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Carbon uptake strategies in the western boreal forest region of Canada : economic considerations Stennes, Brad 2000

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Carbon Uptake Strategies in the Western Boreal Forest Region of Canada: Economic Considerations by Brad Stennes B.Sc. University of British Columbia, 1987 M.Sc. University of British Columbia, 1989 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR T H E DEGREE OF DOCTOR OF PHILOSOPHY In THE F A C U L T Y OF G R A D U A T E STUDIES (Department of Forest Resource Management) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September 2000 © Brad Stennes, 2000 UBC Special Collections - Thesis Authorisation Form http://www.library.ubc.ca/spcoll/thesauth.html In presenting, t h i s thesis i n p a r t i a l f u l f i l m e n t of the., requirements for an advanced degree at the University of B r i t i s h Columbia,. I •. agree that the Library s h a l l make i t f r e e l y a v a i l a b l e ' f o r reference and study. I further agree that permission for extensive copying of t h i s thesis f o r scholarly purpo'ses may be gran'ted by the head of my department or by his or her representatives. I t ' i s . understood that copying or publication of t h i s thesis f o r f i n a n c i a l . g a i n s h a l l not be allowed without my written permission. The University of B r i t i s h Columbia Vancouver, Canada 1 of I 27/09/00 10:55 AM Abstract . Land use change and forest management strategies for carbon (C) uptake are investigated for the boreal forest of Northeastern British Columbia. Deterministic cost-of-mitigation analysis indicates that afforestation does offer some potential for low cost C uptake. However, alternatives within the existing forest base are shown to be high cost and very limited in scope. These strategies include increasing the rotation length, changing the species, age and quality of harvests and more intensive planting. The uncertainty which plagues the climate change problem cannot be ignored. Strategies to meet C uptake and other objectives using traditional multiple scenarios are compared to one that applies fuzzy measures to uncertainties in timber yield, C targets and policy targets. The case study shows that the arbitrary choice of uncertain parameters, often done when employing multiple scenarios, is not appropriate and thus these uncertainties must be modelled explicitly. ii Table of Contents Abstract ii Table of Contents iii List of Tables iv List of Figures v Acknowledgements .'.. vi Chapter 1 Background 1 1.1 Forestry and Climate Change 5 1.2 Cost-of-Mitigation Estimates 9 1.3 Risk and Uncertainty in Forest Planning 14 1.4 Objectives of Research 18 Chapter 2 The Economics of Tree Planting For Carbon Uptake 21 2.1 Afforestation and Carbon Uptake 25 2.2 Substituting Wood for Fossil Fuels 27 2.3 Storing Carbon in Wood Products 37 2.4 Discussion 42 Chapter 3 Land Management Model 45 3.1 Fuzzy Sets for Uncertainty Modelling 51 3.2 Possibilistic Land Management Models 55 Chapter 4 Forest Management and Terrestrial Carbon Uptake 62 4.1 Forest and Agricultural Data and Initial Conditions for the Dawson Creek Region 62 4.2 Carbon 65 4.3 Cost-of-Mitigation for the Dawson Creek Region 68 4.4 Comparison of Alternative Models Incorporating Uncertainty 77 4.4.1 Possibilistic Formulations - Maxmin and Aggregated Opportunity Maximization. 77 4.4.2 Comparing Possibilistic Results to Those From Traditional Scenario Analysis 80 4.5 Testing the Performance of Strategic Thrusts Using Different DM Attitudes Towards Uncertainty 86 4.4 Discussion 90 Chapter 5 Summary and Conclusions 93 5.1 Summary and Conclusions 93 5.2 Policy Implications 96 5.3 Future Research Possibilities 97 Bibiliography 99 Appendices 107 Appendix A Deterministic Model Formulation 108 Appendix B Selected Tables of Inventory and Harvest Patterns 109 Appendix C GAMS Code 116 iii List of Tables Table 1.1: Annual Anthropogenic Flux and Size of the Globe's Carbon Sinks (Gt C) 1 Table 1.2: Greenhouse Gas Emissions Targets Under the Kyoto Protocol for Annex B Countries (2008-2012 Target expressed as Percentage of 1990 Base Year) 4 Table 1.3: Unit Costs of Carbon Sequestration and Summary Information on Technique Used ($US/ton). 11 Table 1.4: Carbon Prices Necessary to Achieve 1990-7% Reduction of Carbon Emissions by the US in 2010 and 2020, 1996 $US/ton 13 Table 2.1: Farmland Area Classified by Land Use (ha) 22 Table 2.2: Net Annual Returns to Current Agricultural Activities ($ per ha) 24 Table 2.3: Carbon Emission Factors for Selected Energy Sources3 28 Table 2.4: Carbon Stored in Ecosystem Components, Saved as a Result of Wood-for-Coal Substitution and Total Carbon Saving when Hybrid Poplar Planted is on Agricultural Land with 15-Year Rotation....32 Table 2.5: Net Annualised Costs of Removing C from the Atmosphere by Substituting Wood Burning for Coal in Electricity Generation, by Region and Current Agricultural Activities ($ per ha) 34 Table 2.6: Annualised Carbon "Removal" Components as a Result of Uptake in Wood Products, Hybrid Poplar Planted on Agricultural Land with 15-Year Rotation (t C ha"1 yr"1) 39 Table 2.7: Net Annualised Costs of Removing C from the Atmosphere by Storing Wood in Products, by Region and Current Agricultural Activities ($ per ha) 40 Table 4.1: Opening Stock Areas by Land Use Type, ha 62 Table 4.2: Remaining Proportion of Original Carbon Remaining from Forest Product Pools, Including that in Landfills 67 Table 4.3: Costs of C Uptake Over 80-Year Time Horizon for Dawson Creek Region 69 Table 4:4: Strategic Mixes For Different Levels Of Carbon Uptake, Deterministic Model (M 3.1)a 71 Table 4.5: Objective and Target Constraint Levels at Successively Higher Levels of Carbon Uptake, Deterministic Model (M3.1) 76 Table 4.6: Description of How Uncertain Model Coefficients (LHS) and Objective Targets are Represented in Model 78 Table 4.7: Achievement of Possibility/Necessity Measures with Maxmin and Oppmax Operators 79 Table 4.8: Strategic Mixes in Different Model Formulations 85 Table 4.9: Net Present Value and Periodic Forest Income for Different Model Formulations with Uncertainty Incorporated, Uncertain Parameters Valued at Means 87 Table 4.10: Even-Flow Harvesting Objective Parameters 90 Table B l : Opening Inventory of Forest land by Age Class 110 Table B2: Coniferous Harvests for Different C Uptake Targets, Deterministic Formulations I l l Table B3: Harvest Strategies for Different C Uptake Targets, Deterministic Formulations 112 Table B4: Pine Harvests for Different Model Formulations, Uncertainty Formulations 113 Table B5: Spruce Harvests for Different Model Formulations, Uncertainty Formulations 114 Table B6: Harvest Patterns for Different Model Formulations, Uncertainty Formulations 115 iv List of Figures Figure 2.1: Costs of Carbon Uptake as a Function of Afforested Area; Western Canada, Hybrid Poplar as a Substitute for Coal Burning, Infinite Time Horizon, with and without Discounting 36 Figure 2.2: Marginal Costs of Carbon Uptake in Western Canada, Hybrid Poplar as a Substitute for Coal Burning, Infinite Time Horizon, with and without Discounting 36 Figure 2.3: Costs of Carbon Uptake as a Function of Afforested Area, Western Canada, Hybrid Poplar Planted for Use in Wood Products, Infinite Time Horizon with and without Discounting 41 Figure 2.4: Marginal Costs of Carbon Uptake through Afforestation in Western Canada, Hybrid Poplar Planted for Use in Wood Products, Infinite Time Horizon with and without Discounting 41 Figure 3.1: Representations of a fuzzy set Mby its membership function f l M and its CC-cut [M]a 52 Figure 3.2: Two fuzzy numbers with trapezoidal membership functions; number a = [ai,a2,h1,h2] with finite main values and spread, n =[n,°°,T|,°o] with infinite right main value and right spread 53 Figure 3.3.Trapezoidal fuzzy numbers = ( ° ° , , ° ° , v f ) and b,L = {bf ,°°,vf , ° o ) 54 Figure3.4: Constraint Etx = et with possibility greater than or equal to (5 59 Figure 3.5: Constraint E,x = e, with necessity greater than or equal to E 59 Figure 4.1: Carbon Sequestration Cost Curves For Dawson Creek Study Area at Different Discount Rates. 70 Figure 4.2: Harvest Volumes of Coniferous Timber 72 Figure 4.3: Harvest Area for Medium Site Pine Over Final Four Periods 73 Figure 4.4: Harvest Patterns by Age Class for Coniferous Timber in Final Four Periods 74 Figure 4.5: Harvest Volumes of Deciduous Timber 75 Figure 4.6: Spruce Harvests in Different Model Formulations Under Uncertainty 82 Figure 4.7: Pine Harvests in Different Model Formulations Under Uncertainty 82 Figure 4.8: Deciduous Harvests in Different Model Formulations Under Uncertainty 83 Figure 4.9: Afforestation Patterns in Different Model Formulations 84 Figure 4.10: Nominal Periodic C Flux, Total Nominal Uptake and Total Uptake in Present Tonnes Equivalents (PTE) 88 Figure 4.11: Tradeoffs Between Cumulative C Uptake and Cumulative NPV Using Different DM Strategies on Uncertainty, Uncertain Parameters Valued at Midpoints 88 Figure 4.12: Periodic Harvest Volumes for Different Model Formulations ofUncertainty, Uncertain Parameters Valued at Midpoints 90 v Acknowledgements The completion of this dissertation would not have been possible without the guidance and insight of a number of individuals. I would first like to thank my supervisor and friend Professor G.C. van Kooten for help in both my general program and in the completion of this dissertation. Dr. van Kooten displays a rare degree of consideration for his students that many other Professors could learn from. I also wish to thank Professor Ilan Vertinsky for his amazing ability to maintain research focus and see the important larger issues in the analysis and results. I wish to thank Dr. Emina Krcmar-Nozic for forcing me to pay attention to the finer details of my basic model and assumptions. I feel very grateful to have worked with such a talented and constructive supervisory committee. I would like to thank Professor Richard Barichello, Professor John Innes and Professor Kurt Klein for their useful comments and valuable criticism of this research work. Finally, I would like to thank my wife and 'best friend' Wendy. Without her love and support, completing my PhD would never have been possible. vi Chapter 1 Background Climate change and related global warming are believed to be caused by greenhouse gases (GHGs) that permit the sun's rays to pass through the earth's atmosphere, but prevent heat from radiating back into space by trapping it. While GHGs include methane (CH4), nitrous oxides (N2O) and a group of artificial gases known as halocarbons (or CFCs), the most dominant GHG (outside of water vapour) is carbon dioxide (CO2), in terms of anthropogenic emissions and potential to affect climate. It is feared that human activities, primarily fossil fuel burning and tropical deforestation, are responsible for increasing the atmospheric concentrations of CO2. This is shown in Table 1.1, which suggests an average 1.3xl09 tonnes (gigatonnes or Gt) of carbon (C) are added to the atmosphere each year as a result of human activities. Compared to the size of global sinks, such as oceans and the soil, which are also indicated in Table 1.1, the contribution of humans is rather small. Table 1.1: Annual Anthropogenic Flux and Size of the Globe's Carbon Sinks (Gt C) Item Average annual flux Approximate sink size C 0 2 sources Emissions from fossil fuels and cement production 5.5 ±0 .5 Net emissions from changes in tropical land uses 1.6 ± 1.0 Total Anthropocentric Emissions 7.1 ± 1.1 Partitioning amongst reserves Atmosphere 3.310.2 800 Oceans 2.0 + 0.8 40,000 Northern Hemisphere forest regrowth 0.5+0.5 — Soils n.a. 1,500 Above ground biomass n.a. 600-700 Inferred Sink (Difference) 1.3 ± 1.5 =43,000 Source: Houghton et al. (1996); n.a. means not available Over the past two centuries, atmospheric concentrations of CO2 have increased by about 25 percent, from approximately 285 parts per million by volume (ppmv) to 356 l ppmv, with most of this increase occurring in the past 100 years. If other GHGs are included, equivalent CO2 levels were approximately 290 ppmv at the beginning of the industrial revolution, 310 ppmv in 1900 and some 440 ppmv by 1995. Mean global surface temperatures have increased some 0.3° to 0.6°C since the mid 1800s, and by some 0.2°-3°C in the last 40 years. Between 1861 and 1910, mean global temperatures remained relatively flat, but were some 0.1 °C below the 1861 level in 1910. Between 1910 and about 1940, temperatures rose by some 0.5°C, remained flat between 1940 and 1975, and then rose a further 0.2°C in the two decades since 1975 (Houghton et al., 1996, p.26).1 Although the majority of scientists now accept that climate change is occurring, there is controversy surrounding the causes of climate change (e.g., Emsley 1996). Climate change is considered by some to be the world's most important environmental policy issue (Clinton and Gore 1993). Average global temperatures are projected to increase by 1.0-4.5°C under a double CO2 atmosphere (Kattenberg et al. 1996). Concern about anthropogenic emissions of GHGs led the World Meteorological Organisation (WMO) and the United Nations Environment Program jointly to establish the Intergovernmental Panel on Climate Change (IPCC) in 1988.2 The first IPCC report was published in 1990; it led to the signing of the United Nations' Framework Convention on Climate Change (FCCC) in Rio de Janeiro in June 1992. The Convention committed signatories to stabilise atmospheric CO2, with developed countries to reduce emissions to the 1990 level by 2000 (article 4). The IPCC's second assessment report was published in 1996 (Houghton et al. 1996) and endorsed by the Second Conference of 'One might have expected a greater increase in mean global surface temperatures after World War II rather than before it, because of the greater increase in fossil fuel use. 2 W M O and UNEP had already convened the First World Climate Conference and established the World Climate Program in 1979. 2 the Parties (COP) to the FCCC. Following this, at the Third COP in December 1997 at •'< Kyoto, Japan, developed countries agreed to curtail their CO2 emissions relative to what they were in 1990.3 Developed countries agreed to varying levels of emissions reductions, given in Table 1.2 (so-called Annex B countries because they are listed in Annex B of the Protocol). The US committed to reduce emissions to 7 percent below 1990 levels by the year 2012 (the actual commitment period for measurement purposes is 2008-2012). E U countries agreed to reduce emissions by 8% of 1990 levels by 2012, as did countries hoping to gain membership to the E U sometime in the future. Canada and Japan agreed to a 6% reduction, while Australia agreed to limit its increase in CO2 emissions to no more than 8% by 2008 and Iceland to an increase of no more than 10%. Other developed countries agreed to limits that fell between the EU's 8% decrease and Australia's 8% increase (Table 1.2). Within the E U , some countries will be required to reduce emissions by less than other countries. Thus, the Netherlands will need to reduce emissions by only 6%, while Germany will reduce them by some 20% or more (because inefficient industries in the East will be closed or rebuilt). The Kyoto Protocol does not commit developing countries to CO2 emission reduction targets, even though their emissions will soon account for more than one-half of total global emissions. 3 The first COP in 1995 issued the "Berlin Mandate" that eventually led to the Kyoto Protocol. 3 Table 1.2: Greenhouse Gas Emissions Targets Under the Kyoto Protocol for Annex B Countries (2008-2012 Target expressed as Percentage of 1990 Base Year) Country Target Country Target Country Target Australia 108 Iceland 110 Portugal 92 Austria 92 Ireland 92 Romania 92 Belgium 92 Italy 92 Russian Fed. 92 Bulgaria 92 Japan 94 Slovakia 92 Canada 94 Latvia 92 Slovenia 92 Croatia 95 Liechtenstein 92 Spain 92 Czech Republic 92 Lithuania 92 Sweden 92 Denmark 92 Luxembourg 92 Switzerland 92 Eur. Community 92 Monaco 92 Ukraine 100 Finland 92 Netherlands 92 United Kingdom 92 France 92 New Zealand 100 United States 93 Germany 92 Norway 101 Hungary 94 Poland 94 Source: Brown et al. (1999) In 1990, overall Canadian G H G emissions amounted to 601 million metric tonnes (Mt) in C02-equivalents4, or 163.9 Mt of C; in 1997 (the latest year for which data are available), emissions amounted to 682 Mt, or 185.9 Mt of C (Analysis and Modelling Group, National Climate Change Process 1999). Business as usual scenarios project annual emissions to rise to 208.3 Mt of C (764 Mt in CC^-equivalents) in 2010 and 230 Mt in 2020. To meet the Kyoto target, Canadian emissions must be 154 Mt C (565 Mt COrequivalents), some 26% (or 54.2 Mt of C) below the level expected in the commitment period. Canada expects a large part of its international commitment to reduce atmospheric GHGs to come from forestry, with perhaps 10 to nearly 25 percent of its Kyoto commitment coming via tree planting (see Canadian Forest Service 1998; Guy andBenowicz 1998: Nagle 1990). The Kyoto Protocol does not call for sanctions against countries failing to meet 4 GHG emissions are expressed in terms of C 0 2 equivalent global warming potentials. For instance CH 4 has a global warming potential of 21 times that of C0 2 , N 2 0 310 and SF6 23,000 times that of C 0 2 (IPCC 1996). 4 their targets—the Protocol is voluntary. Moral suasion will be brought to bear on those countries failing to live up to their agreement, but this will occur only if there is general compliance. With the exceptions of Germany and the UK, most countries signing the F C C C have been unable to meet the Rio target (e.g., Canada's emissions in 1996 exceeded 1990 emissions of CO2 by more than 12%), and most are unlikely to meet the Kyoto target. Nonetheless, countries are committed to reducing anthropogenic GHG emissions in the long run. As an interim measure, policies to remove CO2 from the atmosphere and store it as carbon in terrestrial ecosystems have taken on some importance. Already in 1989, the Noordwijk Declaration that was signed by 68 countries proposed increasing global forest cover as a means of slowing climate change. 1.1 Forestry and Climate Change The emission targets in the Kyoto Protocol are in terms of net emissions, which means that account is given to anthropocentric increases (or decreases) in terrestrial C sinks (Hinchy et al. 1998). The Protocol allows countries to claim as a credit any C sequestered as a result of afforestation (planting trees on agricultural land) and reforestation (planting trees on denuded forestland) since 1990, while C lost as a result of deforestation is a debit. The forest component of the Protocol has several interesting aspects, although each of these is under review as countries seek clarification on the Protocol's interpretation of terrestrial C sinks, especially forest sinks. First, deforestation is defined as a change in land use, so when a site is harvested but subsequently regenerated there is no change in use and only the C credits associated with reforestation 5 are counted, not the costs of C release.5 For example, if a mature forest stand is harvested sometime after 1990 and subsequently replanted before 2008, only growth of the newly established stand is counted as a credit; the debit from harvest is not counted. The amount of C to be credited as a reduction is determined by measuring the inventory on the site at the end of the commitment period minus the inventory at the beginning of the period, divided by the number of years to give the annual value. However, inventory measurement will be difficult and costly, and mean annual increment (MAI) may be used as a fall back for determining C uptake. Second, only deforestation during the period 2008-12 is counted as a debit. Finally, only the commercial (and measurable) component of the trees is counted, so changes in soil carbon, for example, might be ignored. Most countries did not adopt large-scale afforestation programs before the late 1990s, and even reforestation of sites harvested since 1990 will not have occurred before at least the mid 1990s and be ongoing thereafter. For temperate forests, such as those found in Scandinavia, Russia, Canada and much of the US (ignoring the highly productive US South), the major producing countries, the increase in biomass over the first two decades after planting is generally imperceptible. In many instances, growth tables do not even begin until the third or fourth decade. Thus, any measure of C uptake by forests taken in the Protocol's accounting period 2008-2012 will be small, or biased upwards if MAI over the entire rotation is used as a proxy for actual growth. It would appear, therefore, that forest policies are important in the intermediate term, and not the 5At least this is the way some countries interpret the Protocol, but others interpret this differently. 