Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

The impact of using alterative risk views when setting harvest levels on an uncertain harvestable land… Bogle, Timothy Norman 1995

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-ubc_1995-0552.pdf [ 4.06MB ]
Metadata
JSON: 831-1.0075224.json
JSON-LD: 831-1.0075224-ld.json
RDF/XML (Pretty): 831-1.0075224-rdf.xml
RDF/JSON: 831-1.0075224-rdf.json
Turtle: 831-1.0075224-turtle.txt
N-Triples: 831-1.0075224-rdf-ntriples.txt
Original Record: 831-1.0075224-source.json
Full Text
831-1.0075224-fulltext.txt
Citation
831-1.0075224.ris

Full Text

The impact of using alternative risk views when setting harvest levels on an uncertain harvestable land base in British Columbia . TIMOTHY NORMAN BOGLE B.Sc.F., The University of Toronto, 1989 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF FORESTRY in • "• • , ; • THE FACULTY OF GRADUATE STUDIES . : Department of Forest Management . We accept this thesis as conforming to tlie require standard THE UNIVERSITY OF BRITISH COLUMBIA ', September 1995 . © Timothy Norman Bogle, 1995 :, , In presenting this thesis in partial fulfilment 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 by 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 fc>g£ST* \\M&CghA€>^T The University of British Columbia Vancouver, Canada DE-6 (2/88) ABSTRACT In British Columbia, the chief forester is legally required to set harvest levels within a dynamic forest environment. One of the most contentious issues currently is the size of the productive forest that is harvestable. The Forest Service has chosen to portray timber supply over time with a risk neutral approach towards the size of the harvestable land base, while other interest groups would advocate either a risk taking view or risk averse view. This study provides insight into the tradeoffs which are made in setting harvest levels with the three different risk views and a harvestable land base of unknown size for both a coastal and interior example. Harvest levels are determined for decade 1 and 2, using assumed principles for each view, after which time it is assumed that perfect information is in place for the rest of a 100 year planning horizon. Flexibility in harvest level determination after decade 2 is dependent on the harvest level choices made for decade 1 and 2. The indicators used to examine the implications of the different risk outlooks can be categorized as economic, harvest flow stability and state of the system. The indicators were in turn weighted by using one of three probability distributions coinciding with the presuppositions of the three risk views. The numerical results indicate that while large short term economic and harvest flow advantages are achieved through using a risk taking approach, future flexibility and economic value may be foregone. Conversely, using a risk averse view results in highly stable harvest flows over time at the expense of short term economic gain and the possibility of unnecessarily large reductions in harvest level before perfect information is available. It is believed that the risk neutral view, while foregoing some harvest flow flexibility, will result in a more robust strategy in yielding economic values close to those obtained by risk taking while achieving harvest flow characteristics close to those of the risk averse view. Based on the results, modifications to harvest flow policy are suggested as a means of further improving the strategic objectives while maintaining harvest flow policy decline guidelines. Table of Contents ABSTRACT » List of Figures i y List of Tables vi ACKNOWLEDGMENTS .., vii 1. PURPOSE 1 2. ACCOUNTING FOR RISK IN DECISION ANALYSIS 1 3. HISTORICAL CONTEXT 3 i) Pre- 1978 .' 3 ii) Forest Act - Section 7 5 iii) Timber Supply Review 6 iv) Operability, Merchantability, Accessibility, Availability, Sensitivity 7 4. CURRENT SITUATION 8 i) Risk Outlook 8 1) Risk Taking / RT 9 a) Description 9 b) Assumed Action 9 2) Risk Neutral / RN 9 a) Description 9 b) Assumed Action 10 3) Risk Averse/RA 10 a) Description 10 b) Assumed Action 10 ii) Framing the Question 10 5. RESEARCH METHOD 12 i) Land base 12 ii) Growth and Yield 14 iii) Planning Horizon 14 viii) Modeling Platform 14 iv) Initial Harvest Rate • 16 v) Harvest Flow Policy 16 vi) Harvest Forecast Formulation 18 vii) Harvest Forecast Nomenclature 18 ix) Probability Distributions 19 x) Indicators and Probability Weighting 20 1) Economic Indicators 22 iii 2) Harvest Flow Stability Indicators 23 3) "State of the System" Indicators 24 xi) Objective Functions of the Risk Outlooks 24 1) Risk Taking 24 2) Risk Neutral 24 3) Risk Averse 25 6. ANALYSIS RESULTS .' 26 i) Coastal • 27 1) Economic Indicators 27 2) Harvest Flow Stability Indicators 28 3) Probability Weighted Harvest Forecasts 29 4) Inventory Projections 30 6) Probability distributions in the Coastal Context 32 a) Larger probability distribution 32 b) Normal probability distribution 33 c) Smaller probability distribution 34 6) Comparison of Risk Views in the Coastal Context 35 ii) Interior • 37 1) Economic Indicators 37 2) Harvest Flow Stability Indicators 38 3) Harvest Forecasts 38 4) Inventory Projections 39 6) Probability distributions in the Interior Context 40 a) Larger probability distribution .40 b) Normal probability distribution : • 42 c) Smaller probability distribution 43 7) Comparison of Risk Views in the Interior Context :. 44 7. DISCUSSION 45 i) Coastal vs. Interior comparison 45 a) Economic Indicators 45 b) Harvest Flow Stability Indicators 46 c) Harvest Forecast 46 d) State of the System 47 ii) RT/RN/RA futures , 48 8. CONCLUSION :. 49 9. LITERATURE CITED 51 iv APPENDIX A APPENDIX B - Coastal Futures APPENDIX C - Interior Futures List of Figures Figure 1. Decision Tree outlining the choices facing the chief forester in British Columbia 8 Figure 2. The two broad forest categories in British Columbia 12 Figure 3. Age class distribution of the research forest 12 Figure 4. Observed changes in the size of the harvestable land base over time 13 Figure 5. Volume over age curves for the existing and regenerated components of the research forests 14 Figure 6. Harvest forecast developed to support the initial harvest level for each risk outlook 16 Figure 7. Probability of harvestable land base histories with a Larger probability distribution. 20 Figure 8. Probability of harvestable land base histories with a Normal probability distribution 21 Figure 9. Probability of harvestable land base histories with a Smaller probability distribution 21 Figure 10. PWHFs resulting from using a risk taking view in a coastal forest 30 Figure 11. PWHFs resulting from using a risk neutral view in a coastal forest 31 Figure 12. PWHFs resulting from using a risk averse view in a coastal forest 31 Figure 13. Inventory resulting from using a risk taking view in a coastal forest 32 Figure 14. Inventory resulting from using a risk neutral view in a coastal forest 33 Figure 15. Inventory resulting from using a risk averse view in a coastal forest 34 Figure 16. PWHFs for a Coastal forest with a larger probability distribution 36 Figure 17. Coastal Inventory with a larger probability distribution 36 Figure 18. PWHFs with a normal probability distribution for a coastal forest 38 Figure 19. Coastal Inventory with a normal probability distribution 38 Figure 20. PWHFs with a smaller probability distribution in a coastal forest 40 Figure 21. Coastal Inventory with a smaller probability distribution 40 Figure 22. PWHFs resulting from using a risk taking view in an Interior forest 44 Figure 23. PWHFs resulting from using a risk neutral view in an Interior forest 44 Figure 24. PWHFs resulting from using a risk averse view for an Interior forest 45 Figure 25. Interior Inventory resulting from using a risk taking view 46 Figure 26. Interior Inventory resulting from using a risk neutral view 46 Figure 27. Interior Inventory resulting from using a risk averse view 47 Figure 28. PWHFs for an Interior forest weighted larger 48 Figure 29. Interior Inventory with a larger probability distribution 49 Figure 30. PWHFs for an Interior forest weighted normal 50 Figure 31. Interior Inventory with a normal probability distribution 51 Figure 32. PWHFs for an Interior forest weighted smaller 52 Figure 33. Interior Inventory with a smaller probability distribution 53 Figure 34. Comparison of the expected maximum % decline in harvest level between the Coastal and Interior forests by risk view and probability distribution 55 vi Figure 35. Risk view by the largest and smallest harvestable land bases assessed for the coastal example 58 Figure 36. Risk view by the largest and smallest harvestable land bases assessed for the interior example 58. Figure 37. Harvest forecast formulation given an indication of the state of the system 60 Figure 38. Harvestable land base outcome is 73% of the productive coastal forest example 67 Figure 39. Harvestable land base outcome is 66% of the productive coastal forest example with the harvestable land base increasing in the second decade 67 Figure 40. Harvestable land base outcome is 66% of the productive coastal forest example with the harvestable land base increasing in the third decade 67 Figure 41. Harvestable land base outcome is 60% of the productive coastal forest example with the harvestable land base increasing in the second decade 68 Figure 42. Harvestable land base outcome is 60% of the productive coastal forest example 68 Figure 43. Harvestable land base outcome is 60% of the productive coastal forest example with the harvestable land base decreasing in the second decade 68 Figure 44. Harvestable land base outcome is 54% of the productive coastal forest example with the harvestable land base decreasing in the third decade 69 Figure 45. Harvestable land base outcome is 54% of the productive coastal forest example with the harvestable land base decreasing in the second decade 69 Figure 46. Harvestable land base outcome is 49% of the productive coastal forest example 69 Figure 47. Harvestable land base outcome is 73% of the productive interior forest example 71 Figure 48. Harvestable land base outcome is 66% of the productive interior forest example with the harvestable land base increasing in the second decade 71 Figure 49. Harvestable land base outcome is 66% of the productive interior forest example with the harvestable land base increasing in the third decade 71 Figure 50. Harvestable land base outcome is 60% of the productive interior forest example with the harvestable land base increasing in the second decade 72 Figure 51. Harvestable land base outcome is 60% of the productive interior forest example 72 Figure 52. Harvestable land base outcome is 60% of the productive interior forest example with the harvestable land base decreasing in the second decade 72 Figure 53. Harvestable land base outcome is 54% of the productive interior forest example with the harvestable land base decreasing in the third decade 73 Figure 54. Harvestable land base outcome is 54% of the productive interior forest example with the harvestable land base decreasing in the second decade 73 Figure 55. Harvestable land base outcome is 49% of the productive interior forest example 73 vii List of Tables Table 1. Minimum harvestable ages for the two forest examples 14 Table 2. Probability Distributions for the possible outcomes or sizes of the harvestable land base 19 Table 3. Long term economic indicators for a coastal forest 28 Table 4. Economic indicators of expected NPW for a coastal forest 28 Table 5. Harvest flow stability indicators for a coastal forest.. 29 Table 6. Economic indicators of expected NPW with a coastal harvestable land base weighted larger 35 Table 7. Economic indicators of expected NPW with a coastal harvestable land base weighted normal 37 Table 8. Economic indicators of expected NPW^ with a coastal harvestable land base weighted smaller 39 Table 9. Long term economic indicators for an interior forest 42 Table 10. Economic indicators of expected NPW^ for an interior forest 42 Table 11. Harvest flow stability indicators for an interior forest 43 Table 12. Economic indicators of expected NPW for an interior forest weighted larger 48 Table 13. Economic indicators of expected NPW for an interior forest weighted normal 50 Table 14. Economic indicators of expected NPW for an interior forest weighted smaller 51 Table 15. Harvestable portion of the productive land base by Timber Supply Area in British Columbia 65 viii ACKNOWLEDGMENTS I am indebted to the long suffering and kindness provided by my wife and God, neither of whom would allow me to shy away from completing this project. My sincere thanks to my supervisor, Dr. David Tait, for his input and challenging discussions. Also, I wish to extend thanks to the other members of the committee, Dr. Gordon Baskerville and Dr. John Nelson, not to mention, the policy driver behind the choice of this topic, Darrell Errico of the Ministry of Forests, Research Branch. Your patience in my deliberating on this topic is greatly appreciated. Those in Timber Supply Branch of the Ministry of Forests are commended for enduring my double life over this past year. The editorial comments provided by Greg and Jill Lawrance, Karen Bogle and the fantastic map of British Columbia provided by Karen Brandt were invaluable in completing the final draft of my thesis. The research presented in this thesis has been funded in part by the Donald S. McPhee Fellowship. ix 1. PURPOSE One of British Columbia's key natural resources is timber. The chief forester for British Columbia is legislated to assess the extent of the forest resource for specific geographic areas, considering social, environmental and economic objectives. This individual is then required to use professional judgement in determining an appropriate harvest level. The size of the harvestable land base is one area of contention in developing the data and management assumptions used in timber supply modelling. This study details the historical context of harvest level decision making and outlines the current timber supply process in British Columbia. It also defines what harvestability of the productive forest means. The chief forester must consider many factors that could influence timber supply over time. How should uncertainty about the size of the harvestable land base be considered? What are the implications of using different risk views in conjunction with an uncertain future harvestable land base? There are basically three ways of viewing what the harvestable land base is. A person may be risk taking, risk neutral or risk averse. These three risk outlooks are discussed and the implications assessed in order to present the alternative possible futures through simulated adaptive decision making of harvest levels. The Ministry of Forests in British Columbia has chosen to take a risk neutral stance with respect to the size of the harvestable land base. This has brought accusations of excessive conservatism from some and excessive optimism by others. This study provides insight into the strengths and weaknesses of the three risk views given uncertainty in the size of the harvestable land base. It also identifies which risk outlook provides the most robust strategy in terms of satisfying the multiple strategic objectives which the chief forester must consider when determining a harvest level. Given the restrictive nature of this study, (ie. deterministic changes in one variable important to timber supply modelling), the methodology provides a means of quantifying some of the tradeoffs in future harvest flow with a decision made today. The harvest level decision made by the chief forester for a specific timber supply area combines the best available information on many different factors and thus the harvest level choice is a composite of professional judgement on all of the information provided. 