Forestry, Faculty of
DSpace
UBCV
Yan, Yancun
Master of Science - MSc
University of British Columbia
Forests play a crucial role in the global carbon cycle, sequestering atmospheric carbon dioxide and storing it within various ecosystem pools and harvested wood products (HWPs). HWPs can further reduce greenhouse gas (GHG) emissions by substituting carbon-intensive materials and energy sources. This thesis develops an integrated mathematical modeling framework designed to simulate and optimize the climate change mitigation potential of the forest sector in British Columbia (BC), Canada. This framework consists of the Strategic Forest Management Model (SFMM), the Forest Carbon Budget Model (FCBM), and the Wood Product Carbon Model (WPCM), incorporating key carbon indicators such as the total carbon stock of the forest and the net carbon emissions from the forest. The study uses the Prince George Timber Supply Area (TSA) as the case study area. Scenarios ranging from a no-harvest approach to a maximize-harvest approach are simulated to explore the impact of management activities on forest carbon dynamics. In addition, the method used to connect SFMM and FCBM is rigorously tested to ensure the credibility and reliability of the modeling results, demonstrating the framework’s robustness in accurately predicting forest carbon dynamics under various management scenarios. This study also evaluates trade-offs between timber supply and forest carbon management. By employing the epsilon-constraint method, the research generates Pareto front curves that elucidate the quantitative trade-offs between maximizing wood supply versus maximizing total forest carbon stock or minimizing net forest carbon emissions. It reveals the inverse relationship between maximizing wood supply and forest carbon benefits. Extensive sensitivity analyses further examine how variations in the climate impacts of HWPs influence the model’s optimal forest carbon management solution, highlighting the importance of product longevity and substitution effects in carbon forestry decision-making. The research findings underscore important insights for policymakers and forest managers aiming to balance economic and climate objectives during the forest management planning process, ultimately contributing to BC’s goals of reducing GHG emissions and enhancing the forest sector’s role in climate change mitigation.
A Mathematical Modeling Frameworkto Optimize the Climate ChangeMitigation Potential of the ForestSector in British Columbia, CanadabyYancun YanB.Sc., The University of British Columbia, 2022A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Forestry)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)June 2025© Yancun Yan 2025The following individuals certify that they have read, and recommend to the Faculty ofGraduate and Postdoctoral Studies for acceptance, the thesis entitled:A Mathematical Modeling Framework to Optimize the Climate Change Mitigation Potentialof the Forest Sector in British Columbia, Canadasubmitted by Yancun Yan in partial fulfillment of the requirements forthe degree of Master of Sciencein ForestryExamining Committee:Gregory Paradis, Assistant Professor, Forest Resources Management, UBCSupervisorQingshi Tu, Assistant Professor, Wood Science, UBCSupervisory Committee MemberCeline Boisvenue, Adjunct Professor, Forest Resources Management, UBCSupervisory Committee MemberHaibo Feng, Assistant Professor, Wood Science, UBCAdditional ExamineriiAbstractForests play a crucial role in the global carbon cycle, sequestering atmospheric carbon diox-ide and storing it within various ecosystem pools and harvested wood products (HWPs).HWPs can further reduce greenhouse gas (GHG) emissions by substituting carbon-intensivematerials and energy sources. This thesis develops an integrated mathematical modelingframework designed to simulate and optimize the climate change mitigation potential ofthe forest sector in British Columbia (BC), Canada. This framework consists of the Strate-gic Forest Management Model (SFMM), the Forest Carbon Budget Model (FCBM), andthe Wood Product Carbon Model (WPCM), incorporating key carbon indicators such asthe total carbon stock of the forest and the net carbon emissions from the forest.The study uses the Prince George Timber Supply Area (TSA) as the case study area.Scenarios ranging from a no-harvest approach to a maximize-harvest approach are sim-ulated to explore the impact of management activities on forest carbon dynamics. Inaddition, the method used to connect SFMM and FCBM is rigorously tested to ensure thecredibility and reliability of the modeling results, demonstrating the framework’s robust-ness in accurately predicting forest carbon dynamics under various management scenarios.This study also evaluates trade-offs between timber supply and forest carbon management.By employing the epsilon-constraint method, the research generates Pareto front curvesthat elucidate the quantitative trade-offs between maximizing wood supply versus maxi-mizing total forest carbon stock or minimizing net forest carbon emissions. It reveals theinverse relationship between maximizing wood supply and forest carbon benefits. Extensivesensitivity analyses further examine how variations in the climate impacts of HWPs influ-ence the model’s optimal forest carbon management solution, highlighting the importanceof product longevity and substitution effects in carbon forestry decision-making.The research findings underscore important insights for policymakers and forest man-agers aiming to balance economic and climate objectives during the forest managementplanning process, ultimately contributing to BC’s goals of reducing GHG emissions andenhancing the forest sector’s role in climate change mitigation.iiiLay SummaryForests play a critical role in the global carbon cycle. Trees sequester atmospheric carbondioxide and store it in their biomass. Then, the carbon flows into other ecosystem carbonpools and HWPs, and is eventually emitted back into the atmosphere over varying timespans. HWPs can also substitute carbon-intensive materials and energy sources to reduceGHG emissions. Suitable management activities can increase the forest’s potential forclimate change mitigation. This study builds and tests a mathematical modeling frameworkto simulate and optimize the climate change mitigation potential of the forest sector in BC,Canada. It models the carbon dynamics of the forest ecosystem and the downstream woodproduct industry under different management scenarios. Key findings reveal the trade-offs between wood supply and forest carbon management and highlight that the climateimpacts of HWPs are important in determining forest carbon management plans.ivPrefaceThis thesis represents the original work of the author, Yancun Yan. The research wasconducted under the supervision of Dr. Gregory Paradis at the University of BritishColumbia. Throughout this work, I received valuable guidance and support from mysupervisory committee and collaborators. My specific contributions, as well as those of mycollaborators, are detailed below.• Forest Inventory Data: The forest inventory data used to develop the StrategicForest Management Model (SFMM) and Forest Carbon Budget Model (FCBM) wereprovided by my supervisor, Dr. Gregory Paradis.• Conceptualization, Methodology Development, and Validation: Dr. Gre-gory Paradis led the conceptual development of the integrated mathematical model-ing framework and provided extensive guidance in shaping the methodology.• Forest Estate and Carbon Modeling: I adapted and integrated the forest estateand carbon budget modeling scripts, originally developed by Dr. Gregory Paradis.These models were refined by me for model integration, optimization, and validation.ChatGPT was used to generate code suggestions and assist in troubleshooting scriptintegration.• Harvested Wood Product (HWP) Modeling: I was responsible for buildingthe model to calculate the HWP carbon dynamics and substitution effects. Dr.Qingshi Tu provided expert guidance in life cycle assessment to ensure methodologicalsoundness.• Trade-off and Sensitivity Analysis: I conducted the trade-off and sensitivityanalyses, with design guidance, technical support, and feedback from Dr. GregoryParadis, Dr. Elaheh Ghasemi, and Dr. Salar Ghotb.• Manuscript Preparation and Revision: I drafted the entire thesis. Revisionsand feedback were provided by my supervisory committee, including Dr. GregoryParadis, Dr. Kathleen Coupland, Dr. Elaheh Ghasemi, and Dr. Salar Ghotb.Portions of this thesis have been developed into a manuscript titled Forest Managementand Carbon Dynamics: How Harvested Wood Products Affect Forestry Decision-Making invPrefaceBritish Columbia, which will be submitted to a peer-reviewd academic journal for publi-cation. Scripts developed for this research are available at UBC-FRESH/msc walter yan.Generative Artificial Intelligence (GenAI), specifically ChatGPT, was used to supportcoding tasks, generate research ideas, and assist in drafting the thesis outline. All contenthas been critically reviewed and revised by the author.No UBC Research Ethics Board approval was required for this research.viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 Climate Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.2 Forest-Atmosphere Carbon Cycle . . . . . . . . . . . . . . . . . . . 21.1.3 Forest Carbon Management . . . . . . . . . . . . . . . . . . . . . . 21.1.4 Forestry in British Columbia . . . . . . . . . . . . . . . . . . . . . . 41.2 Forest Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2.1 Strategic Forest Management Modeling . . . . . . . . . . . . . . . . 51.2.2 Forest Carbon Budget Modeling . . . . . . . . . . . . . . . . . . . . 51.2.3 Wood Product Carbon Modeling . . . . . . . . . . . . . . . . . . . . 61.2.4 Growth and Yield Modeling . . . . . . . . . . . . . . . . . . . . . . 71.2.5 Forest Carbon Stock and Net Emission . . . . . . . . . . . . . . . . 71.3 Forest Carbon Management Modeling Framework . . . . . . . . . . . . . . 81.3.1 Modeling Framework Overview . . . . . . . . . . . . . . . . . . . . . 91.4 Research Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.5 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11viiTable of Contents2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.1 Study Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Modeling Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2.1 Data Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2.2 Model Execution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.3 Modeling Output Comparison . . . . . . . . . . . . . . . . . . . . . 232.2.4 Stand-level Comparioson Analysis . . . . . . . . . . . . . . . . . . . 242.2.5 Landscape-level Comparison Analysis . . . . . . . . . . . . . . . . . 242.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.3.1 Trade-off Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.3.2 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.1 Forest Inventory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2 Stand-level Comparison Analysis . . . . . . . . . . . . . . . . . . . . . . . . 283.2.1 No-harvest Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2.2 Harvest Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.2.3 Landscape-level Comparison Analysis . . . . . . . . . . . . . . . . . 363.3 Trade-off Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.3.1 Wood Supply vs Total Carbon Stock . . . . . . . . . . . . . . . . . 423.3.2 Wood Supply vs Negative Carbon Emission . . . . . . . . . . . . . 423.4 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.1 Forest Inventory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.2 Stand-level Comparison Analysis . . . . . . . . . . . . . . . . . . . . . . . . 484.2.1 No-harvest Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.2.2 Harvest Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.3 Landscape-level Comparison Analysis . . . . . . . . . . . . . . . . . . . . . 514.3.1 No-harvest Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.3.2 Maximize-harvest Scenario . . . . . . . . . . . . . . . . . . . . . . . 524.3.3 Comparison to Stand-level Analyses . . . . . . . . . . . . . . . . . . 524.4 Trade-off Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.4.1 Wood Supply vs Total Carbon Stock . . . . . . . . . . . . . . . . . 534.4.2 Wood Supply vs Negative Carbon Emission . . . . . . . . . . . . . 544.5 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.6 Contribution of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.7 Limitations of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60viiiTable of ContentsBibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62ixList of Tables3.1 Site information for AUs within the Prince George TSA. . . . . . . . . . . . 31xList of Figures1.1 Forest carbon cycle (Source: USDA, United States Department of Agricul-ture.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Abstract timber yield curve example. . . . . . . . . . . . . . . . . . . . . . . 81.3 Abstract carbon yield curve example. . . . . . . . . . . . . . . . . . . . . . . 102.1 Study area indicating the Prince George TSA. . . . . . . . . . . . . . . . . . 152.2 The integrated forest carbon management modeling framework. . . . . . . . 163.1 Species composition of unmanaged forests in TSA 24. . . . . . . . . . . . . 293.2 Species composition of managed forests in TSA 24. . . . . . . . . . . . . . . 293.3 Age structure distribution of unmanaged forests in TSA 24. . . . . . . . . . 303.4 Age structure distribution of managed forests in TSA 24. . . . . . . . . . . 303.5 Comparison between forest carbon stocks at the stand level under no-harvestscenario. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.6 Comparison between net forest ecosystem emission at the stand level underthe no-harvest Scenario. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.7 Comparison between carbon stock and emission at the stand level with asingle clear-cut applied in period 5. . . . . . . . . . . . . . . . . . . . . . . . 333.8 Comparison between carbon stock and emission at the stand level with asingle clear-cut applied in period 10. . . . . . . . . . . . . . . . . . . . . . . 343.9 Comparison between carbon stock and emission at the stand level with asingle clear-cut applied in period 15. . . . . . . . . . . . . . . . . . . . . . . 353.10 Comparison between carbon stock and emission at the stand level with twoclear-cuts applied in period 5 and period 15. . . . . . . . . . . . . . . . . . . 373.11 Comparison between carbon stock and emission at the stand level with threeclear-cuts applied in period 5, period 11, and period 18. . . . . . . . . . . . 383.12 Comparison between carbon stock and emission at the stand level with fourclear-cuts applied in period 4, period 8, period 13, and period 19. . . . . . . 393.13 Total forest growing stock change under the no-harvest scenario. . . . . . . 403.14 Total forest carbon stock change under the no-harvest scenario. . . . . . . . 413.15 Net forest carbon emission change under the no-harvest scenario. . . . . . . 413.16 Changes in harvested area, harvest volume, and growing stock over timeunder the maximize-harvest volume scenario. . . . . . . . . . . . . . . . . . 42xiList of Figures3.17 Total forest carbon stock change under the maximize-harvest scenario. . . . 433.18 Net forest ecosystem carbon emission under the maximize-harvest scenario. 433.19 Trade-off curves between maximizing wood supply and maximizing totalforest carbon stock with varied HWP half-lives. . . . . . . . . . . . . . . . . 453.20 Trade-off curves between maximizing wood supply and maximizing negativenet carbon emission with varied HWP half-lives. . . . . . . . . . . . . . . . 453.21 Trade-off curves between maximizing wood supply and maximizing negativenet carbon emission with varied HWP half-lives and displacement factors. . 463.22 3D mapping of model sensitivity to HWP half-life and displacement factor. 473.23 Orthographic views of the 3D mapping of model sensitivity to HWP half-lifeand displacement factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47xiiList of AbbreviationsAAC Allowable Annual Cut.AU Analysis Unit.BC British Columbia.BEC Biogeoclimatic Ecosystem Classification.CBM-CFS3 Carbon Budget Model of the Canadian Forest Sector.CO2 Carbon Dioxide.DOM Dead Organic Matter.FCBM Forest Carbon Budget Model.GHG Greenhouse Gas.GYM Growth and Yield Model.HWP Harvested Wood Product.IPCC Intergovernmental Panel on Climate Change.LCA Life Cycle Assessment.libcbm Carbon Budget Model Library.SFMM Strategic Forest Management Model.THLB Timber Harvesting Land Base.TIPSY Table Interpolation Program for Stand Yields.TSA Timber Supply Area.UNFCCC United Nations Framework Convention on Climate Change.xiiiList of AbbreviationsVDYP Variable Density Yield Projection.WPCM Wood Product Carbon Model.ws3 Wood Supply Simulation System.xivAcknowledgmentsI would like to express my deepest gratitude to my supervisor, Dr. Gregory Paradis, forhis unwavering mentorship, insightful guidance, constructive criticism, and encouragementthroughout my graduate studies. His expertise in forest management, mathematical mod-eling, and computer programming, along with his constant support, was instrumental insuccessfully completing this research.I extend my sincere appreciation to my committee members, Dr. Qingshi Tu and Dr.Celine Boisvenue, for their invaluable feedback and technical insights, which significantlyenhanced the quality and rigor of this work.A special thank you is extended to Dr. Elaheh Ghasemi and Dr. Salar Ghotb for theirvaluable contributions to both the trade-off and sensitivity analyses and the revision of mythesis draft. Their expertise and perspectives added depth to the analytical framework ofthis research.My sincere thanks also go to Dr. Kathleen Coupland for her guidance in refiningthe thesis draft and the paper manuscript. Her keen editorial insights and thoughtfulsuggestions played a significant role in strengthening the clarity and presentation of mythesis and paper.I deeply appreciate my family and friends’ unwavering support, patience, and encour-agement throughout this journey. Their belief in me has been a source of strength andmotivation, helping me navigate the challenges of graduate studies with resilience anddetermination.Finally, I would like to acknowledge the financial and institutional support from theUniversity of British Columbia and other funding bodies that made this research possible.xvDedicationTo my family and best friends, whose love and support have been the foundation of myjourney; and to those who have guided and inspired me along the way, shaping my academic,professional, and personal growth.xviChapter 1Introduction1.1 Background1.1.1 Climate ChangeClimate change, characterized by long-term changes in temperatures and weather patterns,is driven primarily by increases in GHG emissions from anthropogenic activities since theIndustrial Revolution [64]. The extraction and combustion of fossil fuels (coal, oil, andgas) are responsible for more than 75 percent of GHG emissions, contributing to nearly90 percent of carbon dioxide (CO2) emissions to date [63]. CO2 plays a dominant rolein climate change, with its enormous increase in atmospheric concentration over the pastfive decades, directly causing global threats to human life and economic stability [46].The contribution of CO2 to climate change has led to the use of CO2 equivalent as astandard unit to