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A macroscale evaluation of forest management in the boreal forest of Canada : linking data and models Lochhead, Kyle Douglas 2019

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A MACROSCALE EVALUATION OF FOREST MANAGEMENT IN THE BOREAL FOREST OF CANADA: LINKING DATA AND MODELS by Kyle Douglas Lochhead B.Sc., Forestry, University of Alberta, 2008 M.Sc., Forest Biology and Management, University of Alberta, 2011 A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (FORESTRY) THE UNIVERSITY OF BRITISH COLUMBIA (VANCOUVER) March 2019 © Kyle Douglas Lochhead, 2019ii  The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled: A Macroscale Evaluation of Forest Management in the Boreal Forest of Canada: Linking Data and Models  submitted by Kyle Douglas Lochhead  in partial fulfillment of the requirements for the degree of Doctor of Philosophy In Forestry  Examining Committee: Dr. Gary Q. Bull Co-supervisor  Dr. Valerie LeMay Co-supervisor Dr. Steven Northway Supervisory Committee Member Dr. Bruce Larson University Examiner Dr. Daniel Moore University Examiner  Additional Supervisory Committee Members: Dr. Olaf Schwab Supervisory Committee Member  iii  Abstract Climate change is altering the nature and condition of vast areas in the boreal forest of Canada. Vulnerabilities associated with drought, fire and forest health are being observed across thousands of kilometres or macroscales. There are great uncertainties in the ecological responses across this macroscale, along with uncertainties in policy and economic responses that need to translate effectively between local and macroscale decision makers. Addressing these uncertainties requires coherent economic and policy analyses that are consistent over different spatio-temporal scales. To meet the challenges, multi-source data must be linked to provide forest information at higher spatial scales, and systems linking ecological and economic information are also needed. Given this informational need, my research question was: How can we improve the linkages of multi-source ecological and economic data to evaluate forest management decisions at macroscales? First, to improve the ecological information, I evaluated alternative multivariate methods to spatially link multi-source data and models of forest attributes for macroscale analysis. The goal was to obtain logical consistency across variables of interest, while improving accuracy and computational simplicity to the analysis. Second, to improve the economic information fed into the analysis, I used price data to develop a multivariate method for generating price information at a finer temporal scale which remains consistent with longer-term price scenarios from global land use models. Third, and finally, I developed a macroscale decision support system (quantify, query and queue, Q3) that demonstrates how to link spatial and temporal ecological and economic information to a forest land-base which is subject to climate change vulnerabilities, the western boreal forest of Canada. As an illustration of the usefulness and relevance of the Q3, I assessed the ability of mitigating drought impacts resulting from possible future climates via planting improved seedling stocks iv  developed in tree genetics and improvement programs. Overall, the methods and the newly developed macroscale decision support system I developed link ecological (e.g., climate change impacts on forests) and economic (e.g., price change) uncertainties enabling the development of appropriate forest and environmental policies, along with forest management practices needed to implement these policies.v  Lay Summary Vast areas in the Canadian boreal forest are becoming increasingly susceptible to climatic changes. Vulnerabilities associated with drought, fire and forest health are being observed across thousands of kilometres or macroscales. The forestry sector, which includes First Nations, industry, and government have struggled to identify an appropriate policy response. There are great uncertainties in how responses will translate effectively between local and macroscale decision makers. Developing a consistent and accurate response that incorporates ecological and economic information is critical for finding a plausible decision space. In this research, I developed a decision support system that links multi-source ecological and economic data to provide information across spatio-temporal scales. Although this system could be used to assess the capacity of Canada’s boreal forest sector to respond to numerous expected climate change challenges, I used this system to examine the further adoption of tree improvement strategies aimed to respond to increasing drought vulnerability. vi  Preface The contributions of committee members to each research chapter are summarized in the tables below. Chapter 2  Research contribution Kyle Lochhead Valerie LeMay Gary Q. Bull Olaf Schwab Steven Northway Total Identify research problem 80 17 1 1 1 100 Designing research 80 15 2 2 1 100 Analyzing data 85 15 0 0 0 100 Manuscript writing 80 17 1 1 1 100 Chapter 3 Research contribution Kyle Lochhead Valerie LeMay Gary Q. Bull Olaf Schwab Steven Northway Total* Identify research problem 73 2 5 2 15 97 Designing research 80 2 2 2 10 96 Analyzing data 65 0 0 0 10 75 Manuscript writing 75 0 15 2 0 92 *Note. Drs Saeed Ghafghazi, Petr Havlik, Nicklas Forsell, Michael Obersteiner and Warren Mabee also contributed to this research chapter and their contribution represents the remaining percentage. In particular, Dr. Saeed Ghafghazi provided a case study to demonstrate the usefulness of this research. vii  Chapter 4 Research contribution Kyle Lochhead Valerie LeMay Gary Q. Bull Olaf Schwab Steven Northway Total Identify research problem 78 2 5 5 10 100 Designing research 80 2 2 6 10 100 Analyzing data 94 1 1 2 2 100 Manuscript writing 77 5 15 3 0 100 A version of Chapter 2 was published as: Lochhead, K.D., LeMay, V.M., Bull, G., Schwab, O. and Halperin, J. 2018. Multivariate estimation for accurate and logically-consistent forest-attributes maps at macroscales. Can. J. Forest Res. 48(4):1-15. doi: 10.1139/cjfr-2017-0221. A version of Chapter 3 was published as: Lochhead, K.D., Ghafghazi, S., Havlik, P., Forsell, N., Obersteiner, M., Bull, G. and Mabee, W. 2016. Price trends and volatility scenarios for designing forest sector transformation. Energ. Econ. 57:184-191. doi: 10.1016/j.eneco.2016.05.001. A version of Chapter 4 was prepared for publication. Lastly, I was second author on a macroscale study from which some the materials were used and referenced in this dissertation. Ghafghazi, S., Lochhead, K.D., Mathey, A.H., Forsell, N., Leduc, S., Mabee, W., Bull, G. 2017. Estimating mill residue surplus in Canada: A spatial forest fiber cascade modeling approach. Forest Prod. J. 67(3):205-218. doi: 10.13073/FPJ-D-16-00031.viii  Table of Contents Abstract .......................................................................................................................................... iii Lay Summary .................................................................................................................................. v Preface............................................................................................................................................ vi Table of Contents ......................................................................................................................... viii List of Tables .................................................................................................................................. x List of Figures ............................................................................................................................... xii Acknowledgements ...................................................................................................................... xiv 1 Introduction ............................................................................................................................. 1 2 Multivariate Estimation for Accurate and Logically-Consistent Forest-Attributes Maps at Macroscales................................................................................................................................... 13 2.1 Introduction .................................................................................................................... 13 2.2 Materials and Methods ................................................................................................... 18 2.2.1 Study Area .............................................................................................................. 18 2.2.2 Imagery and Other Auxiliary Data ......................................................................... 20 2.2.3 Canada’s National Forest Inventory Photo-Plots .................................................... 22 2.2.4 Spatial Matching of Multi-source Data................................................................... 25 2.2.5 Data Splitting .......................................................................................................... 25 2.3 Multivariate Estimation Methods ................................................................................... 26 2.3.1 System of Simultaneous Nonlinear Models ............................................................ 26 2.3.2 Kriging with External Drift ..................................................................................... 31 2.3.3 Variable Space Nearest Neighbour Estimation ....................................................... 32 2.4 Comparisons ................................................................................................................... 33 2.5 Results ............................................................................................................................ 36 2.5.1 SNLM and KED Models ........................................................................................ 36 2.5.2 Comparisons ........................................................................................................... 39 2.6 Discussion ...................................................................................................................... 50 3 Price Trends and Volatility Scenarios for Designing Forest Sector Transformation ............ 53 3.1 Introduction .................................................................................................................... 53 3.2 Materials and Methods ................................................................................................... 56 3.2.1 Biomass Scenarios .................................................................................................. 56 3.2.2 Price Volatility ........................................................................................................ 61 ix  3.3 Results and Discussion ................................................................................................... 64 3.3.1 Biomass Scenarios .................................................................................................. 64 3.3.2 Price Volatility ........................................................................................................ 67 3.4 Case Study: Integrated Price Scenarios .......................................................................... 75 4 Linking Localized Reforestation Decisions to Macroscale Ecological and Economic Impacts in Canada’s Western Boreal Forest............................................................................................... 79 4.1 Introduction .................................................................................................................... 79 4.2 Materials and Methods ................................................................................................... 85 4.2.1 Study Area .............................................................................................................. 85 4.2.2 Forest Estate Model (Q3) ........................................................................................ 87 4.2.3 Ecological and Economic Information ................................................................... 94 4.2.4 Scenarios and Analysis ......................................................................................... 103 4.3 Results .......................................................................................................................... 106 4.3.1 Prioritizing Planting Locations ............................................................................. 106 4.3.2 Vulnerability to Drought ....................................................................................... 111 4.3.3 Financial attractiveness ......................................................................................... 114 4.4 Discussion .................................................................................................................... 115 5 Conclusion ........................................................................................................................... 122 5.1 Contributions to Knowledge ........................................................................................ 122 5.1.1 Overall Importance ............................................................................................... 122 5.1.2 Summary Chapter 2 .............................................................................................. 126 5.1.3 Summary Chapter 3 .............................................................................................. 127 5.1.4 Summary Chapter 4 .............................................................................................. 128 5.2 Limitations ................................................................................................................... 129 5.2.1 Data ....................................................................................................................... 129 5.2.2 Models................................................................................................................... 131 5.3 Future work .................................................................................................................. 132 References ................................................................................................................................... 135 x  List of Tables Table 2.1. Characteristics of the X-variables used as possible predictors for estimating multiple forest attributes. Values were averaged for the 90 m pixel when the spatial resolution was < 90 m. .................................................................................................................................................. 21 Table 2.2. Statistics for forest attributes (Y-variables) using all data for CC (63 428 and 15 025 records for the reference and target datasets, respectively), but using only treed records for the other Y-variables (52 807 and 12 347 for the reference and target datasets, respectively). ......... 24 Table 2.3. Candidate models for the SNLM. P is the number of parameters in the model. AIC is the Akaike Information Criterion calculated as -2 log Likelihood+2P. See Table 2.1 for variable descriptions. .................................................................................................................................. 38 Table 2.4. Accuracies of SNLM, KED and VSNN (k=2) methods. VSNN with k =15 was added for comparison (shaded grey). Statistics were computed using all of the target data and also using the 0 to 10th and the 90 to 100th percentiles of the corresponding Y-variable. Bold indicates a more accurate method (e.g., a lower MD). ................................................................................... 42 Table 2.5. Confusion matrix of broad class species groups for each multivariate estimation method. Classes include: NT (non-treed); D-Aw (>80% Aw); DC (mixed but dominated by Aw); CD (mixed but dominated by coniferous); C-Pj (> 80% conifer, Pj leading); C-Sw (> 80% conifer, Sw leading); C-Sb (> 80% conifer, Sb leading); D-Ot (50 %<Aw < 80% and >20 % other species groups); and C-Ot (50% <conifer < 80% and > 20% other species groups. OA is the overall accuracy. Bold indicates a more accurate method. ..................................................... 44 Table 3.1. Gross Domestic Product (GDP) per capita for each of the three global land use scenarios. ....................................................................................................................................... 58 Table 3.2. Price trends under three projected scenarios ................................................................ 66 Table 3.3. Descriptive statistics of historical (1995-2014) price volatility (%)............................ 69 Table 3.4. Long-term (1995-2014) unconditional correlations of price volatility. ....................... 70 Table 3.5. Estimated C matrix for mGARCH(1,1) model ............................................................ 71 Table 3.6. Estimated A matrix for mGARCH(1,1) model ............................................................ 71 Table 3.7. Estimated B matrix for mGARCH(1,1) model ............................................................ 72 xi  Table 3.8. Average and standard deviation (in parenthesis) of heat generation costs (2015 USD/MWh) based on fuel costs projections using: a) 30 simulation runs of the price trends; and b) constant inflation at 2% annually over the 16-years service life of the systems for the three biomass usage scenarios. Bolded option is the lowest cost. Rankings hold for a 95% confidence interval. ......................................................................................................................................... 78 Table 4.1. Assumed cost structure of forest management activities. All costs in USD currency (2010 dollars). ............................................................................................................................... 97 Table 4.2. Summary of the nine scenarios represented by planting and gain percentages. The 0% gain refers to local stocks, whereas the 10% and 20% gains refer to yield increases using improved stocks. The percent of prescriptions changed is relative to a 0% gain. ...................... 108 Table 4.3. Pearson correlations (ρ) between the change in NPV and averaged stand attributes by FMU (N=77 FMUs). The change in NPV is calculated as the NPV for improved stocks (10% or 20% gain) relative to regular stocks (0% gain) under the assumption of no regeneration failure...................................................................................................................................................... 111 Table 4.4. A comparison of the costs to replant drought vulnerable regeneration with the total cost to initially plant with improved stock. ................................................................................. 115 xii  List of Figures Figure 1.1. A flow chart of the dissertation structure and methods used for linking data and models needed for a macroscale evaluation of forest management ................................................ 1 Figure 2.1. The boreal zone in Canada (Brandt 2009) showing the study area (south of 60° N; boundary is bolded in black) with black squares representing the 2 km by 2 km photo-plots (n=3 298). The dark gray shows areas where forest companies operate. The insert provides a hypothetical photo-plot with delineated polygons and 90 m by 90 m pixel windows. Crossed markings are intersections of major latitudes and longitudes. ...................................................... 19 Figure 2.2. Empirical semi-variograms (solid line) for each Y-variable at a spatial lag of 20 km (points). ......................................................................................................................................... 39 Figure 2.3. Percent root mean square prediction errors (%RMSE; Eq.2.11) averaged over CC, Ht, Age, Vol and Hotelling’s paired T2 (Eq. 2.9) by multivariate estimation method using the target dataset (ntarg=15 025). The k refers to the number of neighbours in VSNN. ................................ 41 Figure 2.4. Actual versus estimated values by forest attribute variable for the target dataset. The grey dashed line represents a 1:1 relationship and ‘r’ is the Pearson’s correlation coefficient. Contour lines depict the numbers of points from low (white) to high (black) densities (ntarg=15 025). .............................................................................................................................................. 43 Figure 2.5. Estimated crown closure (CC) using kriging with external drift (KED) for areas within Canada's boreal forest where forest companies operate; inset maps show all estimated forest attributes for subset of this map. The color ramp displays the minimum (yellow; 0 for all attributes) and the maximum (dark blue; 100 % for CC and species percentages, 45 m for Ht, 300 years for Age and 500 m3 ha-1 for Vol). ........................................................................................ 46 Figure 2.6. Empirical cumulative distributions (CDFs) for the estimated mean annual increment (MAI) by multivariate estimation method using the target dataset. ............................................. 48 Figure 2.7. Ternary diagrams of species percentages for wetland and upland ecological communities. The vertices of each triangle represent 100 % of the labeled species. Contour lines depict the numbers of points from low (white) to high (black) densities (ntarg = 15 025) ............ 49 Figure 3.1. Historical (1995-2014) trends of quarterly prices for forest biomass and energy based markets. Y-axis is the real price (USD in 2010) divided by the mean. Data source: Pink Sheet and FAOSTAT (2015). ................................................................................................................. 67 Figure 3.2. Historical (1995-2014) price volatility for energy based (top graph) and woody residue biomass (bottom graph) markets. Y-axis is the percent change in price. ......................... 68 xiii  Figure 3.3. Conditional correlations. Panel A is the correlation between crude oil and natural gas. Panel B is the correlation between crude oil and woody residue. ................................................ 75 Figure 4.1. Locations where forest companies operate in Canada’s western boreal and the transportation distance of timber to a forest products firm (indicated by dots) that is capable of processing merchantable timber volume. Crossed markings are intersections of major latitudes and longitudes. .............................................................................................................................. 86 Figure 4.2. Q3 work flow (quantify, query and queue) used to link localized decisions (i.e., reforestation in this paper) to macroscale outcomes. .................................................................... 88 Figure 4.3. Annual volume harvested (averaged by 5-year intervals) for the 30-year projection under each scenario. Bold solid lines represent the upper and lower bounds of historical harvest rates ............................................................................................................................................. 107 Figure 4.4. Maps of local stock planting locations forecasted over a 30-year planning horizon. The top map assumes planting (θ) 30% of the total harvest area and the bottom map θ = 70% of the total harvest area (see Eq. 4.7). ............................................................................................. 110 Figure 4.5. Proportions of pixels environmentally sensitive to drought in western boreal FMUs...................................................................................................................................................... 113 xiv  Acknowledgements This dissertation would not be possible without the support of many people. First, I would like to express my deepest gratitude to Prof. Gary Bull and Prof. Valerie LeMay, my research supervisors, for their patience, guidance, encouragement and valuable critiques of this research work. Both were instrumental in expanding my thoughts and skills beyond any of my expectations. My thanks are also extended to Dr. Steven Northway and Dr. Olaf Schwab, my committee members, for encouraging me to approach challenges from diverse perspectives and for supporting the planning and development of this research work. Special thanks are given to Dr. Saeed Ghafghazi, whose keen interests in new computer technologies and expertise in computer programming aided in making very-large scale modelling feasible. This research work would not be possible without the financial support provided by the SmartForests and SpruceUp research projects. Both Prof. Nancy Gélinas at the University of Laval and Prof. Gary Bull deserve a special recognition for acquiring this funding and establishing the Genomics and its Ethical, Environmental, Economic, Legal and Social Aspects (GE3LS) component of these research projects. I wish to acknowledge the entire GE3LS team for their creativity, enthusiasm and passion for promoting healthy and resilient future forests. I am particularly appreciative to Dr. Suborna Ahmed who helped me further my understanding of tree improvement strategies and biometrics.  While at the University of British Columbia, many staff, students and visiting researchers provided valuable sources of data and advice for tackling my ambitious research work. I would like to thank Dr. Tongli Wang for helping gain access to climate data, along with Prof. Nicholas Coops and Dr. Ryan Frazier for providing advice on processing satellite imagery. A special xv  recognition goes to Dr. Jamie Halperin, who helped me navigate the nuances of big spatial data and also to think beyond Canadian borders. I would like to offer my special thanks to Mr. Graham Stinson, Manager of Canada’s National Forest Inventory at the Canadian Forest Service and his staff for responding to my data needs and questions. Finally, I would like to thank my family and friends for encouraging me through this amazing journey. I wish to acknowledge Sean Pledger for helping me remember what forests look like. I wish to thank Dr. Derek Sattler who gave me much needed advice on any topic, both forestry and life. I wish to thank Andre Christensen and James Bartlett for helping me clear my mind through surfing and sailing. I am particularly grateful to Nate Medinski, who kept me sane by encouraging me to ski steeper, bike harder and fish deeper. I am indebted to Kaylee Wallis who has given me never ending support and positivity. Lastly, I would like to offer my special thanks to my mother, father and sister, their patience and love inspires me to continue to work hard and make the world a better place. 