2. ACCOUNTING FOR RISK IN DECISION ANALYSIS For management of a resource to be considered adaptive, it must be flexible to change (Holling, 1978). An evaluation of a range of outcomes in light of their expected impacts is required if potential disaster is to be minimized. Conventional policy analysis has generally been deterministic in approach and attempts are focussed 1 at minimizing conflict as opposed to highlighting difficult tradeoffs (Walters, 1986). Similarly, Walters (1986) indicates that conventional analysis may be focussed on short term objectives while adaptive decision-making promotes long-term objectives. For instance, a method commonly used to incorporate a decision-maker's risk view in conventional analysis is to adjust the discount rate. Using conventional net present value as the sole means of deciding policy issues may create optimal solutions at a unique point in time, but it fails to consider intergenerational inequity (Berck, 1994). For instance, Berck(1994) used net present value for a case study on the redwood forest industry in California, and found that even with perfect information about future land base removals, the net present value was best served by the early liquidation of the redwood resource. Lohmander (1994) has surmised that "...decisions that increase the future level of flexibility (and hence the future expected present value) sometimes reducing the present profit are often found to be optimal in adaptive optimization but never in deterministic models." Therefore two key strategies in effective management are recognizing human motivation as part of the system and confronting future uncertainty (Ludwig, Hilborn and Walters, 1993). Price (1989) outlines several criteria that have been used in conventional decision analysis which allow recognition of human motivation. The maximax criterion states that a decision maker should maximize the maximum opportunity. From a similar perspective, the minimin criterion encourages the decision maker to minimize the minimum possible loss (Fight and Bell, 1977). The minimax criterion states that a decision maker should actually minimize the maximum loss or regret. The Laplace equal probability criterion promotes the use of probability by weighting outcomes equally in order to maximize the expected outcome. This criterion assumes there is no knowledge about the possible states of nature. Price (1989) does indicate that"...choosing the criterion according to the decision-makers' propensities to optimism or pessimism is little better than giving them licence to choose projects intuitively: indeed it is worse in that it permits prejudiced judgement under the guise of objectivity." The combination of indicators into a multi-objective framework has also been widely used but Walters (1986) warns that "multi-objective decision-making can lull the decision-maker into accepting a solution too early by choosing a compromise of bad options." In essence, strategic level decisions are "wicked" problems. The "wicked" problem has been characterized by being interconnected, complicated, uncertain, ambiguous, consisting of conflicting views and possessing societal constraints (Mason and Mitroff,1972). In terms of timber supply management, the decision maker is faced with each of these characteristics despite the fact that the current absolute land base, as identified by the size of the productive forest, can be measured. One of the most contentious issues in British Columbia is the size and age structure of the harvestable portion of the productive forest. Most studies dealing with uncertainty have dealt with pest or fire-related losses. However at this time, serious land use issues as well as increasing technology and high timber prices have produced a high degree of uncertainty about the nature and size of the harvestable land base. 2 3. HISTORICAL CONTEXT i) Pre-1978 In the early settlement of the province, the timber resource was vast and methods of extraction crude. Timber was available through various crown grants and timber licenses, which provided the holder with the exclusive right to the standing timber but not to the land itself. As the extent of the resource became quantifiable, commissions were created to evaluate the state of the forest and commissioners were charged with evaluating cut levels, regional priorities and harvest flow policy. In most cases, the discussion in each commission was centered on maintaining a viable forest industry and in maintaining community stability (Fulton, 1910, Mulholland, 1937). Early in tins century, there was the realization that "over-cutting" was occurring on a local scale on Vancouver Island and in the lower Mainland. At the same time, other areas of the province were being significantly undercut and losses to insect, disease and fire were far outstripping the impact of timber harvesting. Mulholland (1937) remarked that the rapid expansion of the coastal timber industry made "...it...apparent that it will be impossible to avoid a conflict between the desire of private interests to utilize all the mature stands as quickly as markets can be found for the timber and the public interests which require that great basic industries dependent upon natural resources should be regulated on a permanent basis." It was not until the Sloan Commission of 1945, that the idea of regulating the forest resource became a reality. As a result of the report, public sustained yield units were created to begin the transition to "sustained yield" which was defined as " a perpetual yield of wood of commercially usable quality from regional areas in yearly or periodic quantities of equal or increasing volume. "(Sloan, 1945) A specific volume calculation method, the Hanzlik formula was chosen to ascertain the appropriate level of harvesting during the transition from harvesting the virgin timber resource to second growth forests. Vol A Af _ y w l mature , \A AT . ~ D , + 1 V m I immature Rotation After several years of employing the recommendations from the Sloan Report of 1945, Sloan was asked to evaluate the application of the recommendations in a report published in 1956. Several key points of importance to this analysis should be made. Sloan outlined a grave dilemma facing forest management in British Columbia. How should regulation be combined with silviculture, or in other words, when should sustained yield management be postponed with temporary overcutting of the estimated yield capacity versus the need for immediate regulation and loss in future increment? Sloan's view of lost increment is related to the opportunity cost of foregoing the vigorous growth of young managed forest by retaining "decadent" forest which was susceptible to decay due to old age. Sloan argued that the rate of cutting in old growth timber should be related to two objectives: 1) producing an evenly graduated series of age-classes in the reforested lands; 2) removing the old timber soon enough to prevent disastrous losses by insects and fungi (which) add to the loss in increment. Even at this point in time, the Forest 3 Service was accused of ultra conservatism with respect to the assumptions used in the Hanzlik formula (Sloan, 1956). In 1976, Commissioner P.H. Pearse (Pearse, 1976) was asked to evaluate the state of the forest resource and forest management in the province. In summarizing the historical context of harvesting in British Columbia, he re-iterated Sloan's belief that lowering harvest levels would only postpone new growth on stagnant land and shift the cost of declining to the long term harvest level to the citizens of 1976. He also made strong recommendations for improving harvest level determination by accounting for economic, social and environmental considerations which were externalities to the calculation method being used. In his opinion, the appropriate system would possess clear objectives and recognize both economic variables and reasonable assumptions about future trends. At the same time, the use of mathematical optimization methods for timber supply planning was showing a high degree of promise in providing clear analysis and optimal solutions to the wide variety of questions facing forest managers. Pearse felt that by examining various silvicultural strategies and investment patterns, harvest flows could be realistically determined. Mathematical modelling allowed the flexibility to deal with management assumptions and knowledge rather than the inflexible calculation method which did not take into account any obstacles to forest management. The proposed method had a strong basis in mathematical theory and could provide the optimal harvest strategy given the management assumptions and constraints of the day. In addition, a recommendation to combine public sustained yield units into larger aggregate timber supply areas was suggested. These larger areas would be delineated on the basis of timber flow and the communities which processed the resource. This would aid in understanding the social and economic implications of different rates of harvest. Pearse highlighted a unique trend. While the Forest Service was still considered excessively conservative by some, others were beginning to charge the Forest Service with unjustified optimism. There were increasing concerns about high harvest levels and increased government and public interest in the development pattern of the forest industry. Pearse warned the Forest Service to expect an increasing need to harmonize forest operations and other resource users. In light of this, it was suggested that there would be a need for expert and efficient public forest administration to deal with the transition in emphasis from strict timber management to the forest or integrated resources management approach. 4 ii) Forest Act - Section 7 Acting upon recommendations from the Forest Resource Commission (Pearse, 1976), the provincial government of British Columbia changed the emphasis of the legislation from mathematical calculation of the harvest level on small public sustained yield units to a determination based on the professional judgement of the chief forester on larger timber supply areas. Under the current form of that legislation, the chief forester is responsible for determining the harvest level that will be in place for a maximum of five years. By emphasizing the word "determine", the chief forester is bound to consider a list of factors under Section 7 of the Forest Act. The chief forester "...shall consider a) the rate of timber production that may be sustained on the area, taking into account i) the composition of the forest and its expected rate of growth on the area; ii) the expected time that it will take the forest to become re-established on the area following denudation; iii) silvicultural treatments to be applied to the area; iv) the standard of timber utilization and the allowance for decay, waste and breakage expected to be applied with respect to timber harvesting on the area; v) the constraints on the amount of timber produced from the area that reasonably can be expected by use of the area for purposes other than timber production; and vi) any other information that, in his opinion, relates to the capability of the area to produce timber; b) the short and long term implications to the Province of alternative rates of timber harvesting from the area; c) the nature, production capabilities and timber requirements of established and proposed timber processing facilities; d) the economic and social objectives of the Crown, as expressed by the minister, for the area, for the general region and for the Province; and e) abnormal infestations in and devastations of, and major salvage programs planned for, timber on the area." (British Columbia, 1979) The above list provides the breadth of factors relevant to determining an allowable annual cut decision, however the legislation in no way identifies in what fashion the factors must be considered. The act uses the term "expected" but there is no direct context for risk assessment or prioritizing short term and long term implications due to uncertainty in any of the factors. What attitude should the chief forester have towards risk? Obviously, the test of reasonableness can only really be made after the fact. For this reason, the individual responsible for determining a harvest level is in an unenviable position, especially when the current timber supply forecast shows a necessity for a reduction in the rate of harvesting. 5 iii) Timber Supply Review Despite the potential benefits optimization tools could bring, forest management in British Columbia became bogged down in discussion and debate over what the assumptions should be when mathematically modelling forest management. This led to timber supply analyses that were not timely enough to be useful in providing the chief forester with the necessary information to determine appropriate harvest levels. By 1991, renewed concern within the Forest Service over the harvest levels in most timber supply areas precipitated a revisiting of the process of forest estate modelling. A "Review of the Timber Supply Analysis Process for B.C. Timber Supply Areas''(Ministry of Forests, 1991) was undertaken within the Forest Service. The review examined all aspects of the analysis process and came up with recommendations for re-evaluating the timber resource using current management as the qualifier as opposed to the earlier practice of using proposed management. Proposed management had included productive forest as harvestable in a potentially liberal fashion. By placing emphasis on current management, a deliberate course was set in motion which forced forest managers to define the terms of reference upon which timber supply analysis would be built. Emphasis was also placed on the need for an "... expeditious system...to keep pace with rapidly-changing forest resource management."(Ministry of Forests, 1991). For this purpose, a forest estate simulation model was developed. The report also set the Forest Service on a deliberate course in undertaking a Province-wide review of all allowable annual cuts in the span of three years. Concurrent to the timber supply review process, a number of land use planning initiatives were being undertaken within the British Columbia Forest Service. Land use initiatives such as; • the provincial old growth strategy, • Parks and Wilderness for the '90s, • the Protected Areas Strategy (Province of BC, 1993), • regional land use planning under the Commission on Resources and the Environment, • sub-regional land use planning called Land and Resource Management Planning, • and the First Nations Treaty Negotiations,, (Province of BC, 1994) have all increased the uncertainty concerning the size of the harvestable land base. In addition, a significant shift in forest management with unknown harvestable land base implications is the Forest Practices Code of British Columbia Act (British Columbia, 1994), which contains a number of field practices which are expected to lower access to the productive forest. 6 iv) Operability, Merchantability, Accessibility, Availability, Sensitivity As mentioned in section II, the chief forester must use professional judgement in determining a rate of harvest in recognition of the size of the area upon which harvesting will occur. The definition of current management requires a clear identification of the harvestable land base or the land base which will support or sustain timber harvesting for the future. Defining the harvestable portion of the productive forest land base has been a difficult task in British Columbia. The unharvestable lands are those which are "...clearly sub-marginal by virtue of their inaccessible location, elevation, topography or low timber value, unharvestable due to the potential for soil or water damage, or have been made unavailable under a designation for another value such as park or wilderness area" (Pearse, 1976). In British Columbia, the unharvestable portion of the productive forest is determined by what is conventionally called the "netdown" process. Areas or portions of areas are systematically removed from the productive forest dataset until only the net harvestable land base remains. The net harvestable land base has been termed the timber harvesting land base as a means of distinguishing the land base used in timber supply modelling. A list of general netdowns or removals from the productive forest, for timber supply purposes, could include; • non-contributing forest land such as parkland, protected areas, federal reserve lands, etc. (Availability) • a per cent reduction to the land base for environmentally sensitive areas (due to soils, wildlife, avalanche concerns, etc.) (Sensitivity) • low productivity or marginal timber (Merchantability) • problem forest types (stands with unmerchantable characteristics or species composition) • stands deemed inoperable due to steep slopes or inaccessibility (Operability, Accessibility) • per cent reduction to estimate the area used for existing roads • non-commercial forest types The size of the unharvestable land base can range from 10 to 85% of the productive forest land base, depending on the location in the province. Provincially, the long term timber harvesting land base is approximately 34% of the productive forest land in the coastal forest and 47% of the productive forest land in the interior. The current long term timber harvesting land base as a percentage of the productive forest can be seen in Appendix A Table 15 for all timber supply areas currently identified in British Columbia. The terms Operability, Merchantability, Accessibility, Availability and Sensitivity have been used synonymously in this study under the term "Harvestability" or Harvestable. The harvestable portion of the productive forest can change through a shift in forest management objectives, harvesting technology or economics. In order to simplify the discussion and maintain the provincial scope of this study, the term harvestable will be used exclusively. 7 Historically, there has been a steady increase in the size of the harvestable land base due to improved utilization, advanced technology and rising market prices for timber (Pearse, 1976, Binkley et. al., 1993, Williams, 1993). For example, the use of helicopters have increased the accessibility to forested areas. In addition, improvements in modelling forest cover requirements have also included land which would have been removed in previous timber supply analyses (Nelson and Errico, 1993). Counter to this, there has been increased demand placed on the harvestable land base to support non-timber uses such as visual quality (Ministry of Forests, 1993) and the protection of representative areas of BC's natural existing forest (Province of BC, 1993). Herein lies the dilemma. What harvestable land base should be modelled? What assumption concerning the possible changes in the size of the harvestable land'base should a forest manager use today? 4. CURRENT SITUATION i) Risk Outlook As already noted, one key uncertainty which must be addressed by the chief forester in British Columbia when deciding upon a harvest level is the size of the harvestable land base. The productive forest land base, although static in absolute size, may be dynamic in harvestable size. This means that as the conditions for harvestability change, so may the size of the harvestable land base used in timber supply planning. Figure 1 portrays the decision tree expanding the alternative assumptions facing the chief forester in British Columbia, for the first decade. In decade 1, an initial harvest level must be chosen. However, the current timber harvesting land base only accounts for 60% of the productive forest land under the present definition of "harvestable" forest. The action the chief forester will chose may be influenced by an assumption on how the harvestable land base will change in the future. Once the harvest level is chosen, it will be in place for five years. When a new harvest level is chosen at a later date, the harvestable land base could be similar or different but the harvest level chosen today is irreversible. Management Assumption about the size of the harvestable land base Land Base Outcome Larger Management Action Initial Harvest Level LARGER SMALLER Figure 1. Decision Tree outlining the choices facing the chief forester in British Columbia. Status Quo Smaller 8 Three views on risk will be presented as options which the chief forester could use. Each alternative view on risk is assumed to be derived from some basic principles which will be presented in the following sub-sections. For instance, each risk outlook possesses an understanding for how the harvestable land base will change over time. An associated action will be determined based on that understanding. Each outlook will also have certain objectives and goals for the forest. The terms "technically optimistic" and "prudently pessimistic" have been used by Constanza (1989) in describing two of the possible risk outlooks. Fight and Bell (1977) have used the terms "liberal", "neutral" and "conservative" with respect to how management assumptions were considered. Unfortunately, each of these risk outlook descriptors possesses strong historical connotations. In the current context, no judgements should be implied through the use of the terms chosen. The acronyms relating to the risk outlook will be used throughout the discussion. 