measure the climate impact of various GHGs, based on their globalwarming potential [28].To address global climate change, the Intergovernmental Panel on Climate Change(IPCC) was established by the United Nations in 1988 [30], leading to the formation ofthe United Nations Framework Convention on Climate Change (UNFCCC) in 1992 [65].The Kyoto Protocol of 1997 further operationalized the (UNFCCC) by setting emissiontargets for the participating countries [66]. A significant milestone was the negotiation ofthe Paris Agreement under the UNFCCC in 2015, aiming to limit global temperature riseto 2 degrees Celsius above preindustrial levels in the 21st century [67]. This agreementrequires all parties to reduce GHG emissions and achieve net-zero emissions to mitigateclimate change effectively.Nationally, Canada has pledged to reach net-zero GHG emissions by 2050, enacting theCanadian Net Zero Emissions Accountability Act to provide a transparent framework forachieving this target [23]. Despite global efforts to reduce GHG emissions, global warmingtrends persist, with a 0.82-degree increase in global surface temperature between 2011and 2020 [48]. This indicates an urgent need for more ambitious mitigation strategies,including reducing net carbon emissions and implementing negative-emission technologiesin all industries.11.1. Background1.1.2 Forest-Atmosphere Carbon CycleForests are important to the global carbon cycle and have the potential to be a majorcontributor to climate change mitigation. Forests are estimated to absorb around one-third of the atmospheric carbon emitted from fossil fuel use every year since 1990 [49].As dynamic systems, forests constantly sequester, store, and emit carbon [38]. Figure 1.1shows the closed loop of forest carbon in the atmosphere. Forests sequester atmosphericCO2 and convert it to biogenic carbon through photosynthesis by trees and other plantswith growth. Biogenic carbon is fixed in the aboveground biomass of the forest (leaves,branches, trunk), the belowground biomass (roots, rhizomes), dead organic matter (DOM)(deadwood, litter), and soil. Carbon returns to the atmosphere through autotrophic res-piration, decomposition, and oxidation. In addition, natural disturbances, such as fires,diseases, and insect outbreaks, can accelerate these processes [34]. Different parts of theforest, such as biomass and DOM, accumulate and release biogenic carbon, identified ascarbon pools. The amount of carbon stored in each pool at a specific time is called carbonstock. Carbon fluxes are the amount of carbon transferred between different carbon pools.HWPs are also a important part of the forest-atmosphere carbon cycle. Depending onthe type, usage, and end use of HWPs, the carbon they store will gradually be emitted backinto the atmosphere at different speeds [56]. In 2013, IPCC revised that it is mandatoryto consider the HWP carbon pool when estimating total anthropogenic GHG emissions bysources and sinks in land use, change in land use, and the forest sector [27]. In addition tostoring carbon during their lifetimes, HWP s have the potential to replace GHG intensiveand non-renewable materials (material substitution), such as concrete and steel, whichare the two most common building materials in the construction industry worldwide [17].Wood-based bioenergy can also replace fossil fuels and natural gases (energy substitution)[17]. The substitution function of HWPs with other GHG-intensive materials or energysources shows their potential to reduce carbon emissions, thus improving the forest sector’scontribution in combating the global climate crisis.1.1.3 Forest Carbon ManagementManagement is the organized effort to plan, coordinate, and oversee resources and activ-ities to achieve specific objectives efficiently and effectively. It encompasses a variety ofprocesses that guide decision-making, resource allocation, and strategic implementation invarious domains [54]. Forest management, as an application of general management prin-ciples in forestry, is a process of administering and overseeing forest resources to achievespecific economic, social, environmental, cultural, and scientific objectives [16]. It encom-passes a variety of human activities, from low-intensity to high-intensity interventions, withdifferent practices, tools, and techniques [16]. The specific objectives of forest management,such as use or conservation, drive the strategies adopted and influence their long-term im-plementation. For example, the primary focus in commercial forests has traditionally been21.1. BackgroundFigure 1.1: Forest carbon cycle (Source: USDA, United States Department of Agriculture.)on the timber supply, reflecting the dominant management objective of resource extractionand economic return. In the context of global climate change and sustainable development,forest management activities can also play an essential role in climate change mitigationsince human interventions significantly impact the carbon dynamics of the upstream forestecosystem and the downstream wood industry of the forest sector. In 2007, IPCC identifiedthe change in forest management to increase carbon stock at the plot and landscape levelas an important nature-based mitigation option [42]. The IPCC also emphasized, In thelong term, a sustainable forest management strategy aimed at maintaining or increasingforest carbon stocks, while producing an annual yield of wood, fiber, or energy from theforest will generate the largest sustained mitigation benefit. [42]. Therefore, forest carbonmanagement refers to forest management actions, plans, and strategies designed to sys-tematically maintain or increase forest carbon stocks or sequestration of the entire forestsector, considering both the forest ecosystem and HWPs. Canada has around 367 millionhectares of forests that store carbon and regulate climate [45], which is approximatelynine percent of the world’s forests. To achieve Canada’s national emission reduction goalby 2050, improving the carbon storage and emission reduction capacity of its abundantforests is essential through improved forest management activities, which have been identi-31.1. Backgroundfied as one of the most important nature-based climate solutions for Canada [13]. Althoughnatural disturbances, such as wildfires, contribute significantly to carbon emissions fromCanadian forests [36], IPCC do not mandate the inclusion of emissions from natural distur-bances in national GHG inventories [29]. Given the complexity and uncertainty associatedwith modeling emissions from natural disturbances, this study does not include them inits analysis.1.1.4 Forestry in British ColumbiaThe BC province is actively aligned with Canada’s national strategies to combat the globalclimate crisis, having set the mitigation target to reduce GHG emissions by 80 percentrelative to 2007 levels by 2050. Achieving this goal requires decisive mitigation actions inmultiple sectors, including the forest industry [44]. In particular, BC stands out withinCanada for its vast forest resources, covering approximately 60 million hectares of foreststhat store massive amounts of carbon in their ecosystems. The province also leads thenation in the production of HWPs, which contribute positively to climate change mitigationgoals through carbon storage and substitution benefits. Xu et al. [70] and Smyth et al. [59]show the substantial potential for climate change mitigation in the BC forest sector. Thispotential can be realized by improving forest management practices to maximize carbonstorage within forest ecosystems and increasing the production of HWPs with longer half-lives and stronger substitution effects, replacing carbon-intensive materials and energysources. These strategic actions position BC’s forest sector as an enormous contributor inachieving the provincial GHG reduction goal and the broader fight against global climatechange.BC is organized into distinct management units, including 38 TSAs and 34 Tree FarmLicenses [4, 5]. Effective forest management in TSAs requires projecting future timbersupply and determining the allowable annual cut AAC [22]. Timber supply represents theestimated volume of timber that is projected to be available for harvest within a definedperiod under a specific management regime [20]. AAC represents the volume of timber thatcan be harvested sustainably each year in a particular area and serves as a fundamentalregulatory measure to ensure the sustainability of the timber supply [10].However, forest carbon has not been taken into account during the AAC determi-nation of most TSAs in BC. The rationale for AAC determination of some TSAs, suchas Prince George, Fraser, Fort Nelson, and Okanagan, mentioned that more research isneeded to focus on the interrelationship and trade-offs between wood supply and forestcarbon management at the landscape level to support the determination of AAC, althoughthe importance and implications of forest management for climate change mitigation arealso acknowledged and emphasized [22]. Modeling wood supply and forest carbon underdifferent forest management scenarios can provide insights into optimizing managementstrategies to meet both economic and climate goals.41.2. Forest Modeling1.2 Forest ModelingQuantifying forest resources and forecasting forest dynamics are fundamental to forestmanagement planning. Forest modeling is a method of simulating current and future forestconditions by abstracting and conceptualizing key elements and relationships of the forestsystem [55]. Forest modeling has been widely used to help foresters understand forests,predict the future, and make strategic, tactical, and operational decisions at different levels.1.2.1 Strategic Forest Management ModelingIn forest management, developing effective long-term strategies is crucial to maximize theuse of finite resources or to maintain forest ecosystem services [39]. SFMMs serve as im-portant tools to plan forest management activities that meet various objectives. SFMMsare designed to facilitate the forest management planning process, assist decision makersin exploring various forest strategies, simulating and optimizing management plans, andachieving predefined targets [24]. Historically, one of the main focuses of SFMMs hasbeen to ensure a continuous supply of wood in the long term to fulfill economic objectives,which is important to determine AAC. However, current strategic goals underscore a shifttowards ecosystem-based management, focusing on preserving ecosystem health and en-hancing ecosystem services, such as carbon storage and sequestration, over pure timberproduction [24]. This transition reflects a broader understanding of the value of forests,recognizing their important role not only as sources of raw materials but also in globalecological balance, biodiversity conservation, and climate change mitigation.At the technical level, SFMMs are based on mathematical formulations that plan thetreatments to be applied, the specific types of stands to be targeted, the area of the type ofstand to be treated, and the timing of these interventions. Among various methodologiesfor building SFMMs, linear programming, a mathematical method used to determine theoptimal outcome in a model with linear relationships [12], has been used in forest plan-ning since the 1960s to solve many optimization problems in forest operations research,particularly in wood supply [39]. For example, linear programming models can help deter-mine the optimal timing, intensity, and area of silvicultural activities, aiming to maximizethe harvesting yield and efficiency over periods [47, 51]. The Model I linear program-ming approach provides detailed treatment planning for individual or aggregated foreststands, allowing the simulation of sophisticated management actions (e.g., regeneration,clear-cutting) throughout the planning horizon [24], which will serve as the foundation ofSFMM built in this study.1.2.2 Forest Carbon Budget ModelingGiven the important role of forests in the global carbon cycle, international agreements,such as UNFCCC, require countries to monitor, measure, and report on their forest car-51.2. Forest Modelingbon stocks or stock changes to quantify the capacity for forest climate change mitigation.IPCC provides a detailed framework, Good Practice Guidance for Land Use, Change inLand Use, and the Forest Sector. This guide delineates approaches for calculating thechange in carbon stocks and accounting for GHG emissions from forest activities [53]. Itestablishes a solid foundation for building FCBMs. In Canada, the Carbon Budget Modelof the Canadian Forest Sector (CBM-CFS3), which implements the Tier 3 Good PracticeGuidance standard and includes site-specific parameters, has become a standard tool forforest managers to model ecosystem carbon in different management scenarios at standand landscape levels, compare and select the plan that best meets their objectives, andguide sustainable strategies to align with climate change mitigation goals [33]. CBM-CFS3constitutes the core of the Canadian National Forest Carbon Monitoring, Accounting, andReporting System, illustrating the country’s effort to comprehensively and accurately as-sess carbon stock and fluxes in its forests [43]. CBM-CFS3 is designed to integrate andsimulate detailed forest processes, including tree growth, decomposition, and disturbancessuch as harvesting operations, fires, and pest infestations, allowing for a detailed forestcarbon analysis. By integrating these processes, the model can provide information on thenet carbon flux of forest ecosystems—measuring the carbon absorbed through photosyn-thesis against that released through respiration, decomposition, and combustion [33]. Thismodeling approach supports the design of forest carbon management strategies, facilitatingthe evaluation of trade-offs between wood supply and forest carbon management withinthe forest sector.1.2.3 Wood Product Carbon ModelingA systematic assessment that includes the climate impacts of HWP is essential to fullyunderstand and maximize the climate change mitigation of the forest industry. ExistingWPCMs achieve this integration based on two principal functions: (1) tracking HWPcarbon stock over time and (2) calculating HWP substitution effects [9, 31]. One commonway to build the first function is to use half-life parameters to estimate the time that halfof the carbon in the HWP pools returns to the atmosphere due to decay[27]. These half-life values are standardized by the IPCC for three key HWP categories, 35 years for sawnwood, 25 years for wood panels, and 2 years for paper [27]. The second function calculatesthe substitution effect of HWPs using displacement factors, which quantify the reduction ofGHG emissions achieved by substituting non-wood products or energy sources with wood-based alternatives [57]. Displacement factors are calculated based on life cycle assessments(LCA), a framework for analyzing environmental impacts throughout product life cycles[25]. These factors show the important role of HWPs not only in carbon storage but also intheir greater climate change mitigation potential by substituting GHG-intensive materialsand energy sources. Specifically, the national average displacement factors in Canada are2.1 tC/tC for sawn wood and 2.2 tC/tC for panels [57]. These values are estimated by61.2. Forest Modelingreferencing existing LCA studies that compare GHG emissions from wood products tothose from alternative materials like steel and concrete in Canadian construction. Thesereferenced studies assumed functional equivalence between materials, considered emissionsup to the construction phase, used national average data, and treated displacement factorsas constants [57].A common method for deterministically modeling the flow of carbon from harvestedwood into various product pools is through the use of allocation distributions. Thesedistributions define the percentages of harvested timber allocated to different productcategories—such as lumber, plywood, paper, and energy production—based on historicaleconomic data and regional industry practices [9, 31]. This approach enables a structuredassessment of carbon storage and emissions associated with various types of harvested woodproducts, facilitating more accurate evaluations of their role in forest carbon managementstrategies.1.2.4 Growth and Yield ModelingForecasting forest growth and yield is an important component of forest modeling [69].GYM provides a quantitative framework for predicting the development of forest standsover time. This modeling is important to understand how forests grow and respond tovarious environmental conditions and management practices [69]. The essence of growthand yield modeling lies in its ability to simulate the detailed processes of tree growthand mortality within a forest ecosystem. By integrating principles from botany, ecology,mensuration, biometrics, and forest sciences, growth and yield models allow foresters,researchers, and policymakers to make informed and sustainable decisions in many areas,including analysis of timber supply and silviculture planning [18]. The output from GYMsis typically presented as tables or curves, which detail the change in commercial harvestingvolume of forest stands over designated time frames (Figure 1.2), often delineated by species[68]. These data are essential to building forest management and carbon models [6]. InBC, the Table Interpolation Program for Stand Yields (TIPSY) and the Variable DensityYield Projection (VDYP) are two major tools for producing timber yield projections formanaged and natural stands, respectively [18].1.2.5 Forest Carbon Stock and Net EmissionThe total forest carbon stock is the sum of the carbon stored within different carbonpools, such as biomass, DOM, HWPs, which is an important indicator for evaluatingthe role of the forest sector in mitigating climate change. A key consideration in forestcarbon management is the trade-off between maximizing wood supply and carbon stock[35]. Forest management strategies such as prolonging rotation ages, reducing harvestintensity, and adopting no-harvest conservation approaches can increase carbon stock butlead to a decrease in timber supply [1]. Net forest carbon emission is the sum of total carbon71.3. Forest Carbon Management Modeling FrameworkFigure 1.2: Abstract timber yield curve example.emitted from the forest ecosystem and HWPs minus carbon capture from forest growthand the substitution effect of HWPs, which is another essential indicator for evaluating theclimate change mitigation potential in the forest sector. In the context of climate changemitigation, prioritizing the minimization of net forest carbon emissions should be the targetset to maximize the positive climate impact of the forest sector on GHG reduction. Studiessuch as those by Xu [70] and Smyth [59] have modeled the climate mitigation potentialof BC’s forest sector by focusing on reducing net forest carbon emissions, highlightingminimizing this indicator as a practical management goal.1.3 Forest Carbon Management Modeling FrameworkTo evaluate the impact of forest management practices on the carbon dynamics of theforest sector, compare the trade-off between wood supply and forest carbon management,and implement optimal forest management strategies to achieve both economic and climategoals, it is essential to build a robust forest carbon management modeling framework thatintegrates carbon indicators (e.g., total forest carbon stock and net forest carbon