1  1 Introduction Sustainable forest management strategies at macroscales (i.e., larger than landscapes, Urban et al. 1987; Heffernan et al. 2014) have gained considerable relevance particularly in light of the uncertainties related to climatic changes (Lemprière et al. 2013; Kleindl et al. 2018), including associated changes in the type and severity of natural disturbances. In the case of the Canadian boreal forest (~552 Mha, Brandt 2009), uncertainties surrounding future climate directly affect the nature and condition of the forest, including growth and mortality dynamics (Brandt 2013). The changing conditions are expected to increase the frequency and severity of large scale natural disturbances including catastrophic forest fires and pest epidemics, resulting in stock and productivity declines (Flannigan et al. 2005; Gauthier et al. 2014). Conversely, the changing conditions may increase growth rates in some species if temperatures increase (Messaoud and Chen 2011). However, the adaptive capacity of some boreal tree species to tolerate temperature and precipitation variation is uncertain and large-scale mortality may result (Peng et al. 2011; Reyer et al. 2015). There is now evidence that these impacts have already begun (Gillis and Fountain 2016; Hogg et al. 2017). The compounded implications of these changes are very significant for the boreal forest of Canada and there is a general awareness that we need to tackle these challenges at both local and macroscales (Keskitalo 2011; Bull et al. 2018; Kleindl et al. 2018).  There are large uncertainties related to the forest management responses that might be employed under these changing climatic conditions. For example, will there be financial resources available to implement appropriate management actions to ensure the forest can adapt (Spittlehouse 2005; Johnston and Hesseln 2012; Gauthier et al. 2015a; Nilsson 2015)? There are 2  also uncertainties in governance (Cash et al. 2006; Keskitalo 2011). The forest sector actors (including First Nations, private industries and governments) will be the leaders in directing climate change response strategies given their dependency on forest stock and its continued productivity as a means of livelihood and environmental well-being. The anticipated declines in future stocks and growth rates will have serious implications for the raw material supply of forest and energy products (Schwab 2008). Given the spatial and temporal scales of the problem, the dynamics of climate change, and the complex set of actors involved, policy makers have begun to start tackling the problem by considering the potential effects of the macroscale ecological and economic changes (Lindner et al. 2002; Yousefpour et al. 2017).  What does this mean for forest policy in Canada’s boreal forest given that many important forest policies are being formulated by First Nations, private industry and government to combat the threats to future forest productivity and the competitiveness of the forestry sector at the macroscale (Nilsson 2015; Bull et al. 2018)? First, one could increase forest productivity following timber harvests or natural disturbances by planting seedlings with improved genetics resulting from tree improvement programs (hereafter referred to as “improved planting stocks”) that can achieve increased growth rates and increased resistance to biotic and abiotic stressors (Porth et al. 2015). Second, forest policies could be tightly interwoven with climate change policies in Canada since they are very sensitive to macroscale analysis of the boreal forest (Wilbanks 2007). In particular, climate policy targets, which include current forest stocks and forest stock changes, have to consider the commitment to lower greenhouse gas emissions (IPCC 2007). The commitments could drive various national or regional carbon-based policies including the restoring of forest productivity and increase biomass usage financed by carbon taxes and/or offsetting schemes (Hurmekoski and Hetemaki 2013; Smyth et al. 2014). Third, and 3  finally, national and international forest policy (e.g., the Boreal Forest Agreement see http://cbfa-efbc.ca/. accessed Jan 1st, 2018; United Nations Food and Agricultural Organization Global Forest Resources Assessment see http://www.fao.org/forest-resources-assessment/en/, accessed Jan 1st, 2018) reporting requires macroscale information and monitoring systems (Halperin 2017; LeMay and Kurz 2017). These systems will need to incorporate the uncertainties from changing climatic conditions since it will affect everything from future forest productivity, biotechnology application in forests, pricing of timber and products, and international trade in products (Ogden and Innes 2009; Gauthier et al. 2015b; Yousefpour et al. 2017). Given the extensive policy implications of forest management decisions, developing and improving macroscale forecasting models using improved information is critical (Yousefpour et al. 2017; Boucher et al. 2018). Macroscale forecasting models that attempt to link the consequences of forest management decisions to the macroscale have used a variety of methods ranging from spatially explicit ecological landscape simulators (i.e., Boulanger et al. 2018) to economic spatial partial equilibrium methods (i.e., Northway et al. 2009; Latta et al. 2013). Historically, the development of these models has focused separately on ecological, management, or economic perspectives, with very little effort applied to integrating these perspectives (Ogden and Innes 2007). A focus on just one perspective has frequently resulted in different disciplinary focused strategies for conceptualizing the overall system and methods for processing information (Zeide 2003). In addition to the disciplinary silos, we have two broad approaches for building the macroscale models. There are process-based or ‘bottom-up’ approaches to modelling which pieces together components of a system to give rise to more complex systems. Bottom-up approaches use information at finer scales to predict processes at broader scales where empirical data are lacking (Huston et al. 1988). In contrast, the ‘top-down’ 4  approach leverages ideas from hierarchy theory to extrapolate information between scales (O’Neill et al. 1989). The final selection of a modelling approach is largely a function of two things: the availability or scale of the supporting information and the philosophy behind the model development (e.g., predictive or knowledge-generating). Inevitably, models that assimilate ecological and economic macroscale information are forced to compromise with some mixture of disciplines and a mixture of bottom-up versus top-down (Ziede 2003).  Simulation models have been useful to extrapolate across scales because they provide a useful framework to incorporate uncertainties (Marshall 1987). Many types of simulation models have been developed at the macroscale including biophysical models (e.g., Boucher et al. 2018) and state-transition models (e.g., Nabuurs et al. 2002); however, ecological-economic models are of particular interest given their focus on decision making by the forestry sector. The economic decision support systems most often used are either partial equilibrium models (PEM; e.g., Solberg et al. 2003; Buongiorno et al. 2011; Ince et al. 2011; Kraxner et al. 2013; Northway et al. 2013) or the very ambitious general equilibrium models (GEM; ex., Ochuodho and Lantz 2014). The partial equilibrium models are of interest to my work because they focus entirely on the forest sector through components of supply, processing, demand, and interregional trade (Roningen 1997). The PEM models have an advantage in that prices are determined endogenously within the system which is useful for forecasting decisions in the forest sector under various policy scenarios. Using PEM, scenarios describing the future potential of macroscale forests are continually being developed (Nakićenović et al. 1998; Hoogwijk et al. 2005; Kraxner et al. 2013; Lauri et al. 2014) and many of these scenarios are designed to reflect environmental constraints and capacities on the supply of biomass, land use conversion, global 5  environmental policies and commodity trade (Turner et al. 2006; Latta et al. 2013; Lauri et al. 2014).  In the PEM approach, the linkages to ecological processes, including forest stocks and growth changes under future climates and other ecological drivers, have been mainly captured through the development of supply curves (Northway et al. 2013). These upward-sloping curves predict the aggregated behaviour of the forest sector; however, the information being used by these models is commonly spatially and temporally aggregated (e.g., country-level using 10-year time steps), which results in an aspatial or a very spatially coarse ‘top-down’ perspective. For example, the integrated modelling approach used by the International Institute of Applied Systems Analysis (Taylor 2011; Havlík et al. 2011) relies on remote sensing products with lower spatial resolutions (e.g., ~50 km) in estimating the potential supply of forest products at a global scale. Given the resolution of these models it would be very difficult to evaluate localized forest management decisions involving reforestation decisions like prioritizing improved planting stock. Therefore, it is important that forest analysis maintains the relationships between data and models to ensure the proper use of the information at different scales of analysis (Turner et al. 1989; Wilbanks 2007).  To improve the inclusion of both the ecological and economic perspectives within a macroscale model it is critical to incorporate decision making at spatial and temporal scales relevant to forest managers; sustainable forest management requires hierarchal planning frameworks (Bettinger et al. 2005; Schmoldt et al. 2013). At the local or operational scale, stand-level decisions have been the focus which may involve the choice of harvesting boundaries, road development, harvesting equipment and silvicultural prescriptions. These decisions take into account spatial heterogeneity 6  of the forest by incorporating stand-level forest attributes like species composition, age and transportation costs into decision making (Howard and Temesgen 1997). This use of the stand-level spatial scales has been appropriate for preserving the forest managers’ recognition of a stand as an operational unit with a homogenous set of forest attributes (O’Hara and Nagel 2013). Further, these stand or within stand forest attributes have been used as inputs into empirical models to predict future growth and yield (Bokalo et al. 2010). The results of analysis at this stand-level are then linked to higher-level spatial-temporal scales which include regional landscape extents representing management units and planning horizons that span several decades. At the next spatial scale, commonly referred to as the forest management unit level (i.e., > 1 000 ha), decisions (also referred to as assumptions) are further refined to consider ecological and economic objectives that relate to intertemporal costs and spatial prioritization of management activities (Marshall 1986; Davis et al. 2001; Buongiorno and Gilless 2003).  More recently there has been an increased interest in evaluating forest management unit level decisions at the macroscale-level (Smyth et al. 2014; Lemprière et al. 2017; Kleindl et al. 2018). Following Heffernan et al. (2014), the forest macroscale is defined as regional to continental areas that span thousands of kilometres (i.e., larger than landscapes; Urban 1987) and are made up of biological, geophysical and social components that interact with one another and with phenomena at other spatial and temporal scales. This is useful for evaluating policies that drive forest climate response strategies or other national efforts on public policy (e.g., Boreal Forest Agreement, see http://cbfa-efbc.ca/, accessed Jan 1st, 2018; A Vision for Canada’s Forests 2008 and Beyond, see CCFM 2008). To improve the credibility of the analysis it is very useful, if not essential to link the stand, forest management unit and macroscale models to generate ideas that make sense to the forest manager at the local level. Historically this has been a huge challenge 7  since crucial data, information and models were lacking to connect across all scales (Fisher et al. 2008). Arguably, two main components supporting sustainable forest management decisions are the current state of the forest and a management strategy that describes how the current state will look in the future (Marshall 1986; Davis et al. 2001). Forest attributes information describing the forest structure is acquired via a forest inventory system to represent the current state of the forest (Tomppo et al. 2008a; LeMay and Kurtz 2017). Moving from current to future states involves uncertainty and scenarios are commonly used to describe a range of futures that include responses to the uncertainty (Marshall 1987). A very large matrix including both ecological and economic information is needed to support the specific scenarios to be examined. However, information across ecological and economic disciplines rarely have the same spatio-temporal scale (Wilbanks and Kates 1999; Cumming et al. 2006; Wu 2007; Seidl et al. 2013; Kleindl et al. 2018), and often conversion of data into more useful information are needed (Li et al. 2017). Further, desired information may be missing, outdated, or incomplete, particularly for very large land areas of macroscale analyses. A process is needed to spatially and temporally link all data sources and to provide the full information needed at all locations for scenario analyses.  Previous studies assessing forest management decisions at macroscales either omitted or only weakly linked localized forest attributes and economic information (Wilbanks and Kates 1999; Fisher et al. 2008). Commonly, ecological and economic information are summarized for each relatively large spatial extent such as ecological zones or countries (Nabuurs et al. 2002; Wang et al. 2012a) and this information is then used to support the effects of aggregated decision making from individuals in the macrosystem. Several issues have arisen from using the traditional 8  approach. First, the spatial boundaries of these analysis units may change through time. Second, attribute definitions may change across the macroscale and over time (e.g., What is the definition for forest versus non forest? See Halperin et al. 2016). Third, the variabilities of attributes across space are reduced via aggregation, but these variabilities may be critical for adequate scenario analyses (Barber 1985; Bokalo et al. 2010). For instance, consider spatially aggregating species compositions, where two pure species stands representing different species may be aggregated to form a mixedwood classification. The growth and yield of this mixedwood stand can differ relative to the respective pure species stands (Bokalo et al. 2010). Similarly, the greater the aggregation, the larger the amount of information that is lost; however, the variability of forest attributes within a spatially aggregated unit may be important for decision making (LeMay et al. 2008). Fourth, these large spatial scales of analysis units often do not adequately represent important ecological or economic perspectives, thereby distorting the conceptual view of the system (Lindner et al. 2002). Using this traditional approach has frequently resulted in contradictions between the ecological and economic information that support different scales of the analysis (Cumming et al. 2006); these contradictions inevitably produce decision spaces that may not be plausible (Stage 2003). Finally, the traditional approach has resulted in forest management recommendations that are inconsistent across spatio-temporal scales (Wilbanks 2007; Keskitalo 2011; Bull et al. 2018).  Alternatives to the traditional approach just described are now emerging, largely because of research on, and the development of, innovative methods to link multiple informational sources across spatial and temporal scales. These methods can increase the accuracy of information at higher resolutions of scale while reducing costs (Tomppo et al. 2008a; Halperin et al. 2016; Nilsson et al. 2016). One of the first innovative approaches was by Tomppo (1988) who 9  developed methods to link remotely sensed data with forest inventory ground plots to provide wall-to-wall forest attribute information. Since then, a wide variety of estimation methods have been researched and recommended. These methods can be model-free, where no model or probability distribution is assumed (e.g., nearest-neighbour imputation methods in real- or in variable-space), or model-based, where a model with an assumed probability distribution (parametric model) or without an assumed probability distribution (nonparametric model) is explicitly described and used in the estimation process (Fehrmann et al. 2008). Further, methods can be univariate, where each attribute is separately estimated, or multivariate where a vector or matrix of attributes is simultaneously estimated (see Eskelson et al. 2009). In particular, multivariate methods are of interest given a matrix of information is needed to support forest management decisions. However, the application of multivariate estimation methods to the macroscale has been limited with recommendations for the choice of a particular method often based on characteristics observed from univariate applications. Ideally methods for linking data and models of forestry information from the stand to the macroscale would have the following characteristics: 1. Logical consistency both within variable (e.g., forest attributes) definitions, among models and across scales. This implies variable definitions are maintained. For instance, stand height cannot be negative and crown closure must occur within [0,100]. Similarly, disaggregation methods at a finer scale should reproduce the outputs of models or data at broader scales (Schwab and Maness 2010).  10  2. Logical consistency across variables. Forest management decisions require the measurement or estimation of several variables which are often highly correlated (LeMay 1990). These multivariate dependencies should be retained in variable estimates. 3. Accuracy. This implies the method be as close to reality as judged by empirical data. 4. Computational simplicity. The time to solve and or implement the methods should be as fast as possible so as to make the macroscale analysis cost efficient.  In summary, the method used for estimation must be logically consistent, accurate and computationally simple, to obtain the confidence of forest managers (Moeur and Stage 1995; Ohmann and Gregory 2002). Macroscale forest management analyses that do not support these characteristics are likely to produce decision spaces that are implausible (Stage 2003; Cumming et al. 2006).  In this dissertation, the central research question is:  How can we improve the linkages of multi-source ecological and economic data to evaluate forest management decisions at macroscales while ensuring logical consistency, accuracy and computational simplicity across spatio-temporal scales?  To address this question, I focused on the overall goal of developing a forest management decision system that could be used for macroscale problems, but with finer-scale spatial and temporal accuracies (Fig. 1.1). 1   Figure 1.1. A flow chart of the dissertation structure and methods used for linking data and models needed for a macroscale evaluation of forest management  10  To achieve this overall goal, first, I identified, modified, and evaluated methods to link multi-source data and models for macroscales to achieve greater consistency, accuracy and computational simplicity for forest attributes information at a finer spatial scale (Chapter 2). Then, I researched and developed methods for generating price information at a finer temporal scale while remaining consistent with longer-term price scenarios that consider macroscale dynamics captured by global land use models (Chapter 3). Collectively, forest attributes and price information represent key elements in constructing the matrix of ecological and economic information needed to construct a macroscale forest management decision space (Kleindl et al. 2018). For these research chapters, I used data and information from Canada’s National Forest Inventory, freely available remote sensing products, historical price data and global land use models to provide fine and coarse scale heterogeneity information across Canada’s boreal forest zone (~ 552 Mha; Brandt 2009). These sources provided data and information that was: current, updatable, consistent across the macroscale, and met key elements of data quality (i.e., metadata, accuracy, etc.). I then developed a decision support system Q3 (Quantify, Query, Queue) in Chapter 4 that incorporated research outcomes from Chapters 2 and 3 (Fig. 1.1). Since Canada’s boreal forest zone is expected to be greatly impacted by climatic changes resulting in uncertain implications at a macroscale (Price et al. 2013), I used Q3 to evaluate how incremental investments in planting following harvest might be used to mitigate these expected climate change impacts (Chapter 4). Special attention was directed toward planting improved genetic stocks under an anticipated increase in moisture-deficit sites. Collectively, this research contributes towards reducing uncertainties of forest investments, particularly on public forest land, where the allocation of land to timber production and other forest uses is an issue of national importance. The following  11  overview provides an outline of the dissertation while highlighting the research questions posed in each chapter. In Chapter 2, I compared alternative multivariate imputation methods for developing a spatially “wall to wall” forest inventory of Canada’s Boreal forest. Specifically, I evaluated the accuracy and logical consistency of estimated forest attributes for three methods: i) variable space nearest neighbour’s methods (VSNN; commonly used in the forestry literature for developing macroscale maps), ii) a system of nonlinear models (SNLM), and iii) kriging with external drift (KED). The specific research questions were: 1. Can both accuracy and logical consistency objectives be simultaneously met for stand-level attributes over a macroscale using one of these methods, or must one of these be sacrificed because of cost constraints? 2. How does increasing k (i.e., the number of nearest neighbours) in VSNN methods affect accuracy versus logical consistency?   3. Can SNLM be flexible enough to meet logical constraints for various forests attributes, while obtaining accurate estimates of each attribute? 4. Can we achieve the same or greater flexibility than SNE by using KED to allow a smoothing parameter to vary spatially? Based on this research, I recommend a multivariate method to implement across the Canadian boreal zone. In Chapter 3, I developed a forestry sector approach for generating short-term price movements that remain consistent with long-term global land use models. I combined long-term forest sector  12  scenario analysis with high temporal price volatility models parameterized with historical commodity price data. Specifically, the research questions were: 1. Does price volatility from other commodity markets spill over into forest product markets? 2. How can price volatility be linked within existing macroeconomic forestry sector scenario analysis to ensure scenarios are consistent across both time and forest products? In Chapter 4, I used the modelling approaches from the previous chapters to provide ecological and economic inputs into a macroscale decision support system, Q3. The Q3 system simulates localized stand-level investment decisions of the forestry sector at macroscale spatial extents. The model is used to simulate the adoption of macroscale reforestation strategies involving improved genetic stocks by the forestry sector and evaluate the compatibility between financial attractiveness and reducing vulnerability to drought. Here financial attractiveness refers to economically attractive opportunities to enhance the value of the forest which is already in place. Specifically, the research questions were: 1. Where, when and to what spatial extent in the western boreal forest of Canada will improved planting stock likely be adopted?  2. How vulnerable are reforestation strategies adopted by the western boreal forestry industry to future drought?  3. How does drought vulnerability impact the financial attractiveness of planting improved stocks to the forest industry? In Chapter 5, I provide a synthesis of the research along with overall conclusions. I also highlight the main contributions and limitation of this research and future research directions.  13  2 Multivariate Estimation for Accurate and Logically-Consistent Forest-Attributes Maps at Macroscales 2.1 Introduction  Designing resilient landscape strategies for changing environmental conditions has increased the need for forest-attributes information across very large national landscapes or macroscales (Boisvenue et al. 2016a; Kleindl et al. 2018). In the case of the ~552 Mha Canadian boreal zone (Brandt 2009), uncertainties surrounding future climates have raised concerns over possible increases in the frequency and impacts of natural disturbances (Flannigan et al. 2005; Weed et al. 2013). Also, forest management goals increasingly include a broader range of ecosystem services, including a wider variety of forest products, sustaining and providing wildlife habitats, and maintaining water and soil integrity. These changes require policy makers to evaluate the cumulative effects of macroscale ecological and economic changes (Lindner et al. 2002; Kleindl et al. 2018). More comprehensive and complex decision support tools are needed to guide changing forest management and policy; wall-to-wall, spatially-explicit forest-attributes information is needed to support these tools (Bernier et al. 2016; Boisvenue et al. 2016b). Multivariate estimation methods can predict forest-attributes across a landscape by using relationships between forest attributes and auxiliary variables at full-information locations to estimate forest attributes at all other locations with only auxiliary variables. However, for scales ≥ 1 Mha (i.e., macroscales), budgetary constraints limit the number of spatial locations with full-information to only a small proportion of the land area. Also, the diversity of ecosystems across this broad spatial scale is often much greater than for smaller spatial scales. As noted by Moeur  14  and Stage (1995), confidence in this macroscale wall-to-wall forest-attributes information is crucial for developing a plausible decision space to assess and design management strategies.  