1) Risk Taking / RT a) Description In the view of the risk taking (RT), the harvestable land base will increase in size and planning should be made in recognition of it due to: 1. History — The harvestable land base has increased in size through increased accessibility, lower utilization standards and the introduction of non-conventional harvesting systems. 2. Incentive — Anticipation of the harvestable land base increasing will encourage the forest industry to continue to develop strategies and technology for increasing the use of the productive forest. 3. Opportunity Cost — Not planning on the reasonable harvestable land base incurs an opportunity cost in terms of net present value. b) Assumed Action A high harvest level should be chosen in recognition of the certain increase in the harvestable land base. The harvest level should be modelled with a "reasonable" harvestable land base in mind. In this study, the harvest level will be chosen by planning on the harvestable land base actually being 10% larger than it appears, in anticipation of this increase. 2) Risk Neutral / RN a) Description In the view of the risk neutral (RN), the current observed harvestable land base defined by current management practice and harvesting performance should be used as the benchmark in evaluating timber supply due to: 1. History — Past timber supply analyses performed by the British Columbia Forest Service included productive forest optimistically in that some included areas did not have harvesting history to 9 substantiate harvestability. This led to harvest levels in some timber supply areas experiencing immediate declines due to a smaller "active" harvestable land base. 2. Incentive — Including only the productive forest land with proven harvesting history will encourage the forest industry to access currently unharvested stands and prove harvestability. The performance approach could eliminate unsubstantiated speculation on the size of the harvestable land base. 3. Benchmarking — Planning on the current harvestable land base gives the public, the Forest Service and the forest industry an opportunity to discuss the future of timber supply with the understanding of the implications of current management practice. b) Assumed Action A harvest level consistent with the observed size of the harvestable land base is the appropriate harvest level. 3) Risk Averse /RA a) Description In the view of the risk averse (RA), the harvestable land base will decrease in size due to: 1. History — the harvestable land base has been decreasing in size through initiatives that are recognizing the value of the forest for resources other than timber. 2. Incentive — Anticipation of the harvestable land base decreasing will ensure that a relatively constant volume of timber is available. This will spur individuals to research ways of increasing the utilization and value of individual trees, rather than attempting to identify additional areas for harvest. 3. Opportunity Cost — By not planning on the smaller harvestable land base, future flexibility in timber supply is foregone. b) Assumed Action A low harvest level should be chosen in recognition of the certain decrease in the harvestable land base. This will be achieved in this study by planning on a 10% smaller land base than is currently observed to be harvestable and determining a harvest level accordingly. ii) Framing the Question Under the Forest Act, the chief forester is required to weigh the short and long term implications to the province of alternative rates of harvest. The chief forester must also determine what the size of the harvestable land base should be. This study will provide insight into the tradeoffs which will be made in setting harvest levels with three 10 different approaches to risk and a harvestable land base of unknown size. The "best" approach will be deemed to be that which provides the most robust strategy in addressing both the short and long term implications to the province. Robust in this sense means that there is a low expected loss associated with failing to account for changes in harvestable land base size. 11 5. RESEARCH METHOD Datasets describing two forests have been constructed to research the implications of using different land base • Interior assumptions given alternative possible futures. The datasets Coastal describe conditions which are typical to the two broad forest categories in British Columbia, the Coastal and the Interior forests (Figure 2). Figure 2. The two broad forest categories in British Columbia. Land base proportion of total area 0.2 0.18 H 0.16 0.14 0.12 • 0.1 0.08 0.06 0.04 I , , . II • Coastal example • Interior example Figure 3. Age class distribution of the research forest. The total productive coastal and interior forest land base under consideration in this study are 200 000 hectares. Both are considered to be 60% harvestable. Both sample forests are in a state where only 35% of the area is above the minimum harvestable age. The coastal example is characterized by stands with ages either less than 60 years, or in excess of 250 years (Figure 3). Generally the forest of the interior has a vastly different harvesting history than the coastal forest. Intensive logging operations have been occurring for the last 20 to 40 years in the interior, 12 while the coastal forest has been harvested for 60 to 100 years. The interior age class distribution is characterized by forest with stands of many ages but not in any strictly regulated pattern. Changes in the harvestable land base are assumed to be age independent. The proportions found in Figure 3 remain the same, regardless of the size of the timber harvesting land base. This non-trivial simplification was necessary to avoid confounding the impact of harvestable land base changes with age class distribution. In actual fact, a higher proportion of unharvestable land may be covered by mature forest, or a large contiguous area of immature forest may be considered unharvestable. Given the variety of reasons for stands to be considered unharvestable, the age independent method is the easiest to apply and understand. Initial Observed Observed Actual Harvestable Harvestable Harvestable Land B a s e Land B a s e Land B a s e (T imeO) ( T i m e l ) (Time 2) 0 6 6 • 0.66 0.6 < L • 0 . 6 < ^ " 0.6 0.54 < C " - - - - ^ 0.54 0.49 Figure 4. Observed changes in the size of the harvestable land base over time. Figure 4 shows the 3 observation and harvest level determination periods that have been simulated. At time 0, the productive forest is considered to be 60% harvestable. An initial harvest level is chosen. At time 1, the percentage found to be harvestable may have changed, as shown by the three styles of arrows. A new harvest level is chosen based on the observed harvestable land base. At time 2, perfect information is assumed to be made available and the actual harvestable land base is known with certainty. The 3 arrows from the three harvestable land bases observed at time 1, point to the 5 actual harvestable land bases. A new harvest level must be chosen based on the actual harvestable land base. It is assumed that the harvest levels applied to the forest over the first twenty years have been applied to the actual harvestable land base. For example, an actual harvestable land base of 60% is assumed to have three unique histories which are related to changes in the observed harvestable land base over time. This implies that a harvesting history depends on how the size of the harvestable land base has been observed to change and will also be directly associated with risk outlook in Section 5iv. There are 9 possible harvesting histories based on the size of the observed harvestable land base. These are listed after Section 5.vii., which outlines the convention for naming harvesting histories. 13 ii) Growth and Yield For each geographic forest location, only one forest type was used in order to simplify the interpretation of the results. The predominant forest type in the coastal forest is assumed to be a hemlock (Tsuga heterophylla) and balsam {Abies amabilis) mixture. The existing and regenerated yield curves are indicated in Figure 5 by the dark lines The predominant species in the interior is assumed to lodgepole pine (Pinus contorta var. latifolia). The existing and regenerated yield curves are shown in Figure 5 by light lines. A minimum harvest age is generally set to correspond to a user-defined minimum standard. In this study, the maximum long term harvest level is desired, so the minimum harvest age will be set at the culmination of mean annual increment, or culmination age. The harvestable inventory (HI) is defined as the volume of timber above this minimum harvest age at a specific time. The total inventory (TI) is a measure of the total volume of all stands in the forest at a specific time. Minimum Harvestable Age (set at maximum mean annual increment) Location Existing Stands Regenerated Stands Coastal 70 70 Interior 110 80 Table 1. Minimum harvestable ages for the two forest examples. Active management of plantations is assumed to have started 20 years ago. This means that stands 20 years and younger are assumed to be growing as regenerated stands rather than naturally existing stands. 1 4 iii) Planning Horizon The planning horizon during simulation modelling was 200 years. However for graphical representation, the planning horizon is shown as 100 years in length. In addition, all indicators that require summation are summed over the same length planning horizon. This is justified because all risk views have been constrained to remain above or equal to the long term harvest level. In the coastal example, a minimum of the long term harvest level must be reached in period 5, while in the interior the long term harvest level must be attained by period 9. The period length is assumed to be 10 years and age classes also conform to a 10 year wide interval (e.g. 1-10, 11-20, etc.). viii) Modeling Platform The inventory projection model used in this study is the Forest Service Simulator (FSSim). Currently in British Columbia, a great deal of attention has been focussed on trying to incorporate the likely availability of timber on the harvestable land base given operational constraints. For this reason, developments in FSSim allow the analyst to form two types of forest cover constraints in the model. Forest cover constraints are a means of modeling certain forest-level objectives such as visual quality, wildlife or cutblock adjacency. The greenup constraint identifies the maximum percentage of area that may be below a certain age/height. In this study, only 33% of the harvestable land base may be below three metres in height. This implies that a three-pass harvesting system is in place. The old growth constraint ensures the maintenance of older forest by requiring a minimum percentage of the area under consideration be maintained in stands above a minimum age. This latter constraint has not been applied in this study as both forests are assumed to have a timber emphasis. Harvest scheduling in FSSim is based primarily on age ("oldest first") subject to an overall harvest target. The analyst may choose to provide other targets which will over-ride this rule but those features have not been used in this study. FSSim has been used in this study in place of an optimization tool for two distinct reasons. Firstly, the Forest Service is currently using this model for projection system for timber supply modelling. Secondly, this research is meant to evaluate the implications of the different risk outlooks by projecting a reasonably possible future without altering the results through optimizing over the planning horizon. 15 iv) Initial Harvest Rate An initial harvest level must be chosen to represent each risk view. The dark lines in Figure 6 graphically illustrate the initial harvest levels for each risk view. The light lines show the transition of future harvest levels down to the long term harvest level, if the assumptions for each risk view remain constant. A unique harvest projection was determined for each risk view by projecting backwards from the theoretical long term harvest level based upon the growth rate of the regenerated forest and the size of the harvestable land base which the respective view is assumed to be planning on. A strict harvest flow policy was used to determine the initial harvest level. The maximum rate of decline was 10% per decade to the long term harvest level without dropping below this level.1 In this way, the initial harvest level was determined strictly as the harvest level which could be achieved without compromising a decline to the long term harvest level at 10% per decade. harvest volume m3/yr 20000000 -| Coastal example 16000000 -j Risk Taking Risk Neutral 12000000 - Risk Averse 8000000 4000000 Interior example 0 2 4 6 8 10 Decades Figure 6. Harvest forecast developed to support the initial harvest level for each risk outlook. It is assumed in Figure 6 that the projections are simply possible futures based on the implied future as defined by the various risk outlooks. Once the harvest level has been determined, it is considered irreversible while future harvest levels are determined iteratively, based on the size of the harvestable land base at the time of re-determination. Adaptive harvest level determination, which means using a risk view in anticipation of a certain LThe projected decline is similar to harvest forecasts that have been commonly used in British Columbia. Harvesting above the long term capacity of the forest is a management choice that has been acknowledged since the Sloane Commission (1945). 16 future harvestable land base, occurs at time 0 and time 1. Harvest levels determined thereafter are assumed to be planned on perfect information and with the goal of attaining the long-term harvest level. The current harvest level for each forest (i.e. harvest level prior to time 0) has been ignored. In many areas in British Columbia, the current harvest level may be equal to or greater than the Risk Neutral view and in some cases is actually higher than the Risk Taking view initial harvest level. This simplification, while not trivial, has been made to focus attention not on the past, but on the future. v) Harvest Flow Policy Historically, the standard decade to decade change in harvest level was limited to 10% for timber supply modelling purposes. Due to the rigid use of this harvest level decline rate, a common assumption was made by those following the timber supply situation in British Columbia, that the chief forester was bound by this modelling assumption. In the context of the current timber supply review in British Columbia (Section 3.iii.), the harvest flow policy is to allow harvest level declines in harvest forecasts to be generally between 8 and 12% per decade. The current study adopts the harvest flow policy that decadal declines should not exceed 12% when creating harvest forecasts. Another assumption is that if perfect information were available, declines should not exceed 10% per decade. It is also assumed that maintaining the initial harvest level for as long as possible is a harvest flow goal. The risk averse view is assumed to not maintain harvest levels above the long term harvest level unless the increase in harvest level can be maintained for several decades and is not more than 10% above the long term harvest level. Another assumed goal for all risk views will be the achievement of the long term harvest level at the earliest time if a decline below this level occurs. By following these harvest flow guidelines, an opportunity cost is associated with unharvested volume. In some instances, a risk outlook may harvest more volume due to being able to remain above the long term harvest level longer than other views. In another case, an abundance of harvestable inventory may become available at the time when the long term harvest level may be reached as a consequence of high harvest rates in the first decade. Despite the increase in harvestable inventory, the long term harvest level is shown as a continuous volume, or flat line. Irregular flow over the long term is not currently socially acceptable as it does not adequately reflect sustainable harvest levels. 17 vi) Harvest Forecast Formulation Earlier sections have indicated that this study uses an adaptive decision-making approach. At times 0 and 1, the actions or harvest levels are chosen in anticipation of a future harvestable land base outcome. Given uncertainty in the size of the harvestable land base, there can be a cost associated with a bad outcome. In this study, one of the costs may be in the size of the harvest level decline between decades. This will occur mainly with harvestable land base decreases. If the harvestable land base decreases, the harvest level transition which was used in the base harvest forecast may no longer be feasible due to large timber shortages in future decades. In that case, the new harvest level is lowered such that future harvest level declines are kept to the maximum of 12% per decade. The only harvest level declines that will be in excess of 12% per decade will occur in re-determinations of harvest level at times 1 and 2, as these are the decades where the harvestable land base may have been observed to change. vii) Harvest Forecast Nomenclature A system for naming harvest forecasts is used to retain the observed harvestable land base and risk outlook histories. This is used in the legends for the harvest forecasts shown in Appendices B and C: The harvest forecast name above is read from left to right. In the first decade, the harvest level is determined at a certain rate given the current size of the harvestable land base, shown in bold italics, followed by the particular risk view, also in italics. In the second decade, a new harvest level is determined based on the observed harvestable land base, shown in bold print, and the same risk view under examination, shown in italics. In the third decade, the actual harvestable land base is assumed to be known with certainty and it is assumed that the historical harvest levels have been applied to that land base. The actual harvestable land base is denoted in the forecast name by the ending of the forecast name following the dot (i.e. .land). This method assumes that the actual harvestable land base, whatever size it may be, will possess an age class structure directly related to the harvest levels applied to it in the past. In all of the cases examined, the risk outlook is maintained for the first two decades at which point the adaptive determination of harvest level ends and perfect information concerning the harvestable land base is assumed. The following list provides the nine harvesting histories which have been created for each risk view: LandbaseView LandbaseF/ew.land 1 60View 66View.l3 2 60View 66View.66 3 60View 60View.66 4 60View 66View.60 . 