6 short term of the Kyoto Protocol. An exception occurs if high-yielding varieties of hardwood species are used in place of more natural, commercially valuable species, but planting such species could result in adverse environmental consequences such as reduced biodiversity. This situation is examined in Chapter 2 of this dissertation. Planting trees involves more than simply carbon uptake in forest biomass, because what happens to the C balance of the soil and to products produced from harvested timber is also important. Carbon is stored not only in above-ground biomass, but also in decaying material on the forest floor and, importantly, in the soil (Binkley et al. 1997). Wood can substitute for fossil fuels and wood products continue to serve as a C sink for many years after the trees are harvested. Policies can be oriented towards greater substitution of wood for non-wood products (e.g., wood studs rather than aluminium ones) and simply greater use of wood products. Wood products' research is one means of encouraging greater substitution and use of wood, but so are subsidies or other policies that reduce the price of wood products. Planting trees and increasing the supply of wood is one way to reduce prices. In general, it appears that plantation forests are a cost-effective means of sequestering C (Sedjo et al. 1995). The main purpose of cost-of-mitigation studies is to provide benchmarks for comparing alternative strategies, so that the least cost strategies can be implemented.6 Benefits are measured in physical units of C uptake, with some arguing that physical quantities cannot be discounted. For example, the Global Environment Facility (GEF) of the World Bank and United Nations can allocate funds to desirable C uptake projects. In 6 Sequestration strategies, other than those using forestry (or agriculture), being examined by the US Department of the Environment, include geological depositing and pumping liquified C 0 2 into the deep ocean (M. Judge, Globe and Mail, Dec 16 1999). 7 determining project feasibility, GEF recommends against discounting of C sequestered and stored in terrestrial ecosystems in the future, although future costs are to be discounted. Richards (1997) demonstrates that the time value of carbon will depend on the path of marginal damages—that is, on the concentration of atmospheric CO2. If marginal damages are constant over time, then C storage can be discounted at the social rate; the more rapidly marginal damages increase over time, the less future C fluxes (defined as changes in C stock across time periods) should be discounted. In this dissertation, physical carbon is discounted with C uptake expressed in Present Tonnes Equivalent (PTE) (Richards and Stokes 1995). The discounting of physical carbon flows is further discussed below. Examples of investments in tree planting and other carbon-uptake projects for the purpose of "carbon credits" are starting to occur both in Canada and internationally, with speculation that these investments will result in future carbon credits as emissions trading schemes become established. One example of this is a $6 million investment by the Saskatchewan Power Corporation to replant up to 4,000 ha. of northeastern Saskatchewan that was logged decades ago and never successfully regenerated (B. Gord, Regina Leader-Post Nov 4, 1999). Other energy companies are investing in similar carbon offset schemes, such as the recent $25 million investment by Ontario Power Generation Inc. to buy the rights to CO2 emissions permits from a US company that recovers methane from landfill sites (P. McKay, Globe and Mail Oct 26, 1999). Internationally, a large project has been announced by the Toyota Electric Power Company (TEPCO) to plant eucalyptus (and other species) on 1,000 ha of Australian land in 2001, increasing plantings to 40,000 ha over the decade. TEPCO estimates that 8 200,000 tonnes/year of C uptake will be achieved under lease arrangements with landowners managed by Australias State Forest. Although I provide detailed background information on the Kyoto Protocol, due to its very limited definition of changes in carbon pools over time (C-flux), I do not strictly adhere to definitions of the "Kyoto Forest" in this analysis. Instead, in the analyses presented in this dissertation, and subject to the data and assumptions presented, I quantify changes in various carbon pools associated with afforestation, deforestation, reforestation, forest products, and , in the case of land-use changes, soil and litter carbon. This C flux is the basis for both cost-of-mitigation estimates and C targets. 1.2 Cost-of-Mitigation Estimates Numerous cost-of-mitigation studies have been done over the past decade, largely estimating costs in the US. There are a number of issues that can lead to differences in estimates, including differences in cost data^  discount rates and C sequestration levels. However, even if using the same data, the summary statistic used to present the result is critical to its value. There are, in general, three types of summary statistics (Richards and Stokes 1995): 1. Flow Summation Method: Using this method the total carbon captured by a project is simply summed. Carbon sequestered early is not distinguished from that sequestered later on. The cost estimate using this method is the net present value (NPV) of the project divided by total carbon capture. 2. Average Storage Method: Measures the change in average carbon storage over a specified period. This is then divided by the NPV. The only difference between this and Flow summation is the specification of a rotation length. 9 3. Levelization/Discounting Method: This method differentiates costs depending upon when carbon is sequestered. Two possible approaches can be used, each yielding identical results. i. An annualization of the NPV. is done over the project life (similar to an annuity), then divided by the average capture rate in that year. ii. The social discount rate is applied to discount carbon flow back to a summary statistic. This statistic is then divided by NPV. The method used makes certain assumptions about the shadow price of atmospheric carbon. If additional emissions do not cause any damages up to a point, but then catastrophic damage occurs, the correct measure to use is the flow summation method. If, alternatively, a linear relationship exists between the level of atmospheric carbon and damages then the levelization/discounting method is more appropriate. The actions of current public officials do indicate that policy makers prefer early-period reductions of net GHG emissions to those in later periods (i.e., time horizon in the Kyoto Protocol). If one considers the time preference of costs of compliance without equal consideration to the benefits (reduced emissions), all reductions will occur far in the future when the present value of costs is minimized. The fact that policy makers are demanding early-period reductions in GHG emissions through international agreements indicates that physical carbon discounting is appropriate. For further insight consider an example of a system of tradeable carbon permits. Should the market value of an offset permit that sequesters a tonne of CO2 20 years in the future be equivalent in value as one that immediately removes a tonne of CO2? This would be the case with no carbon discounting (after adjusting for risk). A number of the cost of C uptake estimates reported in both Richards and Stokes, a second literature review on carbon sequestration costs (Sedjo et al. 1994) and a more recent study (Sohngen and Alig 2000) are presented in Table 1.3. 10 Table 1.3: Unit Costs of Carbon Sequestration and Summary Information on Technique Used ($US/ton) Study Region Estimate Method Sequestration Costs ($/ton) Afforestation Forest Mgt Moultan and Flow Summation 2-9 6-47 Richards (1990) US Curve Levelized 9-41 n.a. Adams et al. (1993) US Curve Levelized 18-55 n.a. Parks and Hardie (1995) us Curve Levelized 10-82 n.a. Richards et al. (1993) US Curve Levelized 9-66 n.a. van Kooten et al. Flow Summation 6-18 8-23 (1992) Canada Point Levelized 66-187 39-108 Nordhaus (1991) Global Point Levelized 42-114 n.a. Stavins(1999) US Curve Levelized <66 n.a. Plantinga et al. (1999) US Curve Levelized 15-90 n.a. Sedjo(1999) Argentina Point Flow Summation >20 n.a. Source: Adapted from Table 11 in Richards and Stokes 1994, Sedjo et al. 1994 and Table 4 in Sohngen and Alig 2000. Most of the studies develop carbon sequestration cost curves through opportunity costs of afforested agricultural land (Moultan and Richards 1990; Adams et al. 1992; Parks and Hardie 1995; Richards et al. 1993). Adams et al. and Moultan and Richards are similar, both examining the marginal costs of sequestering carbon at levels of 140, 280, 420 and 700 million (short) tons, while Parks and Hardie examine sequestration levels from 45 to 120 million (short) tons. The M C curves in these afforestation studies range from $9 to $90 per ton (SUS), when C discounting (levelization) is used. As a comparison to these forestry cost-of-mitigation estimates, there have been a number of studies on economy-wide costs to meeting targets defined in the Kyoto Protocol. The Energy Information Administration (EIA) of the US Environmental Protection Agency examined the carbon price necessary to achieve the Kyoto Protocol C reduction targets for the US in 2010 and in 2020 (EIA 1998). These estimates were 11 derived from a number of separate groups using different general equilibrium models of the US economy including: < 1. the EIA using the National Energy Modeling System, 2. Charles River Associates (CRA) using the Multi-Regional Trade Model, 3. the Pacific Northwest National Laboratory (PNNL) using the Second Generation Model, 4. the Massachusetts Institute of Technology (MIT) using the Emissions Prediction and Policy Analysis Model, 5. Electric Power Research Institute (EPRI) using the M E R G E model, 6. Data Resources Incorporated (DRI), and 7. W E F A ( W E F A Inc. 1998). Two main scenarios were run with all of these, models, the first being a case in which the US had to reduce emissions by 7% below the 1990 level in the 2008-2020 period without the use of carbon sinks, offsets and international permit trading. The second scenario allowed the use of sinks, offsets and national emissions trading. The carbon prices (1996 $US/ton C) required to achieve the 7% reductions by 2010 and 2020 are given in Table 1.4. 12 Table 1.4: Carbon Prices Necessary to Achieve 1990-7% Reduction of Carbon Emissions by the US in 2010 and 2020,1996 $US/ton MIT EPRI CRA EIA PNNL WEFA Scenario 1 No C sinks, offsets or emissions trading 2010 266 280 295 2020 147 251 316 348 305 221 286 265 360 MIT EPRI CRA EIA PNNL DRI Scenario 2 With C Sinks, offsets and National Emissions Trading 2010 175 114 109 2020 119 188 175 129-163 123-141 100 142 110 131 Carbon prices are very high without the use of sinks, offsets and C trading ranging from a low of $220/ton to a high of $350/ton to achieve a seven percent reduction in 1990 net emissions by 2010. Carbon prices fall by approximately 50% when sinks, offsets and national emissions trading are allowed. Even in this case the costs are significantly higher than those in the upper range of the forestry studies (Table 1.3). Another study on the economic impacts of the Kyoto Protocol was undertaken by the Australian Bureau of Agricultural and Resource Economics (ABARE), which again used a large C G E model to examine carbon prices necessary to achieve Kyoto targets (Brown et al. 1999). The A B A R E study estimated carbon prices in Annex B countries with and without international carbon trading. The global equilibrium price, with international emissions trading was just under $100/tonne (1992 SUS). Estimated C prices from these studies indicate that forest based C uptake is cost competitive in North America, even with international emissions trading. 13 1.3 Risk and Uncertainty in Forest Planning Natural resource planning problems are generally characterized by uncertainty. This is especially true in forestry due to very long planning horizons. This means that risk and uncertainty are probably more important in forestry than most resource management problems. Sources of risk in forest planning include regeneration success, growth and yield, tree survival and economic variables such as prices, costs and discount rates (Pukkala and Kangas 1996). Climatic change can influence all of these factors. Different authors distinguish between the concepts of risk and uncertainty in different ways. One of the first definitions (Knight 1921) was based on knowledge of the probability of an event. Certainty is defined as complete knowledge, risk is partial knowledge and uncertainty is a complete lack of knowledge; In the case of uncertainty, one can not assign numeric probabilities to potential outcomes. Brumelle et al. (1989) define risk as uncertainty with the possibility of undesirable consequences. Finally, Pukkala and Kangas (1996) define risk as uncertainty with the probability of outcomes known. It is important to distinguish clearly between different sources of uncertainty since they need to be handled in different ways. One traditional approach has been simply to rely on a deterministic model that assumes best estimates for the uncertain parameters. In many cases, this approach produces quite different results from one that treats uncertainty systematically. Another widely used approach is scenario analysis, which assumes different values for uncertain parameters. Each scenario represents a set of point estimates for the parameters. The problem with this approach is that, while it sharpens the 14 awareness of decision makers (DMs) about the uncertainties of the consequences of their decisions, the final choice is left to their perception of what is most likely to happen. The need to consider explicitly uncertainty in forest management models is well recognized (Weintraub and Bare 1996). Brumelle et al. (1989) provide a framework for dealing with risk in silvicultural decisions, but the majority of work in forest management under uncertainty deals with the risks of fire and pests. Only recently have other aspects of uncertainty (e.g., with respect to timber yields and production requirements) been introduced in forest management. Given the increasing involvement of multiple stakeholders with conflicting demands, the chance-constrained formulation (Charnes and Cooper 1963) has been suggested as especially appropriate. In this formulation an objective function is maximized while constraints are satisfied with a given probability. Hof and Pickens (1991) applied the chance-constrained formulation in the context of forestland allocation with nondbclining yield constraints and random production targets. Pickens and Dress (1988), Hof, Kent and Pickens (1992), and Weintraub and Abramovich (1995) used the extended chance constraints, formulated by van de Panne and Popp (1963), to analyze problems with random yield coefficients. The original chance-constrained formulation requires the D M to fix thresholds on the probabilities that constraints are satisfied in order to prevent infeasible solutions. If the highest priority is given to the satisfaction of constraints, then one may wish to maximize the chance of meeting the output targets and input availability (Sengupta 1972, p.73; Hof 1993, p.77). A conservative version of this formulation maximizes the lowest 15 chance of meeting the targets (Hof, Kent and Pickens 1992). The chance of not satisfying constraints is spread across the rows in this Maxmin formulation. While the chance constrained approach leads to deterministic LP equivalents in the case of random right-hand sides (production requirements), uncertainty in the technical (timber yield) coefficients results in deterministic nonlinear programs. In addition, the problems with random technical coefficients are analytically tractable only under the assumption of independence between rows in the constraint matrix. Even though one of the recent theoretical results relaxes the assumption of between row independence (Watanabe and Ellis 1994), the complexity of the resulting deterministic equivalent limits its use to small problems. The use of probability assumes a degree of knowledge that often is not possessed by the D M . Furthermore, when precise objectives are incorporated in the decision model as constraints, the use of probability is conceptually inappropriate. The conceptual, data and computational problems associated with probabilistic formulations of the forest land management problem led several authors to incorporate non-probabilistic measures in their models. The approach is to treat uncertain variables as fuzzy sets. Pickens and Hof (1991) employed fuzzy goal programming involving nondeclining production constraints. Mendoza and Sprouse (1989), Mendoza, Bare and Zhou (1993) and Bare and Mendoza (1993) modelled vagueness of the objectives. They used flexible programming (Zimmerman 1996) to maximize overall satisfaction of constraints and objectives under relaxed requirements. 16 Uncertainty in both the yield coefficients and output targets has been considered in forestry by Ells, Bulte and van Kooten (1997). They applied fuzzy multiple objective programming to a static land allocation problem by fixing the level of uncertainty for imprecise technical coefficients, and then maximized the minimum satisfaction of the goals and constraints. Besides the advantage of solving the linear deterministic equivalent, this approach avoids meeting the overall satisfaction of constraints and objectives by treating individual coefficients at the given uncertainty level. In Chapter 3 of this study, I develop a land management model where technical coefficients of the constraint matrix and the right-hand sides of the constraints are uncertain. This model differs from the usual forest planning problem with nondeclining yield by having an additional requirement on stable C flux and permitting variation in the timber production constraint. Timber yield coefficients in the production constraints and C uptake coefficients in the C flux constraints are both functions of standing. wood volume. The relationship between timber production and C uptake in the technical coefficients matrix violates the independence assumption required by the chance-constraint methodology. Thus the traditional chance-constrained model is conceptually inappropriate and computationally infeasible. I extend the chance-maximizing approach in two ways. First, I develop a measure of the aggregated opportunity (see Chapter 3) for meeting objectives and constraints, rather than the minimum opportunity as in the max-min formulation. The minimum satisfaction represents a conservative approach and does not permit tradeoffs between the objectives and/or constraints. Second, I apply the idea of aggregated opportunity to 17 models with uncertainties in both the technological coefficients of the constraint matrix and the right-hand side (RHS) constraints. 1.4 Ob j ectives of Research An important issue that has not been adequately researched in the literature is the uncertainty associated with terrestrial carbon uptake strategies. Estimating carbon flows associated with forestry, agriculture and land-use change is fraught with uncertainty that even threatens the compliance process. This uncertainty is the combination of uncertainties related to climate change and those inherent to forestry (Paoli and Bass, 1996). In this study, I consider several select sources of C uptake uncertainties, such as: • variability of timber yields as a result of weather, climate, a (possible) CO2 fertilization effect, and the intensity of silvicultural treatments; • lack of data on carbon sinks, especially with respect to the life cycle of carbon in wood and wood products; • vague input availability, and; • uncertain objective targets and constraints due to vague societal values and preferences. Governments often regulate timber production goals to maintain employment, while C-uptake goals are the result of negotiations at both the domestic and international levels. This need to introduce uncertainty into economic models of climatic change has been recognized (Leimbach 1996; Schimmelpfennig 1996), also recognized is the need to explicitly incorporate uncertainty into forest management (Weintraub and Bare 1996). However, there is little consensus as to how uncertainty should be modeled. This study contributes to research on forest management by developing methods for characterizing 18 and incorporating uncertainty into forest sector models. These methods are applied to a land-use problem in which economic, carbon uptake and even flow objectives are met in the boreal region of western Canada. The main objectives of the research are twofold. First, I investigate economic issues related to the use of forestry to aid Canada in meeting its international commitments on G H G reductions. The sub-objectives are: 1. To estimate the cost-of-mitigation in the Western Boreal zone of the Canadian prairies through afforestation. 2. To extend these afforestation results, by including the option of changes in forest management along with afforestation, to estimate cost-of-mitigation in the BC Peace River region. My second objective is to investigate the land-use strategies to meet these C targets in conjunction with both economic and stable volume targets under different assumptions on how DMs view uncertainty. In order to meet these objectives I estimate the cost-of-mitigation in the western boreal forest region in Alberta and the Peace River region of British Columbia. This is done by examining the potential for planting trees on marginal agricultural land. A more in-depth analysis of both forest management and afforestation strategies is then performed by using mathematical programming techniques in a decision-framework that recognizes society has more than one goal when determining land use. The goals include achieving a high net present value (NPV), using forests to sequester atmospheric carbon, and maintaining a steady flow of fiber from the forest (to meet employment and community stability objectives). As these are clearly conflicting goals, measurement of 19 tradeoffs, such as the reduction in NPV resulting from increased C sequestration, can be made in this framework. The second objective of this research is accomplished by identifying and implementing a non-probabilistic method of incorporating uncertainty into the decision-making framework. This has not been previously done, with perhaps the exception of Ells, Bulte and van Kooten (1997), although they employed a static model. I apply fuzzy measures to model imprecise timber yield and carbon coefficients and vague targets representing policy objectives (described above). This approach allows a broader interpretation of uncertainty to be addressed and the attitude of the D M toward uncertainty to be incorporated (Dubois and Prade 1993). The research will compare these non-probabilistic method of addressing uncertainty with the more common approach of using deterministic models and multiple scenarios. 