To provide forest-attributes information needed for management, many countries have undertaken a national forest inventory (NFI) that includes ground sampling coupled with remotely sensed imagery (Vidal et al. 2016). Commonly, a systematic sample of ground plots is repeatedly measured over time, providing a continuous assessment using consistent definitions of many forest attributes (Tomppo 2010). For macroscale NFIs, including Canada, ground plots may be partially or entirely replaced by interpreted large-scale photo-plots as a cost-effective option (Magnussen and Russo 2012). Using standardized protocols and viewing stereo-pairs of photos as 3-D images, professional photo-interpreters can measure the crown closure, the species composition based crown closure of each species, and the average height, but other variables are interpreted based on knowledge of the area, information from ground plots, relationships among variables, and other information (Avery and Burkhart 2002; Kershaw et al. 2017). Satellite based(e.g., Landsat) and other available wall-to-wall map information are then spatially and temporally matched with the NFI plots in a multi-sourced forest inventory (Tomppo et al. 2008a; Nilsson et al. 2016). Overall, this multi-sourced information can be used to obtain wall-to-wall estimates of forest attributes at one point in time; these estimates can also be used as inputs into growth and yield models for forecasting different management scenarios (Bettinger et al. 2001; Boisvenue et al. 2016b). Alternative methods have been proposed for obtaining wall-to-wall estimates of forest-attributes using multi-source information. Methods can be univariate, where each forest attribute is separately estimated, or multivariate where a vector or matrix of forest attributes is  15  simultaneously estimated (see overviews by Eskelson et al. 2009 and by Chirici et al. 2016). Further, estimation methods can be model-free, where no model or probability distribution is assumed (e.g., nearest-neighbour imputation methods in real- or in variable-space), or model-based, where a model with an assumed probability distribution (parametric model) or without an assumed probability distribution (nonparametric model) is explicitly described and used in the estimation process (Fehrmann et al. 2008).  In terms of model-free methods, Tomppo (1988) used nearest neighbours imputation methods (i.e., a donor method, termed k-NN by Tomppo) based on proximity in variable-space to estimate each forest attribute (i.e., univariate). Since then, many papers have used variations of univariate kNN (see Chirici et al. 2016). Alternatively, Moeur and Stage (1995) used a multivariate imputation method they termed most similar neighbour (MSN) to estimate a vector of forest attributes simultaneously based on k=1 neighbour. As with variations using kNN, many papers have used variations on MSN, termed variable-space nearest neighbour methods (VSNN) in an overview paper by Eskelson et al. (2009). An extension to doubly-multivariate estimation was demonstrated by Temesgen et al. (2003) who investigated the use of the multivariate VSNN for estimating a matrix of species, sizes and stems per ha (i.e., a tree-list) needed to project each forested stand within a forest inventory. In terms of model-based methods, univariate estimation of each forest attribute has a very long history, including a wide range of linear and nonlinear, parametric and non-parametric methods. Multivariate estimation using model-based methods is relatively more recent than univariate model-based methods, but includes using systems of models (e.g., LeMay 1990; Babcock et al. 2013).    16  Regardless of the method used, estimates of forest attributes must be accurate and logically consistent to obtain the confidence of forest managers (Moeur and Stage 1995; Ohmann and Gregory 2002). Accuracy indicates the closeness of an estimated attribute value to the real value, often measured by summaries of differences between actual and estimated values for full-information spatial locations (Foody 2002). Logical consistency refers to the preservation of attribute definitions and logical relationships (Morrison 1995), as measured by the degree of adherence to logical rules that test for nonsensical values for each estimated attribute and for impossible combinations among estimated attributes (Kainz 1995). Using univariate kNN, optimal accuracy for an estimated forest attribute can be achieved via choosing an optimal combination of the auxiliary variables, the weights associated with each auxiliary variable, the distance metric, and the number of neighbours (McRoberts 2009). Logical consistency for each estimated forest attribute is assured using kNN, since k neighbours are selected from full-information locations and the measured values for the forest attribute are averaged to obtain the estimate for each location with auxiliary variables only. Using univariate model-based methods, careful selection of the model can also ensure logical consistency for each estimated forest attribute. However, logical inconsistencies among attributes may occur using model-free or model-based univariate methods since each forest attribute is separately estimated. Using VSNN with k=1 neighbour selected from full-information locations, logical consistency for each estimated forest attribute as well as across the vector (or matrix) of attributes is obtained (Moeur and Stage 1995; Mauro et al. 2015). This may not be the case using VSNN with k>1 neighbour, since the vector of averages calculated using k donor locations may not be a logically consistent combination of forest attributes (e.g., species compositions than do not occur in nature). Also, estimation accuracy for each forest attribute may be smaller using VSNN with k≥1  17  than univariate kNN, since optimal selection of: 1) auxiliary variables, weights for each auxiliary variable, the distance metric and the number of neighbours may not be possible given the dimensionality of the multivariate problem (Indyk and Motwanu 1998); and 2) accuracy compromises must be made among the vector (or matrix) of estimated forest attributes. Using a multivariate model-based method may provide greater accuracy than VSNN by: 1) developing a simultaneous system of recursive models that allows forest attributes estimated using a model earlier in the system to be used in estimating forest attributes later in the system (Pindyck and Rubinfeld 1981; LeMay 1990); and 2) carefully selecting the auxiliary variable(s) and the model form for each model of the system. While both optimal accuracy and logical consistency are desirable, providing both may be cost-prohibitive for very large spatial scales or macroscales (e.g., Tomppo and Czaplewski 2002; McRoberts 2008; Tomppo et al. 2008b). In this research chapter, I addressed the following main question: Which multivariate estimation method provides the greatest accuracy for a macroscale problem, while maintaining logical consistency among forest attributes? To investigate this, I compared three multivariate estimation methods using a ~390 Mha sub-area of Canada’s boreal forest. For this area, high-resolution multivariate maps of forest attributes needed for macroscale strategic analysis are currently lacking or are outdated (Beaudoin et al. 2014). Specifically, I compared two model-based approaches, a system of simultaneous nonlinear models (SNLM) and kriging with external drift (KED) with the model-free VSNN method to estimate: crown closure percent (CC), average height of dominant trees (Ht), average age of dominant trees (Age), volume per ha for all trees (Vol), and tree species percentages. These attributes describe the current forest and are often the input variables used in stand-level growth models (Bokalo et al. 2010) that underlie many decision-support tools. Given prior research results for smaller spatial scales, macroscale  18  mapping issues raised by Beaudoin et al. (2014), and basic principles underlying these three methods, I hypothesized that: 1) VSNN would be more accurate, since it is model-free; 2) using VSNN with k>1 would increase accuracy, but may adversely affect logical consistency; 3) carefully designing an SNLM would ensure logical consistency of forest attributes, while obtaining accurate estimates of each attribute; and 4) greater accuracy could be achieved by allowing the parameters of the SNLM to vary spatially (KED method). Based on my results, I selected one method and produced multivariate maps (90 m) required for macroscale strategic analysis of Canada’s boreal forest management areas within which forest companies operate (to view these maps see doi: 10.14288/1.0354319). 2.2 Materials and Methods 2.2.1 Study Area The boreal zone of Canada (hereafter, referred to as “boreal”) has a total area of ~ 552 Mha, including ~270 Mha of forest (Brandt et al. 2009). Large areas of pure or mixed coniferous tree species occur, including white spruce (Picea glauca (Moench) Voss), black spruce (Picea mariana (Mill.) BSP), tamarack (Larix laricina (Du Roi) K. Koch), balsam fir (Abies balsamea (L.) Mill.), jack pine (Pinus banksiana Lamb.), and lodgepole pine (Pinus contorta Dougl. var latifolia Engelm.). Deciduous species, particularly aspen (Populus tremuloides Michx.), balsam poplar (Populus balsamifera L.), and paper birch (Betula papyrifera Marsh.), occur in either pure stands or in mixtures with conifers (Brandt et al. 2013). The boreal is bounded in the north by tundra within the arctic zone, in the south by grasslands or temperate forests, in the west by the Rocky Mountains, and in the east by the maritime forests near the Atlantic Ocean. For this study, I confined the study area to south of 60° N, since tree density becomes sparse as the forest  19  transitions to tundra north of this limit (Fig. 2.1). Further, phenological differences between satellite images are more pronounced at these higher latitudes complicating image acquisition and processing (Banskota et al. 2014). Using this northern boundary and excluding major lakes, ~390 Mha remained in the study area.  Figure 2.1. The boreal zone in Canada (Brandt 2009) showing the study area (south of 60° N; boundary is bolded in black) with black squares representing the 2 km by 2 km photo-plots (n=3 298). The dark gray shows areas where forest companies operate. The insert provides a hypothetical photo-plot with delineated polygons and 90 m by 90 m pixel windows. Crossed markings are intersections of major latitudes and longitudes.  20  2.2.2 Imagery and Other Auxiliary Data Multivariate estimation methods rely on a suite of X- (aka, predictor or auxiliary) variables assembled from multiple data sources. For this study, 38 possible X-variables were derived from surface reflectance imagery, climate, topographic and other data assembled for the study area (Table 2.1). Surface reflectance imagery for the boreal forest was retrieved from the Landsat Climate Data Record (USGS Earth Explorer 2013), a Landsat-5 (for scenes selected before 2000 and after 2003) or 7 (between 2000 and 2003) level 2-A product generated by the Landsat Ecosystem Disturbance Adaptive Processing System (Masek et al. 2006). These images provided wall-to-wall, orthorectified, maximally cloud-free coverage at a 30 m resolution. Included with this product were masks for clouds, cloud shadows, water and ice (Zhu and Woodcock 2012). A total of 1 004 images between 1987 and 2010 were acquired to temporally match the varying acquisition years of the NFI photo-plot data (described later). Scene selection was set to the peak growing season (mid-June to August) to reduce phenological differences while recognizing that small differences would be unavoidable over a national geographic extent (Tipton et al. 2010). Images were then masked to remove clouds, shadows and waterbodies. The resulting processed surface reflectance images provided the reflectance measures and vegetation indices described in Table 2.1.   21  Table 2.1. Characteristics of the X-variables used as possible predictors for estimating multiple forest attributes. Values were averaged for the 90 m pixel when the spatial resolution was < 90 m. X-variable Description Spectral Landsat bands (30m)  B1-Blue (0.45 - 0.52 µm); B2-Green (0.52 - 0.60 µm); B3-Red (0.63 - 0.69 µm); B4-Infrared (0.77 - 0.90 µm); B5-Infrared (1.55 - 1.75 µm); B7-Mid-Infrared (2.08 - 2.35 µm)  Landsat indices (30m)              NDVI Normalized difference vegetation index (B4-B3)/(B4+B3) (Rouse et al. 1974)              NDMI Normalized difference moisture index (B5-B4)/(B5+B4) (Jin and Sader 2005)              NLI Nonlinear Index (B42-B3)/(B42+B3) (Goel and Qin 1994)              NBR Normalized burn ratio (B4+B7)/(B4+B7) (Key and Benson 2006)              NSI Normalized soil index [(B5+B3) – (B1+B4)]/[(B5+B3) +(B1+B4)] (Roy et al. 1996)              Albedo Albedo, ∑ Bi7i=1, i≠6 , the sum of reflectances between 0.45-2.35 µm (Lu et al. 2016)  Climatic (1 000m)*               MAP Mean annual precipitation (mm)              PPTsm Summer (June to August) precipitation (mm)              PPTwt Winter (December to February) precipitation (mm)              CMD Climatic moisture deficit                MAT Mean annual temperature (°C)              MTsm Summer (June to August) mean temperature (°C)              MTwt Winter (December to February) mean temperature (°C)              MCMT Mean temperature of the coldest month (°C)              MWMT Mean temperature of the warmest month (°C)              FFP Length of the frost-free period (days)              DD5 Degree-days above 5°C (growing degree days) Topographic (30m)**              Elv Elevation above sea level (m)              Slp Slope angle in degrees               Asp  Angle from north in degrees              CTI  Compound topographic index (Tarboton 1997)  Vector***               SS Canvec+ dataset of saturated soil polygons (0=not saturated; 1=saturated).  Coordinates (m)               AlbX Albers Equal Area Conic X coordinate               AlbY Albers Equal Area Conic Y coordinate  * Seasonal and annual climatic variables were accessed from ClimateNA (Wang et al. 2012b).  ** Accessed from Canada Digital Elevation Data (Geogratis 2013).Eleven variables describing interactions of Elv, Slp and Asp were calculated as per Stage and Salas (2007). *** Accessed from the Natural Resource Canada CanVec+ dataset (Geogratis 2013).  22  Climate, topographic, and other variables were also considered as possible X-variables (Table 2.1). Topographic variables were computed using hydrology tools in ArcGIS v 10.2, including elevation (Elv), slope (Slp), and aspect (Asp) along with 11 interaction terms recommended by Stage and Salas (2007), and CTI (compound topographic index; a variable describing topographic position). The final X-variable was a raster layer of the presence or absence of saturated soils, based on a land cover layer of wetlands and poorly drained soils extracted from the Natural Resource Canada CanVec+ dataset (Geogratis 2013). All layers were resampled to the 30 m pixels to match the surface reflectance imagery using cubic convolution. 2.2.3 Canada’s National Forest Inventory Photo-Plots The aerial photo-plots of Canada’s NFI (see https://nfi.nfis.org/) provided the common forest attributes information (i.e., the Y-variables) used in this research chapter. Although ground plots are available, they were measured on only a subset (1 in 10) of photo-plot locations (Gillis et al. 2005). Using 20 km by 20 km grid spacing across the boreal, a stereo-photo pair (color, 1:10, 000 or 1:20 000) was acquired at each grid intersection. Professional photo-interpreters then used 3D viewing to stratify the 2 km by 2 km photo-plot into many irregularly-shaped polygons according to the harmonized definitions of Canada’s NFI Land-Cover Classification System (Gillis et al. 2005). They classified each polygon as vegetated or non-vegetated (e.g., waterbodies, snow, rock, etc.) land-cover classes. Non-vegetated polygons were not further considered in this research chapter. Since these areas have been mapped across Canada in the CanVec+ dataset, they can be masked out of estimated forest attributes maps. Within the study area, 3 298 photo-plots were classified as vegetated and had cloud-free Landsat-TM/ETM imagery matching the photo-plot acquisition time (Fig. 2.1). Vegetated polygons had been  23  further classified by crown closure percent as treed (≥ 10 %) or non-treed (<10%) based on the FAO (2015) definition, and a series of forest attributes were photo-interpreted for each treed polygon. A subset of these forest attributes was used as the Y-variables in this research chapter (Table 2.2). To reduce the number of Y-variables, species percentages were aggregated into species groups corresponding with those commonly used in stand-level growth and yield models.   24  Table 2.2. Statistics for forest attributes (Y-variables) using all data for CC (63 428 and 15 025 records for the reference and target datasets, respectively), but using only treed records for the other Y-variables (52 807 and 12 347 for the reference and target datasets, respectively).  Attribute  Description  Reference   Target   Mean Min. Max. Std. Dev.  Mean Min. Max. Std. Dev. CC (%) Percent of ground area covered by the vertical projection of tree crown areas.   45. 6 0.00 100.0 28.1  45.3 0.00 100.0 29.1 Species (%) Separation of the CC% into species groups (sum to 100%)                   Aw Populus spp. + Betula spp.  25.4 0.0 100.0 35.9  25.1 0.0 100.0 35.8        Pj Pinus spp.  14.1 0.0 100.0 28.0  14.4 0.0 100.0 28.5        Sb Picea mariana + Larix spp.  46.7 0.0 100.0 41.6  46.5 0.0 100.0 42.0        Sw Picea glauca + Abies spp.  13.2 0.0 100.0 23.7  13.4 0.0 100.0 25.8        Other Remaining spp.  0.6 0.0 100.0 4.5  0.6 0.0 100.0 5.0 Ht (m) Average height of dominant trees  12.5 0.2 42.5 6.3  12.4 0.2 36.4 6.4 Age (Years)  Average age of the leading tree species   77.1 1.0 304.0 37.5  75.3 1.0 290.0 37.2 Vol (m3 ha-1) Total stem volume (live + dead) in for all trees > 1.3 m tall  107.2 0.0 649.0 81.7  106.2 0.0 609.0 82.9 Note: Min. is the minimum, Max. is the maximum and Std. Dev. is the standard deviation. 25  2.2.4 Spatial Matching of Multi-source Data All layers representing the X- and Y-variables were spatially and temporally registered (i.e., matched). A 90 m by 90 m pixel window was extracted from the centroid of each irregularly-shaped polygon (Fig. 2.1). Extracting one pixel window avoided within-polygon dependencies and a larger pixel size mitigated spatial registration issues. Using the centroid avoided polygon edge effects; any 90 m by 90 m pixel window not entirely contained within a polygon boundary was excluded. Then, values for each X- and Y-variable were extracted for each pixel. This resulted in a total of 78 453 full-information locations with both X- and Y- variables.  2.2.5 Data Splitting The full-information locations data were split into a reference (aka, donor for VSNN or model-fitting for SNLM and KED) versus a target (aka, test or validation) dataset as used in other studies (e.g., LeMay and Temesgen 2005; Hall et al. 2006). Although Snee (1977) recommended using n-way validation, Roecker (1991) found marginal improvement over random splitting in the variable-selection setting. Data were split at the photo-plot level to better mimic the multivariate estimation applied to the entire land area (i.e., in application, the reference dataset would contain all full-information locations in a photo-plot, but the target dataset would include only spatial locations outside of photo-plots). The resulting validation dataset had ~20% of the full-information locations (ntarg= 15 025) and the reference dataset contained the remaining ~80% (nref = 63 428).  26  2.3 Multivariate Estimation Methods 2.3.1 System of Simultaneous Nonlinear Models For the first method, a system of simultaneous nonlinear models (SNLM; aka simultaneous system of nonlinear equations; see Judge et al. 1985) representing the relationships between the X- and Y-variables was fitted using the reference dataset (i.e., full-information locations) and this was applied to the target dataset (i.e., locations with auxiliary variables only) following Ver Hoef and Temesgen (2013). Using nonlinear model forms can better reflect known biological relationships (Littell et al. 2006a) and careful choices of these forms can ensure logical consistency for each Y-variable of the system. Then, using a system of models allows for different X-variables in each model of the system. Variables that do not impact the estimated conditional mean of a particular Y-variable (i.e., the estimated Y-variable given the particular set of X-variable values) can be dropped from the model. This allows for more accurate, parsimonious models relative to using a fixed set of X-variables for all Y-variables. Further, a system of models allows for across-model constraints to ensure logical consistency across Y-variables (Babcock et al. 2013). Finally, allowing for a Y-variable of one model to appear as a predictor variable in another model of a simultaneous equations system can improve both accuracy and logical consistency (LeMay 1990; Gujarati et al. 2011a). I specifically used a recursive system of simultaneous nonlinear models, thus enabling an estimated Y-variable to be used as a predictor variable for models later in the ordered system of models (i.e., an instrumental variables (IV) method; see Pindyck and Rubinfeld 1981; Judge et al. 1985; Gujarati et al. 2011a).   27  The SNLM was carefully developed as a logically ordered, recursive system of models to reflect logical, biological relationships for each Y-variable and across Y-variables. Specifically, the SNLM preserved the [0,100] limits of CC and species percentages, the additivity of species percentages (must sum to 100%), and accounted for the interdependencies of CC, Age, Ht, and Vol. The first model was the CC model using a logistic model form that constrains estimates within [0,100]. The estimated CC value (CĈ) was then used to indicate if a location can be considered as treed (CĈ ≥ 10 %) or non-treed, since all non-treed locations have logical zero values for estimated species percentages, Age, Ht, and Vol. CĈ was also available as a possible predictor variable (i.e., using an IV approach) for later models. The species percentages model was next, again using a logistic model form to constrain all estimated percentages to [0,100]. Age, Ht, and finally Vol models followed using nonlinear models to ensure all estimated values were >0, and allowing Y-variables earlier in the system to be possible predictor variables. Details for each model of the system are presented next.  As noted earlier, the CC model was the first model of the SNLM. For this, I used a logistic model: [2.1] Yi100 = πi= ex p(ηi)1+ex p(ηi)       with    ηi= log (πi1-πi) = β0+β'xi+ εi  where Yi is the CC for the ith observation expressed as a percent; πi is CC expressed as a proportion; ηi is the log odds ratio (i.e., logit); β0 is the constant parameter (i.e., intercept of the logit model);  β=(β1,…βl)' is a vector of l parameters associated with the xi vector of predictor variables; and εi is the error term. This model was fit using all full-information locations of the reference dataset and the SAS (v9.4) LOGISTIC procedure. The selection of X-variables was  28  performed using the branch-and-bound algorithm of Furnival and Wilson (1974) to find the model with the smallest AIC, but giving preference to variables that exploit known biological relationships with the Y-variables. The preference variables were AlbY and SS to ensure that crown closure changes with latitude (i.e., should decrease with increasing latitude; Sirois 1992) and changes for saturated versus not saturated soils (i.e., should be lower for saturated soils; Glebov and Korzukhin 1992). For the vector of species percentages model of the SNLM, a generalized version of Eq. 2.1 to a multinomial logistic model was used, where species percentages were considered proportions (e.g., Thompson 1987). [2.2] Yij100=πij= exp (ηij)∑ exp (ηij)Jj=1   with  ηij= log (πijπiJ) = β0j+βj'xi+ εij where Yij is the percentage of the jth species group (j=1…5) for the ith observation and ∑ YijJ=5j=1 =100; πij is species percentage expressed as a proportion; ηij is the log odds ratio for each species group relative to the baseline species group (J=5), meaning  ηi5= log(1) =0; and εij is the error term. This model ensured that all estimated species percentages were in the [0,100] interval and the sum of all the species groups was equal to 100 for each observation. This model was fitted using the subset of the reference dataset considered treed based on CĈ using Eq. [2.1], and using the SAS (v9.4) LOGISTIC procedure with the Newton-Raphson maximum likelihood algorithm. X-variables were selected following the same method as for the CC model. Specifically, SS, MAP, and Slp were the preference variables, since SS would be expected to relate to the presence of black spruce (Sb) which is commonly associated with wetland areas  29  (i.e., saturated soils, Brandt 2009), and MAP and Slp are important abiotic drivers of species composition (Soja et al. 2007). The remaining models for Age, Ht and Vol were fit as a system of simultaneous nonlinear models using the subset of locations in the reference dataset considered treed based on 𝐶?