1 8 5. 60View_60View.60 6. 60View_54View.60 7. 60View_60View.54 8. 60View_5Wiew.54 9. 60View_54ViewA9 The View portion of the harvest forecast name relates to the risk view used in determining harvest levels. A "T" represents an RT view, an "N" represents an RN view and an "A" represents an RA view. As an example, the following forecast, 60T54T. 60 is explained. In this case, the productive forest land base at time 0 is observed to be 60% harvestable and the risk outlook under consideration is the Risk Taking view. A harvest level has been developed in accordance with the corresponding land base assumption and following the harvest forecast formulation explained in Section V. At time 1, the productive forest land base is observed to be 54% harvestable. A re-evaluation of the harvest level is made in accordance with the land base assumption of the risk taking view which is that the actual productive land base is not 54% harvestable but 60% harvestable. The first decade harvest has occurred and it is from this level that the harvest level must decline. At time 2, it is discovered that the productive forest land base is actually 60% harvestable as predicted. The resulting harvest forecast based on this progression is denoted by the long dashed lines in Appendix B, Figure 43 for the coastal example and Appendix C, Figure 52 for the interior example. ix) Probability Distributions Individual harvest forecasts by risk outlook are created for each of the actual harvestable land base outcomes (Appendix B - Coastal, Appendix C - Interior). In the absence of perfect knowledge about the actual size of the harvestable land or the changes which may be observed in the size of the harvestable land base, an aggregating procedure was necessary . A common method of aggregating the outcomes of an uncertain future is to use probability distributions to weight the outcomes to derive some understanding of the tradeoffs inherent in holding a particular risk view (Raiffa, 1968, Price, 1989). Table 2 gives the values used in this analysis to weight individual outcomes by the respective probability of occurrence. Outcome or Portion of the Productive Forest considered harvestable Harvestable Land Base 49% 54% 60% 66% 73% Larger 0 .1 .25 .4 .25 Normal .05 .2 .5 .2 .05 Smaller .25 .4 .25 .1 .0 Table 2. Probability Distributions for the possible outcomes or sizes of the harvestable land base. 19 Figure 7 through 9 illustrate how the probabilities in Table 2 are related to the 9 possible harvesting histories examined in this study. The far right hand side of each figure denotes the actual harvestable land base outcome as a percentage of the productive forest while the values just to the left of the outcome provide the probability associated with that outcome. The sum of the harvest histories for each harvestable land base outcome equals the corresponding values in Table 2. For the duration of this paper, when the harvestable land base is addressed as Larger, Normal or Smaller, it is understood to relate to the probability distribution found in Table 2. Choice of Management Action HL-0 .60 Choice of Management Action Probability of Occurrence L - O . 5 3 HL -0 .66 - L -0 .47 Outcome H L - 0 . 7 3 History Probability 0.25 - S Q - 0 . 3 7 HL-0 .66 0.20 S m - 0 . 1 6 HL-0 .60 0.083 - L - 0 . 6 0 HL-0 .66 0.20 — S O - 0 . 2 S HL-0 .60 0.083 • S m - 0 . 1 5 H L - 0 . 5 4 0.05 - L - 0 . 6 4 HL-0 .60 0.083 S Q - 0 . 3 6 H L - 0 . 5 4 0.05 S m - 0 HL-0 .49 0 LEGEND L-Probability Harvestable land base increases in size S Q - Probability Harvestable land base does not change S m - Probability Harvestable land base decreases in size HL-Size of the Harvestable land base Probability of Occurrence Figure 7. Probability of harvestable land base histories with a Larger probability distribution. 20 D -Choice of Management Action HL-o.eo Choice of Management Action Probability of Occurrence 1-0.31 Sm-0 .52 L - 0 . 2 8 LEGEND L-Probability Harvestable land base increases in size S Q - Probability Harvestable land base does not change S m - Probability Harvestable land base decreases in size HL-Size of the Harvestable land base Probability of Occurrence Outcome H L - 0 . 7 3 HL -0 .66 HL -0 .60 HL -0 .66 HL -0 .60 H L - 0 . 5 4 HL -0 .60 H L - 0 . 5 4 HL -0 .49 History Probability 0.05 0.10 0.16 0.10 0.16 0.10 0.16 0.10 0.05 Figure 8. Probability of harvestable land base histories with a Normal probability distribution. Choice of Management Action HL-0 .60 Choice of Management Action Probability of Occurrence L-o.i3 ^ ' HL -0 .66 LEGEND L-Probability Harvestable land base increases in size S Q - Probability Harvestable land base does not change S m - Probability Harvestable land base decreases in size HL-Size of the Harvestable land base Probability of Occurrence Outcome H L - 0 . 7 3 History Probability 0 HL-0 .66 0.05 HL-0 .60 HL -0 .66 HL -0 .60 H L - 0 . 5 4 HL -0 .60 HL -0 .54 HL -0 .49 0.083 0.05 0.083 0.20 0.083 0.20 0.25 Figure 9. Probability of harvestable land base histories with a Smaller probability distribution. Each probability distribution attempts to capture a broad weighting of the likely states of the future harvestable land base as assumed by the three risk views represented in British Columbia today. While the Larger and Smaller probability distributions are self-explanatory, the Normal distribution requires some explanation. It is assumed that there will be a tendency for the current harvestable land base to remain the same size. For instance, forest that 21 is presently considered unharvestable may in the future become harvestable while other currently harvestable areas may be reserved from harvest. If the forest stands which enter and leave the harvestable land base are of comparable quality and existing condition, there will be no net effect to the harvestable land base. It is also assumed that there, will be a certain tension in changing the size of the harvestable land base as the current harvest level has been predicated on a certain harvestable land base and changes will likely impact on the revenues enjoyed by the present society. For these reasons, the greatest probability is placed on the current harvestable forest with decreasing probabilities of occurrence given to the smaller and larger harvestable land bases. x) Indicators and Probability Weighting In developing indicators, various types were required to provide a breadth of understanding when evaluating the tradeoffs between the actions derived from the risk views and their interaction with an unknown future harvestable land base. The classes used in this study are displayed in terms of: 1. economics; 2. harvest flow stability; 3. state of the system. The following indicators, while not exhaustive, provide insight into the implications of choosing a particular risk view given uncertainty about the size of the harvestable land base. The probability structures provided in the previous section are combined with harvesting information over the first one hundred years. As noted in Section 5.iv., the adaptive or anticipatory harvest level determination process occurs at times 0 and 1. At time 2, the harvestable land base is assumed to be known with certainty and harvest forecasts are developed in keeping with the capacity of that land base. Definitions: decade x = [ xt_I0, xt] for t=10, 20,30,..., 100 Pl = probability of harvestable land base history / (from Figures 7 through 9) Pfj = probability of harvestable land base b (from Table 2)(used in averaging the harvest levels associated with perfect information) di = decadal harvest level decline for harvest history / ht = harvest level in place at time t given a particular harvestable land base history revealed to the decision maker and the decision maker's risk outlook. i = social discount rate t = year N = number of age classes in the forest R = the age class which stands become harvestable Vat = volume per hectare at age class a at time / Aat = area within age class a at time t 22 1) Economic Indicators The expected total net present value2 of a cubic metre of volume harvested ( N P Wp) has been computed for the 100 year planning horizon. NPWT = ]T f 100 A * i=\ tro+o' Two other net present value indicators are calculated to gather insight into possible future economic regret. The expected net present value of volume is calculated beginning in ten years ( N P W 1 0 + ) and again in twenty years ( N P W 2 0 + ) - Tins is used as a means of presenting the distribution of wealth from the forest across several decades. The N P W J Q + indicator measures the value of volume by ignoring the harvests of the first decade and determining the N P W which can be expected from the harvests between the second and tenth decade. The N P W 2 0 + indicator uses the same concept by ignoring the first two decades of harvest and determining the NPW which can be expected from the harvests between the third and tenth decade. Volumes have been discounted by social discount rates of 0%, 2% and 5%. ( f 100 1=1 h. NPW20+ = £ ( f 100 £ o ( l + 0 r-20 The expected total volume harvested (Hj) over the planning horizon is also a pseudo-economic indicator: Total harvest over time should be correlated with increased revenue over time, assuming that equal costs are incurred during harvesting. 9 f f 100 \^\ HT = S Pi I>< z=i V v <=' / 2This assumes that all volume is of relatively equal value. This is a non-trivial simplification as actual monetary value will depend on many factors such as species, grade, final product, etc. 23 The expected percentage decline below the long term harvest level ( D < L T H L ) is used as an indicator of the degree which early harvest levels affect future harvest levels. This is found by dividing the minimum harvest level by the harvest level in place at the end of the planning horizon. 9 ( D <LTHL 2=1 min h. xlOO minimization is for t from 1 to 100 oo J 2) Harvest Flow Stability Indicators The expected maximum decadal decline rate (dmax) is used to characterize the maximum instantaneous change in harvest flow from decade to decade. The harvest levels are dependent upon the harvest history and risk outlook being examined. d, max k-k, ' te(0,10,20,. . . ,100) ht 9 «Lx = Z ( M ) The expected number of decades in the first fifty years with harvest level declines less than the policy decline goal of 12% (Dp^^) provides a means of evaluating how well the harvest forecasts mimic the goal. D Policy I 7=0 1 0 otherwise 0(y+l) <0.12 The expected harvest level decline over the first two decades of simulation was recorded. As an extension of the maximum 12% decline per decade policy goal, the sum of the harvest level declines in the first two decades ( D 2 0 ) s h ° m a n o t exceed 24%. A o = E 9 ( (h -h h -h, ^ " 0 "10 , "10 " 2 0 ;=i Pi* v K The probability weighted harvest forecast (PWHF) will provide an expected harvest forecast for each risk outlook and probability distribution. Each of the nine harvest forecast outcomes is weighted by the appropriate probability for the respective harvestable land base history. ™ f , = E M * = o,i,...,ioo 24 • The expected perfect information forecast (PIF) will provide insight into how closely the PWHF for each risk outlook compares. With perfect information, it is assumed that only one possible harvesting history would occur on the harvestable land base. The harvest methodology used in developing the harvest forecasts shown in Figure 6 was also used in developing a unique harvesting history for each of the five harvestable land bases. Even with perfect information, it is assumed that each of the five ultimate possible land bases could occur (table 2). The expected harvest level associated with perfect information is averaged over the five possible harvestable land bases. PIF<=^Lpbh^ f = o,i,...,ioo 3) "State of the System" Indicators • The expected total inventory (TI) and expected harvestable inventory (HI) time series will be graphed for the 100 year planning horizon as indicators of system flexibility. The impact of the harvest requests of each risk view will depend on the harvesting history being examined and will result in different areas being found in the respective age classes at unique times. 9 N TIt =lLlPlYjVatAat /=0,1,2,...,100 l=\ a=\ 9 f N \ 1=\ V "=R J r=0,l,2,...,100 xi) Objective Functions of the Risk Outlooks Each risk outlook is assumed to have an objective function based on the indicators which the particular view values. 1) Risk Taking The RT view is assumed to value the maximization of net present value of volume at a 5% discount rate as a means of capturing the highest value for the present society given certain harvestable land base increases. Similarly short term regret can be minimized through reducing short term harvest level fluctuations by acting in anticipation of a larger harvestable land base. Finally, increasing the net productivity of the harvestable land base through replacement of slow-growing natural forest with younger 25 managed plantations is a means of capturing the true productivity of the land base and creating future flexibility in harvesting activity. 2) Risk Neutral In representing the risk neutral view, the key indicators are assumed to be a combination of short, medium and long term indicators as a means of understanding the implication of the initial harvest level with the potential risks to future harvest levels. The social discount rate is assumed to be 2%. While net present value of volume is important, future net present value of volume will act as a measure of possible future regret. In maintaining the harvest flow policy guideline of 8-12% harvest level decline rates, the harvest levels enjoyed by past consumers of the resource will not jeopardize the harvest levels of those in the future by necessitating large harvest level declines due to timber supply shortfalls. Another key indicator will be total volume harvested over time as providing an index of the productivity captured through harvesting. While technology and human ingenuity may interact to modify the harvestable land base, using current management as a template ensures that no bias is created which may cause excessive disruptions in future harvest flow. 3) Risk Averse Key indicators for evaluating timber supply in the risk averse outlook are those which focus on minimizing harvest flow instability in the worst case scenario. The discount rate is set at zero under the assumption that the future should not be discounted below the values of the present. Maximizing future net present value in 20 years will ensure that future generations are given economic consideration. Similarly, minimizing the expected harvest level decline below the long term harvest level will maximize future economic value. Maintaining the harvest level decline policy is valued as a means of showing that future harvest level declines can be controlled with some certainty. Also harvest levels should not result in the total inventory declining below the long term total inventory level otherwise the system or harvestable land base has been "over-cut". 26 6. ANALYSIS RESULTS The results from this analysis have been condensed using the aggregation procedure described in Section 5.ix. The actual harvest forecasts for all simulated futures can be found in Appendix B for the coastal example and Appendix C for the interior example. The results for the coastal and interior examples will be shown and followed by a discussion comparing some of the inherent differences between them. Within each example, the probability weighted results will be discussed by economic indicator class followed by the harvest forecast and inventory implications by risk view. Most indicators will be presented in tabular format with the exception of the total and harvestable inventory times series data which are presented in a line graph and a scatter plot representing probability weighted harvest forecasts. Important trends in maximum values of economic indicators will be shaded while harvest flow policy goals will be shaded if the indicators meet the maximum harvest level decline policy guidelines in the tabular data. 27 i) Coastal 1) Economic Indicators Total volume harvested (millions m3) % Decline below the long term harvest level Probability Distribution RT RN RA RT RN RA Larger 145.1 144.2 141.9 8 3 0 Normal 1340 133.8 132.2 13 7 1 Smaller 123.4 123 5 122.9 19 13 1 Table 3. Long term economic indicators for a coastal forest. Some of the short and long term economic implications of applying the harvest rates chosen by each risk view are presented in Tables 3 and 4. Using an RT view is expected to have the highest total harvest, with the exception of being marginally behind the total harvest using the RN view if the harvestable land base is weighted smaller. Expected decline below the long term harvest level will be minimized using an RA view which indicates that planning with an RA view will likely maximize future harvest levels and therefore future value. While using an RT view results in a 20% difference in future harvest level over using an RA view, there is a 20% difference at time 0. N P W T (millions) N P V V 1 0 + (millions) N P W 2 0 + (millions) Discount Rate Land base RT RN RA RT RN RA RT RN RA 5% Larger 3»,283 31.57 29.37 29.es 29.20 27.85 26.46 27 60 27.42 Normal 31.6€ 30.22 28.27 27.16 27.04 26.08 23.38 24.89 25,33 Smaller 38.17 28.86 27.15 24.77 24 84 24.27 20.46 22.13 23.17 2% Larger $$,4$ 64.98 62.35 60.04 60.10 58.80 53.85 55.61 $&M Normal 62 10 60.98 58.89 54.70 55.24 54.60 48.18 50.38 51.3* Smaller $7,91 57.00 55.46 49.60 66.40 50.44 42.82 45.19 0% Larger 145 10 144.25 141.93 126.19 127.06 126.46 108.41 110.86 m$3 Normal 133.75 132.22 115.08 116.56 116 74 98.06 101.00 162.84 Smaller 123.45 123.50 122.90 104.54 106.31 107.43 88.28 91.38 84.16 Table 4. Economic indicators of expected N P W for a coastal forest. NPyV-p is maximized by using an RT view, irrespective of discount rate, with the exception of a Smaller harvestable land base and 0% discount rate. At a 0% discount rate, N P W j equals the total volume harvested which as noted earlier, is maximized in this case by using an R N view. Using an RT view will create a 5% higher N P W T at the 5% discount rate and a 2% higher NPW-p at the 2% discount rate compared to using an RN view. Similarly, harvesting with the RT view will capture 11-13% higher N P W j at the 5% discount rate and 4-7% higher at the 2% discount rate in comparison to using an RA view. 28 The maximum NPW^o+ indicator depends on the social discount rate applied. At 5 % , using an RT or RN view will yield within 0 - 2 % of the maximum. At a 2 % discount rate, using the RN view will consistently yield N P W 1 0 + values between 1 - 2 % higher than the other risk outlooks. At the 0 % discount rate, since using an RA view will harvest more volume after the first decade, a higher N P W J O + is expected if the harvestable land base is weighted normal and smaller. The maximum N P W 2 0 + will likely occur using an RA view at the social discount rates used in Table 5 . The magnitude of the difference between using an RA view and the other two views is directly related to the size of the harvestable land base outcome and the social discount rate used. Using the RA view will yield roughly 4 - 1 3 % higher values than using the RT view and 1 - 5 % higher values than using the RN view. 2) Harvest Flow Stability Indicators With the vast majority of the coastal forest having stands with ages in excess of 2 5 0 years or younger than 6 0 years (recall Figure 3. Age class distribution of the research forests), the allocation of the existing harvestable inventory is crucial to the flexibility of future harvest level declines. Table 5 portrays some harvest flow stability statistics. Maximum % Decline Rate Sum of the first two decades % decline # of Declines < maximum 12% in the first 5 decades Land Base RT RN RA RT RN RA RT RN RA Larger 18 a 8 %%n «.00 4.40 4.65 4.87 Normal 26 16 12 34.35 21.88 ! 