20 Chapter 2 The Economics of Tree Planting For Carbon Uptake Canada expects a large part of its international commitment to reduce CO2 emissions to come from forestry (see Canadian Forest Service 1998; Guy and Benowicz 1998: Nagle 1990). The federal government has created a "Tables" process to examine various means of achieving its C02-reduction commitment (Environment Canada 1998), and afforestation of agricultural lands features prominently in this process (Canadian Forest Service 1998). The focus of investigations into afforestation (Nagle 1990; Guy and Benowicz 1998) has been on identification of suitable (marginal) agricultural lands and the potential growth of trees to be planted. For the most part, economics has been ignored. In this chapter, I seek to rectify this shortcoming by examining the economics of afforestation in Alberta and the BC Peace River region. In particular, this chapter focuses upon the identification of marginal agricultural lands and consideration of the costs of sequestering C on these lands when fast-growing, hybrid poplar is planted. The perspective is longer than that of Kyoto, because the time required to establish plantations for C uptake on a large (massive) scale is too long to have much relevance for the Protocol's commitment period. Rather, I consider the long term, which means finding a use for wood when it reaches maturity. Two uses are examined: substituting wood for coal as a fuel in energy production and storing C in paper and other wood products. I investigate the potential for and costs of terrestrial C sequestration in Northeast BC and Alberta. Current agricultural land uses in the BC Peace River region and the seven Agricultural Reporting Areas (ARA) in Alberta are provided in Table 2.1 (Statistics Canada 1997a, 1997b). In the table, improved land includes non-forage crops, forage, fallow, pasture and other land, while unimproved land contains mainly pasture. 21 Table 2.1: Farmland Area Classified by Land Use (ha) Improved land Unimproved land Region Non-forage crops Forage Fallow Pasture Other Pasture Other BC Peace 137,585 119,584 29,608 96,991 8,372 282,545 150,693 Alberta ARA 1(S east)3 758,862 111,072 409,004 218,121 36,764 2,090,655 36,764 2 (S central)" 1,544,105 135,252 415,483 178,540 32,640 903,954 32,640 3 (S west) 857,419 216,449 83,443 194,053 77,602 1,039,605 129,337 4a (E central) 821,625 115,872 127,406 180,642 18,571 498,009 92,857 4b (E central) 1,055,335 128,412 110,745 186,410 19,614 338,949 117,684 5 (Central) 800,479 435,667 46,080 360,777 47,979 557,366 167,927 6 (N east) 591,720 446,670 76,622 351,051 24,372 685,566 268,096 7 (N west) 1,193,462 334,144 167,958 245,009 28,473 501,393 370,153 a ARAs 1 & 2 have irrigated forage production, are too dry for planting trees and are excluded from further analysis. The agricultural land types considered suitable for afforestation are primarily those associated with forage production and pasture. However, for each sub—region, it is necessary to determine the specific agricultural land use types appropriate for afforestation, and the value of those lands in agriculture. The land suitable for afforestation in the BC Peace River region is a mixture of land in crops, improved pasture and improved idle land. Since unimproved pasture (and crown range) consists mainly of pea vine and vetch that grow under mature aspen stands, it is forested already, and thus cannot be considered for afforestation. The same might be true for the two most northern Alberta regions (ARAs 6 & 7). Nonetheless, I assume that unimproved pasture in these two regions is also suitable for afforestation. If not, then the amount of marginal agricultural land available for planting is some 1.20 million ha less than employed here. The boundaries of the ARAs in Alberta are defined on the basis of soil zones, either brown, dark brown, black or grey. The driest of these are A R A 1, which contains brown soils, and A R A 2 with dark brown soils in the southeast corner of the province. These are characterised by irrigated forage and crop production and are considered too dry for planting trees, although it may turn out that growing trees using irrigation may be an economically viable C uptake option. The remaining ARA's (and the BC Peace), due to higher annual precipitation levels, contain either black or grey soils which I assume are suitable for growing trees (actually a portion of A R A 4 is in the dark brown soil zone, but I assume this is also capable of tree production). Land in crops that can be considered for growing trees is in forage (hay and alfalfa). For ARAs 3, 4 & 5, unimproved pasture is also considered suitable for afforestation. Improved idle land ("other"), improved pasture and land in forage production are also considered to be "marginal" agricultural lands for the purpose of this study. The total amount of marginal agricultural land that I consider suitable for planting to trees is 7.25 million ha. Little economic data is available for improved "other" land, so it is ignored in the analysis. This leaves 7.03 million ha of marginal agricultural land considered suitable for afforestation for C uptake. Estimates of the costs per tonne of carbon sequestered for each of these land types requires data on the net returns associated with the current agricultural activity (the opportunity cost of afforestation), the direct costs of afforestation, and the C uptake associated with the trees to be planted. Budget data, including direct expenses and the capital stock to estimate indirect expenses for forage production in British Columbia are from the Planning for Profit Enterprise Budgets (BC Ministry of Agriculture and Food 1995, hereafter BCMAFF). Net returns are estimates as revenue less direct and indirect costs, and hay establishment costs are averaged over the life of the forage crop (the opportunity cost of land ownership is not included here as it is assumed that the farmer maintains ownership following 23 afforestation). To estimate the differences in returns across regions of Alberta, representative yields and prices obtained from Alberta Agriculture (1998) are used for each of the ARAs. Pasture is treated somewhat differently. A good market exists in both British Columbia and Alberta for private pasture rental. Rents are based on a standardised animal unit month (AUM), which is the forage consumed per month by a 450-kg cow. Using data for each A R A on stocking rates in AUMs per ha (Wroe et al. 1988) and the private market value of an A U M of pasture use (Bauer 1997), the opportunity cost of lost pasture use is estimated.7 The estimated costs per hectare of lost forage and pasture production for all regions are provided in Table 2.2. Table 2.2: Net Annual Returns to Current Agricultural Activities ($ per ha) Forage3 Improved Pasture Unimproved REGION Pasture BC Peace 184.98 34.45 n.a. Alberta, ARA 1 (Southeast) 185.75b 17.51 8.75 2 (South-central) 304.04b 23.64 11.82 3 (Southwest) 310.20 35.82 17.33 4a (East-central) 101.47 24.84 12.42 4b (East-central) 116.80 28.35 14.02 5 (Central) 260.56 46.93 20.26 6 (Northeast) 168.63 58.01 21.04 7 (Northwest) 178.75 34.45 15.15 a Forage is based on the net returns for hay and alfalfa, weighted by the production of each within the region. b ARAs 1 & 2 have irrigated forage production, are too dry for planting trees and are excluded from further analysis. The data is presented for comparison purposes only. The additional cost component that must be accounted for is the direct cost of afforestation, or planting cost. Direct afforestation cost depends on the species chosen 7The bulk of pasture/range use comes from public lands, which have long-term lease agreements. The price associated with these leases is considerably less than the value of forage consumed (Bauer 1997), and thus not reflective of the true social value of forage. 24 for planting. For various regions of the Canadian Prairies, there are different species that could be considered for planting on agricultural land for the purpose of C uptake. For all regions, I consider fast-growing hybrid poplar. I also consider planting a mix of species out of concern for biodiversity, although no attempt is made to value it. Using information from BC's Planning for Profit Enterprise Budgets (BCMAFF 1996), it is assumed that planting costs for hybrid poplar are $ 1270 ha - 1 . 8 2.1 AfforestatioH and Carbon Uptake Carbon is stored in trees (stem, branches, leaves and root), understory, forest litter and forest soils. I calculate storage of C in total tree biomass (including roots) and, although inclusion of C stored in forest soils, floor and understory is still under discussion (Kyoto), I provide some estimates of changes in soil C. Calculation of the stream of C uptake over a specified time horizon requires estimates of tree growth (see Nagle 1990). I employ the Chapman-Richards function: (2.1) v(t)=A(\^-Vt)m, where A is maximum stem wood volume and k and m are parameters (Guy and Benowicz 1998). Hybrid poplar is generally chosen for C uptake because of its rapid rates of growth, and it is considered here. However, many clones exist and "... quoted growth rates of hybrid poplar vary tremendously across Canada and the northern USA making it 8 A n establishment cost of $1270 per ha ($514 per acre) is reported by BCMAFF (1996). Estimates for establishment of hybrid poplar in northern Minnesota are in the range US$285-$338 (C$425-$504) per acre (Agricultural Utilization Research Institute 1997), or close to those used in this study. 25 difficult to estimate average values for each region" (Guy and Benowicz 1998, p.8). Available data on growth rates have been obtained under various management regimes, including fertilisation and irrigation. In this study, I use different parameter values for hybrid poplar in the boreal and prairie regions. For the boreal region, I set ^4=329 and &=0.156; for the prairie region, ,4=270 and £=0.143; m=3.0 for both zones (see Guy and Benowicz 1998). Total C uptake is determined by the wood found in the bole (or commercial component of the tree), which is given by growth function (2.1), multiplied by an expansion factor (=1.57) to obtain total above-ground biomass. Root biomass (R) is related to above-ground biomass (G) as follows, with both measured in tonnes per ha: (2.2) R= 1.4319 G 0 6 3 9 . Finally, the carbon content of timber in the study region averages 0.187 t per m 3 for hardwoods (van Kooten et al. 1993, pp.244-45). To the carbon stored in biomass, I must add the change in soil C . Data on soil C is difficult to obtain. Field trials in the northern Great Plains of the U S indicate that sites with hybrid poplar have an average of 191 tonnes of C per ha in the top 1 metre o f soil, row crops an average o f 179 t of soil C , and grass that is regularly cut 157 t per ha (Hansen 1993, p.435). However, grassland in the more humid eastern portion of the Great Plains rapidly loses some 20% of its soil C when cultivation occurs, implying that native grassland may contain as much as 224 t of soil C per ha, although the amounts would be lower in the more arid western region (p.431). Soil C rebuilds only slowly 26 when cultivation stops. Older stands of hybrid poplar (average 15 years) in Hansen's sample averaged nearly 116 t of soil C per ha (p.435). Guy and Benowicz (1998) note that forest soils in the study region store some 108 tonnes of C per ha compared to cropland that stores some 60 t. Using this last relation and assuming that 2% of the difference is sequestered each year when land is converted from agriculture to forestry, 0.96 t of C yr"1 ha - 1 is added to soil each year for 50 years when an equilibrium is reached (or 48 t ha-1). Determining soil carbon associated with various uses of agricultural land is difficult. Although Hansen (1993) finds row crops store more C than grassland that is regularly cut, I simply assume that there is no difference in the C sink potential of different agricultural land. 2.2 Substituting Wood for Fossil Fuels Most trees grown on agricultural land will be used for pulpwood or burned for energy production, thereby replacing an energy-equivalent amount of fossil fuel in the generation of electricity. I consider the wood burning option first. When wood is burned in place of oil, natural gas or coal, it is necessary to determine the rates of C emissions for similar heating values. The relevant conversion factors are found in Table 2.3. In the study region, electricity is generated using natural gas, coal and hydro, with coal accounting for about 90% of the total. Therefore, I assume that burning wood biomass would replace an energy-equivalent amount of coal. Assuming 187 kg of C per m 3 of poplar biomass and using data in the last column of Table 2.3,1 calculate that some 7.4 GJ of energy are released per m3. However, using the lower range for heating value from the first column, I find that 5.8 GJ of energy are released per m3. Using data in Table 2.3, I find coal releases some 29.4 GJ of energy per tonne. However, Natural 27 Resources Canada (1997) uses a higher heating value (HHV) for sub-bituninous coal of 18.8 GJ per tonne, while the Government of Alberta (1999) reports an H H V of 19.3-26.7 GJ t_ I for coal. Using the latter values for coal, then, if poplar is burned in place of coal, some 2.6-4.6 m 3 of wood are needed for every tonne of coal replaced in order to generate an equivalent amount of energy. Finally, Girouard etal. (1996) report prices of $2.50-$4.00 per GJ as costs for fossil fuels (natural gas, coal and heavy fuel oil). For wood, CSL (1994) indicate a price of $40 per tonne, which translates into an energy price of $2.58 per GJ for the lower range of HHV for wood (Table 2.3). Using the latter price, I obtain a value of $7.50 per m 3 for poplar used in production of electricity. Table 2.3: Carbon Emission Factors for Selected Energy Sources Higher Carbon Carbon Coefficient (incl. Heating Content Carbon 99% combustion Fuel Value b (kg C per kg Coefficient efficiency) (MJ per kg) fuel) (kg C per GJ) (kgCperGJ) Wood . 15.5-19.7° 0.500 25.6 d 25.3 d Coal 29.31 0.707 24.12 23.9 Natural gas 0.0317 (rn3) 0.482 (m"3) 13.78 13.6 Crude oil 42.82 0.850 19.94 19.7 Kerosene (jet fuel) 46.5 0.858 18.45 18.3 Gasoline 47.2 0.869 18.41 18.2 Diesel fuel 45.7 0.865 18.93 18.7 Liquid petroleum gas 50.0 0.818 16.36 16.2 a Power is the rate at which energy is transferred and is usually measured in watts (W), with 1 W=l joule (J) per second (s), with 1 kilowatt hour (kwh)=3.6 x 106 J. One J is the work done when a force of 1 newton (1 N=l kg m s"2) is applied through a distance of 1 meter (m). 1 megajoule (MJ)=106 J ; 1 gigajoule (GJ)=109 J ; 1 petajoule (PJ)=1015 J. See Watson et al. (1996, p.79). b High heating value includes the energy of the condensation of water vapour contained in the combustion of products. In calculating C emissions, Canada and the US use high heating value while the rest of the world uses low heating value (Watson et al. 1996, p.80; Marland et al. 1995). c Low value is converted from Slangen et al. (1997, p.324); high value calculated from data in Table. d Marland and Pippin (1990) It is assumed that hybrid poplar is planted and harvested after 15 years. At that time, the volume of timber available for harvest is 242.8 m 3 per ha in the boreal region and 185.8 m 3 in the prairie region; respective MAIs at age 15 are 12.9 m 3 and 11.1 m 3 . For convenience (to correspond with rotation age) and to ensure a consistent supply of 28 wood in the future, only one-fifteenth of the area available for afforestation is planted in each year. This may be an optimistic assumption as there will undoubtedly be delays (and transaction costs) associated with negotiations between government and farmers, and limits to the amount of area that can be planted in a given year.9 I keep track of carbon build-up in five different accounts, plus the fossil fuel substitution account (see also AACM International Pty Limited 1998). Besides the C saved from fuel substitution, the most important account is the bole or merchantable component of the tree. Equation (2.1) provides the growth of volume for this component, which is translated into C by multiplying by 0.187 t C nf3. Carbon builds up in the bole until year 15, when it is assumed to enter into another account (e.g., wood products) or the atmosphere (by burning). A new stand of trees replaces the old, with the process assumed to continue indefinitely. Next is above-ground biomass, not including the bole component, which consists mainly of branches and leaves. It is found using an expansion factor on merchantable volume and, in this case, constitutes 0.57 of bole volume. When trees are cut, all of the non-merchantable biomass is left on the site as slash. At that time, it enters the litter account, which is treated below. When a new stand of trees is planted, there is re-growth of the non-bole biomass. In this sense, the non-merchantable biomass is treated much like the merchantable component. 9Tree nurseries may not have sufficient seedlings and there are only certain times during the year when seedlings can be planted and expected to survive. I use a 15-year rotation rather than a shorter one to ensure sufficient plantings and a steady future flow of fibre to power plants. 29 Third, carbon in the root pool is calculated from relation (2.2) for hardwoods. I assume a one-time growth in roots, after which decay causes C to enter the soil pool at a rate exactly offset by-the rate at which new growth adds to the root pool. Fourth, it is assumed that soils continue to increase in C content at a rate of 0.96 t per year for 50 years, after which soil C remains in balance (additions to soil C from roots and litter decay equals release to the atmosphere), unless land is converted to a use other than forestry. Then, the overall gain to the soil C sink from afforestation can be determined from the following formula: (2.3a) Cs = cs ^1-(1 + , ) - 5 0 ^ if physical C is discounted (2.3b) Cs = 50 cs, if physical C is not discounted, where Cs is the (discounted) amount of carbon in the sink pool in equilibrium, c s (=0.96 t) is annual addition of C to the soil sink and r is the social discount rate. Finally, the litter pool consists of dead or dying biomass on the forest floor that releases C to the atmosphere through fire and decay and to the soil pool. It is a relatively small pool of C that changes rapidly. I assume that the litter account grows by a constant amount each year for 50 years, after which it is in equilibrium. At that point it is assumed that the litter pool is one-half the non-bole biomass. Equation (3a) can be used to determine the amount of (discounted) C in the litter account (CL) , with C L and c\ (annual addition to litter pool) replacing Cs and cs, respectively. For the boreal region, ci=0.26 t C, while cf=0.20 t C for the prairie zone.10 In addition, there is a spike in the pool's '"Obtained as v(15) m 3 x 0.57 x 0.187 t C m ' x ' / i X 0.02 yr ', where 0.57 converts merchantable volume, v(15), to (non-bole) above-ground biomass with Vi of this biomass in litter after 50 years. 30 biomass at harvest time. It is assumed that the slash component of the litter releases a constant amount of C into the atmosphere over the next 15 years so that it is depleted by the time of next harvest. This carbon spike and subsequent decay is important only if physical C is discounted; otherwise, it is zero. A summary of the carbon sink pools when hybrid poplar is grown and harvested every 15 years is provided in Table 2.4. Carbon uptake is annualised by multiplying total C sink values by the discount rate. In the case of no discounting, however, C uptake is annualised by multiplying by 0.02, because it takes 50 years for the roots, litter and soils pool to reach their equilibrium levels and no C from future growth of trees is included (as discussed above). The annualised values are also provided in Table 2.4. The reason for annualising C uptake is that, once I turn to C savings from fuel substitution, carbon uptake is infinite when physical C is not discounted. But this has its own related problems. In Table 2.4, for example, the annualized C sink values are higher for a 4% as opposed to 2% discount rate. The reason is that a component of the C "removal" is a limited-time stream of benefits that is first discounted and then multiplied by r to annualize it over all time. Unfortunately, there is no good way out of the dilemma if one accepts that C benefits are not to be discounted.11 "See the discussion in Chapter 1 on discounting of physical C. 31 Table 2.4: Carbon Stored in Ecosystem Components, Saved as a Result of Wood-for-Coal Substitution and Total Carbon Saving when Hybrid Poplar Planted is on Agricultural Land with 15-Year Rotation Carbon Account No Discounting3 2% 4% TOTAL CARBON (f C ha"1) Merchantable or bole - Boreal 0 13.2 9.2 - Prairie 0 9.7 6.7 Above-ground biomass - Boreal 0 7.5 5.2 - Prairie 0 5.5 3.8 Roots - Boreal 56.6 47.8 40.8 - Prairie 47.6 40.1 34.1 Litter - Boreal 12.9 16.1 10.2 - Prairie 9.9 12.3 7.8 Soils - Boreal and Prairie 48.0 30.2 20.6 Total C sink - Boreal 117.5 114.9 86.1 - Prairie 105.5 97.8 73.1 ANNUALISED CARBON (t C ha - 1 yr 1 ) Total C sink - Boreal 2.350 2.297 3.443 - Prairie 2.110 1.956 2.923 C prevented from entering the atmosphere due to wood burning - Boreal 3.027 2.626 2.268 - Prairie 2.317 2.010 1.736 Total Carbon Saving - Boreal 5.378 4.923 5.711 (4.217)° (4.233)c - Prairie 4.427 3.966 4.659 (3.397)c (3.453)c When C is sequestered at one time but released later, a zero discount rate leads to no storage. b Calculated using equation (2.4a) or (2.4b). 