̂?. For Age and Ht, I chose an asymptotic nonlinear model to limit the maximum values to logical biological limits, while ensuring non-negative values. [2.3] Yi=α1+exp (θi)+εi   with   θi= β0+β'xi+δ'ŷi where Yi is the Ht or Age for the ith observation in the reference dataset; α is the maximum possible estimated value (i.e., asymptote); δ'is a vector of parameters associated with the ŷi, estimated Y-variables from models earlier in the recursive system; and εi is the error. A Chapman-Richards (C-R) model (Richards 1959) was selected for Vol, because this model form has been widely applied in forestry due to its flexibility, accuracy and biologically meaningful properties (e.g., Zhao-gang and Li 2003). However, we used Ht̂ instead of Agê, since it more directly relates to Vol (e.g., Garcia 2003). [2.4] Yi= αi (1-Bek Ht̂i)11-m+ εi  with  αi=(A0+A'xi+δ'ŷi )  where Yi is the Vol for the ith observation in the reference dataset; αi is the asymptote or maximum Vol; B is a shape parameter; k is a parameter associated with Ht̂i; m is also a shape parameter; A=(A1,…Al)' is a vector of l parameters associated with the xi vector of predictor  30  variables; δ'is a vector of parameters associated with the ŷi estimated Y-variables from models earlier in the recursive system (e.g., CC, species percentage, and Age); and εi is the error. The asymptote parameter was allowed to vary with X-variables and previously estimated Y-variables, since this represents the maximum potential volume at a location and varies with site factors and genetics (Stage and Salas 2007). Although the models for Age, Ht, and Vol were fitted as a system, the selection of X-variables was first performed for each model of the system separately. Linearized versions of Age and Ht were obtained by setting the asymptotes (the 𝛼 parameters) to the maximal values in the reference dataset (Table 2.2). A maximum R2 improvement algorithm (i.e., MAXR in REG procedure) was then used with preference for variables that exploit known biological relationships with the Y-variables. Given that B4, B5 and B7 spectral wavelengths are associated with forest disturbance (Key and Benson 2006) and shadowing effects indicative of older stand structures (Kuusinen et al. 2014), these X-variables were used as preference variables for Age. For the Ht model, B4 was given preference given the sensitivity of vegetation structure to this spectral wavelength (Hall et al. 2006). For the Vol model, a linearized version of the C-R model was obtained by fixing the B and m parameters to 1 and 0, respectively. Following the selection of X-variables, the system was fit using Full Information Maximum Likelihood (FIML) as implemented using PROC MODEL of SAS (v9.4). No error variance models were added since there was no evidence of heteroscedastic error variances in diagnostic graphs.   31  2.3.2 Kriging with External Drift For kriging with external drift (KED), the fitted SNLM was localized by estimating random effects using the reference data (i.e., representing full-information locations) and then spatially interpolating these random effects for target locations (i.e., simulating locations with auxiliary variables only; Schabenberger and Gotway 2005). For KED using a linear model, often the error term is allowed to spatially vary (i.e., residual kriging), which is equivalent to adding in a spatially-varying intercept (Littell et al. 2006a; Lloyd 2007). However, each model of the SNLM system has a zero y-intercept (i.e., no y-intercept). Allowing a spatially-varying error term could result in estimated percentages outside of the [0,100] interval for Eq. 2.1 and 2.2, and in negative estimates for Y-variables of Eq.2.3 and 2.4, thereby affecting logical consistency. Instead, I modified one or more parameters of the model of the SNLM to be random parameters (Schabenberger and Gotway 2005; Littell et al. 2006a), as used by Merz and Blöschl (2003). After preliminary investigations, I included a spatially-varying β0 in the CC model (Eq. 2.1): [2.5] Yi100 = πi= exp (ηi)1+ exp (ηi)       with    ηi= log (πi1-πi) = β0+ zi+β'xi+ εi  where zi~N(0,Σ) is the spatially-varying parameter estimated for each photo-plot that contained the ith observation (i.e., i is nested within a photo-plot); and all other parameters and variables were previously defined for Eq. 2.1. This was repeated for the species percentages model (Eq. 2.2). For Ht and Age (Eq. 2.3) and for Vol (Eq. 2.4), I introduced random effects as follows:  32  [2.6] Yi=α1+exp (θi+ zi)+εi    [2.7] Yi= αi(1-Bekŷi)11-m+ εi   with  αi=(A0+A'xi+δ'ŷi+zi)  To estimate zi, I used the SAS (v9.4) NLMIXED procedure for each model separately, where all other parameters were retained from the previous fit of the SNLM. To apply the spatially-explicit models to the target dataset, the simple kriging (SK) predictor was used to spatially predict zS for each spatial location (s) based on a spatial neighbourhood (Schabenberger and Gotway 2005):  [2.8] ẑs= ∑ λszi nrefi=1  where λs were estimated from a model of the semi-variogram of zi. Several semi-variogram models were fit using ArcGIS v10.2; these were visually compared to the empirical semi-variogram and one model was selected. This was repeated for each of eight cardinal directions (i.e., N, NE, E, SE, S, SW, W, and NW) to check if the assumed stationarity was met with regards to direction (Schabenberger and Gotway 2005). Lastly, to balance cardinal direction within the spatial neighbourhood, at least four neighbours were required within each quadrant. 2.3.3 Variable Space Nearest Neighbour Estimation Unlike the other two methods, VSNN is a model-free method (see Eskelson et al. 2009). The X-variables are used to determine the variable-space distances between reference locations and a target location; the closest neighbours (i.e., k≥1) among the reference locations are used as donors of the Y-variable information for the target location. As k increases, the variability of the estimated Y-variables across the target dataset (i.e., the spatial extent if used in mapping)  33  decreases as the estimated Y-variables for each spatial location approach the vector of means using the entire reference dataset. Two steps were again used, following the use of VSNN by others (e.g., Moisen and Frescino 2002; Halperin et al. 2016). First, univariate kNN was used to estimate CC for locations in the target dataset. Then, 𝐶?̂? (estimated) was used to divide the target dataset into treed versus non-treed locations as with SNLM and KED. For non-treed locations, all other Y-variables were estimated as zero for the target dataset. For treed locations, VSNN was used to estimate the remaining Y-variables for each location in the target dataset using only treed locations of the reference dataset. The X-variables used for the SNLM and KED methods were also used for the VSNN method. All X-variables were standardized (i.e., by subtracting the mean and dividing by the standard deviation) to remove the effects of different measurement scales as in other studies (e.g., LeMay and Temesgen 2005). Although other distance metrics could be used to select neighbours in multivariate variable-space (see Eskelson et al. 2009), I used the distance metric proposed by Moeur and Stage (1995) based on canonical correlation analysis (CCA) between Y- and X-variables, as used by Beaudoin et al. (2014). Unlike Moeur and Stage, I varied k from 1 to 15 and used weighted averages (i.e., inverse-distance in variable-space) of Y-variables from selected neighbours. The R package YaImpute (Crookston and Finley 2008) was used to implement the VSNN methods. 2.4 Comparisons The accuracy and logical consistency of the three multivariate estimation methods were compared using the target dataset. For accuracy, reality was defined by the actual Y-variables of the target dataset. For logical consistency, reality was defined using other non-data driven information to create a rule-based set of criteria, as recommended by Kainz (1995). For CC, Ht,  34  Age, and Vol, I tested the null hypothesis H0: μY = 0 (i.e., vector of mean differences between actual and estimated forest attributes is a zero vector) against the alternative hypothesis that at least one mean difference is not equal to zero. For this, I used Hotelling’s paired T2 statistic (Hotelling 1951), a multivariate generalization of Student’s paired t-statistic. [2.9]       paired T2= ntargy̅'SY-1y̅ where ntarg is the number of full-information locations in the target dataset; y̅ is the mean vector of differences between actual and estimated values for the Y-variables; and  SY is the estimated variance-covariance matrix of these differences. Other accuracy metrics separately calculated for CC, Ht, Age and Vol using the actual (Ys ) versus estimated values (Yŝ) for the target dataset were: 1. Root Mean Squared Prediction Error (RMSPE) defined as: [2.10] RMSPE = √∑(Ys-Yŝ)2ntargntargs=1 2. Percent RMSPE defined as:  [2.11] % RMSPE = 100 (RMSPEY̅) where Y̅ is the mean of actual values for forest attribute Y in the target dataset. 3. Mean difference (MD) between actual and estimated Y-variable values, defined as: [2.12] MD =  1ntarg∑ (Ys-Yŝ)ntargs=1  35  4. Pearson’s correlation coefficient between Ys and Yŝ. To indicate accuracy for extremes of each Y-variable, RMSPE and MD were also calculated using data representing the 0 to 10th and then the 90 to 100th percentiles of the range of actual values for each Y-variable in the target dataset. Accuracy of species percentages was assessed by a confusion matrix of broad species classes. The rules applied to assess adherence to logical consistency were: 1) estimated percent crown closure and all species percentages must be within the [0,100] interval; 2) estimated species percentages must sum to 100; 3) estimated Ht, Age, and Vol values must be non-negative; 4) across-variables ratios must be within bounds of biological reality; and 5) species percentages must be possible based on ecological information. Rules 1, 2 and 3 were met given the steps described in the methods section. Adherence to Rule 4 was not assured using any of the three methods. Although a variety of relationships across Y-variables could be evaluated for Rule 4, I used the ratio of Vol̂  to Agê = MAÎ to look for across-variable inconsistencies, since this growth measure is often used in forest management planning. The cumulative distributions of the actual and estimated MAI values in the target dataset were compared.  To evaluate Rule 5, I used ternary diagrams of actual and estimated species percentages to visually check for illogical combinations. Ternary diagrams map the frequency of percent variables in a two-dimensional space on an equilateral triangle (van den Boogaart and Tolosana-Delgado 2013). Points closer to a vertex of the equilateral triangle represent a larger percentage of the species attributed to that vertex. These species percentages ternary diagrams were obtained for two ecological communities (photo-interpreted land areas), namely: 1) lowlands or areas  36  saturated with water long enough to promote hydrophilic vegetation; and 2) uplands, defined as non-wetland ecosystems. 2.5 Results 2.5.1 SNLM and KED Models Many combinations of spectral, climate, topographical and other X-variables were evaluated. Based on the AIC values, three models for CC and species percentages and two systems of Age, Ht, and Vol models were initially selected (Table 2.3). The CC model with B5, NSI, NDMI, PPT𝑠𝑚, AlbY and SS resulted in the smallest AIC. The species percentage model using SS, NDMI, B5, MTsm, CMD, MAP, Elv and Slp was selected. For the system of Age, Ht and Vol models, the previously estimated CĈ (i.e., log(CĈ)) was selected for Age and Ht models, Pĵ and Aŵ were selected for the Ht model, and Ht̂ was selected for the Vol model. Also, allowing the asymptote (αi) of the Vol model to change with SS resulted in a smaller AIC for the system (Table 2.3). For KED, a random parameter was added to each model of the SNLM as described earlier (Eqs. 2.5-2.7). The estimated random parameter variances for CC, Aw , Pj, Sb, Sw, Age, Ht and Vol were 0.11, 1.14, 7.38, 2.75, 3.53, 0.31, 0.36, and 79 292.93, respectively. Empirical semi-variograms were constructed using the estimates of random effects for each random parameter by location (EBLUP; Schabenberger and Gotway 2005). I found no evidence of directional dependence. The Gaussian semi-variogram model for species percentages and the exponential semi-variogram model for the remaining Y-variables fit the data (Fig. 2.2); spatial correlation was found up to 71 km for the species percentages and up to 300 km and beyond for the other Y- 37  variables. Overall, the evidence indicated that KED should improve the accuracy relative to the SNLM, particularly for CC, Ht, Age and Vol. 38  Table 2.3. Candidate models for the SNLM. P is the number of parameters in the model. AIC is the Akaike Information Criterion calculated as -2 log Likelihood+2P. See Table 2.1 for variable descriptions.  Y  P Models AIC CC [Eq. 2.1] 6 η̂ =17.28 - 0.57SS - 0.15NSI + 12.94NDMI - 13.24B5 - 3.19 x 10-7AlbY 5 272 7 η̂ =15.96 - 0.64SS - 0.13NSI + 10.73NDMI - 13.52B5- 2.93 x 10-3PPTsm - 4.83 x 10-7AlbY 5 224 8 η̂ =15.82- 0.65SS - 0.14NSI + 8.53NDMI - 6.67B4- 1.63 x 10-3PPTwt - 3.57 x 10-7AlbY-3.20 x 10-4Elv 5 252 Species [Eq. 2.2] 32 η̂Aw=7.53 + 7.05 SS -0.11NSI  +0.95MTsm -1.66x 10-2 CMD-1.26 x 10-2MAP + 5.94 x 10-3Elv +0.36Slp η̂Pj =-3.96+ 6.74 SS+0.14NSI +0.57MTsm -2.99x 10-2 CMD-1.00 x 10-2MAP + 5.06 x 10-3Elv +0.35Slp η̂Sb =11.65 + 9.37 SS+8.71 x 10-2NSI +0.16MTsm -3.85 x 10-2CMD-1.03 x 10-2MAP + 1.52 x 10-4Elv +0.05Slp η̂Sw =16.51 + 7.61SS-2.36 x 10-3NSI-0.42MTsm -1.16 x 10-2 CMD-5.83 x 10-3MAP + 3.58 x 10-3Elv +0.39Slp 1 586 36 η̂Aw=-1.99 + 6.72 SS -10.44NDMI + 11.69B5 +1.01MTsm -2.56 x 10-2 CMD-1.57 x 10-2MAP + 4.55 x 10-3Elv +0.39Slp η̂Pj =12.98+ 6.43 SS+25.46NDMI-78.26B5 +1.12MTsm -2.58 x 10-2 CMD-6.35 x 10-3MAP + 5.66 x 10-3Elv +0.39Slp η̂Sb =23.40 + 9.03 SS+18.94NDMI-70.95B5 +0.65MTsm -3.55 x 10-2 CMD-7.06 x 10-3MAP + 5.55 x 10-4Elv +0.11Slp η̂Sw =19.65 + 7.28 SS+11.67NDMI-73.54B5 +6.47x 10-2MTsm -8.11 x 10-3 CMD-2.54 x 10-3MAP + 3.79 x 10-3Elv +0.43Slp 1 352 40 η̂Aw=0.28 + 6.39 SS -3.85NDMI-9.70B5 +0.99MTsm -2.44 x 10-2 CMD-1.54 x 10-2MAP + 4.47 x 10-3Elv +0.38Slp + 9.73B4 η̂Pj =13.06+ 6.16 SS+24.95NDMI-74.29B5 +1.11MTsm -2.50 x 10-2 CMD-6.13 x 10-3MAP + 5.54 x 10-3Elv +0.38Slp −2.86B4 η̂Sb =22.71+ 8.75 SS+15.96NDMI-57.27B5 +0.63MTsm -3.48 x 10-2 CMD-6.90 x 10-3MAP + 4.14 x 10-4Elv +0.09Slp-7.89B4 η̂Sw =23.61+ 7.02 SS+22.17NDMI-118.00B5 +5.50 x 10-2MTsm -7.61 x 10-3 CMD-2.51 x 10-3MAP + 3.68 x 10-3Elv +0.42Slp+20.60B4 1 354 Ht [Eq.2.3] 9 α̂=41.30              θ̂ =-7.12+0.32 Pĵ-0.24Aŵ+106.11B7+1.97 x 10-7AlbX-15.30NDMI-14.27B4-0.88log(CĈ) 1 632 186  Age [Eq. 2.3] 5 α̂=316.30           θ̂ =-1.50-39.81B5+76.92B7 +16.32B4-1.41 x 10-2log(CĈ) Vol [Eq. 2.4] 4 α̂= 549.30        B̂=0.83            K̂=3.03 x 10-2  Ht̂         m=0.62 Ht [Eq. 2.3] 9 α̂=45.1            θ̂ =-7.10+0.33 Pĵ-0.24Aŵ+106.32B7+1.97 x 10-7AlbX-15.30NDMI-14.28B4-0.87log(CĈ) 1 632 180  Age [Eq.2.3] 5 α̂=299.50          θ̂ =-1.90-39.74B5+76.83B7 +16.31B4-1.40 x 10-2log(CĈ) Vol [Eq. 2.4] 5 α̂ i= 551.90-26.01SSi     B̂=0.90      K̂=4.00 x 10-2Ht̂       m=0.56  39   Figure 2.2. Empirical semi-variograms (solid line) for each Y-variable at a spatial lag of 20 km (points).  2.5.2 Comparisons 2.5.2.1 Accuracy Applying the selected SNLM to the target dataset (i.e., validation data) resulted in an average %RMSPE across CC, Ht, Age and Vol of 72% and produced a mean vector of differences nearly equal to a zero vector (paired T2=8.09, p=0.08, Fig. 2.3). RMSPE values for CC, Ht, Age and  40  Vol were 26.4%, 7.4 m, 43.1 years and 76.8 m3 ha-1, and MD values were -2.0%, 1.2 m, -3.6 years, and -0.1 m3 ha-1, respectively (Table 2.4). Estimated values were more accurate for the 0 to 10th percentiles of actual CC, Ht, Age and Vol than for the 90th to 100th percentiles. Correlations between actual and estimated Y-variables ranged from 0.49 for Age to 0.56 for Ht (Fig. 2.4). The overall classification accuracy for the nine species groups was 48% (Table 2.5), with smaller accuracies for more mixed species groups (C-Ot, CD and DC) compared to the more homogenous species groups (C-Sb, D-Aw and NT). In general, coniferous species groups were primarily confused with other coniferous species groups, while the mixed species groups (CD and DC) and D-Aw were primarily confused with each other. The NT group was confused predominantly with the C-Sb group.  The KED method improved the accuracy relative to SNLM for CC, Ht, Age and Vol (Table 2.4) and for species percentages (Table 2.5). The vector of mean differences was also not different from a zero vector (paired T2=7.72, p =0.10, Fig. 2.3). For CC, Ht, Age and Vol, the KED method resulted in the smallest RMSPE among the three methods tested; however, the MD was slightly larger for CC and Vol relative to the SNLM method (Table 2.4). KED also resulted in greater accuracies at the extremes of the 0 to 10th and the 90th to 100th percentiles, with the exception of Age where accuracies were greater using SNLM at the smaller percentile range and for VSNN at the upper percentile range. Correlations between actual and estimated values were largest using KED (Fig. 2.4). Some species percentages accuracies were also slightly greater using the KED method, notably for C-Pj, C-Sb, C-Sw, and D-Aw species groups (Table 2.5). However, classification confusion among species groups was similar to that using SNLM. 41   Figure 2.3. Percent root mean square prediction errors (%RMSE; Eq.2.11) averaged over CC, Ht, Age, Vol and Hotelling’s paired T2 (Eq. 2.9) by multivariate estimation method using the target dataset (ntarg=15 025). The k refers to the number of neighbours in VSNN. 42  Table 2.4. Accuracies of SNLM, KED and VSNN (k=2) methods. VSNN with k =15 was added for comparison (shaded grey). Statistics were computed using all of the target data and also using the 0 to 10th and the 90 to 100th percentiles of the corresponding Y-variable. Bold indicates a more accurate method (e.g., a lower MD).  Y Percentiles (Ranges) ntarg  SNLM  KED  VSNN (k=2)  VSNN (k=15)  MD RMSPE  MD RMSPE  MD RMSPE  MD RMSPE CC (%) 0-10th (0-21) 1 250  10.7 23.8  13.2 23.1  18.3 29.4  25.0 30.2 90-100th (>85) 1 567  -30.4 35.5  -23.9 29.8  -36.1 41.0  -35.8 37.8 All (0-100) 15 025  -2.0 26.4  2.9 24.3  -0.6 29.4  -0.6 24.9 Ht (m) 0-10th (0-3.2) 1 240  2.8 6.4  3.0 5.8  3.5 6.4  7.0 8.7 90-100th (>20.9) 1 234  -6.4 9.6  -8.2 10.4  -7.7 9.8  -7.3 8.5 All (0-36.4) 15 025  1.2 7.4  0.4 6.4  0.79 7.0  1.4 6.1 Age (Years) 0-10th (0-27) 1 234  17.5 31.5  27.3 38.9  28.1 44.3  48.4 56.8 90-100th (>120) 1 975  -44.7 61.9  -39.9 56.1  -36.9 54.5  -34.4 45.5 All (0-290) 15 025  -3.6 43.1  0.9 38.9  6.0 44.3  10.9 38.8 Vol (m3ha-1) 0-10th (0-9) 1 279  32.3 59.8  30.8 56.9  37.5 70.4  53.2 72.2 90-100th (>216) 1 249  -131.7 155.8  -112.9 141.6  -111.9 146.2  -111.0 131.6 All (0-609) 15 025  -0.1 76.8  2.7 70.6  5.1 79.6  9.8 68.7 Note: RMSPE and MD are defined in Eq. [2.10] and [2.12], respectively.  43   Figure 2.4. Actual versus estimated values by forest attribute variable for the target dataset. The grey dashed line represents a 1:1 relationship and ‘r’ is the Pearson’s correlation coefficient. Contour lines depict the numbers of points from low (white) to high (black) densities (ntarg=15 025). 44  Table 2.5. Confusion matrix of broad class species groups for each multivariate estimation method. Classes include: NT (non-treed); D-Aw (>80% Aw); DC (mixed but dominated by Aw); CD (mixed but dominated by coniferous); C-Pj (> 80% conifer, Pj leading); C-Sw (> 80% conifer, Sw leading); C-Sb (> 80% conifer, Sb leading); D-Ot (50 %<Aw < 80% and >20 % other species groups); and C-Ot (50% <conifer < 80% and > 20% other species groups. OA is the overall accuracy. Bold indicates a more accurate method.   Estimated  Method Actual  Total Users Accuracy C-Ot C-Pj C-Sb C-Sw CD D-Aw D-Ot DC NT C-Ot SNLM 0 0 0 0 0 0 0 0 0 0 0% KED 0 0 0 0 0 0 0 0 0 0 0% VSNN (k=2) 4 3 15 2 10 1 0 12 6 53 8% C-Pj SNLM 0 270 200 70 59 21 0 30 105 755 36% KED 0 450 292 77 79 30 0 46 148 1 122 40% VSNN(k=2) 1 422 298 87 53 24 0 25 158 1 068 40% C-Sb SNLM 31 902 4 109 352 535 211 0 415 851 7 406 55% KED 32 785 4 266 303 503 185 0 390 896 7 360 58% VSNN(k=2) 16 621 3 769 271 308 131 0 165 896 6 177 61% C-Sw SNLM 8 163 400 429 119 45 0 91 69 1 324 32% KED 7 159 459 488 133 44 0 100 74 1 464 33% VSNN(k=2) 0 85 196 203 36 25 0 40 50 635 32% CD SNLM 4 78 197 65 111 267 0 204 135 1 061 10% KED 6 74 223 64 110 258 0 209 155 1 099 10% VSNN(k=2) 19 219 578 160 252 214 0 280 279 2 001 13% D-Aw SNLM 0 22 21 12 31 945 0 87 271 1 389 68% KED 0 22 27 13 32 1 027 0 98 312 1 531 67% VSNN(k=2) 0 30 66 38 55 1 169 0 162 276 1 796 65% D-Ot SNLM 0 0 0 0 0 0 0 0 0 0 100% KED 0 0 0 0 0 0 0 0 0 0 100% VSNN(k=2) 0 0 5 0 2 4 0 6 6 23 100% DC SNLM 4 33 79 27 46 477 0 150 123 939 16% KED 3 31 83 36 50 451 0 146 129 929 14% VSNN(k=2) 7 94 200 197 178 376 0 281 215 1 548 18% NT SNLM 2 141 669 55 30 82  37 1 135 2 151 53% KED 1 88 325 29 24 53 0 25 975 1 520 64% VSNN(k=2) 2 135 548 52 37 104 0 43 803 1 724 47% Total 49 1 609 5 675 1 010 931 2 048 0 1 014 2 689          15 025 Producers Accuracy SNLM 0% 17% 72% 42% 12% 46% 100% 15% 42% OA:48% KED 0% 28% 75% 48% 12% 50% 100% 14% 36% OA:50% VSNN(k=2) 8% 26% 66% 20% 27% 57% 100% 28% 30% OA:46%  45  With VSNN, k greatly affected the average %RMSPE across CC, Ht, Age and Vol, ranging from 64% for k =15 to 83% for k =1 (Fig. 2.3). Using k = 1 or 2 resulted in vectors of mean differences close to a zero vector (paired T2 = 0.22 with p=0.99 and 7.0 with and p=0.13, respectively). However, for k > 2, there was at least one mean difference that was significantly different from zero (T2 > 15.01, p <0.0001, Fig. 2.3). Based on these results, k = 2 was selected for most comparisons to the other two methods. Using k = 2, RMSPE values for CC, Ht, Age and Vol were larger than the other methods (Table 2.4). However, the MD for CC was smaller than either SNLM or KED. Also, estimates at extremes were more accurate using VSNN for Age, but not for other Y-variables. Correlations between actual and estimated CC, Ht, Age and Vol were the smallest among the three methods, ranging from 0.39 for CC to 0.52 for Ht (Fig. 2.4). Similarly, the overall classification accuracy for species groups was the smallest (Table 2.5). This was particularly true for NT, resulting from smaller accuracies at the 0 to 10th percentile of CC, which did not improve with increasing k (Table 2.4). However, VSNN with k =2 produced the greatest accuracy for mixed species, namely, CD and DC. Overall, KED was the most accurate of the methods tested, for estimating CC, Ht, Age and Vol and species percentages. The resulting multivariate maps using KED (Fig. 2.5) can be used in decision support analyses and also illustrate the logical consistencies among the estimated forest attributes. For example, the inset maps show taller heights but younger ages nearer the southern boundary, indicating higher site productivities given the more favorable climate for tree growth. Across the Y-variables, Age was one of the most challenging to estimate using SNLM or KED. For the VSNN methods, the most challenging Y variable was CC, especially for the extremes of the 0 to 10th and 90th to 100th percentiles  46   Figure 2.5. Estimated crown closure (CC) using kriging with external drift (KED) for areas within Canada's boreal forest where forest companies operate; inset maps show all estimated forest attributes for subset of this map. The color ramp displays the minimum (yellow; 0 for all attributes) and the maximum (dark blue; 100 % for CC and species percentages, 45 m for Ht, 300 years for Age and 500 m3 ha-1 for Vol). 47  2.5.2.2 Logical consistency All three methods were designed to meet the criteria described in Rules 1 to 3. To assess Rule 4, I examined MAÎ (Fig. 2.6). All three methods were able to estimate cumulative MAI distributions that were similar in shape to the target dataset and values were within biological expectations for the boreal (range = nearly 0.0 to 5.0 m3 ha-1 yr-1 as represented in the reference dataset). However, the VSNN methods using large k values resulted in fewer estimated small and large MAI values representing a loss in variability relative to actual distributions. For Rule 5, under both lowland and upland communities, SNLM, KED and VSNN with k =2 resulted in species assemblages similar to those actual in the target dataset (Fig 2.7). In wetland communities, the target dataset had a large frequency of the Sb group, which was estimated in all of the methods; however, for the VSNN methods the frequency of mixed species grouping was larger than the SNLM or KED (Table 2.5 and Fig. 2.7). This effect was greater for VSNN with k =15 than k =2.  48   Figure 2.6. Empirical cumulative distributions (CDFs) for the estimated mean annual increment (MAI) by multivariate estimation method using the target dataset. 49   Figure 2.7. Ternary diagrams of species percentages for wetland and upland ecological communities. The vertices of each triangle represent 100 % of the labeled species. Contour lines depict the numbers of points from low (white) to high (black) densities (ntarg = 15 025)  50  2.6 Discussion Interest in designing resilient landscape strategies for changing environmental conditions have driven policy makers to use decision support tools that are based on wall-to-wall forest-attributes information. In this research chapter, I compared one model-free (VSNN) and two model-based (SNLM and KED) multivariate estimation methods to examine possible trade-offs between accuracy and logical consistency for forest attributes across a macroscale. A cautionary note is that given the high dimensionality of the problem, I did not compare all possible multivariate estimation methods, nor all possible variations of the methods I did test.  