12**5 4.00 4.20 4.68 Smaller 33 21 15 46.00 31.37 19.56 3.60 3.85 4.47 Table 5. Harvest flow stability indicators for a coastal forest. Table 5 clearly shows that the RA view is expected to minimize declines in all of the stability indicators displayed. The shading in Table 5 indicates where a risk strategy results in a value within the policy space of the respective indicator. Using an RT view is expected to necessitate harvest level declines far in excess of the 1 2 % harvest level decline policy goal in the three probability distributions tested. This is a consequence of maintaining high harvest levels during the adaptive decision making period in anticipation of the harvestable land base increasing in size. All risk outlooks are expected to exceed the decline rate policy to some degree, as indicated by the maximum per cent decline with a smaller harvestable land base and the fact that no risk view is expected to meet the harvest level declines of a maximum of 1 2 % per decade in the first 5 decades. 2 9 3) Probability Weighted Harvest Forecasts harvest volume (m3/yr) 20000000 18000000 16000000 14000000 12000000 -\ 10000000 8000000 6000000 4000000 2000000 0 4 5 6 decades Maximum expected decline rate Larger - 18% Decline Normal - 26% Decline • Smaller - 33% Decline Figure 10. PWHFs resulting from using a risk taking view in a coastal forest. As can be seen by the PWHFs in Figure 10, the possible futures using the RT outlook are highly variable between time 2 and 5. The goal of minimizing the short term harvest level change can be accomplished irrespective of the size of the future harvestable land base as the harvest level decline rate at decade 1 is kept between 6 and 13%. While using an RT view maximizes the economic welfare of the current generation, undesirable harvest flow consequences are anticipated. In the worst case simulation using an RT view, the harvestable land base is decreased in size from 60% harvestable to 49%. The outcome is represented by the harvest forecast, 60T_54T.49, in Figure 46 in Appendix B. In this case, the maximum harvest level decline rate is 45% with a decline of 34% below the long term harvest level. The width of a decline in harvest level below the long term harvest level could be 2 periods with the larger and normal probability distributions and 3 periods with the smaller probability distribution. 30 harvest volume (rrp/yr) 20000000 18000000 16000000 14000000 H 12000000 10000000 H 8000000 6000000 4000000 H 2000000 0 Maximum expected decline rate " Larger - 11% Decline Normal -16% Decline - Smaller - 21% Decline 4 5 decades Figure 11. PWHFs resulting from using a risk neutral view in a coastal forest. Figure 11 represents the PWHF using an RN view. While a maximum expected harvest level decline of 21% occurs at time 2 if the harvestable land base is smaller, the harvest level declines will generally conform to the policy guideline with the largest variation in harvest level occurring after decade 2. The forecast shown by the solid line indicates that with a smaller harvestable land base, a two period wide decline below the long term harvest level is expected. By combining the various harvest flow stability indicators in Table 5 with the possible timber supply futures for the RN view, using an RN view is expected to be less variable than using the RT view. harvest volume (m3/yr) 20000000 n 18000000 16000000 -14000000 -12000000 10000000 8000000 H 6000000 4000000 2000000 H 0 Maximum expected decline rate • Larger - 8% Decline Normal -12% Decline • Smaller -15% Decline 4 5 decades Figure 12. PWHFs resulting from using a risk averse view in a coastal forest. 31 While losses in harvested volume and short term economic values may be incurred, very large gains are expected in future harvest flow stability by using an RA view, as seen in Figure 12 and noted in Table 5. Irrespective of the probability distribution used to weight the harvest forecasts, using the RA view will create harvest levels closer in rate to the long term harvest level than the other two risk views. The largest harvest level declines using an RA view occur after the first decade rather than in the second as planning with the RT or RN views. This can be seen in Figure 12 by comparing all other declines with that occurring at time 1. The RA view maintains lower harvest levels than the other views in all cases in anticipation of harvestable land base decreases. However, the size of many of the harvest level declines anticipated using an RA view are larger than necessary and the harvest level declines could be distributed over numerous decades without necessitating a harvest level decline below the long term harvest level. While planning by the other views will likely require a harvest level decline below the long term harvest level, using an RA will enable harvest levels to remain above it, or in the case of a 73% harvestable land base, actually be at the long term harvest level as shown in Appendix B Figure 38 by the solid line. 4) Inventory Projections Inventory Type by Probability Distribution 20000000 10000000 Total Inventory - Larger Total Inventory - Normal Total Inventory - Smaller — — Harvestable Inventory - Larger - * - - Harvestable Inventory - Normal Harvestable Inventory - Smaller Figure 13. Inventory resulting from using a risk taking view in a coastal forest. Figures 13 through 15 provide the impact of the various harvest levels determined by each risk view on the total and harvestable inventories. In Figure 13, the high initial harvest rates derived using an RT view are expected to remove over 50% of the existing harvestable inventory by decade two. This action has two definite impacts on the system. First, the remaining harvestable inventory must be rationed until sufficient second growth is available to elevate harvests to the long term harvest level. Two, the large area harvested in the first decade will be available for harvest again in decade 7. This creates the apparent convergence of harvestable inventories irrespective of probability distribution between decades 7 and 9. After decade 9, future harvesting at the long term harvest level 32 will lower the harvestable inventory to a level specific to the size of the harvestable land base. The harvestable inventory created by the harvesting pattern of the RT view, could enable an elevation in the harvest level in the seventh decade, as about 50% of the total inventory on the harvestable land base will be of harvestable age. The total inventory is likely to decline below the long term total inventory, but only through decades 2 through 5 at which time stands harvested in the first decade begin adding substantial amounts of immature volume to the total inventory. Inventory Type by Probability Distribution 30000000 Total Inventory - Larger Total Inventory - Normal Total Inventory - Smaller ~~ Harvestable Inventory - Larger " " " " Harvestable Inventory - Normal Harvestable Inventory - Smaller Figure 14. Inventory resulting from using a risk neutral view in a coastal forest. Figure 14 shows the expected impact of the risk neutral harvest rates on the total and harvestable inventory. Only by weighting the total inventory by the smaller probability distribution will the expected decline in total inventory be below the long term total inventory level. By the end of period two, approximately 40% of the harvestable inventory has been removed. This allows the higher harvest rates between times 2 and 5 using an RN view compared to an RT view. As a consequence, the rate of decline in harvestable inventory from decade 2 to 4 is also much steeper than that seen in Figure 13 for the RT view. There still remains a tendency for there to be a large area of harvestable inventory available at time 6 but not to the degree of the RT view as the initial harvest rates using the RN view are 10% below the RT. 33 0 ' 1 2 3 4 5 . 6 7 8 9 decades Figure 15. Inventory resulting from using a risk averse view in a coastal forest. The pattern of harvestable inventory removal created by using RA harvest rates is quite different than using the previous views. At no time is the total inventory expected to decline below the expected long term total inventory on the respective harvestable land base as shown by the lighter lines in Figure 15. In addition, four decades are required before the harvestable inventory is depleted to roughly 40% of the total inventory. Where the harvestable inventories are depleted rapidly and are seen to converge for a brief period after decade 7 under the RT and RN views, the expected harvestable inventories under the RA view remain separate. This fact is directly related to the low initial harvest level and the relative even-flow of the harvest forecasts in Figure 14. 34 6) Probability distributions in the Coastal Context a) Larger probability distribution N P V V T (millions) N P W 1 0 + (millions) N P V V 2 0 + (millions) Discount Rate RT RN RA RT RN RA RT RN RA 5% 13 203 31.57 29.37 29.6S 29.20 27.85 26.46 27 60 ' 27.42 2% 66 49 64.98 62.35 60.04 60.10 58.80 53.85 55.61 55 S2 0% 14510 144.25 141.93 126.19 127 oe 126.46 108.41 110.86 11193 Table 6. Economic indicators of expected N P W with a coastal harvestable land base weighted larger. Table 6 provides insight into the economic tradeoffs between risk views over time if the harvestable land base is weighted larger. As noted earlier, the general trend is that using an RT view will maximize NPyVj, while using the RN view will maximize NPWjq + and using the RA view will maximize N P W 2 0 + - At the 5 % discount rate, the NPW-p is roughly 1.7 million higher than the RN and about 4 million higher than the RA. Similar but slightly smaller differences are shown as the discount rate is reduced. The NP W 2 0 + indicator shows that the RN view is 1.1 million above the RT view. Therefore using an RN view will not quite provide equal economic value of an RT view over time. An RA view may harvest more volume after decade 2 than using an RT view, recognizing that over the planning horizon roughly 3 million cubic metres of volume will be foregone, as shown by the N P W - T / indicator at a 0 % discount rate. Figure 16 identifies the implications of the different risk views on the timber supply forecasts as the probability distribution is weighted towards the larger harvestable land bases. With perfect information, a reasonable transition to the long term harvest level is shown by the dark dashed line. Despite anticipating a larger harvestable land base, using an RT view will cause harvest level deviations from the PIF in decade 2 . Because the thrust of the RT view is anticipation of a steadily increasing harvestable land base, the harvest level in the third decade are expected to decline by 18% to avoid timber supply shortages before suitable second growth volume is available. In the second period, the RN view intersects with the PIF and is expected to capture some of the volume foregone in the first and second decades. In using caution to minimize expected decadal decline, the RA view foregoes value and volume. This is mainly due to an assumed reluctance to raise the harvest level when the "perfect" information becomes available. In terms of total volume, the RT and RN views are able to capture a larger portion of the productivity of the harvestable land base by increasing the amount of area in the forest which is in a faster growing condition. 3 5 harvest volume (m3/yr) 20000000 18000000 16000000 14000000 12000000 10000000 H 8000000 6000000 4000000 2000000 0 - i 1r Maximum expected decline rate Expected Harvest Forecast with Perfect Information 10% Decline • Risk Taking 18% Decline Risk Neutral 11% Decline • Risk Averse 8% Decline Figure 16. PWHFs for a Coastal forest with a larger probability distribution. Figure 17 shows the expected inventory profiles for a harvestable land base weighted larger. Given the cautious strategy of the RA view, the harvestable inventory is reduced at a much slower rate than the other risk views causing fewer slow- growing mature stands to be replaced by faster-growing managed stands. Because the existing inventory is removed over such a long time span, the long term total inventory is actually higher than the RT or RN and approximately 20-25% more harvestable inventory between decades 4 and 8. Using either an RN or RT view is likely to create a similar inventory profile because of the common goal of maximizing total volume harvested. The total inventory for the RT and RN views will reach equilibrium with the long term total inventory by decade 5 while the RA view has not declined to this level by decade 9. Risk view and Inventory Type RT Total Inventory RN Total Inventory RA Total Inventory — ~~ RT Harvestable Inventory - - - - RN Harvestable Inventory ~ R A Harvestable Inventory Figure 17. Coastal Inventory with a larger probability distribution. 36 b) Normal probability distribution N P V V T (millions) N P V V 1 0 + (millions) N P W 2 0 + (millions) Discount Rate RT RN RA RT RN RA RT RN RA 5% 316ti 30.22 28.27 27 16 27.04 26.08 23.38 24.89 2S.3& 2% 60.98 58.89 54.70 55.24 54.60 48.18 50.38 5138 0% 133 99 133.75 132.22 115.08 116.56 116.74 98.06 101.00 102.84 Table 7. Economic indicators of expected N P W with a coastal harvestable land base weighted normal. With a normal probability distribution, the economic indicators can be seen in Table 7 . As noted earlier, the largest expected NPYV-p is expected using an RT view. At a 5% discount rate, the difference is 1.44 million greater than using the RN view, while at 2%, the difference is 1.12 million. Examining the N P W 2 0 + indicator shows the RN view to be 1.51 million larger at 5% and 2.2 million larger at 2% than will be the harvests under the RT view. The future harvest by the RA view will also increase but approximately 1.5 million cubic metres of volume will be foregone as seen by the NPyVj at a 0 % social discount rate. The implied probability distribution using an RN view is the harvestable land base weighted normal. In Figure 18 the RN view PWHF matches the PIF flow with the exception of a small deviation in the fifth decade. Conversely, using an RT view results in harvest levels in the first two decades above what planning on perfect information would have dictated. As a result, harvests at time 2 must decline by 26% in order to allocate harvestable inventory until sufficient second growth volume is available to enable a rise to the long term harvest level. In comparison to the PIF, the RA forecast maintains much lower harvests in the first three decades and thus foregoes opportunity in harvesting but also results in an "unnecessarily large" reduction in harvest level after the first decade compared to that deemed necessary in the PIF created with "perfect" information. 3 7 harvest volume (m3/yr) 20000000 18000000 16000000 14000000 12000000 10000000 H 8000000 6000000 4000000 2000000 0 Maximum expected decline rate Expected Harvest Forecast with Perfect Information 10% Decline Risk Taking 26% Decline Risk Neutral 16% Decline • Risk Averse 12% Decline Figure 18. PWHFs with a normal probability distribution for a coastal forest. The two inventory types are displayed in Figure 19 for the normal probability distribution. The total inventory lines of each risk outlook generally converge by decade 6, despite taking quite different trajectories. The RT view has harvested the slower growing existing inventory faster than the other two views and resulting in a slightly greater harvestable inventory than the other views, despite having the lowest harvestable inventory between time 1 through 6. The RA outlook has applied harvest rates low enough to slowly liquidate the harvestable inventory, as indicated by the much slower rate of decline of the RA Total Inventory and the maintenance of more harvestable inventory between decades 2 through 7. 30000000 Risk v iew and I nventory Type RT Total Inventory RN Total Inventory RA Total Inventory — — RT Harvestable Inventory - - - - RN Harvestable Inventory RA Harvestable Inventory 7 8 9 Figure 19. Coastal Inventory with a normal probability distribution. 