comparison of two modeling approaches. Silva Fennica 35 (4), 425–435. Boyland, M., Nelson J., Bunnell F.L. 2005. A test for robustness in harvest scheduling models. For. Ecol. Manage. 207:121-132. Boyland, M., Nelson J., Bunnell F.L. 2004. Creating land allocation zones for forest management: a simulated annealing approach. Can. J. For. Res. 34: 1669-1682. Caro, F., Constantino, M., Martins, I., Weintraub, A., 2003. A 2- opt tabu search procedures for the multiperiod forest harvesting problem with adjacency, green-up, old growth, and even flow constraints. Forest Sci. 49 (5), 738–751. Daust, D.K., Nelson, J.D., 1993. Spatial reduction factors for strata-based harvest schedules. Forest Sci. 39 (1), 152–165. Davis, L.S., Johnson, K.N., Bettinger, P., Howard, T. 2000. Forest Management: to sustain ecological, economic, and social values. 4th ed. Dubuque, Iowa : McGraw Hill, 2000. Gustafson, E.J., Crow, T.R., 1996. Simulating the effects of alternative forest management strategies on landscape structure. J. Environ. Manage. 46, 77–94. 45  Kimmins, J.P., Mailly, D., Seely, B., 1999. Modelling forest ecosystem net primary production: the hybrid simulation approach used in FORECAST. Ecol. Model. 122, 195–224. Klinka, K. et al. 2000. Tree Species of British Columbia’s Forests. Ministry of Forests and Range. 2007. Tree Farm Licence 48: Rationale for Allowable Annual Cut Determination. Ministry of Forests. 1999. Forest Practices Code. Biodiversity Guidebook. Nalle, D.J., Montgomery, C.A., Arthur, J.L., Polasky, S., Schumaker, N.H., 2004. Modeling joint production of wildlife and timber. J. Environ. Econ. Manage. 48, 997–1017. Nelson, J. 2003. Forest Planning Studio – Atlas Program. Reference Manual Version 6. Faculty of Forestry, University of British Columbia, Vancouver. Nelson, J. 2001. Assessment of harvest blocks generated from operational polygons and forestcover polygons in tactical and strategic planning. Can. J. For. Res. 31: 682–693. Nelson, J., Brodie, J.D., Sessions, J., 1991. Integrating short-term, area-based logging plans with long-term harvest schedules. Forest Sci. 37 (1), 101–122. Nelson, J. and Davis, R. 2002. Is detail impeding strategic thinking? A critical look at spatial detail in forest estate models. Contract report prepared for the Interior Lumber Manufactures Association. Faculty of Forestry, University of British Columbia, Vancouver. 31p. Nelson, J.D. and Finn, S.T., 1991. The influence of cut-block size and adjacency rules on harvest levels and road networks. Can. J. For. Res. 21, 595–600. Ohman, K., Eriksson, L.O., 1998. The core area concept in forming contiguous areas for longterm forest planning. Can. J. For. Res. 28, 1032–1039. Ohman, K., Eriksson, L.O., 2002. Allowing for spatial consideration in long-term forest planning by linking linear programming with simulated annealing. Forest Ecol. Manage. 161, 221–230. Ohman, K., Lamas, T., 2003. Clustering of harvest activities in multi-objective long-term forest planning. Forest Ecol. Manage. 176,161–171. Peter, B. and Nelson, J. 2005. Estimating harvest schedules and profitability under the risk of fire disturbance. Can. J. For. Res. 35: 1378–1388. Remsoft INC., 1996. Design and development of a tactical harvest blocking / scheduling tool. Final Report, Canadian Forest Service. Seely, B., Nelson, J., Wells, R., Peter, B., Meitner, M., Anderson, A., Harshaw, H., Sheppard, S., Bunnell, F. L., Kimmins, H., Harrison, D. 2004. The application of a hierarchical, decision-support system to evaluate multi-objective forest management s trategies: a case study in northeastern British Columbia, Canada. Forest Ecology and Management 199: 283-305.  46  Spittlehouse, D.L. and R.B. Stewart. 