Using the model-free VSNN with k > 2 did provide more accurate results than using SNLM for CC, Ht, Age and Vol. Then, increasing k to 15 (i.e., greater smoothing) provided more accurate results for Ht, Age and Vol relative to KED. These results indicated that using the model-free approach can provide more accurate results as anticipated. Also, increasing k in univariate kNN has been shown to decrease the RMSPE until an optimum k is reached (McRoberts 2009). However, as k increased, the range of estimated CC values shrunk, resulting in less accurate estimates for the 0 to 10th percentile of CC in particular. This is particularly important since these small CC percentiles are used to define non-treed areas. Also, using VSNN with k > 2 compressed the range of MAI values (Fig. 2.6), underestimating areas of both very low and very high productivity forests, greatly impacting macroscale decision support analyses. Further, using VSNN with larger k-values resulted in estimated species compositions that included more species. This would lead to an overestimate of forest area with large species diversity, affecting estimates of ecological services from forests. At the extreme using very large k-values, all areas would be estimated to have all species which could be biologically impossible. Further, the  51  ability to estimate rare species and to assess forest fire risks that change with species composition (Bernier et al. 2016) would be greatly curtailed. Overall, VSNN with k ≤ 2 was needed to meet logical consistency rules, but this adversely affected the accuracies. I found that an SNLM can be carefully designed to meet logical consistency rules, while remaining competitive with VSNN with regards to accuracy. Knowledge of the system being modeled is required, since careful selection of model forms and predictor variables is needed to obtain logically consistent predictions. Haara and Kangas (2012) showed that model-based methods result in greater accuracies relative to VSNN when the specified model was correct. Further, more accurate estimates were obtained for the lower and upper limits of some forest attributes using SNLM versus VSNN. This is particularly important for estimated CC, given its use in delineating treed versus non-treed areas in forest monitoring frameworks (Halperin et al. 2016). Similar results were obtained by Bollandsås et al. (2013) who showed that using a system of models method to estimate diameter percentiles led to greater accuracies for smaller percentiles relative to a VSNN method. As in this research chapter, Hall et al. (2006) demonstrated the use of a recursive system of models to estimate above ground biomass and volume using estimates of CC and Ht from earlier models in the system. They found that nonlinear models were accurate given that forest attributes tend to have a nonlinear spectral reflectance pattern which can be explained by the influence of canopy development, amount of shadow within the canopy, and forest understory effects on spectral response. However, they cautioned the use of locally-fitted models for larger spatial scales. Räty and Kangas (2008) further emphasized the need to allow parameters to vary for local conditions.  52  To allow for locally varying conditions, I used KED and allowed some parameters of the SNLM to spatially vary, resulting in more accurate estimates relative to SNLM. Other researchers showed results similar to our study with accuracy improvements via spatial localization using kriging without (i.e., no predictor variables) and with external drift (Räty and Kangas 2012; Babcock et al. 2013). For our study, I calculated the random effects for each spatial varying parameter at a 20 km spatial scale reflecting distances between NFI photo-plots. This removed abrupt changes at smaller spatial lags noted by Tuominen et al. (2003). I found spatial correlations up to 300 km for the random effects of some forest attributes in our study area (Fig. 2.2). In their study, Liang et al. (2016) mapped global forest productivity and found spatial correlation over thousands of kilometres using residual errors. I found more limited spatial correlation ranges for species percentages (Fig. 2.2) and, correspondingly, the accuracy of KED was similar to SNLM for these attributes. Of the logically consistent methods I tested, KED gave the best results. Overall, accuracies for these estimated forest attributes were similar to other studies using multi-sourced inventories (e.g., Ohmann and Gregory 2002; Hall et al. 2006; Beaudoin et al. 2014) and for macroscale studies looking to develop global-scale maps of forest attributes (Simard et al. 2011).  53  3 Price Trends and Volatility Scenarios for Designing Forest Sector Transformation 3.1 Introduction Many countries are developing national energy strategies or policies that are aimed to reduce their dependency on fossil fuels and at the same time, increase renewable energy use. Biomass is an important renewable energy option, since it is transportable, can be stored, and if produced and used on a sustainable basis, will contribute to greenhouse gas (GHG) emissions reduction targets (IPCC 2007). In particular, the forest sector has embraced the potential to play a role in the emerging woody bioenergy and bioproducts market as a means of diversifying markets and production (Hurmekoski and Hetemaki 2013). In response to these drivers, the emerging forest sector has undergone structural changes (Bael and Sedjo 2006, Palma et al. 2010, Nilsson 2015). One of the key determinants of change is finding profitability when processing logs, residues and other woody by-products. Many firms see the expansion of woody biomass energy production as a means to recover value (Lauri et al. 2014).  The economics of forest residue and wood waste biomass is poorly understood in most countries due to the lack of information on: feedstock supply; trade flow; transportation logistic; and biomass price (Roos et al. 1999). Availability and price of biomass are largely determined by the performance of competing sectors, biomass transportation systems, biomass supply sources, accessibility, and scale and system of production (Graham 2007). Canadian biomass supply chains, for example, rely on the wood fibre made available through processing residues from  54  solid wood, pulp and paper products or logging residue left at harvest sites which makes these sub sectors important determinants of biomass supply costs and volumes (Yemshanov et al.2014). On the other hand, the price of biomass is highly dependent on other energy markets such as the price of oil and natural gas. For example, logs and energy markets are highly correlated (Hartl and Knoke 2014) with energy markets encouraging volatility into various biomass feedstock markets (Onour and Sergi, 2011; Wu et al. 2011) and these ‘volatility spillovers’ or ‘price transmissions’ have increased since the emergence of the biofuels industry (Serra and Zilberman 2013). Added to this are price uncertainties associated with frequent changes in policy and regulatory environments (Moiseyev et al. 2011; Lauri et al. 2012). This complex set of interrelated system of price movements and global environmental policies challenges economic analysis of the forest sector to forecast price and price changes (Kangas et al. 2011). Perhaps one of the most challenging elements of economic forecasting, in general, is capturing price movements and volatility through time and space. Traditionally, price shocks, volatility and the transmission of volatility to other commodities are not commonly considered in forest sector based studies. In contrast, studies focusing on forecasting agricultural markets sector have considered volatility and correlated price movements (e.g., Saghaian 2010; Onour and Sergi 2011; Valin et al. 2014; von Lampe et al. 2014). Of particular interest have been studies assessing the price relationships of oil and ethanol derived from corn or sugar cane (Wu et al. 2011) because evidence of these price movements can be indicative of changes in markets of wood based energy carriers that substitute oil in the production of heating and transport fuels. Work by Kristöfel et al. (2014) showed via univariate generalized autoregressive conditional heteroscedasticity (GARCH) models that price volatility for several woody biomass markets  55  have increased within the last decade which provides greater implications for woody biomass market development. The inability to capture uncertain abrupt changes in price movements, otherwise known as price volatility, can lead to delays in the investment process (Pindyck 1999) or can create opportunities for defensive investments (Henriques and Sadorsky 2011), and as a result, lead to sub-optimal decision making of investments. For example, price volatility in fossil fuel markets was a ‘megaforce’ shaping the sustainability of the European pulp and paper industry (Pätäri et al. 2016). Limited financial resources in conjunction with price uncertainty have become barriers for changing the strategic focus of a capital-intensive forest industry (Näyhä and Pesonen 2014). Therefore, a better understanding of the determinants of price volatility remains a critical area of research since it is a pivotal variable for developing forest sector scenarios.  In this research chapter, I demonstrate an approach to integrate price volatility into forest sector scenario analysis. For this, I used a global land use model to develop price trend scenarios for woody and fossil fuel based commodities. Then, I used time series models parameterized with historical commodity prices to estimate price volatility. An important characteristic of price-time series data is the high, clustered variability; as a result, model errors are expected to be both temporally correlated and heteroscedastic (i.e., not independent and identically distributed). To address this, I developed a multivariate generalized autoregressive conditional heteroscedasticity (mGARCH) model which allows for clustered, correlated price volatilities to move together over time and across markets (Engle and Kroner 1995). Then, I combined price trend scenarios from the global land used models with the corresponding price volatility model for a high temporal  56  resolution economic analysis of price movements. I concluded by highlighting the usefulness of this approach for supporting investment decisions by the forestry sector. 3.2 Materials and Methods 3.2.1 Biomass Scenarios Scenario analysis is a method for dealing with price uncertainties by using combinations of qualitative descriptions of future outcomes and the quantitative modeling of global drivers. Each scenario includes definitions of problem boundaries, current and future conditions, driving processes, and assumptions of critical uncertainties (Swart et al. 2005). Scenarios describing the future global potential of biomass energy are continually being developed (Nakićenović et al. 1998; Hoogwijk et al. 2005; Kraxner et al. 2013; Lauri et al. 2014) and many of these scenarios are designed to reflect environmental constraints and capacities on the supply of biomass, land use conversion, global environmental policies and commodity trade.  The quantitative elements of scenario development typically rely on structural modelling using partial or general equilibrium methods (Serra and Zilberman 2013). These methods have enabled the development of scenarios to describe, for example, trade impacts of an expanding wood-energy market (Ince et al.2011), green-house gas effects of biomass electricity expansion (Latta et al. 2013), and forestry sector outlooks (Northway et al. 2009; Hurmekoski and Hetemäki 2013). One of the objectives of these structural models is to provide valuable insights into the determinants of long-term commodity price movements by taking into account macro-economic drivers. However, these models are formulated to provide information at coarse temporal resolution which leaves investors having to rely on coarse representations of short term price  57  processes. Combining the future price trends obtained from such structural models with price volatility analysis (the mGARCH model from this chapter) would provide the temporal resolution required for short term decision making. In this research chapter, a global land use model called the Global Biosphere Management Model (GLOBIOM, Havlík et al. 2011; Havlík et al. 2014) was used to develop price scenarios for biomass commodities. The GLOBIOM quantifies the competition for global land use between agriculture, forestry, and bioenergy based production sectors. GLOBIOM uses a global recursive dynamic partial equilibrium modelling structure that covers 30 world regions, 18 agricultural crop types, a range of livestock production activities, forest products, first- and second-generation bioenergy, and water (Sauer et al. 2010). Production in the model is spatially explicit, taking land and weather characteristics into account. The market equilibrium is achieved by maximizing the sum of producer and consumer surplus subject to various constraints regarding resources, technology, and policies. Simulation periods can be adjusted from 2000 to 2100 with 10-year-step intervals. For more technical information and references on GLOBIOM see www.globiom.org (accessed July 2nd, 2018).  Three scenarios were developed: business-as-usual; high biomass usage; and no economic growth outlook of the global economy. These scenarios outline key drivers that might differentiate the effectiveness of potential business strategies for a transitioning forest industry to the year 2030. The assumptions made were a combination of WWF (World Wide Fund for Nature, formerly named World Wildlife Fund) Living Forests Report (Taylor 2011), fossil fuel energy forecasts from the US Annual Energy Outlook (US Energy Information Administration, 2010) along with an additional assumption about gross domestic product (GDP) growth per  58  capita (Table 3.1). All currencies are expressed in 2010 US dollars; other currencies and/or other base years were converted using the Organisation for Economic Co-operation and Development (OECD) deflators and exchange rates where necessary (OECD STATS 2015). Table 3.1. Gross Domestic Product (GDP) per capita for each of the three global land use scenarios. GDP (1000 $ cap-1) Global land-use scenario Business-as-usual and high biomass usage  No growth 2010 2020 2030  2010 2020 2030 World 9.29 11.80 14.44  9.29 9.75 10.25 China 6.44 10.53 14.94  6.44 8.87 10.88 Canada 35.23 42.83 50.44  35.23 35.16 35.40 In this research chapter, scenarios of price trends were assumed to represent plausible futures of the global economy. No formal analyses were performed regarding how specific technological advances might evolve during the time frame used here. I focused purely on the rationale behind each scenario by hypothesizing on how events might unfold to produce potentially different futures. The intention was to demonstrate to decision makers the need for flexible strategies in the face of an uncertain global market. More details on the assumptions behind each of these scenarios are in the WWF Living Forests Report (Taylor 2011) and the US Annual Energy Outlook (US Energy Information Administration 2010).  The strength of this scenario analysis is in the linkage between changes in variables like GDP and national biomass policies which will affect biomass markets. The proposed methodological approach in this chapter utilized GLOBIOM and the scenarios from the US Annual Energy  59  Outlook (US Energy Information Administration 2010) to capture these macro-economic processes. 3.2.1.1 Business-as-usual Scenario The business-as-usual scenario is a projection of what the world could look like if consumer behaviour continues on the path of historic trends. This anticipates global land-use changes due to demands for land to supply a growing global human population with food, fibre and fuel, and the continuation of historical patterns of global land-use.  The business-as-usual scenario has six key assumptions. First, the world population will reach 9.1 billion and per-capita GDP will almost triple by 2050. Second, demand for commodities is driven by changes in wealth (measured by GDP) and human population growth. Third, historical trends in aggregate agricultural productivity gains continue. Fourth, the average human consumption rate of food in a country changes according to historically observed relationships with per-capita GDP. Fifth, forestry and agricultural production cannot expand into protected areas; however, unprotected natural habitats can be converted to timber plantations, cropland, and pasture. Sixth, total primary energy use from land-based feed-stocks will double between 2010 and 2050 due to projected energy demand and the competitiveness of technologies and supply chains.  60  3.2.1.2 High Biomass Usage Scenario The high biomass usage scenario will require a global shift towards consumers’ preference of environmentally conscious energy production. As a result, consumption of raw resources will decrease, and there will be an increased emphasis on the use of renewable energy.  The high biomass usage scenario has four key assumptions. First, remaining natural ecosystems identified as important for biodiversity by any one of six separate conservation mapping processes described in Taylor (2011) are protected (i.e., no conversion of these ecosystems to cropland, grazing land, plantations or urban settlements). However, current land uses (i.e., cropland or timber production) in these areas remain constant and continue to produce food or timber. Second, there is a shift from historical trends in the human diet. The total global consumption of animal calories is maintained at the 2010 global average with convergence in per capita consumption across regions (i.e., those now below the global average consume more in the future, while those now above the global average consume less). This scenario means less future demand for animal calories than the business-as-usual scenario. Third, bioenergy feedstock demand is consistent with the 100% renewable energy vision calculated by the Ecofys Energy Scenario (Deng et al. 2010). This contrasts with the business-as-usual scenario in that it assumes a higher carbon price. This makes bioenergy more competitive relative to fossil fuels, while being tempered by higher bioenergy feedstock prices as more bioenergy is used. Fourth, the global loss in natural and semi-natural forest by 2020 was assumed to be zero.  61  3.2.1.3 No Growth Scenario The no growth scenario is narrower in focus in that it only uses GDP per capita as the metric for evaluation and it explores the impacts of a slow growth formal economy at both the country level and the global scale. The focus here is more on the austerity being considered by many national governments combined with fears by the private capital managers to make new investments which increases their risk profile; the combined effect would lead to stagnant or no growth. The key assumption in this scenario is directly linked to GDP per capita change (Table 3.1). Under the no growth scenario, the static GDP per capita being experienced in western countries will continue and will gradually converge with the rest of the world.  3.2.2 Price Volatility  3.2.2.1 Model For the price time series, volatility (v) was expressed as: [3.1] vit=Pit−Pit-1Pit-1   where t is time and the subscript i = {o, n, h, p, s, r} denotes crude oil, natural gas, heating oil, pulp biomass, saw log, and woody residue, respectively. The vector of these price volatilities (vt) or observed errors was assumed to follow a multivariate process: [3.2] vt =  Ηt1/2∙εt where εt represents a vector (6 x 1) of zero-mean, unit variance and multivariate normal iid innovations; Ηt represents the conditional variance-covariance matrix (6 x 6) of vt , with i and j  62  indexing the rows and columns, respectively. To model Ηt, mGARCH models were used. The mGARCH(1,1) model can be decomposed into three terms: a constant term; a first order ARCH term which uses the lagged percent change in prices; and a first order GARCH term which uses the lagged conditional covariance (i.e., (1,1) for ARCH and GARCH, respectively). [3.3] Ηt= CC' + A'vt-1 v't-1Α + Β'Ηt-1Β where 𝐂 is an upper triangular matrix (6 x 6) of constants, so that CC' insures that 𝚮𝑡 is positive definite, 𝚨 is a matrix (6 x 6) of ARCH parameters, and 𝚩 is a matrix (6 x 6) of GARCH parameters. The 𝐀 matrix contains elements aij which are measures of the volatility within the market when i=j and the impacts of markets i to j. The 𝚩 matrix contains elements bij which are measures of the persistence of volatility within the market when i=j and the impacts of other markets i to j.  The elements of the Ηt matrix are thus estimated from the linear combination of the long run average of the volatility (C), the squares and cross products of lagged volatility (vt-1), as well as, the lagged values of the elements of Ηt-1 or the previous forecasted volatility. In this research chapter, this means that the ARCH term (A'vt-1 v't-1Α) represents the contribution of the previous quarterly volatility that would contribute to the price volatility (i.e., new news), while the GARCH term (Β'Ηt-1Β) represents the contribution of the lagged estimate of price volatility (i.e., old news). Since this model was fitted using multiple commodity prices, volatilities within markets can influence the prediction of the volatility in other markets.   63  The parameters C, A and B can be estimated using direct generalizations of the univariate GARCH model of Bollerslev (1986). However, to ensure positivity of the Ηt matrix, Engle and Kroner (1995) proposed an improved parametrization, the BEKK method (i.e., synthesized work on multivariate models by Baba, Engle, Kraft and Kroner, as referenced in Engle and Kroner 1995). For this research, the parameter matrices of the mGARCH model were estimated using a BEKK specification and maximum likelihood techniques within the R package ‘mgarch’ (Schmidbauer and Tunalioglu 2006). A stepwise process was used to approach a parsimonious model whereby non-significant parameters (α =0.1) were fixed at zero and resulting reduced models were compared according to their likelihood and penalized for the number of parameters using Aikake’s information criterion (AIC). The assumptions of an mGARCH model structure are that the volatility is serially correlated, stationary, and heteroscedastic (Engle and Kroner 1995). These assumptions were tested using Box-Ljung tests, a unit root test, and graphically, respectively. Box-Ljung tests were formulated under the null hypothesis of no serial correlation for price volatilities up to 12 lags. The unit root test followed that of an Augmented Dickey-Fuller test, to test the null hypothesis of non-stationarity in the univariate price volatility time series (Gujarati et al. 2011b). 3.2.2.2 Data  In order to parameterize the mGARCH(1,1) model, historic price data were used. Reported quarterly price data for 1995 through 2014 were extracted from several different sources: i) pulp biomass, saw log, crude oil and natural gas price data from the Pink Sheet (World Bank 2012); ii) heating oil price data from the US Energy Information Administration (2010); and iii) woody  64  residue (chips and residues) price data from the FAOSTAT forestry price database with reference to the Swedish Energy Agency (FAOSTAT 2015). Quarterly prices were used, because this was the highest temporal resolution of historical prices that could be sourced at the time of the study. As noted earlier, all prices were standardized to USdollars using the 2010 base rate, using OECD deflators (base 2010) and exchange rates (OECD STATS 2015).  3.3 Results and Discussion 3.3.1 Biomass Scenarios The price levels under the three scenarios are different (Table 3.2). The price of crude oil, natural gas, heating oil, and biomass for saw log under the high biomass usage scenario is the highest, followed by the business-as-usual scenario, then the no growth scenario. The price of biomass for pulp is the highest under the business-as-usual scenario and lowest under the high biomass usage scenario in each of respective years, while its price is the highest under the high biomass usage scenario and lowest under the no growth scenario in year 2030. The price level of biomass for energy under the high biomass usage scenario is the highest. Its price levels under the business-as-usual scenario and no growth scenario are the same in year 2015 and 2020, while in year 2030 the price level under the no growth scenario is a little bit higher. For heating oil, the price level is the lowest in year 2015 under the no growth scenario and highest under the high biomass usage scenario. The direction of these prices is consistent with the scenario descriptions described previously and represent three possible futures. Other studies (Nakićenović et al.1998; Hoogwijk et al. 2005; Kraxner et al. 2013) describing future biomass price scenarios share a common theme, namely, lower fossil fuel dependency,  65  increased growth in GDP, and increased environmental constraints. In many of these scenarios, high fossil fuel prices and low bioenergy prices are evident. Although I choose to use scenarios consistent with the US Energy Information Administration (2010), this analysis of price trends could be used with any plausible future the researcher is interested in, albeit these scenarios were developed with assumptions that are consistent across the price forecasts.  66  Table 3.2. Price trends under three projected scenarios Products Business-as-usual  High biomass usage  No growth 2015 2020 2030  2015 2020 2030  2015 2020 2030 Crude oil  (USD/barrel)a $91.84 $108.10 $123.09  $102.27 $134.04 $167.02  $91.17 $106.53 $119.97 Natural gas  (USD /mill btu)a $9.71 $10.62 $12.08  $10.12 $10.13 $14.12  $8.91 $8.66 $9.68 Heating oil  (USD /gal)a $2.58 $2.97 $3.32  $3.78 $4.77 $5.21  $2.52 $2.88 $3.16 Woody residue (USD /GJ)b $6.91 $8.15 $7.38  $7.40 $8.08 $8.97  $6.91 $8.15 $7.40 Saw log (USD /m3)b $98.57 $102.88 $105.66  $102.70 $106.57 $112.40  $97.05 $99.74 $99.79 Pulp biomass (USD /t)b $79.61 $81.79 $77.49  $77.84 $76.00 $78.11  $79.21 $76.71 $73.87 a: US Annual Energy Outlook (US Energy Information Administration 2010);  b: GLOBIOM 67  3.3.2 Price Volatility The historic, quarterly, price time series data from 1995 to 2014 are presented in Figure 3.1 with each price scaled by its mean. In all commodity markets of this study, correlations in price movements were evident within the last decade (2004-2014). Most notably was the strong positive association of crude oil prices with pulp biomass and woody residues, as discussed by Pätäri et al. (2016). Figure 3.1. Historical (1995-2014) trends of quarterly prices for forest biomass and energy based markets. Y-axis is the real price (USD in 2010) divided by the mean. Data source: Pink Sheet and FAOSTAT (2015). The commodity prices experienced highly clustered volatility between 2004 and 2014 (Fig. 3.2) which was consistent with the work by Kristöfel et al. (2014) and  important for the structural assumptions of the mGARCH model (Engle and Kroner 1995). I calculated descriptive statistics for price volatilities in order to gain some insight into differences across the commodity markets  68  being studied. The unconditional standard deviation varied among the different commodity volatilities, indicating differences in the amplitude of price volatility (Table 3.3). Crude oil volatility ranged between -55 to 39 % while the woody residue volatility was less, ranging between -26 to 19 % (Table 3.3). In general, energy based commodity prices have historically experienced almost double the volatility as of biomass based commodities. Kristöfel et al. (2014) found similar results with wood based biomass volatility being lower relative to the price volatility of agricultural or fossil fuel markets. Figure 3.2. Historical (1995-2014) price volatility for energy based (top graph) and woody residue biomass (bottom graph) markets. Y-axis is the percent change in price. 