38 c) Smaller probability distribution N P V V T (millions) N P W 1 Q + (millions) N P W 2 0 + (millions) Discount Rate RT RN RA RT RN RA RT RN RA 5% 30.17 28.86 27.15 24.77 24.84 24.27 20.46 22.13 i i$AT 2% S5LS1 57.00 55.46 49.60 50.40 50.44 42.82 45.19 45L<11 0% 123.45 123.50 122.90 104.54 106.31 107 43 88.28 91.38 $4.1$ Table 8. Economic indicators of expected NPVV with a coastal harvestable land base weighted smaller. Table 8 shows the NPW economic indicators if the harvestable land base is actually weighted smaller, as is the belief of the risk averse view. In this case, the RA view total volume harvested is much closer to both the RT and RN views than in previous probability distributions as seen by the NPW-p at a 0 % discount rate. By anticipating a smaller harvestable land base, a shift in social welfare between the current generation and future generations becomes evident. The gains using the RT outlook shown in N P W T over the RA view are between 3 and 2 . 4 5 million at the 5 % and 2 % social discount rates. The future expected value using an RA view will be 2 . 7 1 million greater than an RT view at 5 % and 4 . 1 9 million greater at the 2 % discount rate. Depending on the value of unmanaged timber at that future point in time, some regret on the part of the RT view may be felt due to the loss of possible revenue with the shift in welfare from the future to the present. Using an RN view results in N P W T ; values close to those obtained using an RT view, the largest values of N P W J Q + and values of N P W 2 0 + closer to those obtained using an RA view than the RT view. Figure 2 0 graphically illustrates the use of cautionary harvest level determination by the RA view as the harvest level decline is artificially larger at time 1 (solid line) than the harvest level decline deemed necessary under perfect information (dark dashed line). Using an RN view, the harvest flow is interrupted by an expected maximum decline of 2 1 % at time 2 (dotted line) but the declines thereafter are within the policy guidelines. If the harvestable land base is actually smaller, following the RT view (dashed line) may ensure that economic benefits were provided in periods 1 and 2 but at the cost of mid-term stability and economic value between periods 3 to 5 . The harvest forecast developed using the RT view in the first two decades foregoes the harvest level flexibility maintained by using an RA view. 3 9 harvest volume (nrVyr) 20000000 18000000 16000000 14000000 12000000 10000000 H 8000000 6000000 4000000 2000000 0 Maximum expected decline rate Expected Harvest Forecast with Perfect Information 10% Decline ' Risk Taking 33% Decline Risk Neutral 21% Decline • Risk Averse 15% Decline Figure 20. PWHFs with a smaller probability distribution in a coastal forest. While it has been noted earlier in Section 6.i.4., the system impacts resulting from high harvest rates using RT and RN outlooks in the first decade are best seen in the instance of a probability distribution weighted to the smaller harvestable land bases (Figure 21). While high harvest rates chosen by the RT in decades one and two create negative consequences to harvestable inventory between decades 1 and four, the RT Total Inventory (light long dashed line) will exceed the other views in decade 5, and the RT Harvestable Inventory will be larger in decades 8 and 9. A similar but smaller increase can be seen by planning with the RN view. The difference between the harvestable inventory of the RT and RA at the beginning of the 9th decade is relatively equal to that seen in the fourth decade. Even with a smaller harvestable land base, the RA view is not likely to decrease the total inventory on the harvestable forest below the long term total inventory. Riskviewand Inventory Type RT Total Inventory RN Total Inventory RA Total Inventory — — RT Harvestable Inventory - - - - RN Harvestable Inventory RA Harvestable Inventory Figure 21. Coastal Inventory with a smaller probability distribution. 40 6) Comparison of Risk Views in the Coastal Context With an uncertain future harvestable land base, the strategy which is the most robust will be the one which maintains a sense of flexibility without incurring artificial costs in productivity. The age class structure in the coastal example is such that over-estimating the size of the harvestable land base has dramatic impacts on future economic values and harvest level decline rates. Using an RT view will maximize economic goals for the first twenty years and likely will maximize the total volume harvested but at the cost of potentially large harvest level declines and future economic value. Conversely, using an RA view will minimize potential harvest flow instability and thus future economic value but at the cost of short term harvest level declines which may prove to occur prematurely to what perfect information would have deemed necessary and potentially lost opportunity in harvest volume. Using the RN view combines the strengths of the other two risk outlooks. Using the RN view will result in total volume harvested within 0.5% of using the RT view, thus while short term economics are captured using the RT view, mid term economics will be captured using the RN view. In terms of harvest flow stability, harvest level declines are made responsively to the observed size of the harvestable land base. In this way, while potential costs in harvest level may occur, the RN view results in harvest flow indicators which tend to be more like the RA view than the RT view. 41 ii) Interior 1) Economic Indicators Total volume harvested (millions m3) % Decline below the long term harvest level Probability Distribution RT RN RA RT RN RA Larger 40.7 409 40.6 8 2 2 Normal 37.4 37.7 1, 37111 15 5 1 Smaller 34.3 34.5 34 « 21 12 3 Table 9. Long term economic indicators for an interior forest. In the interior forest example, using the RN and RA views will result in the harvest of more volume than the RT view as seen in Table 9 . In addition, determining harvest levels with the RT view will result in larger declines below the long term harvest level than the other two views. A 2 % decline below the long term harvest level is expected by planning with an RA view after probability weighting with the weighted larger probability distribution. This decline is actually indicative of continuing pessimism once the harvestable land base has increased in size. Generally speaking, the RA initial harvest level is only a few percent above the long term harvest level when the productive forest is greater than 5 4 % harvestable. N P V V T (millions) N P V V 1 0 + (millions) N P V V 2 0 + (millions) Discount Rate Land base RT RN RA RT RN RA RT RN RA 5% Larger 3.43 8.93 8.32 8.&1 8.33 7.95 7.67 7 92 7.87 Normal 8.58 8.04 7.08 7.76 7.50 6.94 7.16 7.26 Smaller 8.74 8.28 7.74 I7.3S 7.27 7.01 6.18 6.49 6.61 2% Larger KM 18.45 17.77 17.03 1714 16.85 15.28 15.90 16.04 Normal 17.65 17.28 16.80 15.64 15.72 15.66 13.73 14.30 14.72 Smaller 16.S4 16.21 15.77 14.28 14,42 14.42 12.21 12.84 13.31 0% Larger 40.67 40.93 40.61 35.37 36.11 3$ 28 30.34 31.54 32.16 Normal 37.39 37.67 37.72 32.09 32.85 33.39 27.19 28.40 29.3* Smaller 34.31 34.55 34.77 29.02 29.74 30.44 24.24 25.39 26.52 Table 10. Economic indicators of expected N P W for an interior forest. Table 1 0 illustrates the net present value of volume indicators for the interior example. At the 5 % and 2 % discount rates, the NPyVj using the RT view will be generally 6 % and 2 % larger than the RN view and 1 3 % and 5 % larger than using the RA view. At a 5 % discount rate, using the RT view results in a slightly higher N P W 1 0 + but at a 2 % discount rate, the N P W | Q + using an RN view results are roughly 1 % higher. The N P W 2 0 + indicator is maximized using an RA outlook, with a 3 - 9 % higher performance than using the RT view, depending on the discount rate used. Using an RA view results in N P W 2 0 + 2 - 3 % higher than using the RN view in terms of N P W 2 0 + -4 2 2) Harvest Flow Stability Indicators The interaction between the age class structure of the existing forest (Figure 3) and the minimum harvest age of 110 years can restrict timber supply over time. The existing harvestable inventory must be allocated until younger stands are harvestable. There are essentially two transition periods which occur. The restrictive nature of these transition periods is dependent on the harvest request of the risk view. The first transition period is characterized by allocating the current harvestable inventory until immature existing stands pass the minimum harvest age and are considered harvestable. The second transition occurs in shifting from the harvest of existing natural stands to managed second growth stands. Maximum % Decline Rate Sum of the first two decades % decline # of Declines of maximum 12% in the first 5 decades Land Base RT RN RA RT RN RA RT RN RA Larger ' 13 1«<08 1U<25 $A9 . 4.53 4.83 5.00 Normal 18 12 S 24.97 2104 4.32 4.62 5.00 n Smaller 24 15 10 33.83 25.30 17.06 4.13 4.58 500 Table 11. Harvest flow stability indicators for an interior forest. Table 11 presents the harvest flow stability indicators for the three probability distributions tested. The policy space, as shown by the shading, indicates that both the RN and RA views are likely to maintain the policy decline objectives. In all cases, the RA view is expected to be able to decline at the policy harvest level decline goal of 12% as shown by the score of 5 in the number of declines of maximum 12% in the first 5 decades. Using the RT view will necessitate a maximum harvest level decline beyond the policy goal of 12% and if the future harvestable . land base is weighted smaller, the decline is expected to be twice the desired decline rate. 3) Harvest Forecasts Figure 22 shows the possible futures resulting from using the RT view. While the expected harvest level declines at time 1 are quite small, the maximum expected harvest level declines at time 2 could reach 24%. The solid line and dotted line further indicate that the declines below the long term harvest level, shown in Table 11, could . extend for four decades. In the worst case scenario using an RT view, the maximum harvest level decline rate is 37% and a 27% decline below the long term harvest level is forecast. This forecast is found in Figure 55 of Appendix C and labelled 60T_54T.49. 43 harvest volume (m3/yr) 6000000 -, 3000000 j- n 0 1 2 3 4 S 6 7 decades Maximum expected decline rate • Larger -13% Decline Normal -18% Decline - Smaller • 24% Decline 9 10 Figure 22. PWHFs resulting from using a risk taking view in an Interior forest. While using an RT view appeared relatively unstable, Figure 23 shows the possible harvesting futures under an RN view to change harvest levels over time with far more flexibility. The forecasts still show varying degrees of decline below the long term harvest level. The duration of these declines may be up to four periods in length. harvest volume (m3/yr) 6000000 5000000 2000000 Maximum expected decline rate • Larger - 8% Decline Normal -12% Decline - Smaller -15% Decline 0 1 2 3 4 5 6 7 decades Figure 23. PWHFs resulting from using a risk neutral view in an Interior forest. The harvest flow implications using an RA view can be seen in Figure 24. By maintaining an assumed aversion to planning on the observed harvestable land base, even as the land base increases, an expected decline of 6% from the initial harvest level are forecast, as seen by the dashed line. This is actually lower than the harvest level determined in the third decade and forms a dip in the harvest forecast. This increase is created by weighting the 44 60A66A.73 forecast (Appendix C Figure 47) and the 60A60A.66 forecast (Appendix C Figure 49), where the harvest rates can be elevated at time 2 when perfect information becomes available. harvest volume (m3/yr) 6000000 -, 5000000 A 4000000 L ™ , _ Maximum expected decline rate I ; , 3000000 -Larger - 6% Decline Normal - 9% Decline Smaller -10% Decline 2000000 A 1000000 -0 -I , , , , : 1 , 1 , 1 , 0 1 2 3 4 5 6 7 8 9 10 decades Figure 24. PWHFs resulting from using a risk averse view for an Interior forest. 4) Inventory Projections Figure 25 shows the inventory time series resulting from an RT view. The basic trend in total inventory time series is a reduction below the anticipated long term total inventory level between times 2 and 6. The lowest point in the harvest inventory occurs in decade 7 when the harvestable inventory is 20% of the total inventory. At the beginning of decade nine, the harvestable inventory, resulting from the high initial harvest rates, may be 50% to 60% of the total inventory. 45 volume (m3) 25000000 0 -\ , , , , , , , , , 0 1 2 3 4 5 6 7 8 9 decades Figure 25. Interior Inventory resulting from using a risk taking view. The inventory time series produced by the harvest rates resulting from an RN view are shown in Figure 26. With the starting harvest proposed by the RN, the existing harvestable inventory is reduced at a slightly slower rate than the RT view (Figure 25), enabling more flexibility in setting harvest level decline rates. The future total inventories on the harvestable land base are only expected to decrease below the long term inventory level if the probability distribution is weighted smaller. As with using an RT view, a convergence of the harvestable inventories between decade 8 and 9 is expected as the area harvested in the first decade becomes available for harvest again. At the beginning of the ninth decade, about 50% of the total inventory is harvestable. volume (m3) 25000000 -| 20000000 15000000 10000000 5000000 0 -I , , , , , n , , , 0 1 2 3 4 5 6 7 8 9 decades Figure 26. Interior Inventory resulting from using a risk neutral view. 46 Figure 27 shows the inventory implications resulting from using an RA view. The harvestable inventory is not expected to be depleted below 50% of the total inventory until after decade three if the probability distribution is normal or smaller, or decade five if the probability distribution is weighted larger. The total inventories are not expected to decline below the long term total inventory level at any time. volume (m3) 25000000 -, 20000000 15000000 10000000 5000000 o A , , , , , , , , , 0 1 2 3 4 5 6 7 8 9 decades Figure 27. Interior Inventory resulting from using a risk averse view. 6) Probability distributions in the Interior Context a) Larger probability distribution Table 12 contains the economic tradeoffs in terms of NPW between risk views over time if the harvestable land base is weighted larger. As noted earlier, the general trend is that using an RT view will maximize NPW-j; at the 5% and 2% discount rates, while each risk view will maximize NPWjO+ at its assumed discount rate and using the RA view will maximize N P W 2 0 + - At the 5% discount rate, the N P W 7 ; is roughly 0.5 million higher than the RN and 1.1 million higher than the RA. Similar but slightly smaller differences are shown as the discount rate is reduced. Using an RN view produces N P W 2 0 + v a m e s 0 2 5 million at a 5% discount rate and 0.62 million at a 2% discount rate above using the RT view. However, even within 20 years, the NPW indicators are not different enough to indicate that future economic revenues have been foregone by using an RT view . The reason for this will be seen by the harvest forecasts in Figure 28 and the fact that the using an RN view will result in the highest volume harvested as seen by the NPYV-p at the 0% discount rate. 47 N P W T (millions) N P V V 1 0 + (millions) N P W 2 0 + (millions) Discount Rate RT RN RA RT RN RA RT RN RA 5% 9>43 8.93 8.32 8.51 8.33 7.95 7.67 7 92 7.87 2% 18.80 18.45 17.77 17.03 17.14 16.85 15.28 15.90 ; i6M 0% 40.67 40.93 40.61 35.37 36.11 35 28 30.34 31.54 \ 32*1$ Table 12. Economic indicators of expected N P W for an interior forest weighted larger. Figure 28 presents the harvest forecasts weighted towards the larger harvestable land bases. The dark dashed line shows the harvest forecast with perfect information. Despite presupposing a larger harvestable land base, the interaction between optimism in the second decade and the age class structure which enables steady decline rates within the policy guidelines, the RT view drops below the long term harvest level and is quite different than the PIF. While only declining below the long term harvest level by roughly 8%, the fact that anticipation could lead to unnecessary future declines is a counter to the thesis used by the RT outlook in earlier discussion. The argument was proposed that by not including the potential harvestable land base, the RN and RA views would create unnecessary declines. However, by not fully accounting for the dynamics of the system, the RT outlook is in danger of artificially creating future declines. The economic difference between using the RT and RN comes as a result of the harvest levels not being very different during period 3. Using any discount rate will marginalize any differences in harvest level between decades 4 and 7. As noted earlier, using an RN view will more adequately capture the productivity of the forest due to a flexibility in harvest level decline. The RA view appears to be quite sub-optimal, although the total volume harvested is close to the RT view and the harvest forecast, shown by the solid line, contains the second decade oddity already discussed in Section 6.ii.3. harvest volume (m3/yr) 6000000 5000000 3000000 H 2000000 1000000 I , Maximum expected decline rate i •• 2 4 6 decades • • • Expected Forecast with Perfect Information 10% Decline Risk Taking 13% Decline Risk Neutral 8% Decline Risk Averse 6% Decline Figure 28. PWHFs for an Interior forest weighted larger. 