2004. Adaptation to climate change in forest management. BC Journal of Ecosystems and Management 4(1):7–17. Van Beurden, A. U. C. J. and Douven, W. J. A. M. 1999. Aggregation issues of spatial information in environmental research', International Journal of Geographical Information Science, 13:5, 513–527 Walters, K. 1996. Subdivision of large uniform stands lacking natural bounding features. GIS’96 Symposium, March 1996. Vancouver, BC. 5p. Watts, S. and Tolland, L. (Editors). 2005. Forestry Handbook for British Columbia. Fifth Edition. Vancouver, Forestry Undergraduate Society University of British Columbia  47  APPENDICES Appendix A: Example calculation of age by the area weighted average Table 10. Calculation of age by the area weighted average for scenario H5 (ID 39944) Hexagon ID 39944 39944 39944 39944 39944 39944 39944 39944 39944 39944 39944 Weighted average age  Polygon area (ha) 0.21 0.02 0.04 0.31 2.45 0.36 0.26 0.28 0.05 0.94 0.09  Hexagon area in THLB (ha) 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00  Polygon area (%) 4% 0% 1% 6% 49% 7% 5% 6% 1% 19% 2%  Age  Weighted age 156 186 186 186 186 186 226 226 226 226 246  6 1 1 12 91 13 12 12 2 42 5 197  48  Appendix B: Examples of generalized hexagon blocks  Before spatial generalization for scenario H5 After spatial generalization for scenario H5 Figure 25. The left figure shows overlaid THLB polygons with a hexagon grid (5 ha) for scenario H5. Shaded polygons are non-THLB polygons. The right figure shows generalized hexagon blocks in THLB.  49  Before spatial generalization for scenario H10 After spatial generalization for scenario H10 Figure 26. The left figure shows overlaid THLB polygons with a hexagon grid (10 ha) for scenario H10. Shaded polygons are non-THLB polygons. The right figure shows generalized hexagon blocks in THLB.  50  Before spatial generalization for scenario H20 After spatial generalization for scenario H20 Figure 27. The left figure shows overlaid THLB polygons with a hexagon grid (20 ha) for scenario H20. Shaded polygons are non-THLB polygons. The right figure shows generalized hexagon blocks in THLB.  51  Before spatial generalization for scenario H50 After spatial generalization for scenario H50 Figure 28. The left figure shows overlaid THLB polygons with a hexagon grid (50 ha) for scenario H50. Shaded polygons are non-THLB polygons. The right figure shows generalized hexagon blocks in THLB.  52  Appendix C: Spatial distribution of stand groups for the base case and hexagon scenarios  Base case  Scenario H5  Figure 29. Spatial distribution of stand groups 10 and 15 for the base case and scenario H5. 53  Base case  Scenario H10  Figure 30. Spatial distribution of stand groups 10 and 15 for the base case and scenario H10.  54  Base case  Scenario H20  Figure 31. Spatial distribution of stand groups 10 and 15 for the base case and scenario H20.  55  Base case  Scenario H50  Figure 32. Spatial distribution of stand groups 10 and 15 for the base case and scenario H50.  56  Appendix D: Age class calculation Table 11. Calculation of age class by the area weighted average for scenario H100 (ID 3841) Polygon area (ha) 0.38 6.81 6.71 6.54 6.36 5.53 4.94 4.16 2.52 1.89 1.68 1.64 1.58 1.36 1.16 0.65 0.42 0.23 0.18 0.15 0.12 0.08 0.05 0.02 3.56 5.61 1.76 0.68 0.57 0.09 2.38 1.44 Weighted average age  Hexagon area in THLB (ha) 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24 71.24  Polygon area (%) 0.53% 9.56% 9.41% 9.17% 8.93% 7.76% 6.94% 5.84% 3.54% 2.66% 2.35% 2.30% 2.22% 1.91% 1.63% 0.91% 0.59% 0.32% 0.25% 0.22% 0.17% 0.12% 0.07% 0.03% 4.99% 7.87% 2.47% 0.96% 0.80% 0.12% 3.34% 2.02%  Age  Weighted age  Age class 0 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 146 151 151 151 151 151 181 181  1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 8 8 8 8 8 8 8 8  0 5 5 4 4 4 3 3 2 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 7 12 4 1 1 0 6 4 71 Age class 4  57  

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