0 Values in parentheses are annualised values when account is taken of staggered planting over 15 years, using factor (2.5). Assume that 3.78 m 3 of wood replace one tonne of coal, thereby offsetting the release of 0.707 t C to the atmosphere.12 In the boreal region, then, 242.8 m 3 ha - 1 of wood that is available at harvest time and substituted for coal in generating electricity will prevent the release of 45.4 t C into the atmosphere. Likewise, in the prairie region, 185.8 m ha of 12This assumption (energy from 3.78 m3 wood = energy from 1 t coal) falls in the energy conversion range determined from Table 2.3, but has the added advantage that the same C is released to the atmosphere by wood as with the coal replaced. 32 harvested wood will prevent release of 34.8 t C. This occurs every 15 years, so the annualised C prevented from going into the atmosphere will depend on the interest rate. The annualised values, c B , are determined as follows: (2.4a) cB = rCB f \ (1 + r ) 1 5 -1 i f r > 0 , (2.4b) c B = C B - 15 i f r = 0, where CQ is the carbon that is prevented from going into the atmosphere by burning wood and the term in braces is the usual factor that discounts a stream of benefits accruing at intervals of 15 years into infinity. The annualised values are also provided in Table 2.4. Finally, it is necessary to adjust C uptake and C removal by wood burning for the assumption that it takes 15 years to establish a forest that ensures sustained harvests. The adjustment is done on an annualised basis so that the requirement is reflected in each hectare that is eligible for afforestation. That is, it is assumed that only one-fifteenth of a hectare is planted each year for 15 years, followed by harvest and replanting on that one-fifteenth of a hectare. The conversion factor is: CA (2.5) |^  (1 + r) 1 5 where C4 is the annualised carbon per ha when no account is taken of the staggered plantings. The appropriate values are given in parentheses in the final rows of Table 2.4. When physical C is not discounted, the two values are the same. The B C M A F F (1996) reports that contract harvesting costs for hybrid poplar are $8 per m , while average hauling costs are $10 per m . Alberta Agriculture, Food and Rural Development (1997) employs a figure of $22.05 per m 3 for harvesting and hauling. Since costs of hauling vary by distance to power plants, I assume that harvest plus hauling costs 33 are $18 per m 3 for agricultural areas located near existing power plants (ARAs 3 & 5), $22 per m 3 for areas considered to be an intermediate distance away (ARAs 4a, 4b & 7), and $26 per m 3 for more distant areas (ARA 6 and BC Peace). From these costs, one must subtract $7.50 per m 3 in revenues (or costs saved by not burning coal). I can now calculate the annualised costs of afforestation in the study region for each activity and sub-region. This is done by adding to the values in Table 2.2 the annualised costs of repeated plantings at 15-year intervals, beginning with the current period, plus the annualised harvesting and hauling costs (minus revenues), which also occur at 15-year intervals, but begin after the first rotation. These costs vary with harvest levels and location, and are adjusted to take into account the cost savings from not having to pay for coal. Costs of converting power plants to wood (or building new power plants) and added costs of maintaining and/or improving roads are ignored, as are emissions of CO2 from forestry activities and those saved from no longer having to mine and haul coal. Just as in the case of carbon (Table 2.4), it is necessary to adjust the costs to take into account staggered plantings. The results are presented in Table 2.5. Table 2.5: Net Annualised Costs of Removing C from the Atmosphere by Substituting Wood Burning for Coal in Electricity Generation, by Region and Current Agricultural Activities ($ per ha) Forage3 Improved Unimproved REGION Pasture Pasture BC Peace 388.05 276.47 n.a. Alberta, ARA 3 (Southwest) 386.83 183.45 169.75 4a (Central) 259.63 202.83 193.62 4b (Central) 270.99 205.43 194.81 5 (Central) 350.03 191.69 171.92 6 (Northeast) 375.93 293.93 266.53 7 (Northwest) 347.48 240.52 226.21 34 As increasingly valuable marginal agricultural land is brought into production, (marginal) costs of carbon uptake rise (Table 2.5). Further, rates of C uptake will vary by region—boreal or prairie (see Table 2.4). Using this information, it is possible to determine the marginal costs of carbon uptake as a function of both the cumulative area of land converted to forest and the associated cumulative carbon removed from the atmosphere. The results are summarised in Figures 2.1 and 2.2, where annualised C is on the abscissa in Figure 2.2. Only the cost curves for no discounting and 4% discounting of physical C are provided as the area and amount of C gained are not sensitive to discount rates of 2% versus 4% (when account is taken of staggered planting). The results indicate that, if investment projects are limited to those whose sequestration costs do not to exceed $20 per tonne of C, no more than 0.5 million ha of land would be converted from its current agricultural activity to forestry. This result holds for costs up to $38 per t of C if physical C is not discounted and $49 per t C if costs are discounted (even at a low rate). Suppose costs as high as $50 per t C are tolerated. In that case, 4.8 million ha could possibly be converted if physical carbon is not discounted, resulting in a reduction of C emissions of 22.7 million (undiscounted) tonnes over all remaining time. If C is discounted at 4% (or even 2%), one would convert only 1.6 million ha yielding a total of 7 million tonnes of undiscounted carbon. 35 0% - - - -4% 120 u 100 § 80 u <L> 60 o, rt 40 o u 20 0 0 1 2 3 4 5 6 7 Cumulative Area (mi ha) Figure 2.1: Costs of Carbon Uptake as a Function of Afforested Area, Western Canada, Hybrid Poplar as a Substitute for Coal Burning, Infinite Time Horizon, with and without Discounting •0% 4% O c c o rt <D GO O U 5 10 15 20 25 30 Cumulative Carbon in P T E (mil. tonnes C) 35 Figure 2.2: Marginal Costs of Carbon Uptake in Western Canada, Hybrid Poplar as a Substitute for Coal Burning, Infinite Time Horizon, with and without Discounting 36 The fossil fuel substitution option illustrates how sensitive decisions about how much agricultural land to afforest (C "removals" from the atmosphere) are to costs DMs are willing to tolerate (or the availability of other policy alternatives). If costs above $20 per tonne of C sequestered are intolerable, then the afforestation and biomass burning option is not one that can be relied upon to make a dent in Canada's Kyoto commitments. On the other hand, if one draws the line at $50 per t C, the area that one can expect to afforest is still less than 25% of the total that might be identified for planting by foresters. 2.3 Storing Carbon in Wood Products To investigate the storage in wood products option, I employ the same assumptions as in the case of wood burning, namely, that hybrid poplar is planted and harvested every 15 years. Again the reason for using hybrid poplar is that softwood species grow at too slow a rate and C uptake for rotations that include softwood species is well below that of hybrid poplar. The only different assumption pertains to the merchantable (bole) component of the tree at time of harvest. In the wood-product case, it is assumed that 20% of the bole is waste and burned (as in the previous analysis), with the remainder going into paper products (75%) and wood products such as lumber, posts and OSB (25%) (see Winjum et al. 1998). The question I want to answer is "Does this scenario lead to lower costs for C uptake than other afforestation scenarios?" The C sink components of the ecosystem (litter, roots and non-bole, above-ground biomass) are as before. These are summarised in Table 2.6. Also found in Table 2.6 are the reductions in C resulting because bole waste (20%) is burned, replacing an energy equivalent amount of coal. This is determined as 20% of the amounts in Table 2.4. To 37 obtain carbon fluxes for wood products, assume that proportion p (0<p<l) of the C gets stored in products that decay (release C) at a rate 8 (0<8<1) per year. Then, it is easy to show that the discounted C stored in wood products at time of harvest is: (2.6) [l--iP—- + ( i _ p ) ] C w , l + r - 8 where r is the social discount rate (which could be zero) and C\y is the carbon that goes into wood products when the site is harvested. Skog and Nicholson (1998) argue that paper products have a half-life of one to six years, while lumber in housing has a half-life of 80 to 100 years. Winjum et al. (1998), on the other hand, point out that oxidation rates are 0.02 per year for industrial roundwood products and 0.005 for paper products that end up in landfills. I assume that two-thirds of the paper products end up in landfills, releasing C at a very low rate, while the remainder releases C at a high rate of 0.5; for other wood products, I assume a rate of decay of 0.02. The blended rate of decay, with 75% of wood going to paper and 25% to lumber and other building products, is 0.131. Thus, p=0.8 (since 20% is waste) and 8=0.131. Results are provided in Table 2.6, including sensitivity analysis with respect to values of 8. 38 Table 2.6: Annualised Carbon "Removal" Components as a Result of Uptake in Wood Products, Hybrid Poplar Planted on Agricultural Land with 15-Year Rotation (t C ha 1 yr 1 ) Carbon Account No Discounting3 2% 4% Total ecosystem C sink - Boreal 2.350 2.297 3.443 - Prairie 2.110 1.956 2.923 Coal C saved by waste burning - Boreal 0.605 0.525 0.454 - Prairie 0.463 0.402 0.347 C in wood products - Boreal 8=0.131 2.056 1.511 1.114 5=0.250 1.614 0.414 0.713 5=0.500 0 0.024 0.077 - Prairie 5=0.131 1.574 1.151 0.844 5=0.250 1.236 0.315 0.540 5=0.500 0 0.018 0.059 Total Carbon Savingb - Boreal 5.012 4.334 5.011 (3.712) (3.714) - Prair7ie 4.147 3.509 4.114 (3.005) (3.050) a See notes on Table 2.4. b For the case where 8=0.131. The costs of harvesting and hauling trees is the same as for the case of wood burning, and varies with sub-region as before. The returns are $7.50 per m 3 for waste wood used in place of coal (as before) and, by assumption, $30 per m 3 for remaining wood that goes into products. This yields a blended net return to merchantable wood of $25.50. The net opportunity costs by region are given in Table 2.7. 39 Table 2.7: Net Annualised Costs of Removing C from the Atmosphere by Storing Wood in Products, by Region and Current Agricultural Activities ($ per ha) Forage3 unproved Pasture Unimproved Pasture REGION BC Peace 226.27 114.70 n.a. Alberta, ARA 3 (Southwest) 263.00 59.62 45.92 4a (Central) 135.80 79.00 69.79 4b (Central) 147.16 81.60 70.98 5 (Central) 226.20 67.86 48.09 6 (Northeast) 214.15 132.16 104.76 7 (Northwest) 185.70 78.75 64.44 Marginal cost curves for carbon removal by afforestation and a wood product sink are provided in Figures 2.3 and 2.4 for land area and annual discounted C, respectively. The lowest cost for removing C from the atmosphere in the wood product case is some $11 per t C compared with $38 per t C for the wood burning option. If a cut-off of $20 per t C is chosen, then about 4.1 million ha are converted if physical C is not discounted, yielding a net reduction in C output of 18.5 million tonnes. For low, but positive, discount rates, a $20 limit would reduce the amount of land to be converted to 2.3 million ha and the C saving to 9.9 Mt. If higher costs of $50 per t C are tolerated, 6.5 million ha (28.9 Mt C) of agricultural land are converted in the case of no carbon discounting; this • falls to 5.8 million ha (26.0 Mt C) for a discount rate of 4%. Clearly, the wood products' option is preferred to the wood burning option. Increasing the value of 5 to the levels indicated in Table 2.6 has a dramatic impact on costs of C uptake. This is seen from the significantly lower values of annualised C uptake. Likewise, reducing the value of 8 lowers the costs of C uptake (not shown in the analysis). Our contention is that the values of 8 that I employ are already optimistic and 40 serve as a lower bound on the capacity of wood products, especially paper products, as a carbon sink. •0% -4% U <rt o • u O U 0 . 1 2 3 4 5 6 7 Cumulative Area (mfl. ha) Figure 2.3: Costs of Carbon Uptake as a Function of Afforested Area, Western Canada, Hybrid Poplar Planted for Use in Wood Products, Infinite Time Horizon with and without Discounting 0% •4% O o> a e o . 1-1 O U 0 5 10 15 20 25 30 Cumulative Carbon in P T E (mil. tonnes C) Figure 2.4: Marginal Costs of Carbon Uptake through Afforestation in Western Canada, Hybrid Poplar Planted for Use in Wood Products, Infinite Time Horizon with and without Discounting 41 2.4 Discussion The economics of afforestation were considered, for the cases where harvested wood was used as a substitute for coal in energy production and as a wood-products, carbon sink. Although many of the assumptions are rather optimistic (e.g., planting costs of $1270 per ha when costs as high as $4000 per ha have been reported, low rate of decay for paper products), the results do provide some indication of the possibility for afforestation programs. For a low cost of C uptake of less than $20 per tonne, the wood burning option is not likely to be viable, and one would expect very little (marginal) agricultural land to be planted to trees for this purpose. However, if wood is harvested and wood products subsequently hold C for a long time, then afforestation of marginal agricultural land could be a useful component of Canada's policy arsenal. For C uptake costs of $20 per tonne or less, it may be worthwhile to plant hybrid poplar on 2.3 million ha of a potential 7 million ha of marginal agricultural land. Note that this is less than one-third of the agricultural land that might be identified as suitable for afforestation without the economic thresholds. On this land, some 9.9 Mt of C would be sequestered annually, or some 19.6% of Canada's Kyoto commitment. If these results hold for other regions of Canada, then perhaps as much as 40% of Canada's requirements could be met via afforestation. Although the arguments for C discounting are very strong, I have also included results without physical discounting of C. As mentioned in Chapter 1, the GEF recommends against the discounting of C sequestered (see page 8) and stored in terrestrial ecosystems. I have included the case of no discounting to illustrate the impacts of discounting on the costs of afforestation. 42 Several concerns remain. First, I identified some 1.20 million ha of unimproved pasture as suitable for afforestation in northern Alberta. If this land already has significant crown canopy, costs would go up accordingly. Ignoring this land, will reduce the available marginal agricultural land to 5.73 million ha, and level of afforestation to 1.10 million ha, or 19.2% of available marginal agricultural land. In that case, afforestation in the region would account for no more than 3.8% of Canada's C uptake requirements. If a similar relation holds in the rest of Canada, then afforestation would account for no more than 10% of Canada's Kyoto commitment. Second, it is optimistic to assume that the required area can be planted within a 15-year period, particularly if this is extended to the entire country. The logistics of so doing are likely too great—there may not be sufficient planting stock, trees cannot be planted all year round, some planted areas will not take and will need to be re-established, et cetera. Third, while such problems are one impediment to planting large areas to hybrid poplar, a greater obstacle is that of establishing proper incentives for landowners to grow hybrid poplar. Outright purchase of agricultural land will be financially infeasible, while financial incentives (planting plus annual subsidies) may be difficult to implement as this will require drawing up contracts between landowners and the government agency responsible for the program. Contracting is not costless, and strategic behaviour by landowners could result in much higher costs than anticipated, as well as delays. However, the problem of contracting in such cases is rarely discussed and much less investigated. 43 Finally, no hybrid poplar is likely to be planted before 2000 at the earliest, while large-scale planting may have to wait 5 to 10 years. Not only are there logistical impediments to a "quick start" to planting of hybrid poplar, but there are financing obstacles as well. A planting program would cost at least $750 million in the first year, and that would be an optimistic estimate.13 If planting costs are nearer $4000 per ha, costs would amount to some $1.5 billion in the first year. All these and other biological and economic factors need to be investigated in greater detail. Unless this is done and the right incentives provided farmers, along with long-term guarantees, a large-scale planting program begun in the early 21s t Century may be abandoned before trees even reach maturity. In the remainder of this dissertation, I address more realistic forestry and C flux scenarios. In particular, I examine management alternatives on both forested and marginal agricultural land to meet C uptake and other important objectives. Uncertainty is incorporated into the analysis to examine management strategies to meet these same objectives under different assumptions on uncertainty. The next Chapter describes the land use models used in the case study of Chapter 4. This assumes 100,000 ha are planted in each region at a cost of $1270 per ha, plus the opportunity cost of lost agricultural returns for the first year. 44 Chapter 3 Land Management Model In this Chapter I develop a model that incorporates various land management practices with certain economic, commercial timber output and C flux objectives. Since I allow for the possibility of changing land use, both forestry and agriculture are considered, but the emphasis is on the role of forest management (harvesting, reforestation, afforestation and silviculture) in C uptake. This is a multi-period planning problem with decisions in each period "best" meeting cumulative objectives over the planning horizon, as well as those for each period. Decisions taken in previous periods influence those at the beginning of each planning period, and current decisions affect the future. Boundary conditions in terms of initial land availability, targets on timber and C uptake, and closing stock soil expectation values at the end of the planning horizon are imposed. The objective is to maximize the cumulative net present value (NPV) of products in forestry and agriculture, while meeting specific C sequestration targets (in response to government's climate policy) and maintaining a stable timber flow in order to prevent mills from closing and employment from fluctuating widely. Economic and C benefits depend on the end use of wood; hence, I consider the whole life cycle of a tree, from planting or natural regeneration to its end use, whether as a wood product, or mortality as a result of fire or pests. Let x = x'gMp be the area of land of growth type g, age a and site index s managed by practicep in period te {1,...,T}, geG, seS, aeA 1, peP'^t- l ) . Details of the model are presented in the appendix and its compact form is as follows: 45 Model (M3.1) max Nx s.t. (2) (1) btL<ElX<btu, Vt VTx>v (3) (4) c,L <F,x<ct Cx>c xeX Uncertain coefficients of the model (M3.1) are denoted by tilda (~). Objective function Nx is the cumulative net present value of products in both sectors. The requirement on C uptake is expressed in terms of a flux Ftx = Ctx-Ct_xx, the average change in C stock over the period t, where Ctx is the carbon stored in period t. In a similar fashion, the timber production requirement in a period is expressed in terms of timber flow Etx = Vtx — Vt_xx, were Vtx is the volume of timber harvested in period t. Constraints (1) and (3) represent the requirements for even-flow of timber and stable C flux, respectively. Here, btL and btu are allowable fluctuations of timber flow in period t, while ctL and c" are lower and upper bounds on allowable fluctuations of carbon flux in period t. While the even-flow of timber harvest is seen as a means to maintain stable employment, stable C flux is a way of gradual attainment of C goals. Let Cx denote cumulative net C sequestered over the horizon. Then, constraints (2) and (4) express requirements on timber production in the end period and cumulative. net C uptake, respectively. X\s the feasible set consisting of land availability constraints, conversion of land from agriculture to forestry, or vice versa, forest management and 46 silvicultural investment options, initial and terminal timber and carbon inventories, and nonnegativity constraints. The land-use problem in the context of C sequestration has three distinct groups of objectives: achieving economic and carbon benefits, while maintaining timber production flows to the mills. Model (M3.1) differs from typical timber management models by the additional requirements on C uptake. The nondeclining timber yield requirement from classical formulations of sustainable forest management is replaced by the stable flow requirement. By permitting negative values of lower bounds on timber production or C uptake deviations between periods I allow a decline of timber production and/or C uptake between periods. This makes the model more flexible and able to meet global targets over the horizon. These target constraints are in conflict, especially the C sequestration constraints and the timber output and economic objectives14. There are various sources of uncertainty in the coefficients and parameters of model (M3.1), with their complexity and variety determining the approach taken to analyse the problem. Although some of the coefficients, such as timber yield, may be considered random, it is difficult to provide probability distributions of yield under a changing climate and potential C O 2 fertilization. C coefficients are uncertain because of incomplete information about net C storage in the understory and decay of wood products. Assume product prices and management costs are known with certainty. The only source of uncertainty explicitly modelled in the NPV function is due to uncertainty in harvests, while targets on timber production express vagueness of future regulations on timber production and ongoing negotiations on C uptake targets. 