48 The inventory implications of a harvestable land base weighted larger are shown in Figure 29. While the RN total inventory (light dotted line) is reduced to the expected long term inventory by the fourth decade, the RT total inventory (light dashed line) will decline below the long term total inventory. Conversely, the RA total inventory (light solid line in Figure 29) declines at a slower rate and only meets the expected long term total inventory level at the end of the 100 year planning horizon. The rate of change in the various harvestable inventories is quite different from the initial condition at time zero to that seen at the beginning of the first decade. The higher harvest rate determined using an RT view removes more harvestable inventory than the other views. This creates the necessity to marginally exceed the decline rate policy in harvest flow as seen by the long dashed line in Figure 28. The remaining harvestable inventory is below that of the RN and RA until the end of decade 6, at which time, the RN harvestable inventory equals the RT harvestable inventory. The RA harvestable inventory is maintained at a higher level than the other views and kept between 30 and 50%. of the total inventory. volume (m3) 25000000 -, 0 -1 , 1 , 1 1 , , , , 0 1 2 3 4 5 6 7 8 9 decades Figure 29. Interior Inventory with a larger probability distribution. b) Normal probability distribution The economic indicators for a harvestable land base weighted normal can be seen in Table 13. As noted earlier, the largest expected NPW'p is expected using an RT view. At a discount rate of 5%, the difference is 0.51 million while at 2%, the difference is 0.37 million over using an RN view. Examining the N P W 2 0 + indicator shows the RN view to be 0.22 million larger at 5% and 0.57 million larger at 2% than will be the harvests under the RT view. The total harvest resulting from using an the RA view will be 50 thousand cubic metres higher than the RN view and 330 thousand cubic metres higher than the RT view. 49 NPVVj (millions) N P V V 1 0 + (millions) N P V V 2 0 + (millions) Discount Rate RT RN RA RT RN RA RT RN RA 5% 9.09 8.58 8.04 7.96 7.76 7.50 6.94 7.16 7.26 2% 17.6$ 17.28 16.80 15.64 i i i i i r ™ 15.66 13.73 14.30 mt 0% 37.39 37.67 37 72 32.09 32.85 33.39 27.19 28.40 29.38 Table 13. Economic indicators of expected N P W for an interior forest weighted normal. A normalized probability distribution creates weighted harvest forecasts as seen in Figure 30. In this case, the PWHF resulting from the RN view closely matches the PIF for the first three periods. The small aberrations thereafter are a function of the weighting process. Because harvest level declines are possible that remain within the policy decline rate, it has been assumed that the RN view will maintain the harvest level policy decline rate at the expense of remaining at or above the long term harvest level. Despite following the PIF, the RN view does not harvest quite as much volume as the RA view over the 100 year planning horizon, as seen by comparing the NPW'j; at a 0% discount rate (Table 13). While the RA view foregoes a great deal of volume in the first twenty years, as is evident when comparing the solid line with both the dotted (RN) and dashed (RT) harvest forecasts, the harvest level can be maintained above the long term harvest level for a much longer period of time than the other views. As is expected, using an RT view results in a relatively large decline in harvest rate after the second decade and incurs continued reductions in harvest level until decade 7. harvest volume (m3/yr) 6000000 - i Maximum expected decline rate • • • Expected Forecast with Perfect Information 10% Decline Risk Taking 18% Decline Risk Neutral 12% Decline Risk Averse 9% Decline 1000000 -0 -I 1 1 1 1 , 0 2 4 6 8 10 decades Figure 30. PWHFs for an Interior forest weighted normal. The expected inventory time series are shown in Figure 31. The RN harvest rates are expected to reduce the total inventory to roughly the equivalent of the long term total inventory by decade 4. The total inventory under the RA harvest rates decreases at a shallower rate, while maintaining a higher harvestable inventory until decade 7. The 3000000 2000000 50 RT harvest rates diminish the total inventory at a faster rate than both other risk views and the harvestable inventory is relatively constant between decades 5 through 7 , indicating that virtually all harvestable inventory is harvested to achieve the harvest requests over these decades. By decade 7 , all three outlooks have similar harvestable inventories but achieving the long term harvest level cannot be made by the RN or RT views until the beginning of decade 9 . volume (m3) 25000000 c) Smaller probability distribution Table 14 displays the NPW economic values if the harvestable land base is weighted smaller, as claimed by the risk averse view. In this case, using the RA view will result in the highest total volume harvested, as seen by the NPW-p at a 0 % discount rate. Anticipating a smaller harvestable land base enables future harvest levels to be maintained much higher than when using the other two risk views. The gains for the RT outlook shown in NPW'j; over the RA view are between 1 and 0 . 7 7 million at the 5% and 2% social discount rates respectively, while gains over the RN view are 0.46 and 0.33 million. Using the RA view maximizes the N P W 2 0 + m t n e o r uer of 0.43 million at 5% and 1.1 million at the 2% discount rate. The future expected values attributed to the RA outlook will be higher than the RT. The light solid line in Figure 32 shows the PWHF resulting from the RA view. NPVVj (millions) N P W 1 0 + (millions) N P V V 2 0 + (millions) Discount Rate RT RN RA RT RN RA RT RN RA 5% 8.74 8.28 7.74 7.Z9 7.27 7.01 6.18 6.49 6.61 2% 16.54 16.21 15.77 14.28 1442 14.42 12.21 12.84 mi 0% 34.31 34.55 34 77 29.02 29.74 30.44 24.24 25.39 Table 14. Economic indicators of expected N P W for an interior forest weighted smaller. 51 The PIF in Figure 32 is shown by the solid dashed line. While using an RA view results in harvest levels resembling the forecast developed on perfect information, the other two views show two undesirable features. A decline below the long term harvest level is expected and the decline will be maintained for four decades. While the RN view does remain relatively close to the policy decline goal, the RT view must exchange short term economic benefit for high expected maximum harvest level declines and harvest flow instability. The economic impact which was not apparent in the NPW indicators is that harvest levels between time 4 and 8 will be quite different using an RA view than an RT view. harvest volume (m3/yr) 6000000 Maximum expected decline rate 4 6 decades Expected Forecast with Perfect Information 10% Decline Risk Taking 24% Decline Risk Neutral 15% Decline Risk Averse 10% Decline Figure 32. PWHFs for an Interior forest weighted smaller. The inventory time series quite strongly reflect the impact of higher initial harvest rates applied using the RT and RN views. The RA total inventory reaches the long term inventory level in decade 5, as seen in Figure 33 by the light solid line. The RN and RT total inventories show very rapid declines below the long term total inventory and a low in harvestable inventory is reached at the end of decade 5. By the end of the planning horizon, the higher initial harvest rates of the RT and RN views result in a larger regenerated area than the RA view. This provides some future harvest level flexibility but at the expense of less flexibility between decades 4 and 8. 52 Risk view and Inventory Type RT Total Inventory RN Total Inventory RA Total Inventory — — RT Harvestable Inventory - - - - RN Harvestable Inventory RA Harvestable Inventory Figure 33. Interior Inventory with a smaller probability distribution. 7) Comparison of Risk Views in the Interior Context As noted in the discussion of the coastal forest (section 6.i.6.), a robust risk strategy is required to maintain both harvest level flexibility and harvesting productivity given an uncertain future harvestable land base. The age class structure in the interior example provides both a challenge and an opportunity. Using either an RN or RA outlook will achieve the best total volume harvest over time. The high initial harvest rates chosen by the RT view create a difficult transition in harvesting through the age classes, which the RN and RA views are not as susceptible to. However, despite the opportunity, the challenge occurs in understanding the tradeoff between harvest level declines at the policy rate and the depth of the decline below the long term harvest level. While using an RN view will likely achieve the policy harvest level decline rate, even with a smaller harvestable land base, the decline below the long term harvest level will continue for up to four decades. In an adaptive optimization sense, future harvest levels will best be served by the risk view that is able to maintain the harvest level above the long term harvest level rather than extended periods below. Generally this will be obtained using the RA view, however increasing harvest level declines past 12% per decade would enable the RN view to capture an equal total harvest and eliminate the possible declines below the long term harvest level. 53 7. DISCUSSION i) Coastal vs. Interior comparison The three categories of indicators (economic, harvest flow and state of the system) will be discussed generically in order to compare the differences between the coast and the interior examples. Most of the difference can be directly related to the age class structures of the respective forests (Baskerville, 1992) and their expected growth rates. On the coast, the majority of the forest is in the 250+ age classes so that the harvestable volume per hectare is no longer increasing with time (Figure 3 and 5). Once the existing harvestable inventory older than 250 is harvested, very little area will become harvestable until the large area currently in the 20 year age class becomes harvestable. This can be seen in the harvestable inventory time series by the fact that all risk views (Figures 13 through 15) reduce the harvestable inventory between decades 1 and 4. Harvestable inventory begins to increase in decade five, enabling harvest levels to rise to the long term harvest level in decade six. In the interior example, the harvesting history is much shorter and historical fire frequencies create an age class distribution with a more irregular pattern than on the coast (Figure 3). This means that in the interior example more area is in older immature forest which will become harvestable in decade 1 or 2. This can be seen in Figures 25 through 27 by the fact that the harvestable inventories decline only moderately between time 0 and time 1. If the initial harvest rate does not necessitate the immediate removal of all stands when they reach the minimum harvestable age, volume per hectare yields may still increase, and declines will be necessitated due to the amount of harvestable inventory that is available in any one decade. a) Economic Indicators In the coastal example, using an RT view generally enables the highest total volume harvested over the 100 year planning horizon as a result of exchanging stands which are not adding volume per hectare very quickly and harvesting presently immature stands at the age of maximum mean annual growth. In the interior example, using the RN view enables the highest total volume harvested as the lower initial harvest rates are lower than the RT view and result in greater flexibility in scheduling stands for harvest.. Existing stands which are not harvested exactly at culmination age will still increase in volume per hectare until harvest. The economic indicator of net present value of volume also shows quite different trends between the two examples. The obvious difference lies in the absolute magnitude of the expected values. Given the higher growth potential of 54 the coastal sites, a coastal harvestable land base of identical size to an interior one will support much higher harvest levels. In general, the expected declines below the long term harvest level are very similar in magnitude when comparing a particular risk view in the coastal and interior examples. b) Harvest Flow Stability Indicators Expected Maximum % Decadal Decline in Harvest Rate 35 Larger Normal Smaller • Coast RT E3 Coast RN • Coast RA S Interior RT H Interior RN H Interior RA Figure 34. Comparison of the expected maximum % decline in harvest level between the Coastal and Interior forests by risk view and probability distribution. Figure 3 4 shows the expected decline rates based on risk outlook and probability distribution. In all cases the coastal risk outlooks, as shown by the first three bars in each probability distribution, will exceed the identical risk outlook in the interior, as shown by the second set of three bars. Using an RT view on the coast results in extremely high variability in expected maximum harvest level decline rates, exceeding the decadal decline policy of 12% by possibly two or three times. Using an RN view in the coastal example may also result in exceeding the policy goal unless the harvestable land base increases in size. In comparison, the expected maximum harvest level decline rates for all risk outlooks will be much closer to the policy goal of 12% harvest level decline per decade in the interior. Using an RT view in the interior may actually result a maximum harvest level decline rate within the policy decline rate if the land base increases in size. Using an RN view will likely result in harvest level declines within the policy decline rate. 55 In general, using an RN view results in expected maximum decline rates more closely related to the RA than the RT view. The expected maximum decline rates produced by the risk averse view in either example are actually artifacts of caution as these declines occur at time 1, before perfect information is available. For the other risk views the maximum harvest level declines are expected to occur at time 2, when perfect information is considered to be available. While the RA view may produce unnecessary reductions in harvest flow at time one, using an RT view may create artificially large declines by foregoing harvest level declines in anticipation of the harvestable land base increasing in size. c) Harvest Forecast The harvest forecasts for the different example forests show quite different trends for the risk taking and risk neutral views, while similar harvest futures are seen when using an RA view. In the coastal forest, large expected maximum decline rates are created if the harvestable inventory has not been adequately managed to meet the harvest request. However, after the declines occur, the rise to the long term level can be achieved at the end of the fifth decade (Figures 10 and 11). This rise occurs as a result of managing the large amount of area in the 20 year age class such that once the area reaches the minimum harvest age in decade 5, it is allocated for harvest between decade 5 and 6. In the beginning of decade 7, the area that was harvested in the first decade will be considered available for harvest again. Therefore the expected decline below the long term harvest level occurs for a maximum of two decades. In the interior example, while the maximum harvest level decline rate statistics are not as large as the coastal example, a willingness to maintain the decline rate policy may lead to longer term impacts on timber supply. The expected maximum harvest level declines are shown in Figure 34. In addition, the expected declines below the long term harvest level will be proportionally similar (compare Table 3 with Table 9). However, it is expected that harvest levels will remain below the long term harvest level for about four decades in the interior (Figures 22 and 23). This is a result of not requiring large harvest level declines to avoid serious timber supply shortfalls and assuming that maintaining the policy goal of 12% maximum harvest level decline takes precedence over remaining at or above the long term harvest level. While using an RA view in the coastal example does not create harvest forecasts similar to the PIF weighted towards the smaller harvestable land bases, using the RA view will produce quite similar results in the interior. This fact is due to the increased flexibility in harvest rate that has been shown in the interior example. While anticipating the harvestable land base decreasing in size on the coast necessitates large harvest level decline measures, the age class structure of the interior forest does not create the same necessity in the interior. 56 d) State of the System The system indicators also show quite different trends between the two example forests. The trend in the coastal example tends to show that the minimum harvestable inventory is reached at time 4, with increases thereafter (Figures 13-15). One reason for this is the very large area currently in young managed forest in the coast example due to more intensive harvesting activity (Figure 3). In the interior example, the minimum harvestable inventory is not reached until the beginning of decade 8 (Figures 25-27). In the beginning of decade 9, the harvestable inventory increases by roughly 100% as the area regenerated after the harvest in the first decade becomes available for a second harvest. In addition, the harvestable inventory is not really shown to decline until after decade 2 due to the amount of area in immature stands at time 0 becoming harvestable after the first decade. ii) RT/RN/RA futures The actions of the different outlooks can be seen to maximize their respective objective functions. Using an RT view will almost always maximize net present value of volume using a non-zero social discount rate, enable a minimization of short term harvest level fluctuation and produce future harvesting flexibility once managed stands become harvestable. Using an RN view will generally maximize net present value indicators if the economic considerations begin in ten years, generally maintain the policy harvest level decline rate and only create harvest level declines relative to the size of the harvestable land base. Using an RA view will maximize the net present value indicators if the economic considerations begin in twenty years, result in the least variable harvest flow indicators by choosing harvest rates close to the long term harvest level, minimize the likelihood of declining below the long term harvest level and the total inventory not declining below the long term total inventory. Figures 35 and 36 expose the bounds of the timber supply futures examined in this analysis based on the productivity of the harvestable land bases. 