emis-sion) into SFMMs by connecting them with FCBMs and WPCMs. It is possible to pursuesimilar goals without using the SFMM by manually creating numerous forest managementscenarios, repeatedly running carbon models, and comparing the outputs across scenar-81.3. Forest Carbon Management Modeling Frameworkios. However, this approach is time-consuming and labor-intensive. In contrast, the forestcarbon management modeling framework—integrating multiple forest models—enables ef-ficient identification of optimal management plans that satisfy various objectives and con-straints through optimization algorithms. Traditionally, maximization of wood supply isset as the objective function of the linear programming problems in many SFMMs. In thelast two decades, several studies have been conducted to maximize forest carbon stock asthe objective function to optimize the positive climate impact of the forest sector.Initially, [41] in 2003 integrated carbon indicators into their SFMM by introducingconversion factors from their FCBM to directly calculate the amount of biogenic carbonbased on the volume of commercial wood and soil carbon separately. Later, [7] refinedthis method by setting forest ecosystem carbon storage maximization as an objective func-tion. However, their approach only considers two general carbon pools: biomass and soil.Their approach also approximates the values of each pool using general conversion factors,simplifying the complex forest carbon cycle and leading to inaccuracies in the ecosystemcarbon estimation [7].Building on previous research, [26, 47] proposed an innovative approach using CBM-CFS3 to generate carbon yield curves. These curves represent changes in the forest carbonstock in various pools, including softwood and hardwood biomass (bark, stemwood, fo-liage, branches, and roots), DOM (coarse woody debris, litter from the forest floor anddead roots), and snags (stems and snag branches). An example of these curves is illus-trated in Figure 1.3. In [26, 47], the generated carbon yield curves are built into theirSFMMs to model the temporal dynamics of ecosystem carbon stocks for different standtypes. Subsequently, the objective function in SFMMs is set to maximize the carbon stocksof the forest ecosystem. However, their approach does not account for the carbon stock andthe substitution effects of HWP in optimization problems. To the best of our knowledge,no studies have set the objective of maximizing the total carbon stock of the forest sys-tem, including both the ecosystem and the HWP carbon stocks, as an objective function.Similarly, no studies have aimed to minimize the net carbon emissions of the entire forestsector, considering the combined ecosystem and the HWP net emissions as an optimizationgoal. These gaps highlight opportunities to advance forest carbon management modelingand optimization approaches. Meanwhile, the carbon yield curve method described in[26, 47] can be potentially improved to find optimal management strategies to maximizethe total forest carbon stock or minimize net forest carbon emission while meeting woodsupply targets.1.3.1 Modeling Framework OverviewDuring the literature review, the carbon yield curve method developed by [26, 47] demon-strates the capability to integrate carbon indicators to SFMM to optimize the climatechange mitigation potential of the forest sector in BC. However, these studies did not91.3. Forest Carbon Management Modeling FrameworkFigure 1.3: Abstract carbon yield curve example.include the comparison of carbon modeling outputs from their SFMMs against carbonmodeling outputs from their FCBM, which are used to create their carbon yield curves.This stage is essential to examine the reliability of their forest carbon management model-ing framework to ensure the credibility of any recommendations for management decisions.This study aims to apply, improve, and validate the carbon yield curve method pre-viously proposed by [26, 47]. This framework was further enhanced by systematicallyintegrating different forest models (GYM, SFMM, FCBM, and WPCM). By developinga robust forest carbon management modeling framework, this research seeks to provideguidelines to optimize the climate change mitigation potential of the forest sector in BC.Carbon indicators for total forest carbon stock and net forest carbon emissions havebeen calculated and built into the SFMM with the carbon yield curve method. We devel-oped a rigorous comparison phase to compare the carbon modeling outputs directly fromSFMM against the carbon modeling outputs of FCBM as a reference. This comparisoncan test if the SFMM can replicate the carbon simulation results in libcbm. In doing so,our objective is to provide methods and results that can provide insights into effectiveand sustainable forest carbon management strategies, helping to achieve the GHG reduc-tion goals of BC. The forest carbon management modeling framework developed in thisstudy is scripted in Python 3.10. All scripts, from model construction to data analysis, are101.4. Research Questionspublished on msc walter yan to ensure transparency and replicability.1.4 Research QuestionsThis study aims to explore the central question.How to build a forest carbon management modeling framework to optimizethe climate change mitigation potential of the BC forest sector?The study is structured into the following four subquestions to address this centralquestion.1. How to integrate carbon indicators for total forest carbon stock and net forest carbonemission into SFMMs for mathematical optimization?2. What are the differences between the carbon modeling outputs of SFMM versus thecarbon modeling outputs of FCBM as a reference?3. What are the trade-offs between wood supply and forest carbon management in theBC forest sector?4. How do the climate impacts of HWP affect optimal forest carbon managementstrategies?1.5 Thesis OrganizationThis thesis is structured into five chapters, each addressing different aspects of the study:• Chapter 1 (Introduction) provides an overview of climate change, the forest car-bon cycle, the role of BC forestry in GHG mitigation, and various forest models.It also outlines the study’s research questions, objectives, modeling framework, andsignificance.• Chapter 2 (Methods) details the study area, data preparation, and the devel-opment of the mathematical modeling framework. This chapter explains the con-struction and integration of SFMM, FCBM, and WPCM. It also describes modelvalidation, trade-off analysis, and sensitivity analysis.• Chapter 3 (Results) presents the key findings from model simulations and opti-mization. It includes forest inventory analysis, validation results, trade-off analysisbetween wood supply and carbon management, and sensitivity analysis of optimalforest management solutions to HWP climate impacts.• Chapter 4 (Discussion) interprets the findings about both theoretical and prac-tical implications. It explores the study’s limitations, potential improvements, anddirections for future research.111.5. Thesis Organization• Chapter 5 (Conclusion) summarizes the study’s key findings, contributions, andbroader implications. It also provides recommendations for future applications inforest carbon management and sustainable forestry practices in BC.12Chapter 2MethodsThis project builds a forest carbon management modeling framework to identify forestmanagement strategies that can maximize the climate change mitigation potential of theforest sector in BC. This framework integrates a series of forest models to explore theclimate impacts of various forest management strategies within the study area.The study area section introduces the geographic and forest characteristics of the area ofinterest in this study. The modeling framework section provides a review of the modelingprocesses employed, including data preparation, model execution, and carbon modelingoutput comparison. Finally, the experiments section details the design and methods ofexperiments conducted to systematically explore the differences between setting variousobjective functions for mathematical optimization, trade-offs between wood supply andforest carbon management, and the sensitivity of the modeling framework to HWP half-life and displacement effect input parameter values.2.1 Study AreaPrince George TSA is located in the north-central interior of BC, Canada, covering approx-imately 7.97 million hectares [2] (shown 2.1). As one of the largest management units inthe BC province that plays a crucial role in the BC forest sector, this region was selected asthe study area due to its representativeness of the BC interior forests because of its centrallocation, common forest types, the occupied area (15% of the total timber harvesting landbase in BC), and the economic importance for the provincial timber industry [2]. The for-est composition within the Prince George TSA is predominantly coniferous, with lodgepolepine (Pinus contorta) accounting for 49%, spruce (Picea spp.) for 33%, subalpine fir (Abieslasiocarpa) for 9%, Douglas fir (Pseudotsuga menziesii) for 2%, and cedar (Cedrus spp.)for 1%, which are common BC tree species [2]. Prince George TSA mainly encompassestwo Biogeoclimatic Ecosystem Classification (BEC) zones: Sub-Boreal Spruce (SBS) andEngelmann Spruce-Subalpine Fir (ESSF) [61]. The average site index (a measure of forestproductivity) within TSA varies depending on the tree species and the specific locations,ranging from approximately 10 to 20 years [37]. The annual allowable cut level (AAC) forPrince George TSA is 6,935,023 m3/year, representing more than 15% AAC for the entireprovince [22].Approximately 44% of the study area is crown forest land considered acceptable andeconomically feasible for timber harvesting (around 3.10 million hectares), which is called132.2. Modeling Frameworkthe Timber Harvesting Land Base (THLB) [8]. The rest of the area includes regions withlow timber volume, low site productivity, and accessibility challenges (e.g., steep slopes,remote areas lacking road infrastructure) that make them economically unattractive orinfeasible under current market conditions [2]. In addition, some forest areas are excludedfrom THLB due to legal, ecological, or cultural considerations, such as parks, protectedareas (e.g., wildlife habitat), riparian zones (including lakes, rivers, wetlands, and streams),and sites of cultural significance (e.g., Indigenous archaeological sites) [2].2.2 Modeling FrameworkThe building of the integrated model used for this study required the workflow to be brokeninto three distinct sections: Data preparation, model execution, and modeling outputcomparison (Figure 2.2). The three sections of the modeling framework are described indetail in the following sections.2.2.1 Data PreparationThe forest inventory data utilized in constructing the modeling framework for the selectedstudy area were collected, processed, and prepared in the previous study by [6]. Thisdataset was used as input for GYM, SFMM, and FCBM. The inventory data includesdetailed stand-level attributes, such as stand area, age, THLB, leading species composition,site index, biogeoclimatic ecosystem classification (BEC) zones, and so on. Based onthis information, the study area is classified into different analysis units (AUs). The ageand species distribution of unmanaged and managed stands in the study area are furtheranalyzed and presented in Chapter 3. LCA data necessary to parameterize the WPCM,including HWP product half-lives and displacement factors, were gathered from peer-reviewed literature [59].Generate and Integrate Timber Yield CurvesTIPSY and VDYP are two common GYMs that use forest inventory data to generatetimber yield curves to build SFMM for supporting timber supply analyses and forest man-agement planning in BC [19, 21]. TIPSY produces stand-level timber yield curves for tencommonly studied species (e.g., Subalpine Fir and Engelmann spruce in the study area),developed from stand-level height growth data gathered from individual research studies[19]. The growth and yield curves are extrapolated for species not directly studied byadapting the established curves from those ten primary species. VDYP provides growthand yield simulation for naturally regenerated forest stands based on diverse species com-positions and site conditions [21]. Using historical forest inventory and ecological data,VDYP can forecast future stand characteristics but cannot account for management inter-ventions. In this study, we used the timber yield curves generated from [6] for all AUs in142.2. Modeling FrameworkEsri, TomTom, Garmin, FAO, NOAA, USGS, EPA,NRCan, Parks Canada, Esri, CGIAR, USGS0¯ 100 20050 kmStudy AreaEsri, TomTom, FAO,NOAA, USGS, NRCan, Esri,USGSFigure 2.1: Study area indicating the Prince George TSA.152.2. Modeling FrameworkFigure 2.2: The integrated forest carbon management modeling framework. The frameworkis organized into three discrete sections: Data Preparation, Model Execution, and ModelingOutput Comparison. In the Data Preparation stage, forest inventory data from the selectedstudy area are collected and processed using tools such as VDYP, TIPSY, and libcbm(carbon budget model library) to generate model input data, including timber and carbonyield curves. HWP data, such as product allocation distribution, half-life, and displacementfactors, are also gathered to support the development of the WPCM model. The ModelExecution section integrates two models, ws3 and WPCM, to perform optimization underdifferent scenarios with two primary objectives: maximizing total forest system carbonstock (sum of carbon stock in forest ecosystem and HWPs) and minimizing net forestsystem carbon emissions (sum of carbon emissions from the forest ecosystem and HWPsminus the product substitution effect). In the final Modeling Output Comparison stage,optimized outputs from the ws3 model are compared with baseline outputs from the libcbmmodel to assess consistency and performance. Each component is illustrated using distinctsymbols to denote data sources, processes, and outputs within the workflow.162.2. Modeling FrameworkPrince George TSA (TIPSY curves for all managed forest stands and VDYP curves for allforest stands) [6], with a 350-year projection horizon for forest growth.In [6], a VDYP curve is generated for each AU, and a TIPSY curve is generated for eachAU in managed forests. For forest stands that haven’t been harvested before, their growthwill be simulated based on their VDYP yield curve. Once the forest stand is harvested,it will transition to using a TIPSY curve for growth and yield simulation. Finally, 24VDYP curves and 13 TIPSY curves were generated. When building SFMMs, and FCBMs,the concept of development type is introduced to link attribute curves that describe thechange in key characteristics with a specific AU [50]. Each unmanaged AU has only onedevelopment type linked with a VDYP curve. Each managed AU has two developmenttypes linked with a VDYP curve (when the development type’s last-pass disturbance forthe AU is fire) and a TIPSY curve (when the development type’s last-pass disturbance forthe AU is harvest). When the clear-cut is applied on a managed forest stand that has notbeen harvested, its development type will transit from the one with the VDYP curve tothe one with the TIPSY curve.Generate and Integrate Carbon Yield CurvesTo address research question one of this thesis, we adopted and improved the previouscarbon yield curve method developed in [47] to integrate carbon indicators into our SFMM.libcbm, an open-source Python library specifically coded to behave identically to CBM-CFS3, is used in this study for modeling forest ecosystem carbon to ensure SFMM andFCBM are built in the same programming environment, providing easy model integration[11]. libcbm simulates 21 carbon pools in forest ecosystems, divided into two generalcategories: biomass (10 carbon pools) and DOM (11 carbon pools) [11]. The biomasscarbon pool includes merchantable timber volume, foliage, roots, and other componentsfor softwood and hardwood trees (understory vegetation is not included). DOM includessnags and soils with varying decay rates determined by base decay rates, temperaturesensitivity, and proportion transfer to slow pool [58]. libcbm also simulates 52 carbonfluxes in forest ecosystems. Since natural disturbances are not considered in this study,the only emission source assumed for the forest ecosystem is the decay of the DOM pools.Thirty-seven one-hectare forest stands, representing each specific development type,were simulated for growth from age 1 for over 700 years in libcbm without any manage-ment interventions [19, 21]. This simulation provided detailed projections of carbon stocks(tC/ha/year) and fluxes (tCO2/ha/year), which are used as the carbon yield curves [47].The extended simulation horizon ensures that the oldest forest stands in TSA 24 (≃ 500years old) are projected an additional 200 years into the future to align with the planninghorizon outlined in the SFMM.The carbon stock projections for each development type were summed up and aggre-gated into three carbon curves: biomass, DOM, and ecosystem. Similarly, carbon flux pro-172.2. Modeling Frameworkjections were summed up and aggregated into a single curve: net system emission. Theseaggregated carbon yield curves were integrated into SFMM in a manner analogous to tim-ber yield curves, allowing their use as objective functions and constraints for simulationand optimization. The aggregation of the carbon yield curve streamlines computationalrequirements while maintaining the fidelity required to simulate and optimize essentialcarbon indicators within SFMM. Although the research is using aggregated carbon curves,it is feasible to directly integrate detailed carbon curves (e.g., softwood merchantable car-bon) for specific carbon pools or fluxes in the SFMM model, depending on the researchobjectives, providing flexibility to address different research objectives.2.2.2 Model ExecutionBuild the Strategic Forest Management ModelThe Wood Supply Simulation System (ws3) is an open-source Python package designedto address wood supply planning problems using a Model I linear programming approach[62]. This study uses ws3 to take inputs such as forest inventory data, growth and yieldcurves, management actions, transitions, and scenario parameters to construct SFMMfor simulation and optimization. For simulations and optimizations in this study, a timehorizon of 200 years was selected (starting in 2020), divided into 20 periods of 10 yearseach. The Model I linear optimization problem used to achieve objective functions andmeet the constraints for different scenarios in this study was directly adapted from workpresented in [52] (Equation 2.1). As the most common forest management actions used inBC, clear-cutting and planting are the only two management activities applied to foreststands in this study [15]. Even-flow constraints on harvesting volume and area are appliedto each optimization problem constructed in this study, limiting the variation in bothharvesting volume and area to less than 5% between consecutive periods (Equations 2.3and 2.4).max∑i∈Z∑j∈Jicijxij (2.1)s.t.