69  Table 3.3. Descriptive statistics of historical (1995-2014) price volatility (%).  Commodities (real 2010) Std. dev.  Min. Max. Box-Ljung  (p-value) Unit root test (p-value) Crude oil  0.14 -0.55 0.39 21.28 (0.0461) -6.49 (<0.01) Natural gas  0.22 -0.37 0.55 27.05 (0.007)  -7.68 (<0.01) Heating oil  0.14 -0.43 0.41 22.90 (0.028) -5.60 (<0.01) Woody residue  0.08 -0.26 0.19 20.72 (0.054) -5.31 (<0.01) Saw log  0.06 -0.15 0.17 7.06 (0.854) -7.15 (<0.01) Pulp biomass  0.10 -0.29 0.23 25.22 (0.014) -6.15 (<0.01) The Box-Ljung tests were significant for all of the volatility time series, which provided evidence of autocorrelation, with the exception of saw log prices (Table 3.3). All of the unit root tests (Augmented Dickey-Fuller test) rejected the null (α=0.1), providing evidence of stationarity in the time series (Gujarati et al. 2011). Unconditional correlations of price volatilities showed that there were moderately strong, positive correlations between crude oil, woody residue and pulp biomass prices (Table 3.4). However, there was no evidence of correlation between heating oil versus other price volatilities, which may be advantageous from a risk management perspective. These preliminary analyses suggested an mGARCH model is appropriate for these price vectors. 70  Table 3.4. Long-term (1995-2014) unconditional correlations of price volatility.   Natural gas Heating oil Woody residue Saw log Pulp biomass Crude oil 0.36*** 0.07 0.45*** 0.07 0.44*** Natural gas 1 0.01 0.23** -0.04 0.27** Heating oil  1 0.11 0.06 0.19 Woody residue   1 0.19 0.47*** Saw log    1 0.30*** Note: *significant when α=0.1; **significant when α=0.05; *** significant when α=0.01 Our choice for using an mGARCH model extends the univariate GARCH models developed for woody biomass price volatility by Kristofel et al. (2014). Time series models incorporating in mean autoregressive terms (e.g., vector autoregressive model (VAR), vector error correction models, etc.) offer an alternative to the mGARCH model used in this research chapter. Serra et al. (2011) demonstrated the joint estimation of VEC and mGARCH models and found strong evidence for long-term relationships between oil, ethanol and sugar prices in Brazil from 2001 to 2008. Given the overall objective of this chapter was to link forest sector models with a price volatility model, the models were focused on forecasting volatility. However, price prediction models (e.g., VEC) with GARCH covariance structures might be beneficial by supporting co-integration analyses (i.e., assess long-term price relationships) between woody biomass and fossil fuel prices in future studies.  The single lag mGARCH(1,1) model results indicated that the saturated multivariate model (AIC = 1455) resulted in a lower AIC than the diagonal error covariance model (AIC = 1462). Reducing the model using a stepwise procedure (i.e., setting some parameters in H to 0) resulted  71  in a more parsimonious model with an AIC=1439. This reduced multivariate model was used for volatility forecasting. The matrices of the estimated parameter are provided in Tables 3.5 to 3.7. Table 3.5. Estimated C matrix for mGARCH(1,1) model  Crude oil Natural gas Heating oil Woody residue Saw log Pulp biomass Crude oil 2.266 0.000 0.000 0.000 0.000 0.000 Natural gas  3.615 0.000 0.000 0.000 0.033 Heating oil   3.192* 0.000 -0.957 -0.004 Woody residue    0.000 0.957 0.303*** Saw log     1.127* 0.000 Pulp biomass      0.404 Table 3.6. Estimated A matrix for mGARCH(1,1) model  Crude oil Natural gas Heating oil Woody residue Saw log Pulp biomass Crude oil 0.074 0.195 0.120 -0.044 0.068* -0.167*** Natural gas -0.100*** -0.401*** 0.163*** -0.019 0.056*** 0.228 Heating oil -0.013 0.000 -0.074 0.026 0.009 0.044 Woody residue 0.166*** 0.307 0.195 0.147** 0.064 0.000 Saw log -0.405 0.877** 0.446 0.000 0.037 -0.574*** Pulp biomass 0.153 -0.349 -0.028 -0.047 0.059 -0.016  72  Table 3.7. Estimated B matrix for mGARCH(1,1) model  Crude oil Natural gas Heating oil Woody residue Saw log Pulp biomass Crude oil 0.464*** 0.299 -0.343 -0.152 0.006 0.304*** Natural gas 0.000 -0.324** 0.179* 0.264*** 0.028 0.101*** Heating oil 0.296** -0.230** -0.463*** 0.201*** 0.264*** 0.000 Woody residue  0.000 0.000 1.512*** -0.068 0.430*** 0.000 Saw log 1.248*** -1.126** 0.614 0.391 -0.365** -0.147 Pulp biomass 0.309 2.406*** -0.173 0.403*** -0.198* 0.281** Note: two sided significance test was conducted, *significant when α=0.1; **significant when α=0.05; *** significant when α=0.01 The matrices provided in Table 3.5 to 3.7 can be used as input parameters into the R package ‘mgarch’ (Schmidbauer and Tunalioglu 2006) to provide a forecast of future volatility. These predictions capture the conditional correlation of price movements across markets and provide an estimate of price responsiveness from historically observed volatility. An interesting component of the price responsiveness estimates is the transmission of volatility across commodity markets.  Research has highlighted the transmission of price volatility from fossil fuel energy markets into feedstock markets for biofuels (Wu et al. 2011; Serra 2011). Those studies focused on ‘spillover’ effects from energy markets into non-woody biomass energy feedstocks. The results from this study also provided evidence for fossil fuel induced volatility into woody biomass markets. The volatility in woody residue prices was influenced by crude oil, natural gas and heating oil. In addition, the volatility in pulp biomass prices was also influenced by fossil fuel energy markets. Volatility spill over price transmissions can be used to test the suitability and feasibly of biomass energy investments and provides decision support for a redesigned forest sector.   73  Volatility spill overs are the result of liberalization and integrated markets and have been shown to be driven by cross market hedging and changes in market information. The informational flow (i.e., past volatility) and the time required to process that information varies for each market and subsequently supports different patterns of observed volatility (Ross 1989). Kodres and Pritsker (2002) explained volatility spill overs using financial market contagion, where investors transmit shocks among markets by adjusting their portfolio's exposure to macroeconomic risks. Predictions of price volatility under different macroeconomic scenarios are necessary inputs into a portfolio approach for the forest sector. The multivariate aspect of the mGARCH model estimates the conditional correlation between the volatility of the prices in the model. The estimated conditional correlations were similar in strength to unconditional correlations reported in Table 3.4. However, the correlations in the mGARCH model are conditional on the lagged effects, allowing these to vary from period to period (Fig. 3.3).  As one might expect based on fuel substitutability, there is a high degree of positive correlation between the volatility of crude oil and natural gas prices. If a supply or demand shock results in a short-term increase in the price of crude oil, the price of natural gas is likely to follow. An interesting outcome of the mGARCH model analysis was that the conditional correlation between crude oil and natural gas provided information about the correlation between crude oil and woody biomass. Panel B of Fig. 3.3 illustrates the estimated historical and potential future correlation between volatility in crude oil and woody residue prices. The result of mGARCH model analysis suggests that the correlations between crude oil and woody residue are positive. This provides evidence that the volatility of crude oil and woody residue prices are directional. This is just the kind of result that is useful in the portfolio approach to transitioning the forest  74  sector or through investment opportunities. If a supply or demand shock results in a short-term increase in the price of crude oil, the price of woody residue is likely to increase. On the contrary, if a supply or demand shock results in a short-term decrease in the price of crude oil, the price of woody residue is likely to decrease.  The volatility figures resulting from this study were derived from empirical data which in combination with the price scenarios forecasted with GLOBIOM and the US Annual Energy Outlook (US Energy Information Administration 2010) provide a plausible set of high temporal resolution scenarios required for evaluating investment options. However, estimating price volatility based on changes within scenarios would be more difficult. Zhang and Sun (2001) found evidence that trade restriction led to higher levels of volatility. The utility of a global model like the GLOBIOM to help explore these impacts is critical. Future work should consider perturbing the GLOBIOM supply and demand curves to better understand, in a qualitative way the impact of the different scenarios on price volatility.  75   Figure 3.3. Conditional correlations. Panel A is the correlation between crude oil and natural gas. Panel B is the correlation between crude oil and woody residue. 3.4 Case Study: Integrated Price Scenarios To demonstrate the proposed linkage between price volatility and price scenarios of interest to the bioeconomy, a techno-economic study carried out by Ghafghazi et al. (2010) to identify least cost energy option for a district heating system in Canada was used here as a case study. The case study includes feedstock options considering: i) natural gas; ii) heating oil; and iii) woody residue. Techno-economic assessment studies of least cost energy options for energy systems usually implement naïve approaches to forecast future energy prices during the systems lifetime such as by applying a constant inflation rate over the life of the project (Chau et al. 2009;  76  Ghafghazi et al. 2010; Stephen et al. 2016). In particular, I compare a naïve approach with the mGARCH model and further demonstrate how the mGARCH model could be used in conjunction with scenarios of future biomass energy prices that remain consistent between the US Energy Outlook (2010) and the GLOBIOM.  The configuration of the district heating system and capital cost of different technology options are described by (Ghafghazi et al. 2010). The assessment was focused on identifying the least cost energy option for the baseload system of the district energy centre. The 2.5 MW baseload heat generating system considered in the study is sized such that load variation in the system is minimal when a majority of the annual energy demand (60%) is provided. The seasonal load profile of the base-load system was 5400.00 MWh during winter, 4894.25 MWh during spring, 3650.69 MWh during summer and 5520.00 MWh in fall. Ghafghazi et al. (2010) concluded that utilizing natural gas compared to biomass would provide heat at a lower cost over the 25-year service life of the district heating system.  While the general design considerations and assumptions of the district heating system in this case study are the same as those of Ghafghazi et al. (2010), there were some changes, namely: i) heating oil was considered as an energy option; ii) wood residue biomass was considered rather than wood pellets considered in (Ghafghazi et al. 2010); iii) the service life of the system was set to 16 years; and iv) heat recovery and geothermal were not considered as energy alternatives since the focus was on ranking biomass against fossil fuel options. Projected price scenarios through 16 years of the baseload system’s service-life were generated by a combination of the volatility model developed in this chapter, GLOBIOM, and the US Energy Outlook (2010). Expected future prices of wood based biomass commodities were developed for each scenario  77  using GLOBIOM. These prices were consistent with scenarios of reference, high crude oil and low economic growth within the US Energy Outlook study (2010). The mGARCH model was used to provide 30 forecasted volatility scenarios around the expected price trend using the following equation:  [3.3]  γt= μ + Η̂t1/2∙εt  where γt includes the vector prices of the three commodities at time t used in the techno-economic analysis, 𝛍 is a vector of the price trends from the GLOBIOM and the US Energy Information Administration (2010), and Η̂t is the volatility forecasted using the mGARCH model. The 30 generated fuel costs were then used in the techno-economic assessment to calculate the present cost of the combined capital expenditure and operational expenditure cost of the various energy options. In order to provide a comparison across scenarios, the same analysis was carried out using an average fuel inflation of 2% for the energy options. Using price scenarios from the mGARCH model analysis, the least cost energy option for the district heating system under the “High biomass usage” scenario would be biomass instead of natural gas which is the least cost option in all inflation based fuel projection scenarios (Table 3.8). In comparison to the constant inflation approach, this outcome would not be observed. Moreover, using price scenarios from the mGARCH model analysis allows building confidence intervals around projected heat generation cost over the service life of the district heating system. This analysis allows prices to simultaneously vary through time; therefore, the uncertainty of each price considered the direct influence of that price as well as its joint influence with the other prices. Overall, the combination of a mGARCH volatility model and price trends from GLOBIOM and the US Energy Information Administration (2010) provided an approach to  78  generate prices that maintained logical consistency among models, across temporal scales and the multivariate dependencies of commodity prices that are reflected in historical data.  Table 3.8. Average and standard deviation (in parenthesis) of heat generation costs (2015 USD/MWh) based on fuel costs projections using: a) 30 simulation runs of the price trends; and b) constant inflation at 2% annually over the 16-years service life of the systems for the three biomass usage scenarios. Bolded option is the lowest cost. Rankings hold for a 95% confidence interval. 2015 $USD/MWh a) mGARCH fuel price scenarios b) Constant inflation at 2% annually Natural gas Biomass Heating oil Natural gas Biomass Heating oil Business-as-usual 28.95 (1.69) 29.92 (0.31) 46.68 (1.38) 29.17 30.25 46.17 High biomass usage 29.47 (1.74) 28.48 (0.35) 67.59 (2.15) 30.11 31.28 63.28 No growth 25.38 (1.41) 27.62 (0.33) 45.46 (1.34) 27.35 30.25 45.32   79  4 Linking Localized Reforestation Decisions to Macroscale Ecological and Economic Impacts in Canada’s Western Boreal Forest 4.1 Introduction In the boreal forests of Canada, extreme climate events have triggered large-scale changes to forest conditions and dynamics, which have increased the concerns of Canadians on issues such as forest health, forest productivity and forest economics (Gauthier et al. 2014; Gauthier et al. 2015a). Finding appropriate human intervention responses to these events that are both ecologically and economically sensible is very difficult (Klenk et al. 2011). The ecological and economic dimensions of the challenge must be linked from the local or stand-level, to the landscape-level, and then to the macroscale level, in order to develop strategies and scenarios that are both science-driven and policy-coherent across spatial scales and for different time horizons (Bull et al. 2018). However, the neo-classical view of the investment in silviculture in general provides a barrier for human interventions needed to ameliorate adverse impacts of climate changes (Johnston and Hesseln 2012). Thus, forest management investments in boreal forest of Canada tend to be extensive rather than intensive when compared to other boreal countries (Gauthier et al. 2014; Gauthier et al. 2015a)  Of major concern in the boreal forest of Canada are climate-driven adversities, such as drought, which are currently presenting very serious issues with regeneration success (Allen et al. 2010; Hogg et al. 2017). There is evidence that annual precipitation events now differ in their distribution over the year, suggesting a change in the hydrological regimes (Peng et al. 2011). Along with other extreme events are prolonged drought events, which negatively impact reforestation success and future forest growth rates (Hogg and Schwarz 1997; Wang et al. 2014;  80  Hogg et al. 2017). Research indicates that drought impacts will be regionally-dependent (Bunn and Goetz 2011; Aubin et al. 2018), yet their cumulative effects will impact the entire boreal forests for an indeterminate amount of time (Zhang et al. 2008; Peng et al. 2011; Chen et al. 2016; Boucher et al. 2018). These climatic-driven changes require policy makers to evaluate how forest management strategies, such as planting, can be effective and consistent across spatial scales (Keskitalo 2011; Becknell et al. 2015; Bull et al. 2018). Further, there are many other climate-related events that will also change the direction of forest management policy in areas such as reducing natural disturbance impacts, including insects, diseases, and wildfires, while improving forest productivity through silvicultural interventions, that all need to be consistent from local scales to macroscales for effective policy changes. The second major concern faced by decision makers is that macroscale analysis tools and frameworks have typically been focused on either economic or ecological perspectives with little to no thought given on how to integrate them into forest management (Ogden and Innes 2007; Klenk et al. 2011). For example, many economic spatial partial equilibrium models have been used to analyse forestry sector supply, processing, demand, and interregional trade (Roningen 1997; Northway et al. 2009; Hurmekoski and Hetemäki 2013; Latta et al. 2013). These models rely on aggregated country-level information to develop economic supply curves that provide the linkages to costs incurred from harvesting, reforestation, impacts from climate change, and other costs (Kallio 2010). Using this approach, macro-drivers of timber product prices are projected through time, but the results do not reflect localized and spatial variability of forest resources or localized constraints on forest management decision-making (Schwab 2008). A similar deficiency can be found in ecological models. While ecologically-based tools have been used to determine biophysical potentials of the forests at macroscales (Boucher et al. 2018) and have  81  included localized stand-level information in spatially explicit landscape simulators (Gauthier et al. 2015b; Boulanger et al. 2018), they have not been linked with the economically-based tools that are necessary to evaluate the capacity of the forest industry to respond to climate change (Lindner et al. 2010).  The third concern is linking spatial and temporal scales to develop macroscale forest management strategies and policies that are consistent with operational (i.e., local) action (Wellstead and Howlett 2017; Bull et al. 2018). Traditionally, these multi-scaled relationships have typically been assessed as hierarchical levels of scale from stand to the landscape scale (Bettinger et al. 2005; Schmoldt et al. 2013). Research on methods to link stand and landscape scales to the macroscale (i.e., representing thousands of kilometres) has been limited (Heffernan et al. 2014; Kleindl et al. 2018). Given the complexity of assessing the impact of climate change events, there is utility in strengthening and incorporating spatial-temporal heterogeneity from the macroscale with stand-level forest management attributes like species composition, age, empirical growth and yield models, and local transportation costs (Howard and Temesgen 1997). Maintaining a stand-level focus is still appropriate for preserving the forest managers’ challenges at the operational unit level (O’Hara and Nagel 2013), since this is where practical management actions are taken. However, developing policies to address issues such as climate change requires linking local challenges faced by forest and managers to the macro-scale (Bull et al. 2018; Kleindl et al. 2018).  The fourth concern is the neo-classical view of investment in silviculture (Gregory 1972). Currently, the western boreal forest of Canada is a large area of public boreal forest land where there is limited investment in forest planting. For decades a neo-classical financial analysis  82  approach indicated that planting trees following harvesting is a poor financial investment in the boreal, since most forest stands are slow growing (i.e., <2 m3 ha-1 year-1; see Adamowicz et al. 2003; Schwab et al. 2011; Johnston and Hesseln 2012). The common view was that reforestation investments on public lands should only be undertaken to meet the minimum requirement outlined by regulations, thus supporting an ‘extensive’ forestry approach (Armstrong 2014; Chen et al. 2017). However, there was a mild push back in many jurisdictions where they insisted that for the forest industry to maintain its social license to harvest they are obligated to reforest using local seed sources or provenances for regeneration success (NFDB 2017; Schreiber and Thomas 2017). These basic efforts may not be enough. Changing climatic conditions means that some local provenances may not have the sufficient phenotypic plasticity to survive under new conditions, resulting in regeneration failures (Gray and Hamann 2011; Williams and Dumroese 2013). Alternative stocks may provide a solution. For example, researchers have used yield-gain multipliers (i.e., growth gains for improved versus local stocks) in stand-level growth and yield models, coupled with ground plot data from national forest inventories to support improved planting stock strategies (Nilsson et al. 2011; Jansson et al. 2017; Ahtikoski et al. 2018). To develop a more effective response in Canada, there is an urgent need for macroscale analyses which can assist in the prioritization of locations for forest planting, particularly using improved stocks to improve regeneration success under future climate threats (Lemprière et al. 2008; Lindner et al. 2010). For this, stand-level ecological and economic information would need to be incorporated, to assess whether landscape or regional scale forest management objectives have been met. However, this has been difficult (Smyth et al 2014; Lemprière et al. 2017) in the past, since we did not have the multiscale modelling tools required. As a result, field foresters making forest planting decisions (Howard and Temesgen 1997; O’Hara and Nagel 2013) had limited  83  influence on broader strategies or policies that were attempting to deal with large-scale industrial strategies (Bull et al. 2018), including climate-change response policies.  In this research, I linked localized forest management decisions to a macroscale using a forest estate (i.e., decision support) modelling approach. Forest estate models project future stand attributes under alternative forest management scenarios, simulating timber harvests and subsequent regeneration, while simultaneously considering long-term objectives related to harvest rates, carbon stocks, and other sustainability indicators (Davis et al. 2001; Armstrong and Cumming 2003).  To illustrate the importance of the stand-level to macroscale level tools, I examined forest management scenarios under climate changes for the western boreal forest of Canada. Already, planting seedlings with improved genetics capable of increasing yields and resiliency to biotic and abiotic stressors driven by climate change has been proposed (Hulme 2005; Spittlehouse 2005; Ogden and Innes 2007; Aitken et al. 2008; Seppala et al. 2009; Williamson et al. 2009; Gray and Hamann 2011; Pedlar et al. 2011; Williams and Dumroese 2013; Porth et al. 2015; Bullen 2017; O’Neill et al. 2017). This proposed strategy involves the application of tree improvement technologies to select genotypes from other provenances that are better-adapted to new climate conditions (Hulme 2005; Aitken et al. 2008; Seppala et al. 2009; Williamson et al. 2009; Gray and Hamann 2011; Pedlar et al. 2011; Williams and Dumroese 2013; Porth et al. 2015). For example, using lodgepole pine (Pinus contorta Doug. ex Loud. var latifolia Englm.) provenance tests, Montwé et al. (2016) showed that southern provenances generally had improved drought resiliency, along with improved growth rates except for the most southerly provenances that were the least productive. Ahmed (2016) used a meta-analysis of white spruce  84  provenance tests across Canada’s boreal to predict yields of various provenances based on local climate and site variables. She found 8 to 25% height gains using non-local relative to local provenances.  Broadly speaking, the objective of this research chapter was to develop a decision support tool (labelled as Q3), based on forest estate simulation procedures, to connect the local to macroscales, and integrate ecological-economic variables, in order to improve the linkages between localized forest management decisions and the subsequent macroscale impacts. The value of this approach is that scientific results in fields such as forest genetics applicable at the localized scale can be linked to macroscale forest management strategies and policies aimed to address climate change and forest sustainability. In addition, the approach developed can also help decision makers, always faced with scarce financial resources, set priorities for forest planting locations decisions that can integrate improved planting stocks. The aim is to have healthier, resilient forests that are also attractive for financial investment in the forest sector, given a competitive suite of goods and services can be produced.  Specifically, I illustrated the usefulness of the Q3 tool by: i) identifying the locations across Canada’s western boreal forest where improved stocks would be prioritized for planting; and ii) evaluating the vulnerability of these reforestation strategies to one important climatic stressor, future drought events. The vulnerability of reforestation strategies to drought was determined from: i) projected changes in the hydrologic regime; ii) species-specific exposure and sensitivity to these changes; and iii) the capacity of the forestry industry to plant improved stocks which could mitigate these changes. In particular, planting improved stocks originating from southern  85  climes was assumed to be resilient, while natural regeneration or the use local stocks remained vulnerable to future drought.  