1 4 With slow boreal growth rates, extending rotation lengths (and thus reducing income and harvests) is the most direct means to increase C sequestration. 47 The usual means for dealing with demands of multiple stakeholders is to satisfy the targets set by each group rather than optimize the objective(s). Denote by n the NPV target over the full time horizon. If all objectives and constraints are treated equally, the new model can be formulated as: Model (M3.2) findx s.t. Nx>n btL<Etx<b", Vt VT x > v ctL<Frx<ctu, yt Cx>c xeX Model (M3.2) is a multi-objective model with uncertain coefficients in both the constraint matrix and RHS constraints (targets). I interpret the deterministic equivalent of model (M3.2) as a search for land allocations that satisfy objectives and constraints targets at the predetermined level of uncertainty. This interpretation follows the original chance-constrained concept (Charnes and Cooper 1963). Since there is lack of theoretical justification and empirical data to apply probabilistic constrained programming, alternative measures of uncertainty are applied in this dissertation. Sugeno (1977) generalized the notion of probability by introducing nonadditive fuzzy measures. Denote by Q a measure of uncertainty whereby an element belongs to a set A c U , where U is the universal set. The fuzzy measure is defined as a function from the power set P(U) to [0,1] with two properties: (i) Q(0) = 0; Q(U) = 1; and (ii) V A , Be P(U ): A e B => Q(A) < Q(B). Property (ii) is called monotonicity; it means that"« is 48 an element of A" is less certain than "u is an element of B," when A c B (Klir and Yuan 1995, p. 178). With a fuzzy measure Q, the constraints in model (M3.2) are provided a new interpretation. Denote by a the level at which an NPV target is to be met. Similarly, (3t and yt are the levels to which timber volume and C flux requirements are to be satisfied in each period t. Let p v and Yc be the levels for meeting terminal timber production and cumulative C flux targets, respectively. The given values a, p t, Pv, Yt, Yes [0,1], Vf, may reflect different policies regarding economic benefits, timber production and C uptake. We rewrite (M3.2) as: Model (MS. 3) findx s.t. Q(Nx>n)>a Q{btL<Etx<b»)>$,, yt Q(VTx>v)>$v Q^<Ftx<c")>yt, yt Q(Cx>c)> p c xeX In the chance-constrained approach, a, p t, pv, Yt, Y c G [0,1], Vf, are interpreted as probabilities. In (M3.3), they are interpreted as the "levels of opportunity" Q for meeting constraint targets. Thus, I denote (M3.3) as the opportunity constrained model. The feasible set of this model is the set of x e Xthat satisfy constraints from (M3.3) with the given opportunity levels. The obstacle to implementing this approach is that of determining the opportunity levels for each constraint and/or objective. There are many possible combinations and no guarantee that a feasible solution will result. 49 An alternative is to spread uncertainty over all constraints and/or objectives by maximizing the minimum opportunity for reaching the targets. This is written as: Model (M3.4) max X s.t. Q(Nx>n)>X Q(btL<Etx£btu)Zr\, V f Q(Vrx>v)>'k, Q(ctL<Ftx<ctu)>X, V f Q(Cx>c)>\ xeX Model (M3.4) represents a conservative viewpoint as it maximizes the minimum opportunity (Maxmin). The drawback of this aggregation is that it does not allow trade-offs between various constraints and objectives. As the minimum operator is not always appropriate for combining objectives and constraints, an important issue is that of identifying an appropriate aggregation (Sakawa 1993, p.84). Employ a linear combination of minimum opportunities for the three main groups of objectives. Let P = mint;v{Pt,Pv} and y = mintic{yt,yc}- Then the aggregated opportunity model is specified as: Model (M3.5) max wi a + W2 p +wj y s. t. Q(Nx>n)>a Q(btL<E,x<b»)>$, V f 0 ( f r x > v ) > p Q(ctL<Ftx<c")>y,Vt Q(Cx>c)>y x&X, a, p, y>0 Zi Wj= l ,Wj>0 50 By combining the Maxmin concept with a linear aggregation, the model (M3.5) captures the advantages of two approaches. The Maxmin concept spreads uncertainty over objectives from the same group, while the use of additive aggregation allows trade-offs between objectives. The weights wj and vv? reflect the relative importance of economic and timber production objectives, respectively, while W3 reflects the relative importance of carbon benefits. It is assumed that weights are known with certainty, although this would be rarely satisfied in practice. Hence, future research needs to explore ways of expressing the DMs preferences and incorporating them into the model. Notice that in model (M3.5), a, P and y are no longer given levels of satisfaction, but are variables whose values need to be determined. Before the models developed in this section can be expanded upon (see below), it is necessary to provide precise definitions of the required uncertainty measures. 3.1 Fuzzy Sets for Uncertainty Modelling Model (M3.5) is a general model for maximizing aggregated opportunity that uses a general fuzzy measure Q as a measure of uncertainty. To develop a mathematical programming model, it is necessary to explain what is meant by uncertainty and the fuzzy measures used in (M3.5). Uncertainty is interpreted in terms of fuzzy sets. A fuzzy set M is a mapping from referential set U to the unit interval [0,1] (Dubois and Prade 1989). Each element UG U belongs to M to degree \iu{u), where |J.M(W)=1 implies total membership and \iu{u)=Q implies non-membership. In this representation, U constitutes the abscissa, while the unit interval is on a vertical axis. Another interpretation of a fuzzy set is M={[M]a I ae (0,1]}, where [M]a = {u\ [IM(U) >a} is called the a -cut (Figure 3.1). 51 1 M / a K inf[M]a S U p [ M ] a u Figure 3.1: Representations of a fuzzy set Mby its membership function }XM and its a-cut [M]a Each imprecise parameter in (M3.5) is represented as a fuzzy number <2=[ai,a2,hi,h2], with a trapezoidal membership function such that ai and a2 are the left and right main value, while hi and I12 are the left and right spread, respectively (Figure 3.2). The main value and the corresponding spread can be infinite. If we represent the RHS of inequality Nx>n by the fuzzy number n = (« , ° ° ,T | ,<>° ) , complete satisfaction occurs when net present value is greater than n, with satisfaction less than 1 when the values are below n. There is no satisfaction at all if NPV levels are lower than n-r\, where r| is some given tolerance level. Fuzzy numbers a and n are shown in Figure 3.2. 52 a i a 2 n r| u Figure 3.2: Two fuzzy numbers with trapezoidal membership functions; number a = [ai,a2,hi,h2] with finite main values and spread, n =[n,oo5r|,oo] with infinite right main value and right spread. Constraint btL < Etx<b,u, Vf from (M3.5) will be rewritten as a system of two simultaneous inequalities Etx<b", Vf Etx>btL, Vf Let the R H S of these inequalities be b" = ( 0 0 , ^ , 0 0 , ^ ) and btL = v , £ ,oo ) , fuzzy numbers shown in the Figure 3.3. It is clear that inequalities btL <Etx<btu, Vf are equivalent to equalities £ , x = e,,Vf, where et = (b^,b",vf ,v")is a trapezoidal fuzzy number. Thus, the land management model with imprecise timber yield and C-uptake coefficients, and vague production and carbon targets, represented by fuzzy numbers, is as follows: 53 r1 Figure 3.3:Trapezoidal fuzzy numbers btu = (°°,b",°°,v^) and btL = (bf ,°°,v^,°o). Model (M3.6) max wi a + W2 (3 + W5 y s.t. Q(Nx>n)>a 0 ( £ , x = e,)>p, Vf e(F r x>v)>p e ( J P ( x=/ ; )>y , Vf 0 ( C x > c ) > y JC e^C a, (3, y>0,1,- w,- = 1, w,•> 0 Each constraint of the model (M3.6) has a general form Q(Ajx<bj)>a , or Q(Atx > bj) > a , where Ai is a vector of fuzzy numbers and x is a crisp vector. The term A/X can,be expressed by means of fuzzy addition © and scale multiplication as Atx = dn x, © di2 x2 © • • • © din xn. A level-cut representation of a fuzzy number enables defining operations on fuzzy numbers in terms of arithmetic operations on their level-cuts (i.e., arithmetic operations on closed intervals). The later operations are subject to interval analysis. Fuzzy addition © used in this dissertation is typical for fuzzy applications (Klir and Yuan 1995, p. 105). 5 4 3.2 Possibilistic Land Management Models The fuzzy measure Q covers the range of various measures of uncertainty. Consider two special cases of this measure developed in possibility theory (Dubois and Prade 1993, 1980; Inuiguchi and Sakawa 1994; Inuiguchi, Ichihashi and Tanaka 1989, Buckley 1988). (1) From the monotonicity of Q, it follows that g(AuB)> max{g(A),f2(B)}. Zadeh (1978) named this limiting case a possibility measure, Poss(AuB) = max{Poss(A), Poss(B)}. (2) Following directly from the possibility measure is the necessity measure, Nec(A) = 1 - Poss(A ) (Dubois and Prade 1980). These measures are ordinal, unlike probability which is additive. Therefore, the application of fuzzy measures is more appropriate for reflecting ignorance or imprecision. Furthermore, the use of fuzzy measures allows the development of analytically-tractable chance-constrained like models. Depending on the DM's attitude to uncertainty, possibility or necessity can be used instead of the general fuzzy measure Q in the model (M3.6). The possibility measure reflects the ultimate in optimism. It seeks to avoid situations where achieving any specific objective, constraint or target is impossible. Such optimism is conducive to situations involving multiple stakeholders as it seeks to grant hope to all without making it difficult to find a solution. While the possibilistic formulation is attractive politically, it ignores any information about the strength of belief in the possible. (If there is one set of conditions under which a target can be achieved it is judged as possible and receives the full value of the measure, thus it does not discriminate between solutions that generate more opportunities for realization of the outcome). The necessity measure expresses impossibility of not attaining goals and, thus, it is a conservative or even pessimistic 55 measure. This measure provides a lower bound to probability measure but requires less information. Focusing on necessity means seeking more certainty in achieving objectives. The measure achieves its maximum when an objective is attained with certainty. The minimum reflects situations where the possibility of not achieving goals is at the maximum. When Q from (M3.6) is replaced by possibility Poss, the resulting model is called aggregated possibUity-maximizing (M3.7). The aggregated necessity-maximizing is obtained when necessity Nec is applied (M3.8). Model (M3.7) Model (M3.8) Max w/oc + w?P + wyy max w/8 + W2& + W3§ s.t. s.t. Poss (Nx >n)>a Nec (Nx > n) >8 Models (M3.7) and (M3.8) have the same form and the only difference is in the measure of uncertainty applied, p from (M3.7) is the measure of overall system possibility to meet all production targets, while y represents a possibility to satisfy all carbon constraints. The formulation above treats both P and y as the minimum possibility for meeting production and carbon targets, respectively. Similar reasoning applies for model (M3.8) where 8, e and § are the minimum necessity for meeting economic, production and carbon targets, respectively. Considering the nature of these two measures, value for necessity in (M3.8) never exceeds corresponding possibility in (M3.7) as long as the weights are the same in both models. The three groups of objectives Poss(Etx=et)>$, ^1 Poss(VTx>v) >P Poss(FlX=ft)>y, Vf Poss(Cx>c)>y x eX, a, P, y> 0, Xi w{ = 1, w; > 0 Nec(Etx=et)>£, \/t Nec(VTx>v)>£ Nec(Ftx=ft)>$, yt Nec(Cx>c)>§ x e l , 8, e, <|> > 0, Si Wi = 1, w, > 0 56 are in mutual conflict. It is not possible to improve possibility (necessity) of meeting one of them without worsening at least one of the other two - a Pareto Criterion. Weighting properly each of the three different groups of objectives and adding them up allows trade-To develop deterministic equivalents to the models (M3.7) and (M3.8), possibility and necessity are expressed by set operations. Both possibility and necessity measure the degree of belief that an element belongs to the given set. The former expresses the possibility that an element is situated in a set A, while the latter indicates the degree of certainty that an element belongs to A. If we want to know whether an element z from a set M belongs to A, there are three possible answers: (i) if A contains M then there is total certainty (necessity) that ze A; (ii) if A n M = 0 , then it is impossible that ze A; (iii) otherwise, it is possible that zeA. When M is a fuzzy set, one may evaluate tb what extent A intersects M (possibility of A) and to what extent A contains M (necessity of A) (Dubois and Prade 1989). The values of this evaluation depend on the relationship between A and M . Dubois and Prade (1980) express the degree of possibility and necessity of a set as: (3.1) Poss (A) = sup {<x| A n [ M ] a *0} (3.2) Nec (A) = 1- sup { a| A c n [ M ] a *0} Applying definitions (3.1) and (3.2) to the stable timber flow constraints of (M3.7) and (M3.8), enables us to express these constraints as the set relations between level-cuts of the fuzzy numbers Etx and e,. offs. (3.3) Poss (Etx = el) > p\ Vt (3.4) Nec (Etx = et) >e, Vt o [ £ , x ] p n[e,] p *0 <=> {Etx\_z c[e , ] e 57 In equations (3.3) and (3.4), square braces have the usual interpretation that end points of an interval are included; likewise, round braces indicate that end points are not included. Since uncertain parameters of the model (M3.1), as well as vague targets are presented in terms of fuzzy numbers, equations (3.3) and (3.4) are actually relations between intervals. Here (M) a = {u| | I M ( U ) >a} denotes a strong cc-cut. Let ML(oc) = inf [M] a = inf (M) a and M u (a) = sup [M] a = sup (M) a = sup[ M ] a be the left- and right-hand sides for the a-cut of set M , respectively. Since [ Etx]$ = [Et ]p x is an interval, its bounds can be expressed using the above notation, as £ , ( i (p)jc for the lower bound and £' ( t /(P)x for the upper bound. Using these notations and the interval relationships shown in Figures 3.4 and 3.5, (3.3) and (3.4) can be rewritten as: (3.5) Poss (E,x = et) > p\ Vt <=> E?($)x > e'(P) and Ef($)x< ef(p),Vf (3.6) Nec (E,x = el) >e, Vt Ej-(l-e)x > ef(e) and Ef(\-z)x< {t),Vt 58 1 p £f(p)x e / ( ( 3 ) *,"(P) u Figure3.4: Constraint Etx = et with possibility greater than or equal to P Etx 1 1-8 ~\ / \ / \ / \ / x J.. \ ' / 1 \ / \ / / ^ \ ' \J. JLX .^<<_.. £ 7 \ \ 7 '* x <s— i / / ! \ • \ / \ / \ y \ 7f(l-e)x 4(e) <f(e) u Figure 3.5: Constraint Etx = et with necessity greater than or equal to e Considering that fuzzy equality Etx = et was derived from two simultaneous fuzzy inequalities, then apply relations (3.5) and (3.6) to the net present value, terminal 5 9 harvest and cumulative C flux constraints in models (M3.7) and (M3.8). The level-cut intervals [ « ] a , [v r] p and [c] y are unbounded, so only the first inequality in (3.5) applies. In a similar fashion, constraints in the necessity-maximizing model (M3.8) are converted to standard inequalities by applying relations in (3.6). Possibility and necessity maximizing models (M3.7) and (M3.8) are converted to their deterministic equivalents by means of relations (3.5) and (3.6). Model (MS. 9) Model (M3.10) Max Wj a + W2 p + wj y Max w\6 + w^E. + w$ s.t. s.t. A ^ ( a ) x > « > ) NL(l-5)x>nL($) ^ ( P ) W ( P ) , V t E^l-E)x>ef(E),Vt ^(P)x< C,"(P),V, E»(l-e)x<e»(e)yt F 7 y(p)x>v i(P) • V L Flu(y)x>ftL(y),\ft L VTL(l-e)x>vL(e) FtL(l-^)x>ftL(^yt F,{y)x <r <x),vt ^( i -«D)x< ft"®),vt Cu(y)x>cL(y) CL(\-Q>)x>cL®) xeX, a, p,Ye[0,l] ,IiWi=l,Wi>0 x eX, 6, E, (|>e[0,l], L w{ = 1, w{ >0 Depending on the DM's attitude toward uncertainty, the original linear model (M3.1) with uncertain coefficients is converted into one of the two corresponding deterministic equivalents (M3.9) and (M3.10). While model (M3.1) has 4T+2 linear constraints in x, (M3.9) has 4T+3 constraints in variables x, a, p an<5? y. Similarly, (M3.10) has 4T +3 constraints in variables x, 5, £ and <|>. However, since programs (M3.9) and (M3.10) are neither convex nor concave, attaining a global optimum can be a problem. The constraints of (M3.9) are linear inequalities for fixed a, P and y, while the constraints of (M3.10) are linear for fixed 8, £ and ((). Thus, iterative procedures that use 60 the simplex algorithm can be employed (Inuiguchi, Ichihashi and Tanaka 1989). Hence, a combination of bi-section and the simplex method is used to search for the combination of a, P and y that maximizes the weighted average opportunity, while generating a feasible land allocation x. 61 Chapter 4 Forest Management and Terrestrial Carbon Uptake: A Case Study of Northeastern BC The models developed in the previous chapter are applied to a case study of carbon sequestration in the boreal forest region of northeastern British Columbia (BC). The specific study region is the Dawson Creek Timber Supply Area (TSA) and adjacent agricultural lands of the South Peace River region. 4.1 Forest and Agricultural Data and Initial Conditions for the Dawson Creek Region In British Columbia's biogeoclimatic ecosystem classification (BEC) system, the study region is within the Boreal White and Black Spruce zone. Current land uses (the opening stock in the model) are shown in Table 4.1. Table 4.1: Opening Stock Areas by Land Use Type, ha Land Use Type Good3 Medium Poor Spruce 26,230 73,080 274,950 Pine 29,231 155,830 164,750 Deciduous 150,360 154,870 54,590 Agricultural Land Tame Pasture 83,300 Forage 29,200 Crops 40,000 a Good, medium and poor are defined based on the site index for each species. This is an interesting region with respect to carbon uptake as it includes well developed agricultural and forestry sectors, and is located in a northern latitude where the anticipation from climate model projections is for significant warming, which only adds to the uncertainty about future forest conditions. Substantial portions of the marginal 62 agricultural land in this region directly resulted from deforestation activities, so modelling afforestation strategies for mitigating climate change in this region is quite realistic.15 The time horizon used in the model is 100 years, with all decisions assumed to occur at the end of twenty-year time intervals, although the first twenty-year period is utilized to set up the initial conditions. All decisions are made in the final four periods (80 years). In the model, decisions are based on area land units. Although these units are not spatially accounted for, different land types are identified on the basis of use and measures of capability, such as site index and existing species. The forest sector component of the model consists of three native tree species, spruce, lodgepole pine and aspen, grown on three site classes of land. Once denuded of forest, this land can be replanted, left for natural regeneration or converted to agriculture. Opening stock inventory levels are based on British Columbia Ministry of Forest (BCMoF) estimates for the Dawson Creek TSA of these three species, by site quality and 20-year age classes (see Appendix Table BI). Land availability for forest production results from harvest, catastrophic mortality (fire, pest or disease), or transfer from agriculture. Yield functions are based on management, site quality and species. Inventory numbers are generated from BCMoF estimates for the Dawson Creek timber supply area. Yield functions for managed stands are developed using WinTIPSY (Mitchell, Grout and Macdonald 1995), and those for native stands are developed from the inventory estimates. For the coniferous stands, revenue, tree-to-truck and wood 1 5 Some of this land-use change from forestry to agriculture was facilitated by a Federal-provincial Agricultural Land Development Accord (ALDA) which subsidized the removal of forest cover for agricultural development in BC. 63 conversion costs (conversion to lumber and chips) are based on a combination of BCMoF data (Stone et al. 1996) and a recent cost survey of the BC forest industry (Price Waterhouse 1998). Both costs and the recovery rates of lumber are a function of the species harvested and the site quality. Poorer sites result in higher costs per m 3 and a higher proportion of pulp chips versus lumber. This is important as harvest decisions have ramifications on both economics and carbon flux. Deciduous harvests from native or planted hybrid stands are sold for either pulp or oriented strand board (OSB) production. Cost and return estimates for deciduous products are from BC Ministry of Agriculture (BCMAFF 1996) estimates. Hybrid poplar growth is based on results from a recent study of afforestation for western Canada (Guy and Benowicz 1998; see Chapter 2 for more details). These are short-rotation trees that are, due to limitations of time steps in the model, harvested at their earliest at an age of twenty years. The agricultural sector of the model includes tame pasture and forage production. Tame hay is assumed to be a mixture of alfalfa and grass-legume hay representative for the region. Land available for afforestation is assumed to be in either tame pasture or forage production. If planted, this land can be planted to rapid-growth hybrid poplar or returned to native conifer production (Conversion to or from native forestry is assumed to be with high and medium quality land planted to spruce). A limit of 50% of this available land is available for hybrid poplar planting, the remainder must be planted to native conifers. Hay budgets are developed from estimates for the Peace River region (BCMAFF 1995), while the area of land in different agricultural activities is from the 1996 Canadian Census of Agriculture. 