∑j∈Jixij = 1, ∀i ∈ Z (2.2)(1− ϵp)yp1 ≤∑i∈Z∑j∈Jiµijptxij ≤ (1 + ϵp)yp1, ∀p ∈ O′, t ∈ T (2.3)v−ot ≤∑i∈Z∑j∈Jiµijotxij ≤ v+ot, ∀o ∈ O, t ∈ T (2.4)0 ≤ xij ≤ 1, ∀i ∈ Z, j ∈ Ji (2.5)where182.2. Modeling Framework• Z := set of spatial zones• Ji := set of available prescriptions for zone i ∈ Z• O := set of forest outputs• O′ ⊆ O := set of targeted forest outputs• T := the set of periods in the planning horizon• ϵp := admissible level of variation on yield of targeted output p ∈ O′• µijot := quantity of output o ∈ O produced in period t ∈ T by prescription j ∈ Ji inzone i ∈ Z• v−ot := lower bound on yield of output o ∈ O in period t ∈ T• v+ot := upper bound on yield of output o ∈ O in period t ∈ T• cij := objective function contribution of prescription j ∈ Ji in zone i ∈ Z• xij := proportion of zone i ∈ Z on which prescription j ∈ Ji is applied• yp1 :=∑i∈Z∑j∈Ji µijp1xij , i.e. first-period harvest volume for targeted output p ∈O′Build the Wood Product Carbon ModelThe WPCM built in this study has two main functions: (1) tracking the carbon stockand the emission of HWPs made from the timber harvested in the study area during thesimulation horizon; (2) calculation of the substitution effect of HWPs. This study assumes85 percent (a common utilization rate in BC [59]) of harvested wood is processed into twotypes of HWP: paper and solid wood products (e.g., sawn wood and wood panels) [29].This study selects an average wood density (0.46 ton/m3) from [32] and a conversion factorto calculate the carbon content of the wood (0.5 tons of carbon per 1 ton of dry wood) [53](Equation 2.6). Based on historical data on log availability and use in BC in 2020, thisstudy assumes that 50% of the logs produced are allocated to solid wood products and theother 50% are earmarked to make paper [3] (Equations 2.7 and 2.8).Cwood = ρwoodV Ccontent (2.6)Cp = apCwood (2.7)Cs = asCwood (2.8)192.2. Modeling Frameworkas + ap = 1 (2.9)Chwp = Cp + Cs (2.10)where• V := Volume of harvested wood (m3)• ρwood := Density of the wood (ton/m3)• Ccontent := Carbon content of the wood• Cwood := Carbon stock of harvested wood (ton)• Cp := Carbon stock of paper products (ton)• Cs := Carbon stock of solid wood products (ton)• Chwp := Carbon stock of all HWPs (ton)• ap := Allocation factor for paper products• as := Allocation factor for solid wood productsOnce a HWP starts its life cycle, the IPCC standard first-order decay model is usedto calculate the HWP carbon stock change through time [14] (Equation 2.11 and 2.12).The half-life factor for paper products is two years, and that for solid wood products is 30years [14], which are used to calculate the annual decay constants of first-order decay [14](Equations 2.13 and 2.14).Cp(t+ 1) = Cp(t)(1− kp)10 (2.11)Cs(t+ 1) = Cs(t)(1− ks)10 (2.12)kp =ln(2)hlp(2.13)ks =ln(2)hls(2.14)where• Cp(t) := Carbon stock of paper products at the beginning of the period t• Cs(t) := Carbon stock of solid wood products at the beginning of the period t202.2. Modeling Framework• kp := Annual decay constant of first-order decay given in units for paper products• ks := Annual decay constant of first-order decay given in units for solid wood products• hlp := Half-life for paper products in years, hlp = 2 years• hls := Half-life of solid wood products in years, hls = 30 yearsIn this study, HWP carbon emissions are calculated based on the annual changes in car-bon stocks in each HWP pool. Emitted carbon is converted to CO2 as shown in Equation2.15.Ehwp(t+ 1) =4412(Chwp(t+ 1)− Chwp(t)) (2.15)where• Ehwp(t) := CO2 emission of all HWPs in the period t.• Chwp(t) := Carbon Stock of all HWPs in the period t.The substitution effect of HWPs is calculated based on their displacement factors. Inthe previous literature review, the default displacement factor for solid wood products is2.2 tC/tC, while 0 tC/tC for paper [59]. These parameters are used in Equations 2.16 and2.17.Sp = Cpdfp (2.16)Ss = Csdfs (2.17)Shwp = Sp + Ss (2.18)where• Sp := Substitution effect for paper products• Ss := Substitution effect for solid wood products• Shwp := Substitution effect for all HWPs• dfhwp := Displacement factor for paper products, dfp = 0 tC/tC• dfhwp := Displacement factor for solid wood products, dfs = 2.2 tC/tCThe equations described above are used to build the WPCM to calculate the net climateimpact of HWP in each period. This net impact is determined as the difference betweenthe total CO2 emissions from the HWP pools and the substitution effect, as expressed inthe equation to calculate net forest carbon emission below.212.2. Modeling FrameworkMaximize the Total Forest System Carbon StockThe total carbon stock of the forest sector is the sum of the carbon stock of the forestecosystem and HWPs (Equation 2.19). Therefore, the objective is to maximize the totalcarbon stock of the whole forest system, as shown in Equation 2.20.Csys(t) = Ceco(t) + Chwp(t) (2.19)max∑t∈TCsys,t (2.20)where• Csys(t) := Carbon stock of the whole forest system in the period t.• Ceco(t) := Carbon stock of forest ecosystem in the period t.• Chwp(t) := Carbon stock of all HWPs in the period t.Minimize the Net Forest Carbon EmissionThe net carbon emission from the forest sector is the sum of the carbon emission fromthe forest ecosystem and the HWPs minus the substitution effect of the HWPs (Equation2.21). Therefore, the objective function to minimize net carbon emission from the forestsystem is shown below. All emitted carbon and substitution effects are converted to CO2,as shown in Equation 2.22.Esys(t) =4412(Eeco(t) + Ehwp(t)− Shwp(t)) (2.21)min∑t∈TEsys,t (2.22)where• Esys(t) := CO2 emission of the whole forest system in the period t.• Eeco(t) := CO2 emission of the forest ecosystem in the period t.• Ehwp(t) := CO2 emission of all HWPs in the period t.• Shwp(t) := Substitution effect of all HWPs in the period t.222.2. Modeling Framework2.2.3 Modeling Output ComparisonTo address research question two of this thesis, a series of tests are designed to comparecarbon modeling outputs from the ws3 model with reference carbon modeling outputs fromthe libcbm model (Figure 2.2). Although ws3 and libcbm use similar inputs such as for-est inventory, yield curves, and treatment transitions to estimate forest carbon dynamics,they differ fundamentally in the forest carbon modeling mechanism, which can lead todivergent outputs. libcbm includes a built-in carbon accounting framework that explicitlysimulates fluxes between carbon pools and tracks carbon stocks using deterministic logicparametrized by either built-in default or user-override flux logic parameters[11]. In con-trast, ws3 lacks an internal carbon model and instead relies on carbon stock and flux yieldcurves generated from libcbm as an approximation. This proxy approach is assumed towork perfectly when ws3 is simulated with the specific conditions under which the carbonyield curves were generated (e.g., uniform initial stand age (growing from age 0 at timestep 0) and absence of disturbances through the simulation horizon). Any deviation fromthe initial scenario (e.g., increasing harvesting activities) may lead to modeling distortions,which this study evaluates to assess the reliability and applicability of this approximationmethod across varied forest management scenarios.The degree of alignment between the carbon modeling outputs from two models indi-cates the degree to which ws3 can use its carbon yield curves to replicate carbon simulationresults of libcbm under different scenarios. Specifically, minor deviations between ws3 andlibcbm outputs suggest that ws3 can reliably replicate libcbm’s carbon modeling resultswithin the forest carbon management simulation and optimization framework.First, carbon stocks and emissions were estimated directly based on the integratedcarbon yield curves within the ws3 model. Then, harvesting schedules were generatedfrom ws3 after optimization, which serve as input data for the libcbm model to estimatethe referenced carbon stocks and emissions under this management scenario, to comparewith the carbon modeling outputs of ws3.Subsequently, a comparative analysis was performed, directly assessing the alignmentbetween internally calculated carbon modeling outputs from ws3 and the carbon modelingoutputs from libcbm. This analysis thoroughly quantified differences in forest carbon stockand emissions to evaluate the model’s agreement.The comparison analysis was conducted at two spatial scales under different scenariosfor comprehensive analysis: stand-level and landscape-level, providing insights into modelperformance at different spatial resolutions. It is important to note that this comparisonanalysis exclusively focuses on ecosystem carbon dynamics; carbon stocks and emissionsassociated with HWP are not included in the evaluation.232.2. Modeling Framework2.2.4 Stand-level Comparioson AnalysisIn stand-level comparison analysis, a series of scenarios were designed to systematically as-sess and quantify the reliability and potential errors of the carbon yield curve method usedto integrate ws3 and libcbm at the individual forest stand level. Specifically, 37 one-hectareforest stand test models were created for each development type, simulating growth over200 years starting from age 1. These test models were evaluated under several predefinedharvesting scenarios to assess their stand-alone performance, including no-harvesting, sin-gle clear-cut harvesting conducted at different stand ages, and multiple clear-cut harvestingcycles occurring at various intervals.These selected scenarios encompass different harvesting schedules, enabling a compre-hensive evaluation of the reliability and consistency of the carbon yield curve method acrossdiverse management interventions. Additionally, the scenarios provide insights into howforest carbon dynamics are simulated in ws3 and libcbm respond mechanistically to differ-ent harvesting activities. The no-harvesting scenario serves as a baseline, representing thesimulation of ws3 and libcbm on stand-level growth, carbon accumulation, and ecosystememissions without management disturbance. Single clear-cut scenarios at different standages illustrate how the carbon yield curve method simulates one-time disturbances andsubsequent forest recovery processes, capturing both immediate carbon losses and long-term regeneration dynamics. Multiple clear-cut scenarios simulate more complex scenariosof repeated harvest disturbances, enabling a comparison between cyclic harvesting effects,regeneration timing, carbon removal patterns, and biomass recovery cycles. Collectively,these scenarios can explore the range of stock and emission scenarios provided by thecarbon yield curve method across typical forestry management regimes.However, since the results of most test models in each scenario are very similar, we willpresent the results of only one development type (tsa24 1 2403002 204 2423002) withinthe managed forest area as a representative to avoid redundancy in the analysis. Thisdevelopment type represents forest stands located in the Sub-Boreal Spruce (SBS) BECzone, predominantly composed of lodgepole pine (PL, 67%) and spruce (SW, 33%), witha stand density of 1,700 stems per hectare and an average site index of 18.9. The last-passdisturbance for this development type is harvest. The carbon stock and emission simulationresults from ws3 and libcbm were compared and analyzed in each scenario. The results oflibcbm were assumed to provide a benchmark estimate of forest carbon dynamics, servingas a reference for this analysis.2.2.5 Landscape-level Comparison AnalysisThe landscape-level analyses compare the carbon modeling outputs of ws3 and libcbm un-der two extreme scenarios at the landscape level: the no-harvest scenario and the maximize-harvest scenario with even-flow volume and area constraints as case studies, covering allthe results of the modeling, including the harvested area, the harvest volume, the growing242.3. Experimentsstock (refers to the merchantable volume of all living trees in a given forest), the carbonstock and the emission of the forest ecosystem, HWPs, and the total forest system (sumof forest ecosystem and HWPs) under both scenarios.The no-harvest scenario represents the growth of the natural forest within TSA 24,without human intervention. During the 200-year simulation period, no harvesting activi-ties are carried out. This scenario provides a baseline representing natural forest dynamicswithout management intervention, which is essential to ensure that the forest carbon dy-namics represented by libcbm is maintained in ws3’s carbon accumulation and emissionsimulation over time [33] without human disturbance. Conversely, the maximize-harvestscenario is used to compare the libcbm’s handling of intensive forest management con-straints and harvesting practices, simulating the modeled ecosystem and HWP carbonpools under high-intensity management regimes [35].Comparing these two extreme scenarios ensures the reliability of the carbon modelingframework by examining model outputs under boundary conditions. Analyzing these sce-narios allows for capturing the full range of potential forest management outcomes andidentifying inconsistencies or unrealistic behaviors within the modeling framework.2.3 Experiments2.3.1 Trade-off AnalysisIn this research, the epsilon-constraint method is used to create Pareto fronts for quanti-tatively analyzing trade-offs between wood supply and forest carbon management withinthe study area to answer the third research question three of this thesis [40]. To quantifythe trade-offs between these two competing objective functions (woody supply and forestcarbon), the epsilon-constraint method is used to transform this multi-objective probleminto a sequence of single-objective optimization problems. The epsilon-constraint methodoptimizes one objective function while constraining the other objective functions withinpredefined limits. A Pareto front resulting from the epsilon-constraint method is a setof non-dominated solutions in multi-objective optimization problems, visually illustratingthe trade-offs between competing objectives. A non-dominated solution means no othersolution can improve one objective without worsening another. The Pareto front thus helpsus understand clearly how improvements in one objective may compromise others. [40].Two sets of objective functions were compared for this trade-off analysis. The firstset compares maximizing the total wood supply with maximizing the total carbon stockof the forest system. The second set compares maximizing the total wood supply withmaximizing the negative net carbon emission from the forest system. The negative netcarbon emission from the forest system is calculated by multiplying the net carbon emissionby -1, which represents the amount of carbon emission offset by the forest system. Note thatmaximizing the negative net forest carbon emission is equal to minimizing the net forest252.3. Experimentscarbon emission. The reason for setting the first as the objective function in this analysisis to align it with maximizing the total forest carbon stock, so that we are maximizingtwo different objective functions about forest carbon benefits for comparison. A series ofexperiments were conducted by varying the HWP half-lives and displacement factors toevaluate their influence on the shape and position of trade-off curves between the competingobjectives of wood supply and forest carbon emission. The same epsilon-constraint methodis applied for each unique set of these parameters to generate a corresponding trade-offcurve. All resulting trade-off curves are then combined into a single graph for comparisonand analysis. All harvested wood in this analysis is assumed to be made into a single typeof wood product for simplification.For each experiment to create the Pareto front curve (using the comparison of thefirst set of objective functions as an example), the first step is to run SFMM for twooptimization scenarios: maximize total wood supply and maximize the total forest carbonstock. These runs define the endpoints of the Pareto front, with the maximum total woodsupply corresponding to the minimum total forest carbon stock and vice versa. The epsilonvalue is then determined by dividing the range between the maximum and minimum carbonstocks into ten intervals. The constraints are then applied to the optimization problemincrementally, setting the lower boundary of total forest carbon stock using the minimaltotal forest carbon stock added by multiples of the epsilon value (ranging from 0 to 10).For each iteration, the modeling framework runs to maximize the wood supply under thedefined carbon stock constraint. Finally, the Pareto front curve is made where the x-axisrepresents the lower boundary values for total forest carbon stock, and the y-axis showsthe corresponding optimal wood supply.2.3.2 Sensitivity AnalysisTo explore how the climate impacts of HWP affect optimal forest carbon managementplans (research question four in this thesis), extensive experiments are designed and ap-plied to test the sensitivity of optimal solutions given by the forest carbon managementmodeling framework developed in this study to the half-life and the displacement factorof HWP made from the timber harvested from the study area when minimizing the netcarbon emission of the total forest system. Firstly, all harvested wood is assumed to bemanufactured into a single product type. Then, the product’s half-life is adjusted from1 to 200 years with a one-year interval, while its half-life stays constant (with 0 yearsrepresenting the shortest possible half-life for a HWP and 200 years indicating a very longhalf-life found from a previous study [17]). Third, the HWP displacement factor is variedfrom 0 tC/tC to 2.4 tC/tC in increments of 0.1, while its half-life remains constant. Therange spans realistic scenarios from no carbon displacement (0 tC/tC) to high displace-ment scenarios (around 2.4 tC/tC, which typically represents highly effective substitutionof GHG-intensive materials by harvested wood products) [59]. So, there are 5,000 sce-262.3. Experimentsnarios with specific combinations of HWP half-life and displacement factor, representingvarying climate impacts. The modeling framework is run 5,000 times for each scenarioafterward. Finally, all scenarios’ optimal solutions (sum of harvested wood volume acrossthe simulation horizon) are stored, systematically analyzed, and visualized with Python.27Chapter 3Results3.1 Forest InventoryBased on species composition (first two leading species, biogeoclimatic ecosystem classifi-cation BEC zones, and site index of forest stands), the study area is classified into 24 AUs(11 for unmanaged forests (THLB = 0) and 13 for managed forests (THLB = 1) (Table3.1). The species structure and area distribution for unmanaged forests (forests outsideTHLB) and managed forests (forests within THLB) in TSA 24 are summarized in Figure3.1 and Figure 3.2. In unmanaged forests, the species distribution shows that SubalpineFir covers the largest area, followed by Hybrid Spruce, Trembling Aspen, and EngelmannSpruce. In managed forests, the composition shifts notably. Hybrid Spruce is the mostextensive, followed by Lodgepole Pine, Sub-Alpine Fir, and Engelmann Spruce. The agestructure and area distribution for unmanaged forests and managed forests TSA 24 aresummarized in Figure 3.3 and Figure 3.4, respectively. In unmanaged forests, the overallage structure spans a broad range, from very young stands to those reaching up to 500years, with a relatively even distribution of area across the age classes. In contrast, man-aged forests are dominated by a narrower age span, with stands predominantly maturingup to 400 years, and show distinct peaks at certain age intervals.3.2 Stand-level Comparison Analysis3.2.1 No-harvest ScenarioThe results demonstrate a