57 harvest volume (rrvVyr) 20000000 18000000 16000000 14000000 12000000 10000000 8000000 6000000 4000000 2000000 0 4 6 decades Risk Views: T - Taking, N - Neutral, A - Averse Nomenclature: LandbaseView LandbaseView.landbase Maximum expected decline rate — 60T_66T.73 8% Decline - 60N_66N.73 6% Decline — 60A_66A.73 0% Decline — 60T.54T.49 45% Decline 60N_54N.49 30% Decline — 60A_54A4920% Decline 10 Figure 35. Risk view by the largest and smallest harvestable land bases assessed for the coastal example. >lume (m'/yr) Risk Views: T - Taking, N - Neutral, A - Averse Nomenclature: LandbaseView_LandbaseView.landbase Maximum expected decline rate 2000000 1000000 60T_66T.73 7% Decline 60N_66N.73 0% Decline • 60A_66A.73 0% Decline 60T_54T.49 37% Decline • 60N_54N.49 23% Decline 60A_54A.49 12% Decline Figure 36. Risk view by the largest and smallest harvestable land bases assessed for the interior example. Figures 35 and 36 clearly indicate how disparate the views are with respect to the size of the harvestable land base. In the belief of some people, the dark dashed lines indicate the potential of timber supply based on the harvestable land base expanding. In this instance, the initial harvest level of the risk taking view has no undesirable harvest flow implications. Rather, not choosing a high harvest rate has economic ramifications in the coastal example. The difficulty for the proponents of a risk taking strategy is the realization that harvesting activity is not affecting 58 all of the productive forest and removing harvesting opportunity may not actually ensure the values which are being "preserved" through decreasing the size of the harvestable land base, given the dynamic nature of the system and the old age of mature trees. Alternatively, using the belief of another sector of society, the light lines are more likely representative harvest flows as the harvestable land base decreases in size. Proponents of the risk averse strategy would point out that the development of the productive forest can not be continued at a rate which is irreversible to control. With the diversification of the economy of British Columbia in recent years, fewer people feel a direct impact as a result of changes in harvest level. It is assumed in this study that society generally believes that erratic harvest flows are not connected to the uncertainty present in forest management but rather an indication of poor planning and harvest levels being created for short term economic gain. Between these two risk views, the Ministry of Forests has chosen to represent harvest forecasts using the risk neutral view. While the risk neutral view appears to assimilate the more desirable aspects of the other views, it is not immune to challenge by either outlook if the future unfolds in a direction which the other views supported. Given an uncertain future, it would seem reasonable to set harvest levels in recognition of the size of the current harvestable land base as a means of ensuring that harvestable land base increases are based on evidence rather than speculation and as a means for not incurring unnecessary harvest level reductions. 8. CONCLUSION Fortunately, the chief forester for British Columbia is not faced with harvest forecasts in all timber supply areas where the decline in harvest level to the long term harvest level must begin immediately. The province, in the current round of timber supply reviews, can definitely be seen in its component parts. Each of these parts or timber supply areas, is a unique provincial asset. In this light, the province is actually being managed on a portfolio system. Certain areas, mainly on the coast, are likely in an imminent falldown situation in terms of timber supply. Other areas can maintain the current allowable annual harvest for many decades before changes in harvest level may be necessary. Still other areas are already being harvested at or below the potential long term harvest level. Unfortunately, the local economic impacts of harvest level reductions in specific units are still not well understood, causing some to question the legitimacy of the information used in the allowable annual cut determination process (Binkley, et. al., 1993). However, rescheduling a necessary decline simply necessitates more severe adjustments in the future as noted by Williams (1993) and shown in this study by the harvest level declines resulting from using a risk taking view. Boychuk and Martell (1993) have indicated that the simplest answer to dealing with uncertainty (in their case, with regards to fire losses) was to establish a "buffer stock" by reducing the short term harvest 59 quantity and increasing harvest age. The current analysis concurs with this conclusion but within the context of a potential imminent falldown and an uncertain future harvestable land base, how can this concept be applied in principle? Based on the results of this study, several key tradeoffs are clear if risk taking or risk averse approaches are used. Harvest rates developed in anticipation of increases in the size of the harvestable land base will minimize discomfort in the short term, maximize net present value today and replace slow growing stands with faster growing managed forest. However, only if there is an increase in the size of the future harvestable land base will the mid term harvest flows be kept within the present desired policy decline rates. Strategic decisions such as harvest level may not be purely economic but may involve objectives which define how an enterprise, in this case, the province, wishes to define itself (Gunn, 1991). If a stable wood supply in the future is the highest priority, harvest rates determined in anticipation of decreases in the size of the harvestable land base will maximize harvest flow stability, ensure declines within the policy goal and maintain future harvest level flexibility. But this choice is at the economic opportunity cost of harvest in the short term as well as possibly foregoing the total amount of volume harvested over time. It appears from the forecasts shown in Appendix B and C, that the risk neutral view is the most robust strategy in that action is based on information rather than anticipation. The other risk views attempt to prejudge the future and may create undesirable economic or harvest flow consequences based on the nature of the outcome. Therefore, it would seem appropriate to maintain the risk neutral view. Some preliminary suggestions for harvest flow policy formulation are provided given some knowledge about the possible state of the system for a particular timber supply area. harvest volume rrp/yr 200X30000 Coastal example I Risk Taking Risk Neutral Risk Averse 8000000 A 4000000 A 10 Figure 37. Harvest forecast formulation given an indication of the state of the system. 60 Figure 37 presents a means of improving the solution derived by using the risk neutral view given the preliminary findings of this study. The initial harvest level determined using the RN strategy can be seen by the dark short dashed line. Where greater potential exists for increases in the harvestable land base, harvest rate declines used in harvest projections should be set at the maximum acceptable policy rates, for discussion purposes. This will present a higher initial harvest level and reduce economic opportunity without necessarily depending upon the harvestable land base increasing in size. Where a high risk can be associated with a decrease in the size of the harvestable land base, choosing a harvest flow policy where the initial harvest level is feasible for the first 20 year, followed by harvest level declines to the long term harvest level is suggested. This policy will increase the harvestable inventory buffer in the short term, thus reducing the harvest flow consequences which have already been shown if the harvestable land base decreases in size. This initial harvest level can be seen by the dark solid line in Figure 37, although the level itself will be re-evaluated within five years, at which time new information about the size of the harvestable land base may be available. By using the "mental" harvest flow policy suggested, the chief forester may embrace the uncertainty in the size of the harvestable land base within the framework of the current legislation by providing for the recognition of the short and long term implications of alternative rates of harvest. 6 1 9. LITERATURE CITED Baskerville, G. 1992. Forest analysis: linking the stand and forest levels. IN The ecology and silviculture of mixed-species forests, ed. M.J. Kelty. Kluwer Academic Publ. pp257-277. Berck, P. 1994. Two informational issues in resource modelling. Nat. Res. Model. 8(1): 13-25. Binkley, C.S., M. Percy, W.A. Thompson and I. Vertinsky. 1993. The economic impact of a reduction in harvest levels in British Columbia: a policy perspective. FEPA Working Paper 176. 35pp. Boychuk, D. and D.L. Marten. 1993. Modeling the impact of uncertain forest fire losses on timber supply. IN Proceedings Forest Management and planning in a competitive and environmentally conscious world. Ed. G.L. Paredes. Valdivia, Chile. Mar. 9-12, 1993. pp 95-104. British Columbia. 1979. Forest Act. IN Revised statutes of the province of British Columbia, chap. 140. Queen's Printer, Victoria, B.C. British Columbia. 1994. Forest Practices Code of British Columbia Act. IN Statutes of the province of British Columbia, chap. 41. Queen's Printer, Victoria, B.C. Constanza, R. 1989. What is ecological economics? Ecol. Econ. (1): 1-7. Fight, R.D. and E.F. Bell. 1977. Coping with uncertainty: a conceptual approach for timber management planning. USDA For. Serv. Gen. Tech. Rep. PNW-59. 18pp. Fulton, F.J. 1910. Royal Commission of Inquiry on Timber and Forestry, 1909-1910. Ottawa, Ontario. 153pp. Gunn, E.A. 1991. Some aspects of hierarchical production planning in forest management. IN Proceedings of the International Symposium on Systems Analysis in Forest Resources, compiled by M.A. Buford. March 3-6. 1991. pp 54-62. Holling, C.S. 1978. Adaptive environmental assessment and management. John Wiley & Sons, Chichester, England. 377pp. Lohmander, P. 1994. Adaptive decision-making in forestry. IN Proceedings of the International Symposium on System analysis and management decisions in Forestry: Forest Management and Planning in a Competitive and Environmentally conscious world, edited by G.L. Paredes. Valdivia, Chile. March 9-12. 1994. pp 411-421. Ludwig, D., R. Hillborn and C. Walters. 1993. Uncertainty, resource exploitation and conservation: lessons from history. Science 260:17&36. Mason, R.O. and I.I. Mitroff. 1972 Challenging strategic planning assumptions: theory, cases and techniques. John Wiley & Sons, pp 5-17. Ministry of Forests. 1991. Review of the Timber Supply Analysis Process for B.C. Timber Supply Areas. Final Report (Volume 1). Victoria, British Columbia. Ministry of Forests. 1993. Procedures for factoring recreation resources into timber supply analyses. Rec. Br. tech. rep. 1993:1. 10pp. 62 Mulholland, F.D. 1937. The forest resources of British Columbia. King's Printer. Victoria, British Columbia. 409pp. Nelson, J.D. and D. Errico. 1993. Multiple-pass harvesting and spatial constraints: an old technique applied to a newproblem. For. Sci. 39(1):137-151. Pearse, P.H. 1976. Timber rights and forest policy in British Columbia, report of the British Columbia Royal Commission on Forest Resources. Queen's Printer. Victoria, British Columbia. Price, C. 1989. The theory and application of forest economics. Basil Blackwood Ltd. pp 112-125. Province of British Columbia. 1993. A protected areas strategy for British Columbia. 38pp. Province of British Columbia. 1994. Forest Policy History and Current Initiatives. IN 1994 Forest, Range and Recreation Resource Analysis, pp 267-308. Raiffa, H. 1968. Decision analysis: introductory lectures on choices under uncertainty. Random House, New York. 309pp. Sloan, G. McG. 1945. Report of the Honourable Gordon McG. Sloan, Chief Justice of British Columbia, relating to the forest resources of British Columbia. Chief Justice Gordon Sloan, Commissioner. Queen's Printer. Victoria, British Columbia. Sloan, G. McG. 1956. Report of the Honourable Gordon McG. Sloan, Chief Justice of British Columbia, relating to the forest resources of British Columbia. Chief Justice Gordon Sloan, Commissioner. Queen's Printer. Victoria, British Columbia. Walters, C.J. 1986. Adaptive management of renewable resources. MacMillan Publishing Co., New York. 374pp. Williams, D. 1993. Timber Supply in British Columbia: the historical context & Developing and analyzing management options. IN Determining timber supply and allowable cuts in BC. Seminar Proceedings, Mar 1993. pp9-14, 35-40. 63 APPENDIX A 64 Productive Long Term Forest Harvestable Coast/In Timber Supply Area (hectares) Landbase Harvestable C North Coast 704845 106100 15.1% C Queen Charlotte Isla 348382 60358 17.3% C MidCoast 755191 155580 20.6% C Kingcome 519694 170639 32.8% C Soo 300716 106371 35.4% C Fraser 570266 275083 48.2% C Sunshine 447505 218983 48.9% C Arrowsmith 124619 74436 59.7% C Strathcona 377004 229920 61.0% 1 Wil l iams Lake 3359165 1634707 48.7% 1 Quesnel 1337765 1010383 75.5% 1 100 Mile House 938421 744099 79.3% 1 Lillooet 529269 283194 53.5% 1 Merritt 812512 490793 60.4% 1 Kamloops 1441118 890296 61.8% 1 Okanagan 1403309 971628 69.2% 1 Revelstoke 202098 58342 28.9% 1 Invermere 502492 215985 43.0% 1 Kootenay Lake 589107 273580 46.4% 1 Arrow 404264 200869 49.7% 1 Cranbrook 784814 403445 51.4% 1 Golden 302056 164174 54.4% 1 Boundary 425070 298991 70.3% 1 Fort Nelson 4284500 729070 17.0% 1 MacKenzie 3054385 1098961 36.0% 1 Robson Valley 482407 200342 41.5% 1 Fort St John 2303759 1119.133 48.6% 1 Dawson Creek 1478839 738622 49.9% 1 Prince George 5310879 3450712 65.0% . 1 Cassiar 3667434 366641 10.0% 1 Kalum North 668520 238094 35.6% 1 Kispiox 753395 309090 41.0% 1 Kalum South 199450 99136 49.7% 1 Bulkley 479445 262268 54.7% 1 Morice 1003418 592994 59.1% 1 Lakes 866368 634487 73.2% 1 Cranberry -- - --41732481 18877506 45.2% Table 15 . Harvestable portion of the productive land base by Timber Supply Ares Coastal Total % 34 Interior Total % 47 65 APPENDIX B - Coastal Futures harvest volume (mVyr) 20000000 12000000 A Maximum expected decline rate 60T.66T.73 8% Decline 60N_66N73 6% Decline 60A_S6A.73 0% Decline Figure 38. Harvestable land base outcome is 73% of the productive coastal forest example. harvest volume (m3/yr) 20000000 Maximum expected decline rate 60T_66T.66 20% Decline • 60N_6BN.66 9% Decline - 60A_66A.66 6% Decline Figure 39. Harvestable land base outcome is 66% of the productive coastal forest example with the harvestable land base increasing in the second decade. harvest volume (m7yr) 20000000 Maximum expected decline rate 60T_60T66 11% Decline 60N_60N.66 10% Decline 60A 60A.66 10% Decline Figure 40. Harvestable land base outcome is 66% of the productive coastal forest example with the harvestable land base increasing in the third decade. harvest volume (m3/yr) 20000000 18000000 16000000 14000000 12000000 10000000 8000000 -| 6000000 4000000 2000000 0 Maximum expected decline rate - 60T_66T.60 35% Decline • 60N_66N.60 19% Decline • 60A 66A.60 8% Decline Figure 41. Harvestable land base outcome is 60% of the productive coastal forest example with the harvestable land base increasing in the second decade. harvest volume (m3/yr) 20000000 18000000 16000000 14000000 12000000 10000000 8000000 6000000 4000000 2000000 0 Maximum expected decline rate - 60T_60T.6O 25% Decline • 60N_60N.60 11% Decline - 60A_60A.6O 10% Decline Figure 42. Harvestable land base outcome is 60% of the productive coastal forest example. (m3/yr) harvest volume 20000000 18000000 16000000 14000000 12000000 10000000 8000000 6000000 4000000 2000000 0 Maximum expected decline rate 60T_54T.60 20% Decline 60N_54N.60 18% Decline 60A 54A.60 20% Decline 4 . 6 decades Figure 43. Harvestable land base outcome is 60% of the productive coastal forest example with the harvestable land base decreasing in the second decade. harvest volume (m3/yr) 20000000 18000000 16000000 14000000 12000000 10000000 8000000 6000000 H 4000000 2000000 0 Maximum expected decline rate 60T, _60T 54 40% Decline 60N _60N 54 24% Decline 60A. _60A 54 11% Decline Figure 44. Harvestable land base outcome is 54% of the productive coastal forest example with the harvestable land base decreasing in the third decade. harvest volume (m3/yr) 20000000 18000000 16000000 14000000 12000000 10000000 8000000 6000000 4000000 2000000 0 Maximum expected decline rate 60T. 54T.54 26% Decline 60N. .54N.54 19% Decline 60A. .54A.54 20% Decline Figure 45. Harvestable land base outcome is 54% of the productive coastal forest example with the harvestable land base decreasing in the second decade. harvest volume (m3/yr) 20000000 Maximum expected decline rate 60T_54T.49 45% Decline 60N.54N.49 30% Decline 60A_54A 49 20% Decline 4 6 decades Figure 46. Harvestable land base outcome is 49% of the productive coastal forest example. APPENDIX C - Interior Futures 70 harvest volume (m3/yr) 6000000 Maximum expected decline rate 60T. .66T.73 7% Decline 60 N _66N.73 0% Decline 60A. _66A.73 0% Decline Figure 47. Harvestable land base outcome is 73% of the productive interior forest example. harvest volume (m3/yr) 6000000 Maximum expected decline rate 60T_ .66T.6 - 15% Decline 60N _66N.66 7% Decline 60A. .66A.6 6 0% Decline Figure 48. Harvestable land base outcome is 66% of the productive interior forest example with the harvestable land base increasing in the second decade. harvest volume (m3/yr) 6000000 Maximum expected decline rate 60T.60T.66 10% Decline 60N_60N.66 10% Decline 60A 60A.66 10% Decline Figure 49. Harvestable land base outcome is 66% of the productive interior forest example with the harvestable land base increasing in the third decade. harvest volume (m3/yr) 6000000 Maximum expected decline rate - 60T_66T.60 21% Decline 60N_66N.60 16% Decline - 60A 66A.60 7% Decline Figure 50. Harvestable land base outcome is 60% of the productive interior forest example with the harvestable land base increasing in the second decade. harvest volume (m3/yr) 6000000 Maximum expected decline rate - 60T_60T.60 15% Decline • 60N_60N.60 10% Decline - 60A 60A.60 10% Decline 4 6 decades Figure 51. Harvestable land base outcome is 60% of the productive interior forest example. harvest volume (m3/yr) 6000000 Maximum expected decline rate • 60T_54T.60 12% Decline 60N_54N.60 14% Decline • 60A_54A.60 12% Decline Figure 52. Harvestable land base outcome is 60% of the productive interior forest example with the harvestable land base decreasing in the second decade. harvest volume (m3/yr) 6000000 Maximum expected decline rate • 60T_60T.54 25% Decline 60N_60N.54 12% Decline - 60A_60A.54 10% Decline Figure 53. Harvestable land base outcome is 54% of the productive interior forest example with the harvestable land base decreasing in the third decade. harvest volume (m3/yr) 6000000 Maximum expected decline rate • 60T_54T.54 23% Decline • 60N_54N.54 12% Decline • 60A 54A.54 12% Decline Figure 54. Harvestable land base outcome is 54% of the productive interior forest example with the harvestable land base decreasing in the second decade. harvest volume (m3/yr) 6000000 Maximum expected decline rate • 60T_54T.49 37% Decline • 60N_54N49 23% Decline • 60A_54A49 12% Decline 4 6 decades Figure 55. Harvestable land base outcome is 49% of the productive interior forest example. 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0075224/manifest

Comment

Related Items