4.2 Materials and Methods 4.2.1 Study Area The study area included 77 forest management units (average size = 0.94 Mha; standard deviation (SD) = 1.37 Mha) that define the recent forest industry operating area in the western boreal forest of Canada (hereafter, just “western boreal”). These FMU’s cover ~72.5 Mha and were identified as locations where timber harvesting and reforestation would occur based on the most current forest state as described by the forest attributes information (described later) in the year 2010 (Fig. 4.1). FMU’s are publicly owned by the respective provinces, with management responsibilities like reforestation being mandated to the industry through contractual agreements (i.e., forest tenure; Luckert and Haley 1995; Cumming and Armstrong 2001). Often more than one forest products firm operates within the same FMU and may include clusters of primary and secondary industries (Ghafghazi et al. 2017). Primary industries (e.g., saw mills, some pulp and paper mills) rely on merchantable volume, which can be defined as the volume of trees having greater than 4.88 m of length with a minimum diameter of 15 cm outside bark at stump height (0.30 m above ground) and 10 cm top diameter inside bark (i.e., termed 15+/10); conversely, secondary industries rely on byproducts from these primary industries (e.g., some pulp mills and bioenergy facilities; see Ghafghazi et al. 2017). The implication of a diverse forest products cluster is a demand for species-specific fibre needs (Cumming and Armstrong 2001).  86   Figure 4.1. Locations where forest companies operate in Canada’s western boreal and the transportation distance of timber to a forest products firm (indicated by dots) that is capable of processing merchantable timber volume. Crossed markings are intersections of major latitudes and longitudes. Merchantable tree species within the study area include cold-tolerant coniferous species, particularly: white spruce; black spruce (Picea mariana (Mill.) BSP); tamarack (Larix laricina (Du Roi) K. Koch); balsam fir (Abies balsamea (L.) Mill.); lodgepole pine (in British Columbia (BC) and western Alberta only); and jack pine (Pinus banksiana Lamb., in eastern Alberta, Saskatchewan, and Manitoba only). Deciduous species, particularly aspen (Populus tremuloides Michx.), balsam poplar (Populus balsamifera L.), and paper birch (Betula papyrifera Marsh.) occur in either pure stands or in mixtures with conifers (Brandt 2009). These species represent  87  the major fibre demands that would cascade through the various primary and secondary forest industries as described in Ghafghazi et al. (2017).  Timber harvesting typically uses harvesting systems that emulate natural disturbance agents. Fires, insects and diseases are the major very large-scale natural disturbance agents in the Canadian boreal, causing infrequent, spatially-extensive changes in growing stocks. The growing season of the boreal zone is relatively short at ~175 days (Brandt 2009) with growth rates averaging less than 2 m3 ha-1 yr-1, and maximal rates of 5 m3 ha-1 yr-1. These large scale natural disturbance agents and slow growth rates are factors that support the prescription of clearcutting harvesting systems (NFDB 2017). Following timber harvesting, reforestation is mandatory with objectives often focused on maintaining the pre-harvest species compositions.  4.2.2 Forest Estate Model (Q3) 4.2.2.1 Overview A Q3 forest estate model, representing the modelling phases quantify, query and queue (see Figure 4.2), was developed to link localized reforestation decisions to macroscale ecological and economic outcomes. Although this model could be used to directly evaluate a variety of forest management questions at a macroscale, here planting investment scenarios were evaluated separately for each FMU and results were summarized to the macroscale using all 77 FMUs currently active within the western boreal. An overview of Q3 is provided in this section along with details on the forest estate model processes. Specific details of the inputs used and the scenarios simulated using Q3 are in the sections that follow.   88   Figure 4.2. Q3 work flow (quantify, query and queue) used to link localized decisions (i.e., reforestation in this paper) to macroscale outcomes. 89  Q3 is a Java-based modelling tool that compiles and scales ecological and economic information required for localized forest management decision making. The initial phase of Q3 ‘quantifies’ economic information including prices of forest products and the cost to get the timber to mill gate, and ecological information including current forest attributes maps and growth and yield tables, which are basic input requirements for the forest estate model. Spatially-explicit forest attribute maps provide the location and area information of each pixel (e.g., the 90 m x 90 m spatial resolution and 2010 forest inventory information in this research chapter) along with the forest attributes, namely species composition, crown closure, height, and age classes of each pixel. The shortest distance to a forest products firm (i.e., transportation distance) is also required for each pixel to get estimates of transportation cost. Growth and yield forecasts by stand type (i.e., aggregated spatial unit as described by transportation distance class, species, crown closure, height and age matching forest attributes defined for each spatially explicit pixel) before and after harvest are also obtained using available growth and yield models. The next phase of Q3 ‘queries’ this information to provide the future yield estimates along with the net present value (NPV) for each management prescription by stand type. In the application given in this research chapter, the management prescriptions described the harvesting strategy (i.e., timing) and the subsequent reforestation strategy, including the type and timing of natural, planted local or improved stocks.  The third phase of Q3 ‘queues’ stand types to specific management prescriptions by using a forest estate model. This forest estate model is a Model I linear programming formulation (Johnson and Scheurman 1977) which optimally allocates hectares of various stand types into management prescriptions under the objective of maximizing the NPV over a planning horizon (i.e., 30-years). For this research chapter, the prescriptions assigned for each time (i.e., future  90  year) were: i) no harvest; ii) harvest and use natural reforestation; or iii) harvest and plant with either all local or all improved stocks of the pre-harvest leading species. To emulate current Canadian economic forest management practices, Q3 allows for flow and sustainability constraints. For this study, constraints were placed on: i) the sustainability of each stand type (i.e., ensure that the total area of each stand type remains the same through the 30-year planning horizon); ii) the upper and lower bounds on 5-year harvest flows; iii) the sustainability by insuring non-declining stocks (i.e., the future forest has at least as much merchantable volume as the initial state); iv) the minimum planting effort; and v) the minimum volume harvested in 5-year time period. The output of the queue phase is the area allocated to each management prescription by stand type (i.e., aggregated spatial unit). Next, this information is linked to each pixel of an FMU based on forest attributes to determine the management prescriptions available to a pixel, and a decision of which to prioritize is made on each pixel. In particular, planting prescriptions were prioritized to pixels with drought exposure and sensitivity. Finally, using the list of pixels with their prescriptions, along with costs and prices, the financial attractiveness of the forestry industry was determined using net present value (NPV). In this research chapter, as well as financial attractiveness, drought vulnerabilities of harvested sites were determined by assessing each pixel for drought exposure along with the species-specific sensitivity to drought following harvest.  4.2.2.2 Formulation The Q3 Forest Estate Model was formulated using a Model I (Johnson and Scheurman 1977) approach as stated earlier. For this study, a planning horizon of 30 years and one-year time steps were used for each FMU (n = 77), since this planning horizon generally mimics the length of the tenure rights granted to the forestry sector in the western boreal. Further, the planning horizon  91  affects the motivation for long-term forestry sector investments (Luckert and Haley 1995); however, many options are possible within the Q3 modelling framework. Then, using this planning horizon and the notation in Dykstra (1984, p. 118-128), the objective function was:  [4.1] Max  ∑ ∑ ∑ Cijk𝐾k=1 XijkJj=1𝐼i=1  where Xijk is the number of hectares assigned to stand type i, harvested in period k, and regenerated according to prescription j (i.e., the decision variables to be solved); Cijk is the net present value per ha (see Eq. 4.2) that can be obtained from harvesting stand type 𝑖, harvested in period k, with management prescription j; I is the total number of stand types in the planning area; J is the total number of stand management prescriptions and K is the total number of periods. As noted earlier, stand type is an aggregated spatial unit based on transportation distance and forest attributes namely species, crown closure, height and age. For this research, stand types were characterized by 25 age classes, four crown closure classes, 10 species groups, 15 height classes, and seven transportation distance classes for a total of 105 000 potential stand types in each FMU. Stand management prescriptions used in this research chapter were based on harvest and regeneration strategies. At each time period (k) in the 30-year planning horizon (i.e., k=1 to 30, where k=1 is the initial state in 2010), options were to harvest or not harvest. Then, if harvested, the options for all or portions of the stand type were: i) use only natural regeneration; ii) plant with local stocks; or iii) plant with improved stocks. Prescriptions were confined to a maximum of one harvest and regeneration event in the planning horizon (i.e., only the first pass of a two-pass harvesting system was simulated). Using Q3, NPV for each stand type and management prescription was calculated as:  92  [4.2] Cijk=( ∑ Yijko(Pijko-VCijko))-FCijk3o=1(1+r)k  where Yijko is the yield (various units per ha-1) of product o in stand type i, in period k from prescription j; P is the price ($ per unit of o) ; VC is the variable cost per unit of product o which changes with prescription j and the fuel cost based on transportation distance; FC is the fixed cost ($ ha-1); r is the discount rate; and k is the time period when prescription j was implemented. In this research chapter, all costs and prices were in USD and the products (o) were restricted to saw logs (m3), biomass for pulp (oven dried tonnes), and woody residue for energy (GJ). The product profile for each stand was assumed as: saw logs were 60% of the coniferous merchantable volume (CMV); biomass for pulp was 35% of the CMV plus 85% of the deciduous merchantable volume (DMV) which were converted to a oven dried tonne basis (odt; State of Energy Use in Canada's Wood Products Sector 2015); and woody residue was the remaining 5% of the CMV plus 15% of remaining DMV converted to odt and to GJ using a factor of 18.5 GJ per odt (Ralevic et al. 2010). As noted earlier, constraints on the allocation of management prescriptions can be implemented in the developed forest estate model. For this study, first, the sum of areas of stand type i assigned to any one management prescription k was restricted to be equal to the total area of stand type i at the initial state (k=1 in 2010) (Ai).  [4.3] ∑ ∑ XijkKk=1 = A𝑖𝐽j=1     ∀ i For forest estate planning, volume flow constraints are commonly added to ensure sustained flow of fibre from the planning area. Often, this constraint is based on the volume harvested (F) in a period of time (t) relative to that of a prior period. For this study, the harvest flow period was set  93  to five years, with period t=1 representing the total harvested volume for years 1 through 5, t=2 is for years 6 to 10, etc., and the volume harvested in each period was constrained to be within +/- 5 % of that in the previous period (β=α=0.05, Eq. 4.4 and 4.5). Although yearly harvest rates may fluctuate, 5-year time-steps were used to remain consistent with provincial regulations that require sustained yield based on balancing the harvest rates within a 5-year period (NFDB 2017).  [4.4] (1-α)Ft - Ft+1  ≤ 0    t = 1, …, 5  [4.5] (1+β)Ft - Ft+1 ≥ 0    t = 1, …, 5  Management scenarios are often constrained to ensure that stocks do not decline relative to the start of a planning horizon as a desired condition of the future forest. In this research chapter, a sustainability constraint was included to produce an ending merchantable growing stock inventory equal to or greater than initial (k=1 at 2010) merchantable growing stock inventory (EMI).  [4.6] ∑ ∑ MVijXijJj=1Ii=1  ≥ EMI  where MVij is the merchantable volume (m3 ha-1) at the end of the planning horizon for stand type i with prescription j.  Since planting requires additional costs over natural regeneration, a constraint was included that forces Q3 to allocate hectares for planting in this research chapter. For this, a minimum amount of planting effort constraint (expressed as a percentage, θ) over the planning horizon was included.  [4.7]  θ100∑ ∑ ∑ XijkKk=1𝑗 ∈ 𝑁𝑅  Ii=1 -  ( 1 - θ100) ∑ ∑ ∑ XijkKk=1𝑗 ∈ 𝑃𝑆  Ii=1 ≤ 0   94  where NR and PS are sets of management prescriptions that prescribe natural reforestation versus planted stocks, respectively. Another common constraint is a minimum harvest in each year to ensure sustainability of processing firms. Summing over prescriptions that harvest in time t, the constraint was represented as:  [4.8]  ∑ ∑ VHijkXijk Jj=1Ii=1 ≥  MVHk  ∀ k where VHijk is the merchantable volume (m3 ha-1) harvested in period k for stand type i with prescription j; and MVH is the minimum required annual volume harvested. MVH was assumed the same for all k periods and was determined as 40% of the average annual volume harvested from the non-restricted model (i.e., excluding Eq. 4.8) following Palma and Nelson (2009). The last constraint added ensured that non-negative hectares were assigned to any of the management prescriptions for any stand type. This could feasibly occur for management prescriptions yielding negative NPVs. [4.9] Xijk ≥ 0        ∀ i, j, k Each FMU formulation was solved using the Lp_solve v 5.0 Java library (Berkelaar et al. 2005; http://web.mit.edu/lpsolve/, accessed June 24th, 2015).  4.2.3 Ecological and Economic Information 4.2.3.1 Prices Price scenarios needed for Eq. 4.2 were developed for crude oil (to be used as a surrogate for diesel fuel cost $ L-1), saw logs ($ m-3), biomass for pulp ($ odt-1), and residue ($ GJ-1) using a combination of price scenarios forecasted from global land use models and a price volatility  95  model as demonstrated in Chapter 3 (see also Lochhead et al. 2016). In particular, price scenarios for saw logs, biomass for pulp and residues were determined from the global biosphere model (GLOBIOM; see Havlík et al. 2011; Havlík et al. 2014). GLOBIOM uses a global recursive dynamic partial equilibrium modelling structure that covers 30 world regions, 18 agricultural crop types, a range of livestock production activities, forest products, first- and second-generation bioenergy, and water (Sauer et al. 2010). Market equilibrium in GLOBIOM is gained by maximizing the sum of producer and consumer surplus subject to various constraints regarding resources, technology, and policies (see www.globiom.com, accessed July 6th 2017). Using GLOBIOM, a business-as-usual scenario describing what the world could look like if consumer behaviour continues on the path of historic trends as outlined in the World Wide Fund living forests report (Taylor 2011) was used to forecast long-term prices. Since crude oil price was not forecasted in GLOBIOM, a business as usual scenario was used from outlook reports by the US Energy Information Administration (2010). In this research chapter, the resulting long-term business-as-usual price forecast was used within Q3.  Finally, the price volatility information represented by the mGARCH model of Chapter 2 provided short-term price movements, which were used later in the analysis to indicate the sensitivity of forecasted scenarios to short-term price changes. All price forecasts were localized for the period covered in the planning horizon of this study (i.e., initial state in 2010 with a 30-year planning horizon) using yearly price data from 2010 to 2015 from Mundi index (see https://www.indexmundi.com/commodities/, accessed July 28th 2017) and Random Lengths (see http://www.randomlengths.com/in-depth/monthly-composite-prices/, accessed July 28th, 2017) and then converted from commodity prices to log ($ m-3), pulpwood ($ odt-1) and energy ($ GJ-1)  96  following Ghafghazi et al. (2017). Also, crude oil prices were converted to diesel prices using a rule-based conversion (TBA 2013).   4.2.3.2 Cost Structure The cost structure included harvesting, regeneration, and transportation components (Table 4.1). Harvesting costs were categorized by harvesting phase, including road and site maintenance, “tree to truck” felling and yarding, and overhead costs. For natural regeneration, costs included site preparation and silvicultural surveys. For planting using local stocks, silviculture costs were based on the minimum amount of effort needed to meet government regulations of establishment and performance following harvesting. The planting costs were based on the maximum effort for planting (~$1500 ha-1) as reported in the Alberta timber damage assessment costs of reforestation (Alberta Agriculture and Forestry 2018), assuming that this would be similar for all provinces in the western boreal. I assumed no additional costs in using improved stocks over the cost of local stocks. Improved stocks may have additional costs over producing local stocks (e.g., 4 to 7 cents per seedling based on B.C. Government 2017); as a result, the analyses in this paper demonstrate an upper bound of the value of using improved stocks to the forestry sector. The transportation cost structure was conditional on the transportation distance, the timber volume to transport, and the forecasted fuel price ($ L-1). The minimum transportation distances were obtained for each 90 m pixel using a spatial road dataset (Geogratis 2013) overlaid with locations of forestry industry facilities within the western boreal (Ghafghazi et al. 2017). Network Analyst in ArcGIS v10.2 was used to find the optimal route (i.e., least-cost distance) between the pixel and the closest mill capable of processing logs. The resulting transportation distances were aggregated into seven classes represented by the midpoints 12.5, 37.5, 62.5, 87.5, 112.5, 162.5 and 200 km as shown in Fig. 4.1.  97  Table 4.1. Assumed cost structure of forest management activities. All costs in USD currency (2010 dollars). Type Cost Assumption (various units) Description Variable Overhead  $ m-3 = 9.52 - 0.015 * VH  Related administration and supervisory activities attributed to operations (i.e., “tree to truck”, transportation, basic silviculture) Variable Tree to truck  $ m-3 = 20.61 - 0.01979 *VH Includes expenses for landings, skid trail construction, felling, skidding and bucking, loading, crew transportation and any contractor profit under conventional ground based skidding Variable Fuel (i.e., diesel) cost (DC) $  = f(crude oil price) Price of diesel determined from a rule based conversion from crude oil following Transportation Business Associates (TBA 2009). Variable Number of truck loads (NL)  NL= (VH*0.5)/20 The number of truck loads per hectare of forest, assuming a 20 tonne capacity trailer. Variable Hauling  $ ha-1 = NL* (D/60)*(85.7 + DC*30) The cost to haul logs from the landing to the mill gate. D is the distance (km) to a processing facility, with trucking assuming an average speed of 60 km hr-1.  Fixed Natural Regeneration $ ha-1 = 1000 Relying on natural regeneration processes including seed sources and seed dissemination. Includes site prescription, preparation, surveying the establishment and performance following harvesting.  Fixed Planting local or improved stocks a $ ha-1 = 2500 Includes site prescription, preparation, surveying the establishment, performance following harvesting, cost of tree seedlings, planters and supervision.  Note: VH is the merchantable volume (m3 ha-1) harvested; a Costs based on natural regeneration plus those in the Alberta timber damage assessment costs of reforestation (ASRD 2014).  98  4.2.3.3 Forest Attributes For the initial state of the western boreal, spatially explicit, ‘wall to wall’ forest attributes information was used. As described in detail in Chapter 2 of this dissertation (see also Lochhead et al. 2017), this information was estimated using a kriging with external drift (KED) method to provide a multivariate forest attribute map at a pixel resolution of 90 m for the year 2010. The KED method involved fitting a simultaneous system of nonlinear models with spatially varying parameters using information available from Canada’s National Forest Inventory database. The forest attributes (a.k.a., Y-variables) were species percentages, crown closure (CC), average height (Ht) and age, and the predictor variables (a.k.a., X-variables) were variables extracted from Landsat TM/ETM+ imagery, interpolated climate variables, topographic variables, and other remote sensing products. The resulting KED method was applied to entire the boreal forest in Canada to obtain estimates of all forest attributes for each 90 m pixel (found at doi: 10.14288/1.0354319; accessed July 27, 2017). The resulting forest attributes maps were intersected with FMU boundaries of the western boreal (www.databasin.org, accessed June 24th, 2017). Although the FMU boundaries were determined by provincial administrative decisions and these may change over time, they represent the current size and distribution for planning and implementing forest management activities including reforestation (Gauthier et al. 2015b). Within each of these FMU boundaries, a spatial layer describing the productive forest area (PFA) was created and used to mask out non-productive forest areas. Non-productive forest area can be defined differently across the western boreal; the definitions used in this research chapter were from the National Forestry Database (NFDB 2017). For Alberta and British Columbia (BC), the PFA was defined as all pixels capable  99  of yielding merchantable volume (i.e., 15+/10 as defined earlier) of ≥ 50 m3 ha-1 by 140 years. For Saskatchewan, the PFA was defined as all pixels capable of obtaining a merchantable volume mean annual increment ≥ 0.5 m3 ha-1 yr-1. Finally, for Manitoba, the PFA included all pixels capable of eventually producing merchantable volume. These definitions required yield estimates over time, which were obtained using the growth and yield meta-model developed in this research chapter as next described.  4.2.3.4 Growth and Yield To define the PFA for each FMU and to forecast future forests under different scenarios for ecological and economic valuations, a growth and yield model was needed. The Mixedwood Growth Model (MGM) was selected as the basis for growth and yield forecasts; this model includes the stand types of the study area and was validated using permanent sample plot data established across the western boreal (Bokalo et al. 2010). MGM forecasts growth, yield, regeneration, and mortality at a tree-level (distance independent) allowing for species composition changes over time. Tree-level forecasts can then be aggregated to obtain growth and yield per ha for all species, as well as by species and size class. As a tree-level model, MGM requires a tree list (i.e., species, tree size, and stems per ha by tree) or at least a stand table (i.e., species and stems per ha by diameter at breast height (DBH) class). However, Bokalo et al. (2010) developed a method for obtaining estimated tree-lists given stand-level characteristics, and then these estimated tree-lists can be used as inputs to MGM. Using this approach in this research chapter, MGM outputs were obtained for a wide variety of stand types. Then, a meta-analysis of these MGM outputs was used to obtain yield tables for each stand type and management prescription in this macroscale analysis.   