consistency between the ws3 and libcbm models for the sim-ulation of carbon dynamics in different carbon pools and emissions under the no-harvestscenario. As observed in Figures 3.5 and 3.6, the trends in carbon stocks for both modelsfollow closely aligned trajectories, with negligible divergence throughout the simulationperiod. In particular, for the net carbon emission from the ecosystem, the absolute per-centage difference between the results from ws3 and libcbm remains 0.00% for the entiresimulation horizon. For the ecosystem carbon stock, the absolute percentage difference be-tween the results of ws3 and libcbm remains 0.00% during the initial five periods, slightlyincreasing to an average of 0.04% throughout the simulation horizon.283.2. Stand-level Comparison AnalysisBL SX AT SESpecies0100000200000300000400000500000600000700000800000Area (ha)Figure 3.1: Species composition of unmanaged forests in TSA 24. The x-axis displays dom-inant tree species codes: AT = Trembling Aspen (Populus tremuloides), BL = SubalpineFir (Abies lasiocarpa), SE = Engelmann Spruce (Picea engelmannii), and SX = SpruceHybrid (Picea engelmannii × Picea glauca). The y-axis indicates each species’ total un-managed forest area, measured in hectares (ha).SX PL BL SESpecies0.00.20.40.60.81.01.21.41.6Area (ha)1e6Figure 3.2: Species composition of managed forests in TSA 24. The x-axis displays dom-inant tree species codes: PL = Lodgepole Pine (Pinus contorta), SX = Spruce Hybrid(Picea engelmannii × Picea glauca), BL = Subalpine Fir (Abies lasiocarpa), and SE =Engelmann Spruce (Picea engelmannii). The y-axis indicates each species’ total managedforest area, measured in hectares (ha).293.2. Stand-level Comparison Analysis0 100 200 300 400 500Age (year)020000400006000080000100000120000140000Area (ha)Figure 3.3: Age structure distribution of unmanaged forests in TSA 24. The x-axis repre-sents the age classes of the forests, grouped in 10-year intervals (years), while the y-axisindicates the total area occupied by each age class, measured in hectares (ha).0 100 200 300 400Age (year)050000100000150000200000250000300000350000Area (ha)Figure 3.4: Age structure distribution of managed forests in TSA 24. The x-axis representsthe age classes of the forests, grouped in intervals (years), while the y-axis indicates thetotal area occupied by each age class, measured in hectares (ha).303.2. Stand-level Comparison AnalysisTable 3.1: Site information for AUs within the Prince George TSA. AUs areidentified using a numeric coding system (e.g., 2401000), where the first digits representTSA subdivisions, and subsequent digits indicate stand attributes (including BEC zones,site index classes, and species distribution subdivisions). There are two BEC zones (Sub-Boreal Spruce [SBS], Engelmann Spruce-Subalpine Fir [ESSF]) and two timber harvestingland base status (THLB: 0 indicates unmanaged stands excluded from timber harvesting,and 1 indicates managed stands available for harvesting). Stand density is expressed asthe number of trees per hectare. Average species distributions are provided, includingdominant species (Spp1 and Spp2) along with their respective average percentages withineach AU. Site productivity is represented by the site index in meters (SI), indicating thepotential height growth of dominant tree species at a reference age. Additionally, the totalarea occupied by each AU (in hectares) is included.AU BEC THLB Density Spp1 Spp1 (%) SI Spp2 Spp2 (%) Area (ha)2401000 SBS 0 1500 SW 55 9.8 PL 38 5957922402000 SBS 1 1600 SW 55 13.9 PL 38 5712652403000 SBS 1 1600 SW 55 18.0 PL 38 7701772401001 ESSF 0 1300 SE 73 4.6 PL 21 2945742402001 ESSF 0 1400 SE 73 7.8 PL 21 3222672403001 ESSF 1 1500 SE 73 10.7 PL 21 4716152401002 SBS 1 1700 PL 67 13.0 SW 33 4118812402002 SBS 1 1700 PL 67 15.8 SW 33 4394012403002 SBS 1 1700 PL 67 18.9 SW 33 5134252401003 SBS 0 2400 SW 57 8.5 PL 25 1471842402003 SBS 1 2500 SW 57 12.5 PL 25 1518022403003 SBS 1 2500 SW 57 16.5 PL 25 1681852401004 ESSF 0 1400 SE 82 7.9 PL 13 938332402004 ESSF 1 1500 SE 82 10.6 PL 13 1128252403004 ESSF 1 1500 SE 82 13.3 PL 13 1615482401005 SBS 0 1600 PL 62 7.9 SW 31 749642402005 SBS 0 1600 PL 62 10.7 SW 31 769442403005 SBS 0 1600 PL 62 12.8 SW 31 800572401006 SBS 0 1500 SW 55 6.8 FDI 38 740952402006 SBS 0 1500 SW 55 9.8 FDI 38 731152403006 SBS 0 1500 SW 55 12.8 FDI 38 857112401007 SBS 1 1600 SW 55 13.9 FDI 38 693172402007 SBS 1 1600 SW 55 16.9 FDI 38 645212403007 SBS 1 1600 SW 55 19.9 FDI 38 751713.2.2 Harvest ScenarioSingle Clear-cutFigure 3.7, Figure 3.8, and Figure 3.9 show an analysis of the carbon stock and emissionsimulated by ws3 and libcbm models under the application of a single clear-cut event atdifferent periods (period 5, period 10, and period 15). The results indicate that, acrossall scenarios, the simulations of the biomass carbon pool of both models remain closelyaligned. However, a notable deviation emerges in the DOM carbon pool and net forestecosystem carbon emission immediately after the clear-cut is applied, with the magnitude313.2. Stand-level Comparison Analysis0 2 4 6 8 10 12 14 16 18 20Period050100150200250300350Stock (tC)libcbm Ecosystem Stockws3 Ecosystem Stocklibcbm Biomass Stockws3 Biomass Stocklibcbm DOM Stockws3 DOM StockFigure 3.5: Comparison between forest carbon stocks at the stand level under no-harvestscenario.0 2 4 6 8 10 12 14 16 18 20Period202468Emission (tC)libcbm Net Ecosystem Emissionws3 Net Ecosystem EmissionFigure 3.6: Comparison between net forest ecosystem emission at the stand level underthe no-harvest Scenario.of this deviation progressively decreasing in subsequent periods. The results show that thetiming of the clear-cut impacts the degree of deviation: the earlier the clear-cut occurs,the larger the initial divergence.Multiple Clear-cutsIn this experiment, we applied multiple clear-cuts to the forest stand, increasing the num-ber of harvests from 1 to 4. In addition, the rotation time between successive harvests323.2. Stand-level Comparison Analysis0 2 4 6 8 10 12 14 16 18 20Period150200250300350Stock (tC)libcbm Ecosystem Stockws3 Ecosystem Stock0 2 4 6 8 10 12 14 16 18 20Period0255075100125150Stock (tC)libcbm Biomass Stockws3 Biomass Stock0 2 4 6 8 10 12 14 16 18 20Period140160180200220240260Stock (tC)libcbm DOM Stockws3 DOM Stock0 2 4 6 8 10 12 14 16 18 20Period202468Emission (tC)libcbm Net Ecosystem Emissionws3 Net Ecosystem EmissionFigure 3.7: Comparison between carbon stock and emission at the stand level with a singleclear-cut applied in period 5.333.2. Stand-level Comparison Analysis0 2 4 6 8 10 12 14 16 18 20Period180200220240260280300320340Stock (tC)libcbm Ecosystem Stockws3 Ecosystem Stock0 2 4 6 8 10 12 14 16 18 20Period020406080100120140Stock (tC)libcbm Biomass Stockws3 Biomass Stock0 2 4 6 8 10 12 14 16 18 20Period160180200220240260Stock (tC)libcbm DOM Stockws3 DOM Stock0 2 4 6 8 10 12 14 16 18 20Period202468Emission (tC)libcbm Net Ecosystem Emissionws3 Net Ecosystem EmissionFigure 3.8: Comparison between carbon stock and emission at the stand level with a singleclear-cut applied in period 10.343.2. Stand-level Comparison Analysis0 2 4 6 8 10 12 14 16 18 20Period200225250275300325350Stock (tC)libcbm Ecosystem Stockws3 Ecosystem Stock0 2 4 6 8 10 12 14 16 18 20Period020406080100120140160Stock (tC)libcbm Biomass Stockws3 Biomass Stock0 2 4 6 8 10 12 14 16 18 20Period180200220240260Stock (tC)libcbm DOM Stockws3 DOM Stock0 2 4 6 8 10 12 14 16 18 20Period20246810Emission (tC)libcbm Net Ecosystem Emissionws3 Net Ecosystem EmissionFigure 3.9: Comparison between carbon stock and emission at the stand level with a singleclear-cut applied in period 15.353.2. Stand-level Comparison Analysiswas extended for each scenario. Figures 3.10, Figure 3.11, and Figure 3.12 demonstratethat the biomass carbon stock simulation results of ws3 and libcbm remain aligned almostidentically in all harvest scenarios. For net carbon emissions from the forest system, itsvalue is reset to the initial level immediately after each harvest, followed by a gradualdecline until the next harvest. The longer the forest is allowed to grow or regeneratebetween harvests, the smaller the deviation between the ws3 and libcbm simulations be-comes, leading to greater consistency between the models. However, for DOM carbon,increasing the harvest intensity will constantly increase its simulation deviation betweenws3 and libcbm. The more clear-cuts applied in the forest stand, the more DOM carbonwill be overestimated.3.2.3 Landscape-level Comparison AnalysisNo-harvest ScenarioInitially, the volume of forest growing stock in the study area is 7.49 × 108 m3. Thisvolume experiences rapid growth during the first ten decades, peaking at 1.40× 109 m3 inperiod 14, before slightly declining in the last 60 years (Figure 3.13). At first, the totalcarbon stored in the forest ecosystem is 1.39× 109 tons, distributed between the biomassand DOM pools at 4.67 × 108 tons and 9.26 × 108 tons, respectively. During the firstdecade, the DOM carbon stock decreases slightly but then increases gradually throughoutthe simulation period (Figure 3.14). The largest deviation between the models in theDOM carbon pool occurs in the first period, with a difference of 1.27%. This differencedecreases steadily, reaching 0.00% in period 11, before increasing slightly to 0.28% at theend of the simulation. The average percentage difference between the two models is 0.42%for ecosystem carbon stock, 0.41% for biomass carbon stock, and 0.42% for DOM carbonstock. In contrast, the biomass carbon stock exhibits rapid growth in the first 75 years,followed by a slight decline. Figure 3.15 illustrates the results for net carbon emissions fromthe forest ecosystem under the no-harvest scenario, as modeled by both ws3 and libcbm.Initially, the emission starts at a relatively high value of −9.11× 105 tCO2, which rapidlydecreases to −4.25× 106 tCO2 over the first five decades. Subsequently, the sequestrationrate slows, and the emissions gradually increase to −4.03 × 105 tCO2 over the next 15decades.Maximize-harvest ScenarioWhen setting the maximization of harvest volume as an objective function and maintainingan even flow harvest area and volume as constraints, the harvested area remains relativelystable in most periods, fluctuating between 369,000 and 408,000 hectares (Figure 3.16a).The same amount of area is harvested for each period between periods 2-12 (368,873 ha),and the amount increases to 407703 ha for periods 13-20. The harvest volume also stays363.2. Stand-level Comparison Analysis0 2 4 6 8 10 12 14 16 18 20Period150175200225250275300325Stock (tC)libcbm Ecosystem Stockws3 Ecosystem Stock0 2 4 6 8 10 12 14 16 18 20Period020406080100120140Stock (tC)libcbm Biomass Stockws3 Biomass Stock0 2 4 6 8 10 12 14 16 18 20Period140160180200220240260Stock (tC)libcbm DOM Stockws3 DOM Stock0 2 4 6 8 10 12 14 16 18 20Period202468Emission (tC)libcbm Net Ecosystem Emissionws3 Net Ecosystem EmissionFigure 3.10: Comparison between carbon stock and emission at the stand level with twoclear-cuts applied in period 5 and period 15.373.2. Stand-level Comparison Analysis0 2 4 6 8 10 12 14 16 18 20Period160180200220240260Stock (tC)libcbm Ecosystem Stockws3 Ecosystem Stock0 2 4 6 8 10 12 14 16 18 20Period020406080Stock (tC)libcbm Biomass Stockws3 Biomass Stock0 2 4 6 8 10 12 14 16 18 20Period140160180200220240260Stock (tC)libcbm DOM Stockws3 DOM Stock0 2 4 6 8 10 12 14 16 18 20Period202468Emission (tC)libcbm Net Ecosystem Emissionws3 Net Ecosystem EmissionFigure 3.11: Comparison between carbon stock and emission at the stand level with threeclear-cuts applied in period 5, period 11, and period 18.383.2. Stand-level Comparison Analysis0 2 4 6 8 10 12 14 16 18 20Period140160180200220240260Stock (tC)libcbm Ecosystem Stockws3 Ecosystem Stock0 2 4 6 8 10 12 14 16 18 20Period0102030405060Stock (tC)libcbm Biomass Stockws3 Biomass Stock0 2 4 6 8 10 12 14 16 18 20Period120140160180200220240260Stock (tC)libcbm DOM Stockws3 DOM Stock0 2 4 6 8 10 12 14 16 18 20Period4202468Emission (tC)libcbm Net Ecosystem Emissionws3 Net Ecosystem EmissionFigure 3.12: Comparison between carbon stock and emission at the stand level with fourclear-cuts applied in period 4, period 8, period 13, and period 19.393.2. Stand-level Comparison Analysis0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0Period0.00.20.40.60.81.01.21.4Volume (m3)1e9 Growing StockFigure 3.13: Total forest growing stock change under the no-harvest scenario.relatively stable during the simulation horizon. The harvest volume in the first 8 periodsexperiences slight fluctuations and then stays constant between periods 9 and 15 (7.45×107m3) (Figure 3.16b). The constant harvest volume increases to 8.23× 107 m3 in period 16and continues until the end. The growing stock exhibits a continuous declining trend over20 periods. It starts with 6.57× 108 m3 in period 1 and gradually decreases to 3.98× 108m3 in period 20 (around 2% periodic decrease in average) (Figure 3.16c).However, ws3 projects lower values of ecosystem stocks than libcbm during the first 13periods but higher values in the last 7 periods (Figure 3.17. The greatest deviation occursin the previous period (2.20%). In contrast, ws3 initially projects a higher DOM stock,which declines until period 9 before gradually increasing until the end of the simulation.In general, the average percentage differences are 1.04% for the ecosystem stock, 0.06% forthe biomass stock, and 1.17% for the DOM stock, demonstrating that the integration of thecarbon indicator at the landscape level remains robust, even under scenarios of intensiveharvest.On average, the net predicted ecosystem emissions differ by 80.94%, with ws3 generallyestimating higher emissions than libcbm (Figure 3.18). This divergence remains relativelysmall during the first eight periods, with ws3 projecting slightly lower emissions than403.2. Stand-level Comparison Analysis0 2 4 6 8 10 12 14 16 18 20Period0.00.20.40.60.81.01.21.41.6Stock (tC)1e9libcbm Ecosystem Stockws3 Ecosystem Stocklibcbm Biomass Stockws3 Biomass Stocklibcbm DOM Stockws3 DOM StockFigure 3.14: Total forest carbon stock change under the no-harvest scenario.0 2 4 6 8 10 12 14 16 18 20Period4.03.53.02.52.01.51.00.5Emission (tC)1e6libcbm Net Ecosystem Emissionws3 Net Ecosystem EmissionFigure 3.15: Net forest carbon emission change under the no-harvest scenario.libcbm during the first six periods. In the subsequent 12 periods, the divergence becomesincreasingly pronounced, reaching its peak at 100. 47% at the end of the simulation, atwhich point ws3 estimates emissions that are approximately two times higher than thoseof libcbm.413.3. Trade-off AnalysisFigure 3.16: Changes in (a) harvested area, (b) harvest volume, and (c) growing stock overtime under the maximize-harvest volume scenario.3.3 Trade-off Analysis3.3.1 Wood Supply vs Total Carbon StockThe trade-off analysis used the epsilon-constraint method to effectively visualize the re-lationship between the maximization of wood supply and total forest carbon stock (Fig-ure 3.19). The resulting Pareto Fronts exhibit a non-linear inverse relationship betweenthese two competing objectives, with the endpoints representing optimization extremes.Maximizing wood supply corresponds to the lowest total forest carbon stock, while maxi-mizing forest carbon stock results in zero wood supply.For example, in the scenario with a half-life of 30 years, the maximum wood supplyachieved is approximately 1.58 × 109 m3, associated with a total forest carbon stock ofaround 2.40 × 1010 tC. As the carbon stock constraint increases, wood supply declinesalong the curve, reaching approximately 3.0× 1010 tC at the zero wood supply point.Similarly, for hl = 60 years, the curve begins at about 1.58 × 109 m3 of wood volumewith a corresponding carbon stock near 2.48 × 1010 tC. For hl = 90 years, the maximumwood supply is also around 1.58×109 m3, with the starting carbon stock at approximately2.52× 1010 tC.Across the three half-life scenarios, the curves converge from similar harvesting levelswith varied carbon stock toward the same terminal point near 3.0× 1010 tC in the forestcarbon stock and zero harvest volume. The intermediate points on each curve representfeasible trade-offs.3.3.2 Wood Supply vs Negative Carbon EmissionThe trade-off curves in Figure 3.20 illustrate the relationship between maximizing woodsupply and maximizing negative forest carbon emissions, revealing a clear inverse trendbetween these two objectives. In this case, the displacement factor for the single HWP423.3. Trade-off Analysis0 2 4 6 8 10 12 14 16 18 20Period0.00.20.40.60.81.01.2Stock (tC)1e9libcbm Ecosystem Stockws3 Ecosystem Stocklibcbm Biomass Stockws3 Biomass Stocklibcbm DOM Stockws3 DOM StockFigure 3.17: Total forest carbon stock change under the maximize-harvest scenario.0 2 4 6 8 10 12 14 16 18 20Period0.000.250.500.751.001.251.501.752.00Emission (tC)1e6libcbm Net Ecosystem Emissionws3 Net Ecosystem EmissionFigure 3.18: Net forest ecosystem carbon emission under the maximize-harvest scenario.433.4. Sensitivity Analysisderived from all harvested wood is set to zero, meaning there is no substitution effect.The endpoints of the Pareto fronts represent the optimization extremes: maximum woodsupply results in minimum negative net carbon emissions, while maximum negative carbonemissions correspond to zero wood supply.Across all scenarios, the maximum wood supply is approximately 1.58 × 109 m3. Theminimum emissions achieved vary between approximately −1.2 × 109 tCO2 and −0.8 ×109 tCO2, with longer half-lives yielding more negative values. For example, the 30-yearhalf-life curve begins around −1.20× tCO2 and ends approximately −0.16× 109 tCO2 innegative net emissions. In comparison, the 60-year and 90-year half-life curves begin near−1.02 × 109 and −0.85 × 109 m3, respectively, and terminate at the same ending point−0.16× 109 tCO2 with zero wood supply.The trade-off patterns observed in Figure 3.20 closely resemble those in Figure 3.19,where shorter half-lives result in steeper Pareto curves and sharper reductions in woodsupply under tighter emission constraints.Additional trade-off curves are shown in Figure 3.21, representing combinations ofHWP half-lives and displacement factors. Curve names indicate the pairing (e.g., 1.5 60represents a displacement factor of 1.5 tC/tC and a half-life of 60 years). These results showthat the maximum harvest volume ranges from approximately 1.44 × 109 m3 (0.0 30) toover 1.59×109 m3 (e.g., 1.5 55). The minimum emissions achieved vary significantly acrossthe configurations, from around −1.15 × 109 tCO2 (0.0 30) to slightly positive emissionsexceeding 1.15× 109 tCO2 in higher displacement factor and high half-life scenarios (e.g.,1.5 55, 1.5 60).Overall, as the half-life and displacement factor increase, the trade-off curves shifttoward the upper-right portion of the plot and become increasingly horizontal.3.4 Sensitivity AnalysisFigure 3.22 presents a 3D map of the optimal solution, defined as the total harvestedwood volume over 20 periods, across 5,000 scenarios with varying combinations of HWPhalf-lives and displacement factors.The results show a clear relationship between these two parameters and the model’sdecision to harvest. In the dark blue region—corresponding to low half-life and displace-ment factor values (bottom-left corner of the Figure 3.23 surface and Figure 3.23a)—thetotal harvest volume remains at zero. As either parameter increases, the model beginsselecting harvest options, with the total volume rising