64 The economics of pasture production are treated somewhat differently. There is an active market in this region for private pasture rental. The rents are based on the forage consumed by a 450-kg cow, during one month, known as an animal unit month (AUM). To estimate the value of a hectare of pasture requires an estimate of stocking rate (AUM/ha) and the prevalent rent ($/AUM). Stocking rates (Wroe et al. 1988) and the private market value of pasture rental (Bauer 1997) are based on those in the neighboring Alberta Peace region. The first time period in the analysis covers the period 1980-2000. Initial conditions are used to calibrate the models to mimic this period using annual allowable cut levels from the 1994 Timber Supply Review (BCMoF) for both coniferous and deciduous harvests. The model is forced, using bounds on the harvest activities, to meet the A A C levels in the first period. Setting up the models to portray first period harvest levels is important as allowable volume deviations and C flux in later periods use the initial period as a reference point. The same first period conditions are used in all model formulations and scenarios in this dissertation. 4.2 Carbon Accounting for carbon is a key element in this analysis. The absolute size of carbon stock in various pools is not important, but rather the change in this stock or C flux. The carbon measure of interest is the flux associated with a number of carbon pools, including the aboveground biomass of forests, soil carbon in the case of conversion between forestry and agriculture, and forest products16. As in Chapter 2, when tree planting on 1 6 I assume that soil carbon associated with forested ecosystems does not change as long as there is no change in land-use. Afforestation or deforestation result in soil C-flux. 65 agricultural land, there is a build up of soil carbon until it reaches the steady state associated with the forested ecosystem. The assumptions on carbon buildup are described in Chapter 2 and are not repeated here. The emissions or C debits associated with harvest and removal of forest products is also accounted for. Carbon storage increases with tree growth, and is reduced by disturbances such as harvest17. With harvest, for instance, 90% of the merchantable volume is assumed to leave the forest. The carbon associated with the difference between merchantable and total volume, adjusted for foliage, branches and stumps, remains in the forest, entering either a fast or slow release pool. The factor to scale-up the carbon in total volume to account for above ground, non-bole biomass is 1.57 (Guy and Benowicz 1998). The proportions of biomass that enter either fast or slow release pools and the associated decay rates are from Kurz et al. (1992). There are four general forest product categories in the model. Coniferous timber is cut into lumber with the remainder going to chips for pulp. The lumber is assumed to be 70% construction grade lumber and 30% other lumber (Kurz et al. 1992). Deciduous harvests are sold, as logs, for either pulp or OSB production. The amount of product from each pool that ends up in landfills must also be accounted for. These products are not immediately lost to the atmosphere either. Decomposition rates also exist for those forest products that end up in landfills. Estimates of the amount of carbon from the product pools remaining over time are given in Table 4.2. These estimates include both the amount of carbon still remaining in wood products and that in landfill sites. When wood or paper products leave forest product pools, many end up in landfills with very little 1 7 Carbon losses due to catastrophic loss is not debited against the C flux for the period, nor is the new growth following these losses counted as a credit. 66 decay. In fact the literature suggests that some portion of the carbon in landfills will remain there almost indefinitely (Skog and Nicholson 1998). Table 4.2: Remaining Proportion of Original Carbon Remaining from Forest Product Pools, Including that in Landfills Year Lumber Coniferous Deciduous OSB Pulp Pulp 0 0.98a 0.48 0.38 0.78 20 0.92 0.41 0.33 0.74 40 0.84 0.33 0.26 0.67 60 0.74 0.24 0.19 0.59 80 0.61 0.15 0.12 0.48 100 047 O i l O09 0.38 Source: Calculations based on Kurz et al. 1992 a These are losses in the first year, for instance construction lumber lost to cutting etc. in construction process. While product pools contain considerable amounts of carbon derived from forest activities, different age and site qualities result in a different proportioning of timber into forest products even for the same species. Therefore, forest management decisions have an impact on product pools as well as on the carbon associated with standing timber. An important issue in multi-period modeling of carbon sequestration is discounting. There is a clear problem if discounting is utilized for the market costs and returns in the model but not for the physical carbon. There will be an obvious bias towards sequestering carbon in later periods. This has been well recognized in carbon sequestration research, and the discounting of physical carbon has been used in a number of studies (see Chapter 1 for a detailed discussion). Here, physical discounting of carbon is utilized to determine cost per unit of carbon sequestered and for the level of carbon used to meet cumulative C targets. In other words, if 1,000 kilotonnes (ktonnes) of carbon is the cumulative C uptake target, physical carbon is discounted back to derive a 67 net present equivalent carbon measure. A discount rate of 4% is used in this analysis, the same as used for economic variables.18 4.3 Cost-of-Mitigation for the Dawson Creek Region Utilizing forestry for C uptake must be considered a component of a national strategy for reducing net emissions. For this purpose, increasing terrestrial carbon sinks is an efficient means to meet international obligations if it is lower cost than alternatives, such as fossil fuel substitution (e.g., natural gas for oil) or other energy sources (e.g., wind, solar). The deterministic model formulation described in Chapter 3 (Model M3.1) is used to estimate a marginal cost curve for carbon uptake in our study area. Model output provides the lowest cost combination of land-use and forest management strategies for each level of sequestration. The cost curve is traced out by running the model at successively higher levels of C uptake, then measuring the NPV at each level subject to a hard constraint limiting volume deviations to +/- 10% of the initial period harvest. These results are given in Table 4.3. The discount rate of 4% is commonly employed for long-term forestry investment. For a further discussion of appropriate discount rates in forestry see Heaps and Pratt (1989). 68 Table 4.3: Costs of C Uptake Over 80-Year Time Horizon for Dawson Creek Region Cumulative Uptake (C in PTE ktonnes) MC AC $/tonne 250 24 16 500 32 21 750 32 25 1000 38 28 1250 46 30 1500 105 42 1750 307 72 2000 480 111 2250 infeasible infeasible Comparing these estimates to the numbers presented in Table 1.3, the marginal costs are quite similar to the previous estimates for levels of 250 to 1,250 ktonnes, after which the costs estimated here are much higher. Most of the results from other studies given in Table 1.3, and estimated for the Canadian prairies in Chapter 2, are for afforestation of marginal agricultural lands, which is the strategy used to generate the low cost levels of sequestration in Table 4.3. However, when the marginal agricultural land is fully employed and more costly forest management alternatives must be included in the strategic mix, costs are much higher. The marginal cost curve represented by the cost data in Table 4.3 (4% discount rate) and changing the discount rates to 2% and 6% are given in Figure 4.1. The effect of changing the discount rate is evident from the marginal cost curves in Figure 4.1. Much greater carbon uptake is possible with the lower discount rate, and at a lower marginal cost. Less of the uptake occurs in the early periods in this case. The strategy of delaying C uptake to later periods is known as 'backloading', and is common in dynamic cost-of-mitigation studies that use low or zero C discount rates. 69 500 n 450 -400 -0) 300 § 250 S 200 150 100 50 0 250 500 750 1000 1250 1500 1750 2000 2250 ktonnes Carbon (PTE) Figure 4.1: Carbon Sequestration Cost Curves For Dawson Creek Study Area at Different Discount Rates. There are a number of possible strategies that can be employed to meet C uptake objectives within the model. The first is to replant marginal agricultural land with either hybrid poplar or native conifers (limited to spruce for afforestation). The next alternative is to alter the harvest strategy by generally lengthening the rotation and changing the harvest mix. Finally, the proportion of regenerating denuded sites by planting increases. When C uptake constraints are not included, most reforestation occurs by natural regeneration. The DMs use of these strategies with no C constraints, and at C uptake levels of 1000, 1500 and 2000 ktonnes, are given in Table 4.4. 70 Table 4.4: Strategic Mixes For Different Levels Of Carbon Uptake, Deterministic Model (M 3.1) a Level of Uptake Range None 1000 1500 Ktonnes 2000 Early Period Afforestation ('000 ha) Hybrid Poplar 0 -50 ++ ++ ++ Native Conifers 0 -44 - H -Reforestation By Planting 6% - 25% - ++ Early Harvestsb ('000 ha) Spruce 163 - 192 + ++ ++ Pine 78 - 130 ++ + mid Aspen 0- -110 ++ _ _ _ _ _ _ Hybrid Poplar 0 -98 mid ++ ++ Late Harvests ('000 ha) Spruce 67 -105 — _ ++ Pine 97 -177 ++ _ _ Aspen 0- -235 ++ _ _ _ _ _ Hybrid Poplar 0- -133 ++ ++ ++ a The method of deriving criteria for rating the strategies is based on splitting the range Of alternatives into five equal intervals. The meaning of each is: - - very weak, - weak, mid is neutral, + strong and ++ very strong. b Early harvests refer to those in periods 2 and 3, while late harvests are those in the final two periods. When C uptake is not considered as a priority, (1) no afforestation of agricultural land occurs, (2) there is little emphasis on planting, and (3) early period native species harvests are at their highest level. As C sequestration is imposed on the system at successively higher levels, afforestation occurs with hybrid poplar, then conifers. The more rapidly growing hybrid poplar planted on marginal agricultural lands displaces harvests of aspen. A higher proportion of denuded land is planted, rather than left for natural regeneration, which incurs higher costs but allows for more rapid growth. Details on the harvest volumes of coniferous timber in the different time periods are provided in Figure 4.2. 71 No Uptake • 1000 ktonnes 0 1500 ktonnes • 2000 ktonnes CO 45,000 40,000 35,000 30,000 £ 25,000 | 20,000 " 15,000 10,000 5,000 0 Period i f The pattern of coniferous (pine and spruce) harvest volumes over time indicate that in period 2, harvests are lowered as C uptake is increased , rotation length is increased. There is little change at 1,000 ktonnes, but, for the case of 1,500 ktonnes and the maximum uptake case, second period harvests are reduced. This, along with shifts in planting are why it is so costly to sequester carbon after about 1,500 ktonnes (see Figure 4.1 for marginal costs). The category of coniferous harvests that show the most change across levels of C uptake is medium site pine. Harvest levels for medium site pine (in thousand ha) are shown in Figure 4.3. Harvest for the initial time period is suppressed as it is set to be the same for all model runs. 72 140 120 100 OB -C 80 o  o 60 40 20 0 I No Uptake 11000 ktonnes • 1500 ktonnes m 2000 ktonnes 3 4 Time Period Figure 4.3: Harvest Area for Medium Site Pine Over Final Four Periods The area of medium pine is greatly reduced in the second period as successively higher C uptake is levied on the system. Referring back to Figure 4.2, second period harvest volumes do not fall for the 1,000 ktonne uptake case. The reason is that, in the second period, "poor site" spruce harvests are much higher for 1,000 ktonnes of C-uptake. Another notable difference in harvest patterns is for poor site pine which has harvests greater than 50,000 ha in the no uptake case. These harvests completely cease whenever C uptake becomes an objective of policy. Figure 4.3 gives harvest patterns by age class for coniferous timber. 73 U No Uptake B 1000 ktonnes • 1500 ktonnes El 2000 ktonnes 350 300 250 co 200 o o o 150 100 50 rlTff"rbrH i I IT 0 40-60 60-80 80-100 100-120 120-140 140+ Age Class Figure 4.4: Harvest Patterns by Age Class for Coniferous Timber in Final Four Periods The general result regarding harvest patterns by age is that, as more C uptake is required, harvests tend to be delayed, or in some cases timber is not cut. This is illustrated most clearly in Figure 4.4 by the reduction in 40-60 year old harvests as C uptake becomes a more important factor for policy. Moving from no uptake to the target of 2,000 ktonnes of C, the area of harvests in this age class falls from approximately 170,000 to 85,000 ha Most of the change is on medium sites, especially pine. There is little change on good sites, except at the highest level of uptake. Total deciduous harvest volumes (native plus hybrid poplar) for these same four cases are given in Figure 4.5. 74 j II No Uptake • 1000 ktonnes • 1500 ktonnes • 2000 ktonnes 25,000 20,000 g 15,000 o p 10,000 5,000 0 1 2 3 4 5 Period Figure 4.5: Harvest Volumes of Deciduous Timber In the three final periods deciduous harvest volumes seem quite similar across levels of C uptake. However, hybrid poplar makes up a larger proportion for targeted uptake levels of 1,500 and 2,000 ktonnes. In fact, in these two cases, hybrid poplar completely displaces deciduous harvests from native species after the initial time period. There are only small native deciduous harvests at the 1,000 ktonne C uptake target in later periods. Table 4.4 gives the objective function and target constraint values for these different levels of carbon uptake. One other pattern is evident when examining the coniferous and deciduous harvest patterns in Figures 4.1 and 4.3. In the case of no carbon uptake, the entire harvest volume in period 2 is made up of coniferous timber. As more C uptake is required, a larger proportion of total harvest volumes are deciduous, mainly hybrid poplar. Deciduous harvests fall off in later periods for the higher levels of sequestration. 75 Table 4.5: Objective and Target Constraint Levels at Successively Higher Levels of Carbon Uptake, Deterministic Model (M3.1) Level of Uptake (ktonnes) None 1,000 1,500 2,200 NPV ($ '000) 1,093,810 1,019,970 985,640 825,320 Harvest Volume ('000 mJ) Period 1 . 42,420 42,420 42,420 42,420 Period 2 38,180 38,180 38,180 38,180 Period 3 33,940 33,940 33,940 33,940 Period 4 29,700 29,700 29,700 29,700 Period 5 25,460 25,460 25,460 25,460 Carbon Flux (ktonnes Nominal) Period 1-2 -2,690 2,020 2,070 2,135 Period 2-3 -4,430 0 2,120 3,490 Period 3-4 -4,420 814 1,190 2,528 Period 4-5 -5,030 0 0 1,350 Nominal Forest Net Income ($ '000 Nominal) Period 1 523,240 463,090 471,040 388,020 Period 2 527,540 445,610 328,900 205,460 Period 3 124,520 230,190 246,380 240,390 Period 4 158,330 140,600 194,790 263,920 Period 5 -94,100 103,010 131,380 175,020 Nominal Agric Net Income ($ '000 Nominal) Period 1 155,220 155,220 155,220 155,220 Period 2 155,220 139,530 141,600 124,880 Period 3 155,220 137,610 137,610 80,000 Period 4 155,220 137,610 137,610 80,000 Period 5 155,220 137,610 137,610 80,000 If C sequestration is not included as one of the target constraints, there is a considerable negative C flux in the model. Overall harvest volumes by period at different levels of C uptake are quite similar, the difference being the species, age and site quality that make up the harvest. When no C uptake is required, the most economically attractive timber is liquidated as early as possible, resulting in high early period incomes and much lower incomes in the later periods (a result driven primarily by discounting). 76 No agricultural land is transferred to hybrid poplar production as traditional agriculture yields higher returns. 4.4 Comparison of Alternative Models Incorporating Uncertainty The preceding analysis has been accomplished in a deterministic modeling framework (Model M3.1). It is important to recognize the high level of uncertainty in long-term climate change modeling, and how this affects management strategies to achieve C uptake targets and the attainment of other important (and competing) objectives. For this purpose, I introduce uncertainty into the land-use problem of C uptake in the Dawson Creek region. I compare model formulations based on the fuzzy measures of uncertainty (possibilistic formulations) from Chapter 3 (M3.7) and (M3.8) to those based on traditional scenario analysis. Land use strategies under the assumptions for each of these models are compared to those of a base case (1,500 ktonnes C uptake) resulting from Model M3.1, as described in the previous section. 4.4.1 Possibilistic Formulations - Maxmin and Aggregated Opportunity Maximization There are a number of target objectives that are used in the possibilistic model formulations. These targets are in three main categories: • economic, which includes a target for cumulative net present value (NPV); • volume with periodic volume deviation targets and a minimum final period harvest; and • C targets that include periodic flux targets and a discounted cumulative C sequestration target. 77 These objective targets, along with technical coefficients for merchantable timber volume and carbon are modeled as fuzzy numbers. The means of meeting the three objectives is very different in the possibilistic formulations than in the traditional mathematical programming approach. The deterministic models maximize NPV subject to hard targets on C and volume deviation constraints. In the possibilistic models all three objectives are treated as soft targets, subject to the allowable deviations in the fuzzy numbers used. A description of how uncertainty is modeled in the LHS and RHS parameters of the mathematical programming model is described in Table 4.6. Table 4 .6: Description of How Uncertain Model Coefficients (LHS) and Objective Targets are Represented in Model Coefficient/Target Type of Fuzzy Number Particulars Merchantable Volume Coefficient Symmetric Triangle +/- 10% of estimated coefficient Carbon Coefficient Symmetric Triangle +/-10% of estimated (c) coefficient Cumulative NPV One-sided Trapezoid Range 50% to 100% Optimal NPV Merchantable Volume Trapezoid Deviations +/- 4,240,000 m 3 Deviations Spread 50% Final Period Minimum One-sided Trapezoid 50% Initial Period A A C Harvest Deviation 50% Period Carbon Flux Trapezoid Flux +/- 750 ktonnes (PTE) Spread 50% Cumulative Discounted One-sided Trapezoid 1,500 ktonnes (PTE) Carbon Uptake Deviation 50% Deterministic results from the previous section are important as they are used to establish NPV and C targets for the final model formulations. The NPV target is the maximum NPV attained by the deterministic model without C uptake targets. The 78 economic cutoff for C uptake is set at a marginal cost of $100/tonne (4% discount rate), which leads to a cumulative C target of just over 1,500 ktonnes over the 80-year planning horizon. The deterministic model with C uptake set at this level is referred to as the base case for the remainder of the analysis. As discussed in Chapter 3, there are a number of alternative operators that can be used in the objective function of a multiple objective model. The two that are considered here are the commonly employed Maxmin operator {Model (M3.4)} and the aggregated opportunity (Oppmax) operator {Model (M3.5)} defined in Chapter 3. The results of using these two operators are compared assuming a D M using both the Possibility and Necessity measures of uncertainty. Table 4.7 gives the achievement of the Necessity and Possibility measures using the two operators. Table 4 . 