sharply, forming a “cliff” patternon the surface. In this transitional region (roughly displacement factors between 0.6–1.5tC/tC and half-life between 0-200 years), the harvest volume increases rapidly from 0 toover 1.2× 109 m3, creating an unstable zone with high output sensitivity.Beyond these thresholds, when both the half-life exceeds approximately 100 years and443.4. Sensitivity AnalysisFigure 3.19: Trade-off curves between maximizing wood supply and maximizing total forestcarbon stock with varied HWP half-lives (hl = half-life).Figure 3.20: Trade-off curves between maximizing wood supply and maximizing negativenet carbon emission with varied HWP half-lives (hl = half-life).453.4. Sensitivity Analysis1.0 0.5 0.0 0.5 1.0Emission (tCO2) 1e90.00.20.40.60.81.01.21.41.6Volume (m³)1e9Curves1.0_301.2_501.5_601.2_401.2_301.5_500.0_301.5_550.5_30Figure 3.21: Trade-off curves between maximizing wood supply and maximizing negativenet carbon emission with varied HWP half-lives and displacement factors (curve name =displacement factor + half-life).the displacement factor surpasses 1.0 tC/tC, the harvest volume approaches its upperbound, leveling off around 1.45 × 109 m3—a value nearly identical to the optimal har-vest volume under the maximize-harvest scenario (the yellow region in Figure 3.22 andFigure 3.23a).The side view (Figure 3.23b) isolates the influence of half-life, keeping the displacementfactor constant along the y-axis. Here, total harvest volume remains low when the half-life is below 50 years, but increases sharply between 75–125 years, particularly when thedisplacement factor is high. The total volume reaches over 1.4× 109 m3 when the half-lifeexceeds 150 years with a medium level of displacement factor (around 1.1 tC/tC).The front view (Figure 3.23c) highlights the effect of the displacement factor, withhalf-life held constant on the x-axis. When the displacement factor is below 0.6 tC/tC, theharvest volume stays near 0, even with half-lives up to 200 years. In contrast, displacementfactors above 1.0 tC/tC result in a substantial increase in harvest volume, especially formoderate-to-high half-lives. Once the displacement factor exceeds 1.5 tC/tC, the modelopts for nearly full harvest volume (above 1.4× 109 m3) even when the half-life is 0.463.4. Sensitivity Analysis0255075100125150175200Half-life (years)0.00.20.40.60.81.01.21.41.61.82.02.2Displacement factor0.00.20.40.60.81.01.21.41e9Total harvested volume (m³)0.00.20.40.60.81.01.21.4Total harvested volume (m³)1e9Figure 3.22: 3D mapping of model sensitivity to HWP half-life and displacement factor.25 50 75 100 125 150 175 200Half-life (years)0.00.20.40.60.81.01.21.41.61.82.02.2Displacement factorXY-plane (Top View)25 50 75 100 125 150 175 200Half-life (years)0.00.20.40.60.81.01.21.4Total harvested volume (m³)1e9 XZ-plane (Side View)0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2Displacement factor0.00.20.40.60.81.01.21.4Total harvested volume (m³)1e9 YZ-plane (Front View)0.00.20.40.60.81.01.21.41.6Total harvested volume (m³)1e90.00.30.60.91.21.51.82.12.4Displacement factor0255075100125150175200Half-life (years)Figure 3.23: Orthographic views of the 3D mapping of model sensitivity to HWP half-lifeand displacement factor: (a) top view (XY-plane), (b) side view (XZ-plane), and (c) frontview (YZ-plane).47Chapter 4Discussion4.1 Forest InventoryThe forest inventory analysis in TSA 24 reveals distinct differences in species compositionand age structure between unmanaged (THLB = 0) and managed (THLB = 1) forests.Unmanaged forests are dominated by Subalpine Fir (BL), followed by Spruce Hybrid (SX),Trembling Aspen (AT), and Engelmann Spruce (SE) (Figure 3.1). These forests exhibit adiverse and uneven-aged structure, with stands ranging from young regeneration to over400 years old. This pattern reflects natural disturbance regimes such as fire and suggests alandscape shaped primarily by ecological processes rather than silvicultural interventions.In contrast, managed forests are characterized by a distinct shift in species compositionand age structure. Hybrid Spruce (SX) and Lodgepole Pine (PL) dominate the managedland base (Figure 3.2), indicating strong influence from deforestation and reforestationpractices that prioritize commercially valuable, fast-growing conifers. The age distributionof managed forests is more homogeneous, with a concentration of area in younger and mid-rotation classes (less than 200 years old) and fewer stands in older age classes. This reflectsdecades of harvesting, planting, and stand-replacing treatments aimed at maintaining asustainable and productive timber supply.The differences observed between managed and unmanaged forest areas have directimplications for carbon dynamics. Managed forests may support higher short-term car-bon sequestration rates due to rapid biomass accumulation in young stands, but unman-aged forests can contribute substantially to long-term carbon storage through older, high-biomass stands. Furthermore, unmanaged forests offer important structural complexityand ecological functions that support habitat diversity and long-term ecosystem stability[60].4.2 Stand-level Comparison AnalysisThe stand-level comparison analysis provided a detailed examination of the carbon yieldcurve method used to connect ws3 and libcbm in a single one-hectare forest stand underscenarios with no harvest, single clear-cut, and multiple clear-cuts. This analysis also pro-vided insight into the impact of forest management activities on stand-level forest carbondynamics simulated in ws3 specifically, with comparisons to the carbon modeling outputfrom libcbm serving as a reference.484.2. Stand-level Comparison Analysis4.2.1 No-harvest ScenarioThe stand-level no-harvest scenario shows sustained carbon accumulation in biomass andDOM pools over time. Negative net forest ecosystem carbon emissions throughout thesimulation horizon highlighted the role of the forest as a carbon sink. ws3 carbon modelingoutputs closely matched libcbm results, with deviations averaging below 0.05% (Figure 3.5.This minimal difference highlights the fidelity of carbon yield curve integration for ws3 inmaintaining the carbon dynamics simulated in libcbm. The nearly identical results of bothmodels suggest that the carbon yield curve method is reliable for long-term carbon stockprojections in forest stands without human intervention.4.2.2 Harvest ScenarioSingle Clear-cutSingle clear-cut scenarios show immediate removal of biomass carbon stocks after the clear-cut, followed by recovery phases driven by regrowth. Recovery trajectories varied withharvest timing, with later clear-cuts delaying the peak of biomass carbon recovery. DOMcarbon stock initially increased due to carbon transfer from biomass to the DOM pool, butgradually declined as decomposition outpaced the new carbon inputs. Although the carbonsimulation results from ws3 and libcbm are nearly identical under the no-harvest scenario,deviations primarily emerge in the DOM pool and net forest ecosystem emission whenharvesting activities are applied. These discrepancies can be attributed to the underlyingmechanisms of the ws3 model. In ws3, when a forest stand is clear-cut, ws3 resets theage of the stand to zero, assuming that 100% of biomass is removed from the stand. Themechanism works well for modeling the biomass carbon stock, as the forest biomass andits carbon storage are highly correlated. However, for the DOM carbon pool and the netemission of the forest ecosystem, their carbon yield curves in ws3 have high initial valuesat age zero due to the spin-up process [6], and these values are used immediately afterharvest, causing overestimation of them.This process contrasts with that of libcbm, where DOM carbon accumulates incremen-tally, and harvesting events facilitate carbon transfers from the biomass pool to the DOMpool. When the harvest is postponed, the forest has a longer period to grow or regenerate,leading to greater biomass accumulation and increased carbon flow into the DOM pool andemitted back into the atmosphere eventually. As a result, the peak DOM carbon stock andnet forest ecosystem emission at harvest time will be higher and more closely aligned withthe initial values of the carbon yield curve that ws3 employs to represent DOM carbonstock and net forest emission, thereby reducing deviations at that time. Conversely, if theinterval between successive clear-cutting events is insufficient for forest regrowth, the DOMcarbon stock and net forest emission at harvest will fall below the initial values of their re-spective carbon yield curves, exacerbating deviations. In summary, while the carbon yield494.2. Stand-level Comparison Analysiscurve method effectively simulates biomass carbon dynamics in ws3, it introduces inaccura-cies in the representation of DOM carbon stock and net forest ecosystem carbon emission.These results highlight the sensitivity of the DOM carbon stock and net ecosystem emis-sion modeling deviation in the ws3 model to the timing of clear-cut events, particularlywhen they occur early in the simulation period, with the effect gradually diminishing asthe ecosystem recovers over time.Multiple Clear-cutsIn multiple clear-cut scenarios, repeated harvesting compounded the impacts on forestecosystem carbon dynamics. Each clear-cut results in an immediate reduction in biomasscarbon stocks, with subsequent recovery phases influenced by the timing and frequencyof harvesting. Recovery trajectories for biomass carbon stocks are truncated with shorterintervals between harvests, reflecting diminished regrowth periods and the cumulative de-pletion of biomass reserves over time. For DOM carbon stock, the impact of multipleclear-cuts is more complex. Each harvest event transfers a certain amount of carbon fromthe biomass pool to the DOM pool. The carbon stock DOM initially increases after eachharvest as a result of this influx, but subsequent decomposition gradually reduces thesestocks over time. When clear-cuts occur at shorter intervals, the DOM pool does not haveenough biomass carbon input. This results in lower overall DOM carbon stock in libcbmcompared to scenarios with fewer or more widely spaced harvests. Net ecosystem emis-sion fluctuated between high values immediately after harvest and negative values duringrecovery, reflecting the cyclical nature of carbon fluxes in intensively managed stands.Comparisons between simulations ws3 and libcbm in multiple clear-cut scenarios re-veal greater discrepancies than in single-cut scenarios. These deviations are particularlypronounced in the DOM carbon pool. Same to single-cut scenarios, ws3 assumes that theforest stand resets to age zero after each harvest, using the initial values of the carbonyield curves as starting points for post-harvest carbon stock and flux. Although this ap-proach aligns well with the dynamics of biomass carbon, it leads to elevated DOM carbonstock due to the high initial values of the DOM spin-up [6]. With each successive harvest,the cumulative effects of this assumption become more pronounced, resulting in increasingdeviations between ws3 and libcbm carbon simulation. For net ecosystem emission, thetiming and frequency of clear-cuts also influence the degree of divergence between ws3 andlibcbm. When clear-cuts are spaced further apart, there is more time for forest growth andregrowth, resulting in more biomass carbon flow to the DOM carbon pool and becomingemissions after harvest, reducing discrepancies. In contrast, closely spaced harvests resultin higher deviations due to the lower post-harvest DOM and net forest carbon emission.These findings underscore the need for refinements in ws3 to better account for DOMcarbon dynamics and net ecosystem emissions before and after harvest. Specifically, incor-porating more nuanced modeling of DOM decomposition rates and post-harvest residue504.3. Landscape-level Comparison Analysismanagement could improve the alignment between ws3 and libcbm. Furthermore, extend-ing the carbon yield curve methodology to account for cumulative harvesting impacts andage-related variability in DOM carbon stock and net ecosystem emission would improvethe accuracy of the modeling framework’s carbon simulation in scenarios with intensiveforest management.4.3 Landscape-level Comparison AnalysisThe landscape-level comparison analysis of the carbon yield method was performed bycomparing the outputs of ws3 and libcbm under two contrasting scenarios: no-harvest andmaximize-harvest. These scenarios provided a comprehensive evaluation of the method’sability to simulate the forest carbon dynamics represented in libcbm on the landscapescale. The results demonstrated the reliability and robustness of the carbon yield curvemethod in modeling large-scale forest carbon processes while also identifying areas thatrequire refinement.4.3.1 No-harvest ScenarioIn the no-harvest scenario, the landscape-level comparison analysis highlighted sustainedcarbon accumulation in both biomass and DOM pools over the 200-year simulation horizon.The biomass carbon dynamics mirror the changes observed in the growing stock due to thestrong correlation between the biomass carbon stock and the wood volume of living trees.The forest ecosystem functioned as a persistent carbon sink, with net emission remainingnegative throughout the simulation period, sequestering CO2 from the atmosphere. Thebiomass carbon stocks increased rapidly during the initial simulation periods due to forestgrowth. Meanwhile, the DOM stock exhibited a slower but steady increase driven bythe dynamics of natural litterfall and decomposition. The carbon yield curve methodperformed exceptionally well in this scenario, with deviations from libcbm averaging below0.5%. This close alignment confirmed that the method succeeded in modeling the carbondynamics of unmanaged forests at the landscape scale as represented in libcbm.Without harvesting activities, the carbon modeling outputs of ws3 and libcbm exhibitnearly identical trends, confirming the successful integration of the carbon yield curvesinto the ws3 model (Figure 3.14 and Figure 3.15). Both models show a steady increasein the ecosystem carbon stock during the simulation horizon. However, ws3 consistentlyestimates slightly lower values of ecosystem carbon stocks compared to libcbm. Thistrend is also reflected in the biomass carbon pool. In particular, there is no deviationbetween the simulation results for the net ecosystem emission from ws3 and libcbm duringthe simulation horizon. This close alignment between the two models suggests that ws3can reliably simulate the total carbon dynamics of the ecosystem for unmanaged forestlandscapes in ws3 under the no-harvest scenario.514.3. Landscape-level Comparison Analysis4.3.2 Maximize-harvest ScenarioUnder the maximize-harvest scenario, the simulation applied intensive harvesting whilemaintaining even-flow constraints on both harvested area and volume. As shown in Fig-ure 3.16a and 3.16b, harvested area and volume remained relatively stable across mostperiods, with slight increases in later years potentially reflecting management responsesto regrowth or operational shifts. Meanwhile, the continuous decline in growing stock(Figure 3.16c) indicates that removals consistently exceeded forest regrowth.Carbon modeling outputs from both ws3 and libcbm exhibited consistent trends underthis scenario. Biomass carbon stocks declined steadily due to ongoing harvests, while DOMstock remained relatively stable. Net forest carbon emission, however, showed greatervariability (Figure 3.18).For biomass carbon, both models projected nearly identical declining trajectories, re-flecting the impact of continuous harvest. However, discrepancies emerged in the estimationof DOM stock: libcbm predicted a steady decline, whereas ws3 maintained more stablevalues.The most significant divergence occurred in net ecosystem carbon emission. While themodels agreed perfectly under the no-harvest scenario, substantial differences arose in themaximize-harvest case (Figure 3.18). In particular, ws3 consistently overestimated netemission in the latter half of the simulation horizon, with deviations reaching up to 100%.This likely results from the cumulative effect of how ws3 resets post-harvest stand age tozero, applying initial values of carbon yield curves, which inflate DOM fluxes.Despite these discrepancies, the overall emission trends remain aligned across models.As such, it is still feasible to use ws3 for optimization purposes, provided that the finalcarbon outputs are accurately reported using libcbm results.4.3.3 Comparison to Stand-level AnalysesThe landscape-level comparison analysis findings share several parallels with the stand-levelanalyses, particularly regarding the high alignment of biomass carbon simulations betweenws3 and libcbm and the limitations observed in DOM and net ecosystem emission predic-tions. Similarly to the results at the stand-level, the discrepancies in DOM carbon and netecosystem emission arise primarily from the simplified modeling assumptions used by ws3for post-harvest conditions. However, the DOM carbon discrepancy is less evident at thelandscape level, potentially moderated by large areas of forests that are unmanaged andless intensively managed (ws3’s DOM simulation is more accurate for these forests). Nev-ertheless, the net ecosystem emission discrepancy is magnified at the landscape level dueto the cumulative effects of harvesting in larger areas. Both comparison analyses demon-strate the capacity of the carbon yield curve method to support large-scale forest carbonmanagement modeling and planning. The method facilitates strategic decision-making tobalance timber production and climate mitigation objectives by providing estimates of car-524.4. Trade-off Analysisbon stock in the ecosystem. However, the observed deviations in net ecosystem emissionpredictions highlight the need for model refinements to improve the accuracy of emissionsimulation in ws3 under intensive harvest scenarios at the landscape level.4.4 Trade-off Analysis4.4.1 Wood Supply vs Total Carbon StockThe trade-off analysis clearly illustrates the inherent conflict between maximizing woodsupply and total forest carbon stock, as visualized in the Pareto Fronts generated by theepsilon-constraint method (3.19). The non-linear inverse relationship between these twoobjectives highlights the competing priorities of timber production and climate mitigation.Maximizing wood supply leads to the lowest forest carbon stock, reflecting the immediateloss of biomass carbon due to harvesting. In contrast, prioritizing the total carbon stockof forests results in a no-harvest strategy, emphasizing the importance of standing biomassand undisturbed ecosystems in maximizing forest carbon storage.The role of the half-lives of HWPs in moderating these trade-offs is noteworthy. Short-lived HWPs exacerbate the trade-offs because of their limited carbon retention capacity.Rapid carbon release from short-lived HWPs reduces their ability to offset the reductionin forest carbon stock. This dynamic is reflected in the steeper Pareto Fronts for scenarioswith a 30-year half-life HWP. In contrast, the production of longer-lived HWP reduces theseverity of trade-offs by extending carbon storage beyond the forest ecosystem. The flatterPareto Fronts for scenarios with a 90-year half-life HWP suggest that HWP with extendedcarbon retention capabilities play a better role in mitigating the trade-offs between woodsupply and forest carbon