7 : Achievement of Possibility/Necessity Measures with Maxmin and Oppmax Operators Economic Volume Carbon a 3 Y Necessity Maxmin 0.12 0.12 0.12 Oppmax 0.75 0.50 0.04 Possibility Maxmin 0.95 0.95 0.95 Oppmax 0.95 1.00 0.95 With Necessity, switching from the Maxmin to the compensatory Oppmax operators leads to much different results. Under Maxmin all three sets of objectives result in a level of Necessity of 0.12. With Oppmax, a small sacrifice in the level of achieving the carbon objective results in large increases for the other two objectives. The As discussed in Chapter 1, $100/tonne ($ Cdn.), although at the high end of forestry estimates for C sequestration costs, is less than the shadow price of carbon necessary to achieve the levels of C 0 2 emissions agreed to in the Kyoto Protocol by the US of $1007ton ($US). 79 overall strategies in terms of decision variables in the model are also markedly different. The differences include more aggressive harvests of late period spruce with Maxmin versus pine with Oppmax, much more reforestation through planting with Maxmin, and higher levels Of afforestation with native conifers in the Maxmin case. In the case of Possibility, there is little change in either the levels of possibility for each goal or the strategy employed between the two operators. The reason is that under Maxmin the level of possibility is very high (remember, these are normalized). This means that very little improvement can be gained through the use of the compensatory operator Oppmax. There is little difference in the strategies chosen using the Maxmin and Oppmax operators and Possibility. In the case of Necessity, there are large differences in the strategies. The Necessity results show a serious limitation with the Maxmin operator. Once the Necessity level of 0.12 is achieved for each of the objectives, no further improvement is sought. In this case higher NPV can be achieved with no loss in the other objectives, an unsatisfactory result. As Oppmax allows tradeoffs between the different objectives, this problem does not occur. For the remaining analysis in this Chapter, the Possibilistic results presented are with the compensatory Oppmax operator. 4.4.2 Comparing Possibilistic Results to Those From Traditional Scenario Analysis Scenario analysis involves the base case, optimistic and pessimistic scenarios, along with lax and strict management policy regimes. In the base case, technical coefficients are given mid-values of corresponding intervals and targets are not relaxed from initial levels. In the case where the D M is assumed to be optimistic, uncertain technical 80 coefficients are assumed to occur at values as high as possible. With a pessimistic D M , the uncertain technical coefficients are valued at the lowest level in the defined intervals. For both types of D M , targets are set at their most easily attained values (easy targets) and their most difficult (hard targets). The scenario describing the optimistic D M with easy targets is known as Opteasy, that which describes an optimistic D M with hard targets is Opthard, that with a pessimistic D M and easy targets is Pesseasy and finally Pesshard describes the Pessimistic D M with hard targets. Naturally, in the scenarios assuming a pessimistic D M , targets are more difficult to meet than in the base case or optimistic scenarios. I compare these multiple scenario results to the model formulations using the Possibility and Necessity measures of Models (M3.3) and (M4.4). These formulations use the compensatory operator to aggregate Possibility/Necessity for meeting the objective target levels. The results from using these measures are referred to as Possibility and Necessity. The harvest patterns associated with these different model formulations are given in Figures 4.6 to 4.8 (for a detailed table of harvest patterns in the different models see Appendix Table A4). There are large differences in the harvest patterns of spruce in the different models. Period 2 harvests are highest with the two scenarios representing a pessimistic D M and the Possibility scenario. The smallest area of spruce harvests in this period occur in the Opteasy and Necessity scenarios. The other noticeable differences are in late period poor spruce harvests, which are more aggressively harvested in the case of the Pesshard scenario and the D M using Necessity as a measure of uncertainty. 81 H Opteasy • Opthard • Base Case • Peseasy • Peshard El Possibility • Necessity 180 1 2 3 4 5 Time Period Figure 4.6: Spruce Harvests in Different Model Formulations Under Uncertainty El Opteasy • Opthard • Base Case • Peseasy • Peshard • Possibility • Necessity 140 -120 -1 2 3 4 5 Time Period Figure 4.7: Pine Harvests in Different Model Formulations Under Uncertainty 82 B Opteasy • Opthard • Base Case • Peseasy • Peshard B Possibility H Necessity 140 1 2 3 4 5 Time Period Figure 4.8: Deciduous Harvests in Different Model Formulations Under Uncertainty Early period pine harvests are similar across scenarios except in the case of the Opteasy scenario. The larger differences across scenarios for pine harvest patterns are in the later periods. For these late-period pine harvests, the largest area cut is for the Necessity scenario. The increases in harvest area are for poor site pine, of which over 130,000 ha are harvested in this scenario in the final two periods. The only other case in which any poor site pine is harvested is for the Pesshard D M , in which 51,000 ha are harvested. Figure 4.8 gives the area of deciduous harvests in each period for the different scenarios. In all of the scenarios, harvests of native deciduous timber cease in period 2. There is no harvest of any deciduous timber in the two scenarios with easy targets and the Possibility scenario. In the remaining scenarios, hybrid poplar is harvested in the second 83 period, with the highest harvests in the case of the pessimistic D M with hard targets. In the fourth and final periods, the Opteasy scenario and the cases with DM's using Possibility and Necessity all harvest native deciduous timber. No native deciduous timber is harvested after the initial time period (which uses a constraint to force deciduous harvests) in all remaining scenarios. B Opteasy B Opthard • Base Case El Peseasy B Peshard 1 Possibility • Necessity Hybrid Poplar, Hybrid Poplar, Spruce, Period 1 Spruce, Period 2 Period 1 Period 2 Figure 4.9: Afforestation Patterns in Different Model Formulations Figure 4.9 shows the early period afforestation patterns for the different methods of modeling D M attitudes towards uncertainty. The highest initial period planting of hybrid poplar on agricultural land occurs in the scenario where a D M is assumed to use the Possibility measure. The lowest levels are for both the optimistic DM's with either easy or hard targets. In the case of the Pesshard D M , hybrid polar planting is at an intermediate level, but this is the case in which afforestation using native conifers is the highest. The only other case in which native conifers are planted on agricultural land is 84 for the D M using the Necessity measure of uncertainty. It should be noted that, with an additional 50,000 ha of good and medium spruce planted by the Pesshard D M , and 32,000 of good and medium spruce in the Necessity scenario, there is no increase in good or medium spruce harvests (refer back to Figure 4.6). These agricultural plantings of native conifers are left for carbon storage. Table 4.8: Strategic Mixes in Different Model Formulations Optimistic Base Pessimistic Poss Nec Range Easy Hard Case Easy Hard Early Afforestation ('000 ha) -- -- - - - - ++ Hybrid Poplar 40-51 - - - - - - - - ++ - - mid Native Conifers 0-50 Refer. By Planting 9% - 24% - - - - - - - ++ ^- mid Early Harvests" ('000 ha) Spruce 154-195 ++ - + + + + + + + Pine 101-123 ++ - - - - ++ + mid Aspen 0 - - • - -Hybrid Poplar 50-98 - - + ++ ++ ++ - - ++ Late Harvests ('000 ha) Spruce 74- 100 - - + ++ - - ++ - ++ Pine 90-230 mid - mid - + ++ Aspen 0-44 - - - - - - - - - - ++ Hybrid Poplar 106-113 ++ + ++ ++ ++ ++ a The method of deriving criteria for rating the strategies is based on splitting the range of alternatives into five equal intervals from lowest to highest. The intensity of using each decision listed are then assigned as, - - meaning very weak, - is weak, mid is neutral, + is strong and ++ is very strong. b Early harvests refer to those in periods 2 and 3, while late harvests are those in the final two periods. Summary information on the strategic mix employed by different model formulations is given in Table 4.8. These results show that different DMs will chose different land-use strategies. Comparing the base case and the strategy chosen by the Opteasy D M , there is more afforestation of hybrid poplar and greater early period spruce and pine harvests. The strategies chosen by the Pesseasy and Opteasy DMs are quite similar, however the strategies chosen by the Pesshard and Opthard DMs share very little 85 in common. Afforestation, harvest and reforestation strategies in this case are all quite different. Likewise the strategic mix of the DMs using the Possibility and Necessity measures are completely unlike each other, or any of the other strategies outlined in Table 4.8. 4.5 Testing the Performance of Strategic Thrusts Using Different DM Attitudes Towards Uncertainty The results of the previous section illustrate the strategic thrusts employed by DMs depending on how they view and manage resources under uncertainty in both the technical dimensions of the problem and the decision objectives (targets). To assess the performance of these different strategies in meeting objective targets requires assumptions on the future states of uncertain parameters. For this purpose, I examine the strategies from the previous section under the assumption that uncertain parameters occur at their expected values (interval midpoints). The strategic mix chosen by each D M in the previous section is modeled with parameters valued at these levels. The first objectives I examine are economic (NPV) targets. Select economic performance measures under the different strategic thrusts are presented in Table 4.9. Not surprisingly, the lowest NPV is for the strategy chosen by the pessimistic D M facing hard targets. The D M using the Necessity measure, also a very pessimistic strategy, achieves a much higher cumulative NPV than the Pesshard D M . The highest NPV is for the Opteasy D M , although the NPV achieved by the Pesseasy D M is nearly identical. 86 Table 4.9: Net Present Value and Periodic Forest Income for Different Model Formulations with Uncertainty Incorporated, Uncertain Parameters Valued at Means Necessity Pessimistic Optimistic Possibility Hard Easy Hard Easy NPV ('000 $) 925,440 834,380 1,036,930 993,790 1,039,810 1,014,640 Forest Income (' 000 $ nominal) Period 1 454,430 381,100 472,080 475,850 475,730 461,530 Period 2 207,950 263,620 459,620 338,850 501,500 428,540 Period 3 287,650 259,460 221,080 229,930 119,440 240,590 Period 4 72,580 163,310 177,800 238,180 190,760 198,470 Period 5 149,020 115,390 41,780 78,850 48,920 101,709 Mean 234,250 236,580 274,470 272,330 267,270 286,170 Standard Dev. 146,150 102,710 186,680 146,840 208,390 153,960 Also shown in Table 4.9 are the levels of forest income ($ nominal) in the different periods under each D M strategy. The mean periodic forest income is very similar for all strategies except for Necessity and Pesshard, which have lower mean incomes. The strategy employed by the Pesshard D M also has the least variation in income, with much less variability in income between periods than any of the other strategies. The success of the different strategies in meeting C targets is shown in Figure 4.10. The highest level of discounted (PTE) C uptake occurs with the strategy that achieved the lowest NPV, that of the Pesshard D M . The cumulative C uptake target of 1,500 ktonnes is exceeded in this case with total C uptake of 1,633 ktonnes. The other 'pessimistic' strategy, that of the D M using Necessity achieved 90% (1,467 ktonnes) of the C uptake as the Pesshard D M with a 10% increases in NPV. The incremental cost of the additional carbon sequestered by the Pesshard D M is $550/tonne (PTE carbon units) as compared to the strategy of the D M using necessity. 87 • Necessity • Pesshard • Pesseasy • Opthard • Opteasy B Possibility 8000 7000 -1000 -2000 Total Total (PVE) Period Figure 4.10: Nominal Periodic C Flux, Total Nominal Uptake and Total Uptake in Present Tonnes Equivalents (PTE) 1800 1600 1400 UJ 1200 > ^ 1000 w a> c c o 2 o 800 600 400 200 • Necessity! Pesshard < Pesseasyx Opthard* Opteasy® Possibility 200 400 600 NPV $million 800 1000 1200 Figure 4.11: Tradeoffs Between Cumulative C Uptake and Cumulative NPV Using Different D M Strategies on Uncertainty, Uncertain Parameters Valued at Midpoints. 88 The tradeoffs between economic (cumulative NPV) and C uptake targets under the different strategies are explicitly shown in Figure 4.11. The tradeoffs between economic and C uptake targets are clear in this figure. Moving from the lowest level of uptake (Opteasy) through to Possibility there is little loss in cumulative NPV, but a large increase in C uptake. After that point, the strategies with difficult targets and pessimistic DMs yield large amounts of NPV for additional units of C uptake. In the case of this particular tradeoff, easy versus hard targets results in more similar results than whether a D M is optimistic or pessimistic. The results in Figure 4.11 only show two of the three objective targets. The performance of the different strategic thrusts in meeting the even-flow constraint is provided in Figure 4.12. The strategies used by the Pesshard D M and the D M using the Necessity measure involve higher late period harvests than any of the others DMs. Those facing relatively easy targets harvested very little in the late periods. To better describe how the strategies of different DMs perform in terms of the even-flow objective, some simple descriptive statistics are presented in Table 4.10. The Necessity scenario results in both the highest total volume harvest and the least variability in those harvests between periods. The Pesshard D M also harvests large cumulative volumes, but variability between periods is higher than in the case of Necessity. The third highest volume is harvested by the Possibility D M , who would harvest more with less variability between periods than do the Pesseasy, Opteasy or Opthard DMs. 89 CO E o o • Necessity • Pesshard • Pesseasy • Opthard • Opteasy H Possibility Figure 4.12: Periodic Harvest Volumes for Different Model Formulations ofUncertainty, Uncertain Parameters Valued at Midpoints Table 4.10: Even-Flow Harvesting Objective Parameters Necessity Pessimistic Optimistic Possibility Hard Easy Hard Easy Cumulative Volume 187,300 182,260 158,420 162,196 156,391 164,440 Range 12,000 17,430 23,560 20,694 22,419 17,810 Strd Deviation 4,384 7,190 10,826 7,625 9,994 7,989 4.4 Discussion In the deterministic world, forestry does appear to have a role in helping meet Kyoto targets in the boreal region. Afforestation, and some limited management alternatives in native forests result in costs lower than the $100/tonne equilibrium which other studies indicate is the approximate shadow price of carbon (for the US) necessary to meet the Kyoto net emission target. Strategies to achieve high C uptake include afforestation, 90 increased planting intensity and a general increase in rotation length. Harvest patterns are also changed by a move from pine to spruce harvests (especially late period harvests). With the explicit incorporation of uncertainty quite different strategies are employed by the DMs to meet the objectives. This is best illustrated in the case of the D M using Necessity, an extremely pessimistic measure of uncertainty. Although the C uptake target is the most binding in this case, the overall management strategy is quite different than with high C uptake in the deterministic case. Necessity ensures that goals/targets are met with certainty, while possibility looks for solutions that allow for the possible achievement of goals. This means that more information is known about a solution in the case of necessity. Two different operators were employed in the possibilistic analysis, the commonly used Maxmin and the Oppmax operator (introduced in Chapter 3). With possibility, the choice of operator had negligible effect on the overall strategy to meet the objective targets. With necessity however, the choice of operator had a large effect on the solution strategy. In the case of Maxmin, the binding objective (Carbon) resulted in a level of necessity of 0.12. With little or no relaxation in the achievement of the C target, economic and volume targets can be met at much higher levels. Oppmax allows these tradeoffs, which changes the overall strategy. Oppmax does have the limitation that the objective function and weights for the three objectives must be specified. In this analysis equal weights were used for the three objective targets. There are marked differences between the strategies employed by a pessimistic D M using the possibilistic approach (Necessity) and the pessimistic D M using hard t targets in the more traditional multiple scenario analysis. Likewise, the strategies 91 employed by optimistic DMs using the two approaches to modeling uncertainty are quite different. The very nature of this problem means that predicting the future level of technical coefficients and thus achievement of objectives is very difficult. Making the bold assumption that these technical coefficients occur at their arithmetic means, the only scenario that meets or exceeds the 1,500 ktonne target on C uptake is Pesshard. The Necessity scenario also achieves a high C uptake of 1, 470 ktonnes while achieving a higher NPV and a more even-flow of fibre harvests. The cost of the additional C sequestered in the Pesshard versus Necessity is over $550/tonne. 92 Chapter 5 Summary and Conclusions In this chapter, the principal contributions of the research are summarized, some policy implications are pointed out, and some suggestions for future research are made. 5.1 Summary and Conclusions The research of this study contributes to knowledge in climate change and forestry research in three major areas: • It benchmarks the costs of forestry alternatives in the boreal forest to meet international commitments on C uptake. • It develops and utilizes an approach to modeling uncertainty that is both innovative and appropriate to this particular problem. • It examines the strategic mix that a D M must utilize to simultaneously meet C uptake, timber volume and economic objectives under uncertainty that is characterized by vagueness and imprecision. The costs of achieving G H G emissions targets agreed to in the Kyoto Protocol are high in North America relative to most other developed countries. This has led to interest by local policy makers in increasing terrestrial forest sinks as a means to help meet these targets. Although forestry offers some potential for low cost C uptake, costs do become prohibitive after a point. Determining a management strategy to utilize forestry up to that point is the main purpose of the cost-of-mitigation analysis in this dissertation. The analysis in Chapter 2 examines cost-of-mitigation with a specific focus on afforestation of marginal agricultural lands in the grain belt region of Alberta and 93 Northeastern British Columbia. In this chapter, it is shown that using the harvested timber for more traditional forest products (pulp and lumber) results in lower costs of C uptake than i f harvested timber is used for biomass energy production. The results show the importance of economic thresholds on suitable land types for afforestation. At a threshold price of $20 per tonne of C, and assuming that the harvested biomass is used in the manufacture of forest products (wood and pulp), 32% of the potential marginal agricultural land identified in this study would be planted. At a higher threshold of $50 per tonne C, over 80% of identified lands are used for afforestation and with the threshold of $100 per tonne, all of the identified land becomes eligible for afforestation. Afforestation and forest management strategies within the working forest are examined using a case study focusing on northeastern BC in Chapter 4. The results from this analysis show that, in a deterministic world, afforestation of marginal agricultural land and limited management within the existing forest base can accomplish C uptake at a reasonable cost compared to alternatives outside of forestry. In this case, C uptake is accomplished subject to maintaining an even flow of fibre. Most mitigation strategies within the existing forest base are shown to be high cost and limited in scope due to very slow growth in the boreal region. The most effective in-forest strategies for minimizing the costs of C uptake are to increase rotation length and reduce harvests (which results in a reduction in regional economic activity). Although the cost-of-mitigation analysis is interesting, estimating C flux associated with forestry and land-use change is fraught with uncertainty, possibly impeding compliance with carbon, volume and economic objectives. In light of international agreements such as Kyoto, compliance with such targets is becoming an important issue. 94 Managing the uncertainties associated with climate change is a difficult task. The quality and amount of information we possess about many of the parameters of this problem are not sufficient to assess probabilities. In addition, the level of complexity required to model these problems renders them computationally intractable. As highlighted by the lack of international consensus, the problem involves many new policy issues, where even the quantifiable targets have not been resolved. Traditional modeling methods for dealing with these complexities generally involve the use of multiple scenarios. This technique assumes that the D M has the ability to observe the potential solution set and consequences, choose one likely outcome, and implement the corresponding solution. In this dissertation, models have been developed to incorporate explicitly uncertainty of two distinct types—those uncertainties associated with biophysical system parameters and, perhaps most important in terms of the carbon debate, uncertainty in the policy domain (i.e., uncertainty with respect to objectives). This was accomplished using two distinct and very different measures of uncertainty with roots in fuzzy set theory, namely, necessity and possibility. Using either of these measures allows the incorporation of the DM's attitude towards uncertainty without having to fix the values of uncertain parameters. This is an important issue as the complexity of this problem means that fixing the values of these parameters is nothing but a guess. The results from the case study of the Dawson Creek Timber Supply Area and surrounding agricultural land show that the interaction of strategic features over time is hard to predict. Changes in the strategic mix are not monotonous along a continuum from pessimism to optimism. The strategies chosen by pessimistic or optimistic DMs 95 explicitly incorporating uncertainty do not resemble those from DMs modeled using the multiple scenario approach. This result makes the use of multiple scenarios for this problem inappropriate. Instead, uncertainties in both objectives and parameters must be modeled explicitly. 5.2 Policy Implications The study region in the case study of Chapter 4 consists of 1.2 million ha, of which nearly 10.5% constitute marginal agricultural land. These indicate that upwards of 1.5 million tonnes of discounted C (discounted at 4%) can be sequestered in the region at an average cost of about $40 per tonne or less. This amounts to an average of about 1.3 tonnes per ha, or about 52 kg per ha per year. If this is applied to all of Canada's productive boreal forestland and surrounding marginal farmland, then some 10-15 Mt of C annually might be sequestered via this option. This amounts to at most 7.5% of Canada's annual Kyoto-targeted reduction, well below the 2 2 % envisaged by the forest industry (CPPA 2000). Only if short-rotation, hybrid poplar plantations replace logged or otherwise denuded forests might forest management become a competitive alternative to other methods of removing CO2 from the atmosphere. Hybrid poplar plantations are also the only cost-effective, competitive alternative when marginal agricultural land is afforested (see also, van Kooten et al. 1999, 2000). However, the negative environmental effects of hybrid poplar plantations, such as reduced biodiversity, disease, caterpillar problems and loss of scenic amenities, limits their viability as a tool for emissions reduction. 96 There remains a great deal of uncertainty about planting hybrid poplar on a large scale because this has not been done previously. For example, it is likely that unaccounted for and unknown transactions costs associated with afforestation will increase C-uptake costs above what has been estimated. Outright purchase of agricultural land will be financially infeasible, while financial incentives (planting plus annual subsidies) may be difficult to implement as this will require drawing up contracts between landowners and the government agency responsible for the program. Contracting does have costs, and strategic behaviour by landowners could result in both higher costs than anticipated, as well as delays. In addition, there is uncertainty about (current and future) prices of timber products (including what wood fetches as fuel) as well as agricultural products. If afforestation occurs on a global scale, carbon leakage from the early harvest of extant forestlands followed by their conversion to a non-forestry land use could reduce the effectiveness of afforestation strategies. Large future increases in the supply of fibre from these afforestation programs may influence C flux from the existing forest base as future fibre prices are reduced. Early harvests can be expected to occur in anticipation of lower future prices. Forest landowners would liquidate extant forest stocks in response to anticipated lower fibre prices and convert land to another use (Sohngen and Sedjo 1999). 5.3 Future Research Possibilities The study region considered in this dissertation, the Dawson Creek Timbers Supply Area and adjacent marginal agricultural lands of Northeastern British Columbia, is in some ways unique in that much of the marginal agricultural land was originally deforested a 97 century or less ago, making it an ideal candidate for afforestation. Using these results to make inferences about the rest of the boreal forest in Canada, or other temperate zones, is risky. Similar analysis should be performed on other areas in the boreal forest. However, it is the inherent uncertainty of the problem addressed here that requires further research. The innate weakness of the science surrounding climate change, its effect on forests and the feedback effects of tree growth on climate, pose an important challenge for future research. As improvements are made in the understanding of the biophysical relationships, some uncertainty can be reduced, but much will remain. The reason is that projections of future climate change, the effect of forest growth and forest management on removing CO2 from the atmosphere, and the policy environment are and remain a source of uncertainty that is difficult to model. While possibilistic programming and fuzzy set theory were used in this study, assumptions were made about the forms of the possibility distributions on the technical coefficients in the model and the weights used to represent the different targets in the objective function. Research is required to determine appropriate functional forms, as is research to elicit information that can improve the fuzzy membership functions. 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Zimmermann, H.J., 1991, Fuzzy Set Theory - And Its Applications, Kluwer Academic Publishers Boston/Dordecht/London. 106 Appendices 107 Appendix A Deterministic Model Formulation The general structure of the deterministic model formulation for the forest sector is given in equations A . l to A . 10. (A.1) Max NPV= Z Z Z Z Z [ R g > s > m > a j t V g , s , m , a X g > s > m > M - C S T g ^ a X ^ m a t ] / ( \ + i)1 subject to : (A.2) TV t - T V t l < vtargett (A.3) carbt -carbt j >ctargett (A.4) X g ) S m a > t - 0Sg,s,m,a,t for t = = 0,Vg,s,m, a (A.5) RP g > s >t-^g,s>m>a,t <0 for a = l,m = l,t = = l,.,T,Vg,s (A.6) N R g ; M - X g ; S m ; M <0 for a = l,m = 2,t = l,.,T,Vg,s ( A J ) Xg,s,m,a-l,t-l "Xg,s,m,a,t -Hg,s,m,a,t " Fg,s,m,a,t <0 fort = l,..,T,a.= 2,.,8,Vg,s,m ( A ' 8 ) §5Hg,s >m,a,t + m| Fg,s,m,a,t + T A F g > s > t - R P g > S ) t - N R g > s > t - T F A g > s > t <0 fort = l,.,T,Vg,8 ( A 9 ) | ? S 5 V , m , a H g > S f m , M - T V t <0 for t = 1,,T ( A - 1 0 ) |5gi:Cfes.ni,axg,s,m,a,t " c a r b t <0 fort = 1,.,T Where the index g is species, s is site quality, m is management, a is age, t is time period, and T is terminal period. For coefficients and variables, R is revenue, V volume/ha, X is land use type, CST is the cost coefficient, TV is total volume in a period, carb is carbon in a period, OS is opening inventory, RP is replanted forest, NR is natural regeneration, H harvest, F is fire loss, TFA is transfer from forest to agriculture, TAF is transfer from agriculture to forest and C is the carbon coefficient. 108 Appendix B Selected Tables of Inventory and Harvest Patterns 109 r * , OX) \< , + T f I i-H I FH IN O o o oo o 00 o o I 1—1 o I o ° 8 " T f ° ^ r o ^ uo o ° ° 2 ON T f ^ UO T f 0 4 — ' < N 0 ° ° P ON 00 ^ r o NO 1 r—i CO o o <= CO ON 12 00 NO * T f " O N " £ £ 2 g O r o ^ ro" T f £ O O O r-- oo oo ^ > ^ C N ro" ro' ° ° / - « ON NO O T f ON < N " oo r-i C N O O O O ON NO ro^ r o r-; ON" -< w T3 g i* s o -2 o U O O o C N C N o o r o O ON T f C N T f C N ^ ^ O r o O O o O uo oo o ON oo^ NO^ wo ,—T r-" C N o" r o T f C N C N o o o ON T f C N ro^ T f T f o" T f ON — ' NO T f O f-O O T f UO C N C N O C N o o C N O O NO T f ^22 ,-, ° ° p NO r -•^O r o uo e S o -2 o •B o T J o O ^ ^ o o r- oo o | o m ' , " T f O O O t-- uo T f NO^ 00^  C N ro" C N —T r o O O C S 3 oo P ^ r o t C N (X" T f UO 1 0 O O O ON C N r o °\ °\ ^ ro" oo" r - T C N T f r - . O O O r o T f C N NO r o t-» 0 " T f ~ C N C N >—' o o O o o oo NO I C N T f o T f ro" O ^ 00 - H ~ uo" uo" C N Tf" o T f o o NO O o r - H ON NO" T 3 O O a B -3 V-i o o PH 110 Table B2: Coniferous Harvests for Different C Uptake Targets by Site Class, Deterministic Formulations. Level of Uptake (ktonnes) None 1000 1500 2200 Pine Harvests '000 ha Good Period 1 27.9 27.9 27.9 27.9 Period 2 0.9 0.9 0.9 0.9 Period 3 0.3 0.3 0.3 0.3 Period 4 19.8 19.8 19.8 23.5 Period 5 3.9 3.9 3.9 6.4 Medium Period 1 3.5 3.5 3.5 3.5 Period 2 116.6 60.2 45.3 9.1 Period 3 12.1 55.9 54.5 67.6 Period 4 17.6 11.5 19.1 28.8 Period 5 86.7 61.2 57.0 38.2 Poor Period 1 0 0 0 0 Period 2 0 0 0 0 Period 3 0 0 0 0 Period 4 30.6 0 10.1 0 Period 5 18.7 18.9 10.6 0 Spruce Harvests '000 ha Good Period 1 21.3 21.3 21.3 21.3 Period 2 2.6 2.6 2.6 2.6 Period 3 0.7 0.7 0.7 0 Period 4 11.8 11.8 11.8 15.5 Period 5 4.8 4.8 4.8 6.4 Medium Period 1 4.3 4.3 4.3 4.3 Period 2 13.9 11.1 11.1 8 Period 3 1.5 2.0 2 2.6 Period 4 25.8 3.6 1.1 2.7 Period 5 2.8 19.5 36.1 34.7 Poor Period 1 0 0 0 0 Period 2 72.7 139.0 102.0 152.5 Period 3 91.2 36.6 44.7 25.1 Period 4 28.7 20.1 38.8 20.1 Period 5 0.5 7.6 7.6 25.4 111 Table B3: Harvest Strategies for Different C Uptake Targets, Deterministic Formulations. Level of Uptake (ktonnes) None 1000 1500 2200 '000 ha Pine Harvests Period 1 31.4 31.4 31.4 31.4 Period 2 117.5 61.1 46.2 10.0 Period 3 12.4 56.2 54.8 67.9 Period 4 68.0 31.3 49.0 52.3 Period 5 109.3 84.0 71.4 44.6 Spruce Harvests Period 1 64.3 64.3 64.3 64.3 Period 2 89.2 152.7 115.7 163.1 Period 3 93.4 39.3 47.4 27.7 Period 4 66.3 35.5 51.7 38.3 Period 5 8.1 31.1 48.5 66.5 Deciduous Harvests Period 1 122.8 122.8 122.8 122.8 Period 2 0 0 36.8 41.8 Period 3 110.2 56.3 56.3 56.3 Period 4 89.0 93.4 56.3 56.3 Period 5 146.2 56.3 56.3 56.3 112 l l o es a s a. £ o , 5 4 ai • es IPQ CS CS IW £ © © © ^ ° ^ ON CO ° ° ON £ ©' o 3 ON r o °9 ON £ d © 2 ^ <^ ON co ° ° ON £ © d 2 co' . ON CO . 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T f r- ^ vd ^ CN O ^ VO > 0 T f in © oo vo CN T f p Os CN i— i d T f d Os vd d , — < " ro T f m T f in vo NJ ro m T f m oo r-- O T f T f ro 00 vq d in Tf' Os vd od d in ro in m CN CN vo ro so ro T f "1 ro vo T f VO m K N d VO ~ CN vo ro VJ OJ CS = T f o o •c -c -c -a -c <u <u a) u a> PL, PH PH PH PH <—I CN ro O O m O a, <Z3 oo CN CN OO ro t-- T f vd Os od ro in m vo CN ro O oq m os oo oo CN CN ro ro ro od vd vd vd ro in m in CN CN ro ro ro vd vd vd m m m oo CN p ro C O ro vd vd vd in m m oo CN CN ro ro CO ro vd vd vd ro m in m oo CN CN CO CN t-; O vd C N in m vo Vi > 5 - 1 <N ro * T J -a 2 o o g -c -c -c o m a> <u 3 PH PH PH a T 3 O T f -a o •£ PH 115 Appendix C G A M S Code 116 rH ft O JJ ft rl ~ \ co 0 E rfl <u o tt) ft a- ft •H u ft A rd - •H .fl tt) £ -* u -ft fl xl \ 0) 0 U 00 0 in a u ft * 0 * 0 u CO H Cn H A tt) fl — — ft 6 0) rH XI O u p< tt) CO 73 fl * rd tt) rl O U m a) ft tt) ft rH fl 4J M-1 -rl M-1 H O CD tt) tt) ft JJ <u tn rd fl rd e A A CO >N (1) tt) JJ Xl rH -H - H O 3 U tt) i—I -H 4J tt) DI (0 M rH ft rd fl tt) CO Xl fl W O 1 ft U tt) U XI -H CT •H x) fl tt) <u > m rH rH rd 4-> 6 rH fl tn -H JJ -H -H -ri rd rd £ co tn 4-> to £ rl o Cn jJ £ rd Cn rd cn JJ cn cn XI XI O O -H -H rH rH tt) tt) ft ft tt) £ •H JJ JJ CO u -H XI X) o O -H -H rl rl <U tt) ft ft 0) tt) E E -H *rH JJ JJ Xi XI JJ rH rH -H fl X! 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J J -rt fl tt) rH 0) rd fl pa P Q SH >H tt) tt) 0 rH 1 C SH - r t U > T l ft A fl fl 0 &H rd rd E E u MH ( rd Tt T l Dl 3 -rt tt) -H o J J -rt - r t XI C O E E rH rH fl fl + + 1 rH C C rd O SH rH SH rl tt) C O J J fl ft ft rH rH t cd rd rH 01 X) C J XI fl C O tt) O C O C D o 0 o o J J J J t rH rH rH 0 rH rd 0 J J rl fl XI fl fl > > — -^^  1 rd J J 0 SH A SH SH Jfl C O -rt -rt J J 0 0 rH SH 1 U rH rH M H O 0 rd rd J J tt) MH </> xl XI XI XI XI XI -rt O • ^ 1 1 fl rd rd T l J J J J O rH rH ft C Q J J J J C J C J tt) rH . 1 j j SH SH fl fl fl fl J J ft ft fl 0 TJ SH SH u u u MH , — , 1 rH fl fl rd TJ -rt tt) 0 0 -rt C O TJ J J 0 u fl fl 0 0 tt) tt) X! > > X! i fl J J J J rH O > TJ ft ft J J fl -rt 0 -rt -rt MH MH E E C J tt) tt) SH I C J rH rH SH tt) C fl C O rfi J J SH J J SH T l T l rd i -rt fl fl J J ft > -rt rd TJ TJ J J tt) cn tt) C O tt) tt) XI XI rH rH tt) U U U i SH u ( J CD 0 rH -rt - r t -rt > tt) 0 ft E £ u u rd rd £ — -— fl i Dl -rt - r t tt) 01 XI MH ft SH >H > rd SH rH 01 fl fl SH SH J J J J -rt 1 tt) rd SH U >H rd rd 0 0 X) XI -rt XI -rt fl c rH rH 0) tt) 0 o SH + + £ i fl Dl Dl 0 )H >. 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H I—ll—ll—IrHi—ll—ll—IrHi—I JJ ^ H PI : : : M (N H — z = = C N H s f = = = = : ft ft--- ft ft ft = T l f l f l r H r H r H f l f l f l T l O f t f t f l f l f l f t f t f t O o o o f t f t f t u u o o 3 0 ) 0 1 0 0 0 0 ) 0 1 0 1 3 O T J T J O I O I O I T J T J T J U — 0 J * * T J T l T J * * * — 0) „ TJ — -— * * * —. .— .—. — TJ JJ * 0 1 D 1 — — — D 1 D 1 D ) JJ * — •— — Dl Di D) — — — »• 0) D l f t f t — — — ftftft Dl Dl — — -H -H ft ft ft-H - H . - H — — rH T l ,fl XI -H -H -H XI Xl X! rH T! O O O. XI X' XI O O O • 0-ft O X I X I O O O X I X I X I ft O fl 3 S H S H X ) X ) X ! S H S H S H - fl 3 . T) X l r d r d S H S H S H r d r d r d T i XI 0 S n o o c d c d c d o o o O S H SH c d - - C J O U - - - SH cfl ft O 0 1 0 1 - - - 0 I D 1 D 1 ft O X * - — — 0 1 0 1 0 1 — — — X I * o — D i E E — — — E E E o — 01 * = — flflEEEflflfl * = — — H E c n c n f l f l f l c n c n c n H E 01= fl + + cncncn + + + -~ 01= fl — — c n — — + + +— — — — — — cn ftft+jjjj — — — J J J J J J J J ftft + - H r H — — — J J J J J J — — — — - H r H — XI fl JJ 01 01 ' i—I i—I i—I i—I X l f l J J U ft— O l O l r i l H S H C d r d r d r d O ft — X l U O V l r l f l f l f l f l f l f l f l X 1 O 0 SH 0) 3 rfl Xl O O O -H -rl -H -H S H C L ) 3 C d T J j J J J J J M H M H M H M H M H M H M H r f l T i j - l U - K J J J J J J J J J J J J J J J J J J J J O - K J J •K — <&</></></></></}•</)•</}•</>•</>• * — -CO 01 Dl — — — — — — — — — — 01 01 — O f t r H C N H r O C N H s J i r O C N r H O f t r H Qt -rl I I I I I I I I I I ft -H I r H X l J J J J J J J J J J J J J J J J J J J J H X JJ ftO ftO-T 3 X I 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 TJ rQ 01 CH — — —• — — — — — — —' SH — • K H H H H H H H H H H - C d r H 0 1 O 0 1 O -— ftftftftftftftftftft — O E - flflflflflflflflflfl E - r H fl01TJTJTJTlTlTlTiTlTlTi fl01Ti cn O O O O O O O O O O W — O £ J H J H S H M J H S H S H S H S H S H E S H l l f l f t f t f t f t f t f t f t f t f t f t l l f l f t c n x l x l x l x l x l x l x l x l x l x l c n x l — + U O O U O O O O O O — + o o o h H ft -rl x l o o ft - H XI o o o h3 149 * * * •K * * * * r H ro T ro C N H 7 = C N r H = - = •— zz r — — — ' — ft ft — ' ----- ft ft ft r H r H ft ft ft i-H r H r H fl fl r H r H r H fl fl fl ft ft fl fl fl ft ft ft u u ft ft ft C J U U tt) 1) C J C J o 0) tt) tt) TJ TS tt) CU tt) XI XI XI * * TJ XI X) * * * * * .—. *—. * * * ,—. .—* .—. .— .—, 01 cn — Di Di D l - = • "— Cn D l —T — — ' i-H * * * -K * r H * * * * * ft ft ft ft ft 7 .—. * * * — .— • .—. * * * .— — . • H - H ft ft ft - H - H - H r —^ — . 77 77 7 * —. .—. —. : fl J f l - H - H • H fl fl fl fl —. H ro L ro C N r H fl ,—. H ro 1 1 ro C N r H U C J fl fl fl U C J U cn 1 z r C N r H r r cn 7 7 = C N r H r fl fl u C J C J fl fl fl 0 C N — ' -—' 7 7 7 ~— -—' "—• O C N ' — ' 7 7 '— —- —-SH H fl fl fl SH SH SH cj r fl fl — r —f fl fl fl U 7 fl fl — fl fl fl rS rS rH H M rS rS rS tt) — cn cn X J fl fl cn cn cn tt) cn C Q fl fl fl C Q C Q cn C J C J rS rS rS C J C J U TS fl 0 0 cn cn C O o 0 0 TJ fl 0 o C O C Q C Q 0 O o U U U - - - * cn u u 0 0 0 o C J C J * cn o C J 0 o O C J U C J cn Cn cn cn Dl r H o tt) tt) u u o cu cu tt) r H O tt) tt) C J u C J CU tt) cu -—' -—- 3 D l Dl * - rs u X! XI cu tt) tt) X l XI TJ (S C J TJ T l tt) tt) tt) TS TJ TJ e e £ B B > cu * * X l XJ TS * * * • > tt) * * TJ TJ TJ * * * A A B B e fl fl fl C J x l r H r H * * * r H r H r H U T l r H r H * * * r H r H r H C O cn fl fl A cn cn cn fl * rS rS r H r H r H (6 rS rd fl * rd rd r H r H r H rd rd rd + + cn cn cn + + + — r H > > rS rS (S > > > — r H > > cd rd rd > > > . + + + ,—, ,—. . — ,—. + rS u C J > > > C J C J U + rS C J u > > > u C J C J 4 J J J . .—. .— J J 4 J 4 J J J > fl fl U C J C J fl fl fl > fl fl o C J C J fl fl fl •—- — J J J J — — —- -— 4-1 C J —- — fl fl fl -— •— — 4 J C J — — fl fl fl — -— — cu tt) — — — r H r H r H r H fl + + — — -— + + + ~— fl + + —- -— + + + tt) tt) SH H W rS rS rS rS r H -—- + + + ,— , ,— r H -— . ,— + + + , ,—, ,—. u SH fl fl fl fl fl C fl . + 4 J 4 J . . . .— 4 J 4 J 4 J 4 J + 4 J 4 J J J J J J J 4 J fl fl 0 0 0 - H - H - H - H fl — — ' J J J j — -— — ' — fl — -— 4 J 4 J 4-> -— — — — 4 J 4 J 4-1 MH MH MH MH MH MH cn tt) tt) — — ~—- r H r H r H r H cn J J tt) tt) — ' — — r H r H r H r H 4 J 4 J J J J J J J J J J J J J J J 0 * tt) tt) SH SH SH rS rS rS (0 0 —- tt) tt) u SH SH rd rd cd rd «/> ^/^ </> </> </> </> O 0 >H SH fl fl fl C C fl fl 0 0 SH SH fl fl fl fl fl fl fl ,—, ,—. .—. .— .—. ^ r H fl fl 0 0 0 - H - H - H - H r H fl fl 0 0 0 - H - H - H - H TS J J J J J J MH MH MH MH MH MH MH T l 4 J J J J J MH MH MH MH MH MH MH C N i H ro C N r H T f ro C N r H * J J J J J J J J 4 J J J J J 4 J 4 J J J * J J 4 J J J - J J J J J J J J J J J J J J l l i l 1 l i l 1 r H </> </> </> • C / > • C / > </> </> </> </> r H </> </> </> </> </> </> </> </> </> 4 J 4 J 4 J J J J J 4 J J J J J J J rS ^ 7 — - •~~7 rS ^ ^ - — — > ,—. ,—, , ,—, .—. .—. .—, . . ,—. . . > ,— . , .—, .—. , . .—. .—, ,—. . . .—, cn D l Dl D l Dl D l Di Di Di C J r H C N r H ro C N r H Tt< ro C N r H C J r H C N H ro C N r H T f ro C N r H fl 1 1 1 i 1 1 i t 1 1 fl t 1 1 t 1 t 1 i 1 1 r H r H r H i-H r H r H r H r H r H * ni J J J J 4 J J J J J J J J J 4 J J J J J * J J J J 4 J J J J J J J J J J J J J J J 0 0 0 0 0 o o o o i f C r H r H r H r H r H r H r H r H r H r H cu C r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H o 0 T l X l X l X l x f X l XJ X) XI fl fl fl fl fl fl fl fl fl fl fl fl fl fl fl fl fl fl fl fl fl fl 0 0 0 0 0 0 0 0 O cn cn cn cn cn cn cn cn cn cn cn cn cn C Q C Q C Q C Q C Q C Q CQ cn cn S H rH u u SH SH SH SH SH 0 0 0 0 0 0 o O o o o o o 0 o O O O O O o o ft ft ft ft ft ft ft ft ft x l 0 0 0 0 0 0 0 0 0 0 TJ 0 0 0 0 0 0 0 0 0 0 - f l fl fl fl fl fl fl fl fl r H r H r H r H r H r H r H r H r H r H r H r H i-H r H r H r H r H r H r H r H u 0 u u C J U u U U II XI XI XI XI XI TJ T l XI TJ TJ II TJ TJ TJ TJ TJ TJ TJ TJ TJ T) ft rH * ft — O = tt) C N T l = TJ — * ft rH rH rd ft > U o cu fl TJ — TS + * rH J J rd — > rH CJ • fl ft — rH + fl ~ ft O ft — fl O TJ 3 * J J rH J J rd <J> > — u fl r H * I tt) J J fl — 0 rH ft • rH CU ft rH TJ fl TJ ft ft II fl TJ ft ft r H r H ft ft U CJ 0) tt) TJ TJ TJ TJ * * r H r H rd rd > > CJ U fl fl + + J J J J tt) 4) tt) 4) SH SH fl fl J J J J J J J J •c/> </> C N r H I I J J J J ft ft rH rH fl fl ft ft ft ft fl fl TJ XI fl cn O o fl cn O cj O J ft r H ft XJ CJ ft 150 0 E o u a - H Cn < * * * * * * •_— — -_ ro CM rH CN H 7 : r 7- •— — — —- —- ft ft ft ft ft ft rH rH rH rH rH rH ft ft ft ft ft ft U u U U U U 0 0 0 0 0 0 TJ T i T i T J T i T ) T i T J TJ T ) TJ T ) * * * * * * rH rH rH rH rH rH (tJ rfl rfl cd cd nJ > > > > > > u CJ CJ u 0 u r f l r f l A r C r f l r f l — ~ ~ + + + + + + . , . .—. .—. . 4-> 4-1 4-1 4-1 4-> 4J — —- — — -— -— — rH rH rH rH S H u SH rfl cfl rfl rfl fl fl fl C fl C fl 0 0 0 - H • H - H - H HH M-1 M-4 M-1 M-1 M-1 M-1 4J 4J 4-1 4-1 4-) 4-1 4-1 •CO CO •CO Vi Vi •CO •CO-ro (N iH sf CO CM H 4-1 4J 4-> 4-) 4J 4-1 4-1 rH rH rH rH rH rH rH ft ft ft ft ft ft ft rH rH rH rH rH rH rH fl fl fl fl fl fl fl ft ft ft ft ft ft ft ft ft ft ft ft ft ft fl fl fl fl fl fl fl T) TJ T ) T J T i T J T i ft rH ft • CJ 0 I T i T J • * rH 1 r f l > CJ r f l ro = = = ro CN rH = CN H s f = = • .= = ft — rH ft ft rH CJ ft 0 U TJ 0 T f T) * T i rH * r f l > 4J rfl — > rH CJ • r f l + ft" — rH + 4J fl — — ft • O -i-H T i * rH . 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SH cn ft 0 CJ CJ 0 0 4J Cl rH J J -H CO rJ OJ 4J -H CO rH C M T i ft fl 01 0) Pri £ > I D Ti X I SH co ft 0 CJ CJ I D | D rl -X J TS E ft J J J J U fl ft rH I D P J 

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