stock. This finding underscores the importance of promotinglong-lived wood products in sustainable forest management and climate change mitigationstrategies.Despite the moderating effect of longer half-lives of the HWP, the analysis confirmsthat maximizing total forest carbon stock inevitably requires a no-harvest approach. Thisoutcome reflects the intrinsic conflict between carbon storage and harvesting activities,as the removal of biomass directly reduces forest carbon stock and limits the ecosystem’scarbon storage potential. These results highlight the need for forest carbon managementstrategies that optimize harvest levels, prioritize long-lived HWPs, and account for trade-offs between economic output and climate objectives.Furthermore, the non-linear nature of the Pareto Fronts indicates that the opportunitycosts of increasing forest carbon stock constraints are not uniform. The sharp declines inwood supply at intermediate points suggest that small increases in forest carbon stock goalscan result in disproportionate reductions in wood production. This observation reinforcesthe importance of carefully balancing forest carbon objectives with timber productionneeds to achieve target outcomes.534.4. Trade-off AnalysisIn conclusion, this trade-off analysis demonstrates the role of HWP half-lives in shapingthe relationship between wood supply and carbon stock. By extending carbon retentionand mitigating trade-offs, long-lived HWPs can enhance the climate benefits of timberharvesting. However, the fundamental conflict between these objectives requires a nuancedapproach to forest management that integrates both economic and climate considerations.These findings provide valuable information for policy-makers and forest managers lookingto balance timber production with climate change mitigation in the BC forest sector.4.4.2 Wood Supply vs Negative Carbon EmissionThe relationship between wood supply and negative carbon emission highlights the complexinterplay between harvest intensity, forest carbon dynamics, and HWP climate impacts.As shown in Figure 3.20, the inverse relationship between these objectives underscoresthe challenges of achieving negative emissions while maintaining high-level wood produc-tion. Maximizing the wood supply at one extreme results in minimal negative emissions,as increased harvesting results in more emissions and reduces the forest ecosystem’s se-questration capacity. In contrast, prioritizing negative carbon emissions leads to a zerowood supply (when the substitution effect is not included), emphasizing the importanceof undisturbed ecosystems in achieving sustained carbon sequestration. Negative carbonemissions are achieved when the combined effects of carbon sequestration in forest ecosys-tems and the substitution effect in HWP exceed the carbon released through decompositionand product decay. The results of the analysis reveal that the intensity of harvesting di-rectly influences the balance between these factors, shaping the potential for achieving andsustaining negative emissions.The role of HWP half-lives in influencing these trade-offs is noteworthy. Short-livedHWPs exacerbate the trade-offs by quickly releasing stored carbon back into the atmo-sphere, as reflected in the steeper Pareto Fronts for scenarios with a 30-year half-life HWP.These steep trade-offs indicate that short-lived HWPs provide limited climate benefits andcannot offset the carbon losses associated with intensive harvesting. On the other hand,longer-lived HWPs, such as construction materials with a 90-year half-life, mitigate trade-offs by extending carbon storage outside the forest ecosystem. The flatter Pareto Frontsfor these scenarios reflect the ability of long-lived HWPs to achieve negative emissionswhile allowing higher levels of wood supply, underscoring their role in reducing the tensionbetween economic and climate goals.The similarity between the trade-off patterns observed in Figure 3.19 and Figure 3.20highlights the inverse relationship between maximizing wood supply and forest carbonbenefits and the important role of HWP carbon storage capacity in shaping these relation-ships. In particular, when substitution effects are excluded in the trade-off analysis forwood supply versus negative forest carbon emission, a similar pattern is repeated betweenthe two trade-off analyses.544.5. Sensitivity AnalysisFigure 3.21 extends this analysis by incorporating both HWP half-lives and displace-ment factors, offering a more comprehensive view of their impacts on the trade-off betweenmaximizing wood supply and negative forest carbon emission and interactions betweenthese parameters. The upward and horizontal shifts in the Pareto Fronts with increasinghalf-lives and displacement factors illustrate the synergistic effects of these factors in bal-ancing wood supply and negative carbon emission. Longer half-lives improve the durabilityof carbon storage in HWPs. At the same time, higher displacement factors amplify thesubstitution benefits by reducing the emission of alternative materials and energy sources.Together, these effects reduce trade-offs between maximizing wood supply and negativecarbon emissions, creating opportunities to align economic and climate objectives.The convergence of trade-offs at higher half-lives and displacement factors in Figure3.21 demonstrates the potential of forest management strategies to achieve both goalssimultaneously. When HWPs combine long-lasting carbon storage capacity with strongsubstitution benefits, the optimal solutions for maximizing negative carbon emission alignclosely with those for maximizing wood supply. This finding reinforces the importance ofpromoting the production and utilization of durable HWPs in forest-based climate strate-gies. It also highlights the need for policy interventions, such as incentives for long-livedproducts and investment in wood-based construction, to fully realize these synergies.In summary, the trade-off analysis between wood supply and negative carbon emis-sion reveals the influence of HWP half-lives and displacement factors in mitigating theinherent tensions between these objectives. Forest managers can reduce trade-offs andalign economic productivity with climate mitigation goals by prioritizing the productionof long-lived HWPs and maximizing their substitution benefits. These findings provide astrong basis for the development of integrated forest management strategies that supportboth sustainable timber production and effective climate change mitigation.4.5 Sensitivity AnalysisThe sensitivity analysis highlights the important role of HWP climate impacts, specificallythe half-life and displacement factor, in determining optimal forest management strategiesto maximize negative carbon emissions from the forest system. The results reveal a stronginteraction between these parameters, demonstrating that higher values enable greateralignment between economic and climate objectives.At low half-lives and displacement factors, the no-harvest strategy emerges as optimal,reflecting the inability of HWP to offset the carbon emissions associated with harvesting.However, as these parameters increase, the optimal harvest level increases, underscoringthe importance of durable long-lived HWPs with effective HWP substitution benefits. Thesharp transition in harvest volumes observed at intermediate parameter values emphasizesthe need for precision in managing this balance. Small changes in either half-life or dis-554.6. Contribution of the Studyplacement factor within this transition range can have disproportionately large impacts onforest management outcomes. It highlights the need to seriously consider carbon forestrydecision-making when HWP’s half-life and displacement factors fall in this unstable region.The three orthographic views provide additional information on the relative impor-tance of these parameters. Although half-life primarily influences the temporal durationof carbon storage, the displacement factor drives immediate climate benefits by replacingemission-intensive materials and energy sources. The strong influence of the displacementfactor, particularly at higher values, highlights its important role in maximizing the climatebenefits of HWPs. However, the climate benefit limitations caused by short-lived HWPs,even with high displacement factors, underscore the need for strategies that optimize bothparameters simultaneously for forest-based climate change mitigation.Notably, the analysis demonstrates that the goals of maximizing timber production andachieving climate mitigation can converge under favorable conditions, such as producingHWP with long half-lives and high displacement factors. This finding provides importantinformation for BC forest policy and practice. It suggests that forest management strategiesthat emphasize the production of long-lived, durable HWPs with strong substitution effectscan reduce trade-offs between economic and climate objectives, creating synergies thatsupport forest carbon management.These findings reinforce the importance of investing in technologies and policies thatimprove the positive climate impact of HWPs. For example, promoting more wood use inconstruction, developing recycling pathways, and prolonging product life can amplify theclimate benefits of HWPs. In addition, efforts to refine displacement factors and optimizetheir application in forest carbon models can enable more precise carbon managementstrategies and improve forest decision-making.In conclusion, the sensitivity analysis underscores the important role of the HWP cli-mate impacts in forest carbon management. By increasing product half-life and displace-ment factor values, it is possible to achieve sustainable harvesting while maintaining strongclimate benefits. These insights provide an important foundation for advancing integratedforest management strategies that align economic productivity with climate mitigationgoals.4.6 Contribution of the StudyThis study contributes to the advancement of forest carbon modeling by building an innova-tive forest carbon management modeling framework for the BC forest sector. It integratesws3 with libcbm through the carbon yield curve method, then links to a WPCM, whichallows simulation and optimization of the carbon dynamics of the whole forest system invarying management scenarios. The research advances and provides an example of the [47]method at both the stand level and the landscape level, demonstrating its effectiveness in564.6. Contribution of the Studycapturing fluctuations in forest ecosystem carbon dynamics in different harvesting strate-gies. The results confirm that the method can replicate libcbm carbon stock estimates inno-harvest and maximize-harvest scenarios at the landscape level, reinforcing its reliabilityin modeling carbon stock of unmanaged and managed forests in BC.A key contribution of this study is the identification of systematic overestimations inpost-harvest carbon dynamics within ws3, particularly DOM stock at the stand level andnet ecosystem emission at the landscape level. The study reveals that ws3 resets the ageof the stand to zero after harvest, using static initial values for the carbon yield curves,leading to inflated DOM carbon stock and exaggerated emission estimates. These devia-tions become more pronounced under high-rotation-frequency harvest scenarios, where thecumulative effect of resetting results in greater discrepancies between ws3 and libcbm insimulating DOM carbon stock and net ecosystem emission over time. By quantifying theselimitations, this research highlights the necessity of redefining post-harvest decompositionmodeling in ws3 to represent real-world carbon fluxes more accurately.Another important contribution of this study is the detailed trade-off analysis betweenwood supply management and forest carbon management, providing quantitative insightsinto how the intensity of harvesting affects total forest carbon stocks, net emissions, andlong-term climate benefits. The study constructs Pareto Frontiers to illustrate these trade-offs, demonstrating that maximizing timber supply leads to lower forest carbon stock andnegative emissions, while prioritizing forest climate benefits may necessitate a no-harveststrategy. In particular, the research identifies that long-lived HWPs (e.g., constructionmaterials with a half-life of 90 years) help mitigate these trade-offs by extending carbonretention beyond the forest ecosystem. The results also emphasize the role of the substitu-tion benefits HWP, showing that higher displacement factors allow economic and climategoals to be aligned more effectively.The study also incorporates a large-scale sensitivity analysis that evaluates 5, 000 dif-ferent combinations of HWP half-lives and displacement factors, mapping their impacton optimal forest carbon management strategies when minimizing net carbon emissionfrom the entire forest system. The findings highlight that increasing HWP half-lives anddisplacement factors can largely reduce trade-offs between timber supply and carbon ben-efits, shifting the optimal solution to achieve a win-win between economic and climatebenefits. These insights underscore the importance of considering the HWP climate bene-fits, promoting long-lived HWPs, and increasing their substitution benefits in forest carbonmanagement. The results also reveal the necessity of incorporating advanced product LCAinto forest carbon modeling.Finally, this research provides strong policy-relevant findings for the BC forest sector,supporting the design of climate-focused forest management strategies. By refining ws3’spost-harvest carbon flux modeling, enhancing HWP tracking mechanisms, and integratingmultiobjective optimization, this study lays the groundwork for future improvements in574.7. Limitations of the Studysustainable forest carbon management.4.7 Limitations of the StudyDespite its contributions, this study has several methodological and modeling limitationsthat should be addressed in future research. One of the primary limitations is the post-harvest carbon reset mechanism in ws3, where the harvested stands are reset to age zero,leading to overestimated DOM carbon stock and net ecosystem emission. This assumptiondoes not accurately reflect the gradual DOM decomposition and the continued carbon cy-cling within harvested stands, which can lead to inflated DOM stock (in the short term)and ecosystem emission estimates (in the long term), especially in intensive harvest sce-narios. Future refinements should incorporate dynamic DOM decomposition modeling tobetter simulate post-harvest carbon stocks and emissions.A key limitation of this study is the exclusion of natural disturbances such as wildfires,insect outbreaks, and extreme weather events, which play a significant role in shaping for-est carbon dynamics. The assumption of a stable and uninterrupted forest growth cyclemay lead to an overestimation of the long-term carbon storage and sequestration and themitigation potential of HWPs. In reality, disturbances can cause sudden and substan-tial carbon losses, transferring carbon from biomass into the DOM pool and atmosphere.Without taking these stochastic events into account, projected carbon benefits can be un-realistically high, resulting in possible misinterpretations of the role of the forest sectorin climate mitigation. Future studies should incorporate dynamic disturbance models tobetter simulate the effects of large-scale disturbances on forest carbon dynamics.Furthermore, the study relies on the carbon yield curve method proposed by [47] in2008, which is static and does not dynamically adjust to environmental changes. Althoughthese carbon yield curves can help ws3 estimate forest carbon efficiently, they are simpli-fied representations of forest carbon dynamics in the natural world. This means that theeffects, disturbances, and changes in forest growth rates due to climate change are notexplicitly captured in the long-term simulation. Given the increasing influence of risingtemperatures, the effects of CO2 fertilization, and changing precipitation patterns on for-est productivity, integrating climate-sensitive growth and yield curves into SFMM wouldimprove the precision of long-term carbon projections.A further limitation of this study is its simplified approach to HWP carbon accounting,which does not fully capture the variability in product allocation and market dynamics.The research assumes that all harvested timber is deterministically allocated into two gen-eral HWP categories with fixed ratios, disregarding fluctuations in product type, produc-tion processes, and market distribution over time. In reality, HWP allocation is influencedby many factors, such as economic demand, technological advancements, and regionalmarket conditions, which can significantly alter the proportion of wood used for long-lived584.7. Limitations of the Studyversus short-lived products. The assumption of fixed allocation ratios may oversimplifythe dynamic interactions between upstream forest management and downstream productmarkets, leading to potential biases in estimating long-term carbon storage and emissions.Future research could improve this by implementing a market-based product allocationfunction, allowing product distributions to change dynamically based on historical marketand economic data.This study also applied IPCC’s first-order decay method to estimate HWP carbonstorage, assuming static half-life values for each product category. However, this simplifiedapproach does not account for variations in product longevity due to reuse, recycling, orlandfill retention. For example, construction lumber can be reused multiple times beforeeventual decay, while paper and packaging materials rapidly decompose or are incinerated.In addition, regional differences in recycling infrastructure and landfill practices can influ-ence the actual decay trajectory of HWPs, altering carbon release patterns over time. Toimprove cy, future research should consider building more detailed product decay functionsbased on dynamic LCA, incorporating regional recycling rates, end-of-life disposal meth-ods, and carbon retention factors from landfills instead of applying fixed half-life values.In addition to carbon storage, the study models HWP substitution effects using fixeddisplacement factors, which oversimplifies the complexity of how HWPs replace fossil-intensive materials or energy sources. In reality, the benefits of substitution vary basedon multiple factors, including the type of wood product, the regional energy mix, and thecarbon intensity of alternative materials and energy sources. For example, the wood usedin long-lived construction can displace steel and concrete, generating significant emissionreductions, whereas bioenergy feedstocks may have lower or even negative displacementeffects if harvested in an unsustainable way. By assuming static displacement values,the study can misestimate the net climate benefits of HWPs under different market andpolicy conditions. Future models should incorporate sector-specific displacement factors,recognizing that different wood products provide different levels of emission displacement.Furthermore, the study treats HWP half-life and displacement factors as independentvariables in sensitivity and trade-off analyses, even though these two factors are interde-pendent. In reality, long-lived HWPs generally have higher displacement factors, as theyremain in use for extended periods while replacing high-carbon materials. Conversely,short-lived HWPs usually provide lower long-term substitution benefits, as their carbonis quickly re-released into the atmosphere. By treating these factors separately, the studycan overstate the range of possible trade-offs and fail to capture synergies between long-lived wood products and enhanced substitution benefits. A more accurate approach wouldinvolve joint probability modeling or integrated optimization techniques that account forthe simultaneous effects of product carbon longevity and material/energy substitution.59Chapter 5ConclusionThis study developed a mathematical modeling framework to simulate and optimize theclimate change mitigation potential of the BC forest sector by integrating SFMM withFCBM with [47]’s method and a WPCM. The research systematically evaluated [47]’smethod at both the stand and the landscape levels, compared the dynamics of forestcarbon in different management scenarios, explored trade-offs between wood supply andforest carbon management, and examined the sensitivity of the optimal model solution tothe climate impacts of HWPs.The results show that the carbon yield curve method works well when simulating theecosystem carbon stock (almost perfect for the biomass stocks) at the stand and land-scape level, especially under no-harvesting or less intensive harvesting scenarios. However,this study identified systematic deviations for the simulation of post-harvest DOM carbonstocks and net emissions within ws3, revealing the need for improved post-harvest decom-position modeling. The trade-off analysis shows that while optimizing wood supply andcarbon benefits inherently conflict, this trade-off can be partially mitigated by increasingHWPs half-life and optimizing their substitution benefits. The sensitivity analysis high-lights the significant influence of HWP half-life and displacement factor on determiningoptimal forest carbon management plans.Beyond methodological contributions, this research provides important information forsustainable forest carbon management and climate policy. This study offers insight intosystematically considering the trade-off between balancing economic and climate objectiveswhen making forest management plans. The findings reinforce the importance of promot-ing long-lived HWPs in construction and extending their carbon retention capabilities toimprove their positive climate impact. Efforts must also be made to increase the HWPsubstitution benefits.Looking ahead, this study underscores the necessity of developing and integrating dy-namic natural disturbance and climate-sensitive growth and yield modeling to improvethe forest carbon management modeling framework developed in this study. Given the in-creasing frequency and intensity of wildfires, insect outbreaks, and extreme weather events,future models must better capture the risks associated with natural disturbances and cli-mate variability to improve the accuracy of estimating forest carbon dynamics. Further-more, more sophisticated HWP allocation and carbon accounting models could improvethe simulation accuracy of HWP climate benefits.60Chapter 5. ConclusionIn conclusion, this research improves the scientific methodology for optimizing forestmanagement strategies in the context of climate change mitigation. Although certainsimplifications remain, the proposed framework offers a scalable and adaptable approachto modeling forest carbon dynamics and informing evidence-based policy decisions. As theglobal push for climate action intensifies, continued refinements to the established forestcarbon modeling framework will be essential in supporting sustainable forest strategiesthat align with economic and climate objectives.61Bibliography[1] Abderrahmane Ameray, Yves Bergeron, Osvaldo Valeria, Miguel Montoro Girona, andXavier Cavard. Forest carbon management: A review of silvicultural practices andmanagement strategies across boreal, temperate and tropical forests. Current ForestryReports, 7(4):245–266, 2021.[2] BC Ministry of Forests. Prince George Timber Supply Area Rationale for AAC Deter-mination. Government Report, British Columbia Ministry of Forests, Lands, NaturalResource Operations and Rural Development, 2017. Available online: https://www2.gov.bc.ca/gov/content/industry/forestry/managing-our-forest-resources/timber-supply-review-and-allowable-annual-cut/allowable-annual-cut-timber-supply-areas/prince-george-tsa [AccessedApril 24, 2024].[3] BC Ministry of Forests. 2020 Major Timber Processing Facili-ties in British Columbia. https://www2.gov.bc.ca/assets/gov/farming-natural-resources-and-industry/forestry/fibre-mills/mill_list_report_2020.pdf, 2020. [Online]. Accessed: Apr. 2, 2024.[4] BC Ministry of Forests. Timber Harvesting Rights - Tree Farm Li-cences (TFL). https://www2.gov.bc.ca/gov/content/industry/forestry/forest-tenures/timber-harvesting-rights/tfl, 2024. [Online]. Accessed: Nov.19, 2024.[5] BC Ministry of Forests. Timber Supply Area Designations. https://www2.gov.bc.ca/gov/content/industry/forestry/managing-our-forest-resources/timber-supply-review-and-allowable-annual-cut/allowable-annual-cut-timber-supply-areas/timber-supply-area-designations,2024. [Online]. Accessed: Nov. 19, 2024.[6] Ce´line Boisvenue, Gregory Paradis, Ian MS Eddy, Eliot JB McIntire, and Alex MChubaty. Managing forest carbon and landscape capacities. Environmental ResearchLetters, 17(11):114013, 2022.[7] Charles P-A Bourque, Eric T Neilson, Chris Gruenwald, Samantha F Perrin, Jason CHiltz, Yvon A Blin, Geoffrey V Horsman, Matthew S Parker, Christie B Thorburn,Michael M Corey, et al. Optimizing carbon sequestration in commercial forests by62Bibliographyintegrating carbon management objectives in wood supply modeling. Mitigation andAdaptation Strategies for Global Change, 12(6):1253–1275, 2007.[8] British Columbia Forest Practices Board. Glossary of Terms. https://www.bcfpb.ca/news-resources/glossary/, 2024. [Online]. Accessed: Dec. 18, 2024.[9] Pau Brunet-Navarro, Hubert Jochheim, and Bart Muys. Modelling carbon stocks andfluxes in the wood product sector: a comparative review. Global Change Biology, 22(7):2555–2569, 2016.[10] Canadian Forest Service. Forest Glossary - Allowable Annual Cut (AAC). https://cfs.nrcan.gc.ca/terms/read/301, 2024. [Online]. Accessed: Apr. 2, 2024.[11] CAT-CFS. libcbm documentation. https://cat-cfs.github.io/libcbm_py/, 2024.[Online]. Accessed: Apr. 2, 2024.[12] George B. Dantzig. Linear Programming 1: Introduction. Princeton University Press,Princeton, NJ, 1963.[13] C Ronnie Drever, Susan C Cook-Patton, Fardausi Akhter, Pascal H Badiou, Gail LChmura, Scott J Davidson, Raymond L Desjardins, Andrew Dyk, Joseph E Fargione,Max Fellows, et al. Natural climate solutions for Canada. Science Advances, 7(23):eabd6034, 2021.[14] HS Eggleston, Leandro Buendia, Kyoko Miwa, Todd Ngara, and Kiyoto Tanabe. 2006IPCC guidelines for national greenhouse gas inventories. 2006.[15] Environmental Reporting BC. Trends in Silviculture in B.C. (1987–2019). https://www.env.gov.bc.ca/soe/indicators/land/silviculture.html, 2021. [Online].Accessed: Mar. 19, 2025.[16] Forest Stewardship Council. Forest Management: Practical tools for thriving forests.https://fsc.org/en/forest-management, 2024. Accessed: 2024-12-03.[17] Aixin Geng, Hongqiang Yang, Jiaxin Chen, and Yinxing Hong. Review of carbonstorage function of harvested wood products and the potential of wood substitutionin greenhouse gas mitigation. Forest Policy and Economics, 85:192–200, 2017.[18] Government of BC. Growth and Yield Modelling. https://www2.gov.bc.ca/gov/content/industry/forestry/managing-our-forest-resources/forest-inventory/growth-and-yield-modelling, 2024. [Online]. Accessed: Apr.2, 2024.[19] Government of BC. Table Interpolation Program for StandYields (TIPSY). https://www2.gov.bc.ca/gov/content/industry/63Bibliographyforestry/managing-our-forest-resources/forest-inventory/growth-and-yield-modelling/table-interpolation-program-for-stand-yields-tipsy,2024. [Online]. Accessed: Apr. 2, 2024.[20] Government of BC. Sustainable Forest and Timber Management. https://www2.gov.bc.ca/gov/content/industry/forestry/managing-our-forest-resources/silviculture/timber-management-goals, 2024. [Online]. Accessed: Apr. 2, 2024.[21] Government of BC. Variable Density Yield Projection(VDYP). https://www2.gov.bc.ca/gov/content/industry/forestry/managing-our-forest-resources/forest-inventory/growth-and-yield-modelling/variable-density-yield-projection-vdyp,2024. [Online]. Accessed: Dec. 18, 2024.[22] Government of BC. Allowable Annual Cut - Timber Supply Areas. https://www2.gov.bc.ca/gov/content/industry/forestry/managing-our-forest-resources/timber-supply-review-and-allowable-annual-cut/allowable-annual-cut-timber-supply-areas, 2025. [Online]. Accessed: Mar. 10,2025.[23] Government of Canada. Canada’s Climate Plan Overview. https://www.canada.ca/en/services/environment/weather/climatechange/climate-plan/climate-plan-overview.htm, 2024. [Online]. Accessed: Apr. 2, 2024.[24] Eldon A Gunn. Models for Strategic Forest Management. In Handbook of OperationsResearch in Natural Resources, pages 317–341. Springer, 2007.[25] Michael Z Hauschild, Ralph K Rosenbaum, and Stig Irving Olsen. Life cycle assess-ment, volume 2018. Springer, 2018.[26] Chris R Hennigar, David A MacLean, and Luke J Amos-Binks. A novel approach tooptimize management strategies for carbon stored in both forests and wood products.Forest Ecology and Management, 256(4):786–797, 2008.[27] Takahiko Hiraishi, Thelma Krug, Kiyoto Tanabe, Nalin Srivastava, Baasansuren Jam-sranjav, Maya Fukuda, and Tiffany Troxler. 2013 Revised Supplementary Methods andGood Practice Guidance Arising from the Kyoto Protocol. Intergovernmental Panelon Climate Change Switzerland, 2014.[28] John T Houghton. Climate change 1995: The science of climate change: contributionof working group I to the second assessment report of the Intergovernmental Panel onClimate Change, volume 2. Cambridge University Press, 1996.[29] IPCC. 2019 Refinement to the 2006 IPCC Guidelines for Na-tional Greenhouse Gas Inventories. https://www.ipcc.ch/report/64Bibliography2019-refinement-to-the-2006-ipcc-guidelines-for-national-greenhouse-gas-inventories/,2019. [Online]. Accessed: Dec. 3, 2024.[30] IPCC. History of IPCC. https://www.ipcc.ch/about/history, 2024. [Online].Accessed: Apr. 2, 2024.[31] G Jasinevicˇius, M Lindner, K Pingoud, and M Tykkylainen. Review of models forcarbon accounting in harvested wood products. International Wood Products Journal,6(4):198–212, 2015.[32] Elma I. Kennedy. Strength and Related Properties of Woods Grown in Canada, 1965.[Online]. Accessed: Apr. 2, 2024.[33] WA Kurz, CC Dymond, TM White, G Stinson, CH Shaw, GJ Rampley, C Smyth,BN Simpson, ET Neilson, JA Trofymow, et al. CBM-CFS3: A model of carbon-dynamics in forestry and land-use change implementing IPCC standards. EcologicalModelling, 220(4):480–504, 2009.[34] Werner A Kurz, CH Shaw, Celine Boisvenue, G Stinson, J Metsaranta, David Leckie,Andrew Dyk, Caroline Smyth, and ET Neilson. Carbon in Canada’s boreal forest—asynthesis. Environmental Reviews, 21(4):260–292, 2013.[35] TC Lemprie`re, WA Kurz, EH Hogg, C Schmoll, GJ Rampley, D Yemshanov,DW McKenney, R Gilsenan, A Beatch, D Blain, et al. Canadian boreal forests andclimate change mitigation. Environmental Reviews, 21(4):293–321, 2013.[36] James MacCarthy, Alexandra Tyukavina, Mikaela Weisse, and Nancy Harris.Canada’s Record-Breaking 2023 Wildfires Released Nearly 4 Times More Carbon thanGlobal Aviation. https://www.wri.org/insights/canada-wildfire-emissions,2024. [Online]. Accessed: Dec. 3, 2024.[37] Shirley Mah and Gordon D. Nigh. SIBEC Site Index Estimates in Support of ForestManagement in British Columbia. Technical Report 004, British Columbia Ministryof Forests, Research Branch, Victoria, BC, 2003.[38] Yadvinder Malhi, Patrick Meir, and Sandra Brown. Forests, carbon and global climate.Philosophical Transactions of the Royal Society of London. Series A: Mathematical,Physical and Engineering Sciences, 360(1797):1567–1591, 2002.[39] Susana Mart´ın-Ferna´ndez, Eugenio Mart´ınez-Falero, and Miguel Valent´ın-Gamazo.Optimization methods to identify the best management plan. Quantitative Techniquesin Participatory Forest Management, pages 421–498, 2013.[40] George Mavrotas. Effective implementation of the ε-constraint method in multi-objective mathematical programming problems. Applied Mathematics and Compu-tation, 213(2):455–465, 2009.65Bibliography[41] F.R. Meng, C.P.A. Bourque, S.P. Oldford, D.E. Swift, and H.C. Smith. Combiningcarbon sequestration objectives with timber management planning. Mitigation andAdaptation Strategies for Global Change, 8(4):371–386, 2003. doi: 10.1023/B:MITI.0000005615.40897.dc.[42] Gert Jan Nabuurs, Omar Masera, Kenneth Andrasko, Pablo Benitez-Ponce, RizaldiBoer, Michael Dutschke, Elnour Elsiddig, Justin Ford-Robertson, Peter Frumhoff,Timo Karjalainen, Olga Krankina, Werner A. Kurz, Mitsuo Matsumoto, WalterOyhantcabal, Ravindranath N.H., Maria Jose´ Sanz Sanchez, and Xiaquan Zhang.Forestry. In B. Metz, O.R. Davidson, P.R. Bosch, R. Dave, and L.A. Meyer, editors,Climate Change 2007: Mitigation. Contribution of Working Group III to the FourthAssessment Report of the Intergovernmental Panel on Climate Change, chapter 9,pages 543–584. Cambridge University Press, Cambridge, United Kingdom and NewYork, NY, USA, 2007.[43] Natural Resources Canada. Carbon Budget Model. https://natural-resources.canada.ca/climate-change/climate-change-impacts-forests/carbon-accounting/carbon-budget-model/13107, 2024. [Online]. Accessed:Apr. 2, 2024.[44] Natural Resources Canada. Climate Change Impacts of Forests - Mit-igation. https://natural-resources.canada.ca/climate-change/climate-change-impacts-forests/mitigation/13097, 2024. [Online]. Accessed:Nov. 19, 2024.[45] Natural Resources Canada. How Much Forest Does Canada Have?https://natural-resources.canada.ca/our-natural-resources/forests/state-canadas-forests-report/how-much-forest-does-canada-have/17601,2024. [Online]. Accessed: Dec. 3, 2024.[46] Natural Resources Defense Council. Global Warming 101. https://www.nrdc.org/stories/global-warming-101, 2023. [Online]. Accessed: Apr. 2, 2024.[47] Eric T Neilson, David A MacLean, Fan-Rui Meng, Chris R Hennigar, and Paul AArp. Optimal on-and off-site forest carbon sequestration under existing timber supplyconstraints in northern New Brunswick. Canadian Journal of Forest Research, 38(11):2784–2796, 2008.[48] NOAA National Centers for Environmental Information. Global Climate Report -Annual 2020. https://www.ncei.noaa.gov/access/monitoring/monthly-report/global/202013#:~:text=The%20decadal%20global%20land%20and,C%20(%2B1.12%C2%B0F), 2020. [Online]. Accessed: Nov. 14, 2024.66Bibliography[49] Yude Pan, Richard A Birdsey, Jingyun Fang, Richard Houghton, Pekka E Kauppi,Werner A Kurz, Oliver L Phillips, Anatoly Shvidenko, Simon L Lewis, Josep GCanadell, et al. A large and persistent carbon sink in the world’s forests. Science, 333(6045):988–993, 2011.[50] Gregory Paradis. ws3 Package Documentation: 2. Wood Supply Models. https://ws3.readthedocs.io/en/dev/Chapt1.html#development-types, 2024. [Online].Accessed: Nov. 27, 2024.[51] Gregory Paradis, Luc LeBel, Sophie D’Amours, and Mathieu Bouchard. On the risk ofsystematic drift under incoherent hierarchical forest management planning. CanadianJournal of Forest Research, 43(5):480–492, 2013.[52] Gregory Paradis, Mathieu Bouchard, Luc LeBel, and Sophie D’Amours. A bi-levelmodel formulation for the distributed wood supply planning problem. Canadian Jour-nal of Forest Research, 48(2):160–171, 2018.[53] Jim Penman, Michael Gytarsky, Taka Hiraishi, Thelma Krug, Dina Kruger, RiittaPipatti, Leandro Buendia, Kyoko Miwa, Todd Ngara, Kiyoto Tanabe, et al. Goodpractice guidance for land use, land-use change and forestry. 2003.[54] Stephen P Robbins, Rolf Bergman, Ian Stagg, and Mary Coulter. Management. Pear-son Australia, 2014.[55] Stephen R Shifley, Hong S He, Heike Lischke, Wen J Wang, Wenchi Jin, Eric JGustafson, Jonathan R Thompson, Frank R Thompson, William D Dijak, and JianYang. The past and future of modeling forest dynamics: from growth and yield curvesto forest landscape models. Landscape Ecology, 32(7):1307–1325, 2017.[56] Kenneth E Skog and Geraldine A Nicholson. Carbon cycling through wood products:the role of wood and paper products in carbon sequestration. Forest Products Journal,48(7):75–83, 1998.[57] Carolyn Smyth, Greg Rampley, Tony C Lemprie`re, Olaf Schwab, and Werner A Kurz.Estimating product and energy substitution benefits in national-scale mitigation anal-yses for Canada. GCB Bioenergy, 9(6):1071–1084, 2017.[58] Carolyn Esther Smyth, JA Trofymow, WA Kurz, CIDET Working Group, et al. De-creasing uncertainty in CBM-CFS3 estimates of forest soil carbon sources and sinksthrough use of long-term data from the Canadian Intersite Decomposition Experiment.Victoria: Pacific Forestry Centre, Canadian Forest Service, 2010.[59] CE Smyth, Z Xu, TC Lemprie`re, and WA Kurz. Climate change mitigation in BritishColumbia’s forest sector: GHG reductions, costs, and environmental impacts. CarbonBalance and Management, 15:1–22, 2020.67Bibliography[60] Ira J Sutherland, Elena M Bennett, and Sarah E Gergel. Recovery trends for multipleecosystem services reveal non-linear responses and long-term tradeoffs from temperateforest harvesting. Forest Ecology and Management, 374:61–70, 2016.[61] UBC Centre for Forest Conservation Genetics. About BEC and BGC Units. https://cfcg.forestry.ubc.ca/resources/cataloguing-in-situ-genetic-resources/about-bec-and-bgc-units/, 2025. [Online]. Accessed: Mar. 10, 2025.[62] UBC-FRESH. ws3 - Wood Supply Simulation System. https://github.com/UBC-FRESH/ws3, 2024. [Online]. Accessed: Nov. 27, 2024.[63] United Nations. Causes and Effects of Climate Change. https://www.un.org/en/climatechange/science/causes-effects-climate-change, 2023. [Online]. Ac-cessed: Apr. 2, 2024.[64] United Nations. What Is Climate Change? https://www.un.org/en/climatechange/what-is-climate-change, 2024. [Online]. Accessed: Apr. 2, 2024.[65] United Nations Climate Change. What is the United Nations Framework Con-vention on Climate Change? https://unfccc.int/process-and-meetings/what-is-the-united-nations-framework-convention-on-climate-change,2024. [Online]. Accessed: Apr. 2, 2024.[66] United Nations Climate Change. History of the Convention. https://unfccc.int/process/the-convention/history-of-the-convention#Essential-background,2024. [Online]. Accessed: Apr. 2, 2024.[67] United Nations Climate Change. The Paris Agreement. https://unfccc.int/process-and-meetings/the-paris-agreement, 2024. [Online]. Accessed: Apr. 2,2024.[68] U.S. Forest Service. CENTRAL HARDWOOD NOTES: Introduction to ForestGrowth And Yield. https://www.nrs.fs.usda.gov/pubs/ch/ch_notes/ch_5_01.pdf, 2024. [Online]. Accessed: Nov. 19, 2024.[69] Aaron R Weiskittel, David W Hann, John A Kershaw Jr., and Jerome K Vanclay.Forest growth and yield modeling. John Wiley & Sons, 2011.[70] Zhen Xu, Carolyn E Smyth, Tony C Lemprie`re, Greg J Rampley, and Werner AKurz. Climate change mitigation strategies in the forest sector: biophysical impactsand economic implications in British Columbia, Canada. Mitigation and AdaptationStrategies for Global Change, 23(2):257–290, 2018.68
Thesis/Dissertation
eng
Forestry
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Paradis, Gregory
A mathematical modeling framework to optimize the climate change mitigation potential of the forest sector in British Columbia, Canada
Text