100  For the meta-analysis, a series of stand types were simulated up to 200 years using MGM. The initial MGM inputs describing the stand types were based on altering: i) site index (SI; i.e., 8 to 24 m by 2 m; nine levels); ii) regeneration delay (i.e., breast height age 14 to 34 years by 4 years; five levels); iii) species group, as defined by both broad cover group (i.e., D, deciduous dominant; C coniferous dominant; CD, mixed-wood with coniferous dominate; DC, mixed-wood with deciduous dominant) and leading conifer species (Sw, white spruce and Abies spp; Sb, black spruce and Larix spp.; P, Pinus spp.; 10 levels). The result of using these initial MGM inputs is a representative tree-list including an estimate of tree density (trees ha-1). Further, to account for variability in western boreal growth and yield, a stand density factor was included with three levels (based on 25%, 50% and 100% of the tree per ha estimate from MGM). This information was then compiled and used to simulate a total of 1 350 stand types (i.e., nine SI * five starting ages * 10 species groups * three density factors) for each of the four provinces (5 400 MGM simulations). Using the MGM outputs for the simulated stand-types, a meta-model for merchantable volume per ha over time was developed using:  [4.10] Ŷ=aAgebe-cAge where Ŷ is the estimated merchantable volume per ha for coniferous and deciduous species separately, and a, b, and c are parameters that vary with stand type. To obtain estimates of a, b, and c, PROC MODEL of SAS v9.4 was used in a parameter prediction approach (Littell et al. 2006b). These parameters varied by province and output of stand-level information predicted by MGM which provided a link to forest attribute information in each pixel of the western boreal. The MGM simulation with projected stand-level attributes (species group, crown closure, age  101  and height) that was closest to the corresponding forest attributes in a pixel was used to represent the growth and yield for that pixel. As an indication of plausibility of the yields, the merchantable volumes of ground plots established within Canada’s National Forest Inventory (Gillis et al. 2005; see nfi.nfis.org, accessed July 6th, 2017) were compared to yields using the meta-model. Correspondence between measured and estimated yields was similar with a root mean squared prediction error of 50.8 m3 ha-1. Since the MGM yield forecasts were based primarily on permanent sample plots located in naturally regenerated stands, these yields were adjusted for planted stands and thus assumed the same species composition will be planted and the initial planting densities will be similar to the density during establishment. First, since planting seedlings reduces the regeneration delay, the volume vs age trajectories using the meta-model were shifted to the left to lower the age at which a particular yield would be achieved. These shifts were based on the Huang et al. (1994) study of the number of years to reach 0.3 m (stump height) in naturally regenerated stands. Additionally, for improved planting stocks, yields were increased using a multiplier approach that assumes a percent increase of yields at all ages (i.e., 10% and 20% increases in this research chapter). Although other methods for projecting yield gains have been used, this multiplier approach is simple to apply in macroscale analyses and has been used in a large number of studies and locations (Newton et al. 2003; Jansson et al. 2017; Ahtikoski et al. 2018).  4.2.3.5 Drought Vulnerability Drought vulnerability (DV) of harvested sites was assessed following Johnston and Williamson (2007) and Aubin et al. (2018) by defining DV as a function of: i) drought exposure given  102  projected future climates (E); ii) species-specific sensitivities to these projected climates (S); and the adaptive capacity of the forestry industry (AC). Drought exposure was based on the climate moisture index (CMI), which is the difference between annual precipitation and potential evapotranspiration (see Hogg 1997). The CMI map projected for future climates (2011-2040) at a 1 km resolution by Hogg et al. (2016) was used to obtain CMIs for each harvested pixel at the end of the planning horizon. For this forecast, Hogg et al. (2016) used the Canadian Earth System Model (v2) to simulate a representative concentration pathway (RCP) scenario that assumes continued emissions increases (i.e., an anthropogenic radiative forcing of +8.5 W m-2 in 2100 relative to pre-industrial levels; IPCC 2014). Pixels with negative CMIs indicated moisture deficits while positive CMIs indicated moist conditions. However, the impacts of drought exposure will be conditional on species-specific traits. Following Aubin et al. (2018), species-specific sensitivities (thresholds) to drought exposure were calculated using spatial maps of historical CMI (1971-2000) and species distributions. Historical CMI distributions by species were calculated and the 5th percentiles of these distributions were used to indicate species-specific thresholds for drought exposure. Aubin et al. (2018) calculated the species CMI (mm) thresholds for mature tree species as: -5.2 for deciduous species; -4.4 for lodgepole pine; -3.9 for white spruce; -2.2 for black spruce; and 0.1 for jack pine. While Aubin et al. (2018) and Boucher et al. (2018) scaled these thresholds based on species-specific mature tree sensitivities, for regenerating trees; I assumed a high sensitivity for tree seedlings and directly used these thresholds. Lastly, the capacity of the forestry industry to mitigate drought exposure and sensitivity was based on the proportion of a pixel prioritized for planting with improved stocks, where a higher proportion indicates increased capacity. Using exposure, sensitivity and capacity of the forest industry, drought vulnerability for each harvested pixel was calculated using:  103  [4.11]  DVs = ESs – Cs where ESs is the proportion of the sth harvested pixel with a CMI below the threshold of the leading species; and Cs is the proportion of the pixel prioritized for planting improved stocks. A high DVs value indicates a high amount of the regenerating forest will be vulnerable to drought over the planning horizon. DVs values were then summed for each scenario over all harvested pixels in an MU.   4.2.4 Scenarios and Analysis  Historical harvest rates of 34.4 to 43.1 Mm3 yr-1 for 2010 through 2015 in the western boreal (assuming 18% of BC’s annual harvest rate was within the western boreal; NFDB 2017) were used to adjust the discount rate in all scenarios. Initially, several base simulations were run with different discount rates (between 0 and 6% by 1%). For these base simulations, greater than 50% of the harvested area was constrained to be planted in order to mimic the averaged planting percent over to 2010 to 2015 period. The VH (Eq. 4.8) was then summarized over all FMAs of the study and compared to the historic harvest rates. Using this process, a discount rate of 4% was selected for use in all simulations, since the initial 2010 to 2015 harvesting rates were within the historic bounds. Using this selected discount rate, nine scenarios were simulated by varying two factors: i) percent of the total harvest area prioritized for planting (i.e., planting effort); and ii) the yield gains over natural regeneration. For the percent of total harvest area planted, three planting efforts were assessed (i.e., θ in Eq. 4.7 set to 30%, 50%, or 70%). These levels represent plausible planting effort levels determined from historical data on the area planted in each  104  province (NFDB 2017). For the yields gains, three gain levels were included, specifically: i) 0%, indicating local stocks (i.e., same yields as for natural regeneration, but with a reduced regeneration delay); ii) a 10% increase relative to local stock yields using improved stocks; and iii) a 20% increase relative to local stock yields using improved stocks. These yield gains were based on plausible yield gains from provenance trials for white spruce reported in Newton (2003) and Xie and Yanchuk (2003), as well as simulations using the growth and yield meta-model developed by Ahmed (2016).  For the nine scenarios, initially all post-harvest areas were assumed to have successfully regenerated (i.e., 0% mortality rate). These simulation results were used to compare the planting effort and gain alternatives in terms of harvest rates over time, financial attractiveness, the locations of planted stands, and total area planted. To examine impacts of drought stress on financial attractiveness, the scenarios were reassessed using differential rates of mortality from drought stress (i.e., based on CMI species-specific thresholds), specifically: 10%, 25% or 100% (i.e., all died). The mortality rate was implemented on harvested pixels (or proportions of pixels) under drought stress (i.e., ESs > 0) that were either naturally regenerated (i.e., areas not planted as simulated for all gain levels) or planted using local stocks (0% gain only). For areas with regeneration failures due to drought-related mortality, additional planting using improved planting stocks to meet regulated regeneration requirements was assumed at a cost of the mortality rate multiplied by a fill planting cost of $1 500 ha-1 for the portion of the pixel that was under drought stress. Finding productive and drought-resistant genotypes may be difficult as trade-offs between growth and heat drought resistance have been demonstrated (Bigras 2005). However, stocks selected from southern boreal climes tend to have greater drought-resistance since they tend to experience drier growing conditions. Thus, these stocks would likely have  105  greater survival rates relative to local stocks or natural regeneration under future droughts from climate changes (Wang et al. 2006). For this research, I assumed that drought-resistant genotypes would be obtained through tree improvement programs. For each scenario, the financial attractiveness of the forestry sector was assessed using net present value (Eq. 4.2) for 20 realizations of price volatility around the price scenario. Note that the price volatility model was incorporated into the analysis after Q3 had solved the forest estate model under the business as usual price scenario. Including price volatility indicated the uncertainty of investments in planting due to future price movements, since increases in forest product prices can lead to increased attractiveness for investments into reforestation (Sohngen et al. 1999) including planting improved stocks. These price volatility realizations allowed saw log, biomass used for pulp production, woody residues for energy, and fuel for transportation prices to simultaneously vary through time; therefore, the uncertainty of each price considered the direct influence of that price as well as its joint influence with the other prices (see Lochhead et al. 2016; Pianosi et al. 2016). Financial attractiveness was then assessed as an average and standard deviation of these 20 price realizations. To compare the financial attractiveness across scenarios, the difference in total NPV between using improved stocks (10% or 20% gain scenarios) versus local stocks (i.e., a 0% gain) was divided by the area planted for each FMU and labelled as ΔNPV.  106  4.3 Results 4.3.1 Prioritizing Planting Locations For all reforestation scenarios and assuming 100% regeneration success post-harvest (i.e., 0% mortality rate), the annual volume harvested (i.e., shown as averages by 5-year period) showed declining trends over the 30-year planning horizon, especially for the 30% planting scenarios with a decline of 5% per 5-year period (Fig. 4.3; Eq. 4.4 and 4.5). The annual volume harvested was greater than the lower bound of the historic harvesting rates initially in the 30-year horizon for all scenarios, but less than the lower bound of the historic harvesting rates towards the end of the 30-year horizon for all but the 70% area planted scenarios which were very close to the lower bound. As expected, planting improved stocks with 10 or 20% yield gains increased the total volume harvested (across the 30 year planning horizon) by 2.74 to 5.17 Mm3 over using local stocks. Using improved stocks with 20% yield gains increased the annual volume harvested by ~1 Mm3 yr-1 relative to planting stocks with a 10% gain. Thus, the difference in the annual volume harvested between a 10% and 20% yield gain scenario was smaller relative the difference between using local stocks (0% yield gain) versus improved stocks (10% or 20%). Note that yield gains from genetic stock could also consider gains from reducing losses to insects and disease which was not included in this analysis. Stand types selected for harvest had an average volume per ha ranging from 145.1 to 153.4 m3 ha-1, increasing with the planting area percentage (θ in Eq. 4.7). Across the scenarios, the majority (~90%) of volumes harvested were coniferous species. The annual area harvested over the 30-year horizon ranged between 242 200 to 238 300 ha yr-1, with the 30% and 70% planting scenarios resulting in the largest and smallest areas harvested over the 30-year planning horizon,  107  respectively (Table 4.2). The area planted for each scenario was the minimum planting effort for that scenario.   Figure 4.3. Annual volume harvested (averaged by 5-year intervals) for the 30-year projection under each scenario. Bold solid lines represent the upper and lower bounds of historical harvest rates 108  Table 4.2. Summary of the nine scenarios represented by planting and gain percentages. The 0% gain refers to local stocks, whereas the 10% and 20% gains refer to yield increases using improved stocks. The percent of prescriptions changed is relative to a 0% gain. Plant (%) Gain (%) Average Harvest Volume             (m3 ha-1) Average Harvest Area          (1 000 ha yr-1) Percent of prescriptions changed (%) Planted Area by Leading Species (%)a   Transportation Class Area Planted (%) b Sw Sb P Aw 0-25 26-50 51-75 76-100 101-150 151+ 30 0  145.3 237.0 . 22.9 46.0 13.8 17.3 19.4 15.3 15.3 13.5 11.0 4.9 10 145.2 238.0 5.7 22.1 42.9 14.9 20.1 18.8 14.9 14.6 13.2 11.0 4.9 20 145.1 238.3 6.9 21.9 41.6 15.1 21.4 18.3 14.6 14.3 13.0 11.0 4.9 50 0  149.6 229.6 . 25.1 46.5 14.7 13.7 28.4 23.8 24.2 22.4 17.8 9.4 10 149.4 230.5 6.4 24.1 44.8 15.4 15.7 27.9 23.8 23.6 21.7 18.1 9.4 20 149.3 230.9 8.0 23.9 44.1 15.4 16.6 27.5 23.6 23.6 21.7 18.2 9.3 70 0  153.4 226.2 . 26.6 47.6 15.5 10.3 37.2 33.8 34.2 31.2 25.8 15.2 10 153.3 227.3 6.5 26.0 46.5 15.6 11.9 37.2 33.7 34.2 31.2 25.9 15.2 20 153.2 227.6 7.8 25.7 46.0 15.6 12.7 37.1 33.8 34.1 31.0 25.9 15.2 a Sw- white spruce and Abies spp.; Sb -black spruce; P-pine; and Aw –aspen and other deciduous species. b Transportation distance classes in kilometres. 109  The spatial locations prioritized for planting local stocks determined from Q3 are presented in Figure 4.4. Alberta and BC had the largest harvest areas corresponding with the highest total areas planted; Saskatchewan and Manitoba had the smallest. As the planting effort increased from 30% to 70%, the selected planting locations were in similar pixels within each FMU, but the percentage of the pixel that was planted increased (Fig. 4.4). The change in management decisions from planting improved stock relative to local stocks ranged between 5.7% to 8.0% within a given planting effort scenario (Table 4.2). Stand types prioritized to planting local (0% gain scenarios) or improved stocks (10% and 20% gain scenarios) were predominately coniferous species (63.5 to 74.2 %) with white spruce and black spruce as the leading species. Increasing the planting percentage resulted in less area planted with deciduous species (Table 4.2). Although the area allocated to planting local or improved stocks occurred across a range of transportation distance classes, increasing the planting effort resulted in planting more pixels with shorter transportation distance. For the baseline scenario with a 0% mortality rate, the average difference in NPVs resulting from yield gains using improved planting stock versus local stocks (i.e., ΔNPV; standardized to per ha using planted area) were between $10.45 (SD = 3.05 ) to $37.29 (SD = 11.5) ha-1 across FMUs and planting scenarios (the 30% planting was the largest ΔNPV). The ΔNPVs declined with several indicators of the initial state of the FMU including the average distance to the processing facility, average stand age, and percentage of merchantable volume as coniferous (i.e., negative correlations; Table 4.3). This indicated greater benefits for younger deciduous or mixed stands nearer to a processing facility, but the average distance to the processing facility and average age had greater impacts (i.e., stronger correlations) than the percentage of merchantable volume as coniferous.   110   Figure 4.4. Maps of local stock planting locations forecasted over a 30-year planning horizon. The top map assumes planting (θ) 30% of the total harvest area and the bottom map θ = 70% of the total harvest area (see Eq. 4.7).    111  Table 4.3. Pearson correlations (ρ) between the change in NPV and averaged stand attributes by FMU (N=77 FMUs). The change in NPV is calculated as the NPV for improved stocks (10% or 20% gain) relative to regular stocks (0% gain) under the assumption of no regeneration failure.  Plant (%) Gain (%) Average Productive Forest Area Stand Attribute a Average Distance to Processing Facility Average Stand Age Percentage of Merchantable Volume as Coniferous 30 10 -0.214  -0.226 -0.346 20 -0.151  -0.167 -0.296 50 10 -0.540  -0.422 -0.381 20 -0.523  -0.433 -0.433 70 10 -0.510  -0.394 -0.332 20 -0.492 -0.402 -0.338 a Averages were area-weighted by stand areas. Regular type indicates very low correlations, italics indicates low correlations and bold indicates moderate correlations.  4.3.2 Vulnerability to Drought Between 2010 and 2040, a total of 2.38 Mha of the western boreal PFA (7.57%) was projected to be exposed and sensitive (hereafter, just ES) to drought under an extreme climate scenario (i.e., RCP +8.5 W m-2; Fig. 4.5). Areas ES to drought occurred throughout the western boreal, but more commonly occurred in southern FMUs. Over the PFA, 61.5% of the FMUs had some area ES to drought. However, there was a predominance in Alberta (1.30 Mha) and Saskatchewan (1.03 Mha). In Alberta, areas ES to drought were found in 19 of the 20 FMUs. In Saskatchewan, areas ES to drought were found in all 19 FMUs. Five of the FMU’s in each of British Columbia and Manitoba had areas ES to drought, but total ES areas were only 0.02 and 0.03 Mha, respectively.   112  Only 0.80 to 0.82 Mha of the ES area would be harvested under the 0% gain scenarios (i.e., using natural regeneration and local stocks). The majority of harvested area that was ES to drought was in Alberta and Saskatchewan. The majority of stand types harvested that were ES to drought were in species groups with conifer dominated black spruce and pine (C-Sb and C-P), mixedwoods (deciduous and conifer) with conifer dominated by black and white spruce (CD-Sb and CD-Sw) and conifer dominated white spruce (C-Sw). 113   Figure 4.5. Proportions of pixels environmentally sensitive to drought in western boreal FMUs. 114  4.3.3 Financial attractiveness   The total NPV to the forest industry from harvesting drought exposed and sensitive stands ranged between $1 191.9 M to $1 510.6 M with the 30% planting scenario resulting in the largest NPV. Using an assumed 10% regeneration mortality rate for naturally regenerated stands (all gain scenarios) or local stocks (0% gain scenario only), the total reforestation costs incurred from replanting the portions of harvest areas ES to drought ranged from $25.5 M to $78.7 M over the 30-year planning horizon depending on the planting effort (Table 4.4). Overall, considering the replanting costs needed for complying with reforestation obligations provides evidence that initially prioritizing planting locations with improved stocks (i.e., yield gains or 10% or 20%) would be a more financially attractive reforestation strategy relative to planting local stocks and replanting the drought vulnerable areas.  Including the costs to replant drought vulnerable natural regeneration and local stock, the average ΔNPV resulting from planting improved stocks (i.e., 10% or 20% gain) relative to planting local stocks (i.e., 0% gain) ranged from $19.66 (SD =3.06) to $44.32 (SD = 11.53) ha-1 for a 10% regeneration mortality rate and $ 33.48 (SD = 3.06) to $ 54.87 (SD = 11.53) ha-1 under 25% regeneration mortality rates. The resulting increase in ΔNPV from increasing the mortality rate of drought vulnerable regeneration was an indication of the cost savings from initially planting drought vulnerable areas with improved stocks versus having to replant the drought vulnerable local stocks (i.e., pay an additional $1 500 ha-1 on top of the $2 500 ha-1).   115  Table 4.4. A comparison of the costs to replant drought vulnerable regeneration with the total cost to initially plant with improved stock.  Plant (%) Gain (%) Replanting Cost ($ M) Cost to Plant Improved Stock @ the Planting Percentage ($ M) 10% Mortality 25% Mortality $40 ha-1 $70 ha-1 30 0 78.7 196.7 . . 10 62.2 155.5 35.7 62.6 20 63.3 158.4 35.3 61.9 50 0 76.3 190.8 . . 10 44.8 111.9 66.5 116.4 20 45.0 112.5 66.2 115.8 70 0 73.4 183.6 . . 10 25.3 63.4 107.5 188.2 20 25.5 63.9 107.3 187.7 4.4 Discussion Linking localized forest management decisions to macroscale outcomes is needed to inform policy makers of our capacity to respond to climate change (Keskitalo 2008; Lindner et al. 2010). In particular, planting stocks with improved yields has been proposed as means to mitigate the adverse impacts of changing climates (Hulme 2005; Spittlehouse 2005; Ogden and Innes 2007; Seppala et al. 2009; Gray and Hamann 2011; Williams and Dumroese 2013; Gauthier et al. 2014; Porth et al. 2015; Bullen 2017), including anticipated increases in drought events. While increasing the post-harvest planting, particularly using more improved stocks, will initially increase planting costs, the overall regeneration costs may decrease via reductions in plantation vulnerability. In this research chapter, a macroscale decision support system, Q3, was developed and used to examine regeneration scenarios using improved stocks. The aim was to build a tool that could start to examine the net financial benefits of using more improved stock for reducing the vulnerability of reforestation to drought in the western boreal of Canada.  116  Determining these costs is necessary for collaborative macroscale policy development (Bull et al. 2018). The costs and benefits of a macroscale adoption of improved planting stocks are partially dependent on the state of the forest, markets for products and services, and management constraints (Guo and Costello 2013). To examine the costs and benefits assigned requires high-resolution spatio-temporal information that can serve as the foundation for linking macroscale decision support systems (here, Q3) to localized management decisions (Lindner et al. 2010; Lemprière et al. 2013). Q3 provided a means to link localized reforestation decisions to macroscale outcomes, improving evaluations of the capacity of forest management strategies to mitigate climate-change vulnerability (Gauthier et al. 2015b; Aubin et al. 2018).  In this chapter, Q3 was applied to the western boreal forest in order to find better answers to particular strategic questions: 1. Where, when and how much improved planting stock should be planted?  2. How should we prioritize the planting across the macroscale?  3. How effective will the planting be in addressing vulnerability of the forest to a climate stressor such as drought? The choice of a planting location affects the projection of yield gains from improved stock because of heterogeneity in site productivity and vulnerability to future climate threats. The planting locations determined by Q3 were found capable of reproducing historic harvest volumes under different assumptions of planting effort and yield gain from improved planting stocks. For a given planting effort, the macroscale impact of a 10 or 20% yield gain from planting improved stocks increased harvesting rates in the beginning of the planning horizon relative to using local  117  stocks, supporting an allowable cut effect (ACE; Schweitzer et al. 1972). The ACE estimated from Q3 totaled (over the 30 year planning horizon) 2.74 to 5.17 Mm3 and translated into NPV gains of $10.45 to $37.29 ha-1; however, not all of the FMU’s would result in an ACE. FMUs characterized by shorter transportation distances, along with relatively younger stand ages and a smaller percentage of coniferous volume would achieve greater financial returns from planting improved stocks. Under future changes to climate in Canada’s boreal, increasing natural disturbance events may increase the spatial extents of young stands with a lower percentage of coniferous volumes (Williamson et al. 2009). The lower transportation costs decrease costs, whereas the other attributes generally reduce yields and therefore value, providing greater incentives to invest in improved stocks that increase yields (Sohngen et al. 1999). Despite its controversy (Luckert and Haley 1995; Weetman 2002), an ACE is important to demonstrate to macroscale policy maker’s one potential value stream to the forest industry (Binkley 1980). It is important to note that this indicator of financial attractiveness is highly influenced by the discount rate (i.e., 4%; Adamowicz et al. 2003) which triggers a debate on which discount rate to use, if any. There is evidence in Canada that first nations, private forest industries and governments may choose a lower discount rate (Stern 2008; e.g., 1.4%) and this could increase the value generated by an ACE. Further, the relatively short 30-year planning horizon in this study limited the value generated from an ACE; however, this planning horizon mimicked the duration of tenure rights allocated on these public lands (Luckert and Haley 1995). Lastly, as a cautionary note, yield gains by using stocks that mitigate other factors, for example, reducing insect and disease incidences were not accounted for in this analysis, but this would increase the forest value stream (Schwab et al. 2011).  118  As well as increased yields, reforestation strategies using improved stocks can be financially attractive as a cost minimization strategy under policies with stand establishment constraints. Considering an extreme climate change scenario (RCP +8.5 W m-2) for 2010 to 2040, the macroscale simulations suggest that a total of 0.80 to 0.82 Mha (~12%) of the post-harvest stands will be exposed and sensitive to drought and are thus, at risk for regeneration failure. The cost of replanting these sites was found to be higher than the costs of planting improved trees across the macroscale. Re-planting due to the improper selection of planting stock drastically increases the reforestation cost and thus, a macroscale adoption of improved stock contributed greatly to the forest industries value stream. Given the ability of Q3 to link local to macroscales, it was shown that at a risk of 25% of the drought vulnerable area would require replanting (i.e., 3% of the total harvest area); a planned macroscale adoption of improved planting stock at a cost of $40 ha-1 would be a financially attractive strategy relative to having to replant these areas. This result presents evidence that the conventional perspective of an ‘extensive’ approach with a reactive view of climate change is likely to be more costly under future climate change threats. In contrast, a planned macroscale adoption of improved stock can be a financially attractive strategy to mitigate these costs when considering drought vulnerability and stand-establishment constraints. Dymond et al. (2015) showed that proactive management through improving the resiliency of forested landscapes can be an economically viable option. A macroscale adoption of improved planting stock is important for tree improvement programs to achieve economic feasibility via economies of scale where costs of producing improved stocks can be spread over a greater area (Schreiber and Thomas 2017). The ability of tree improvement programs to find both a productive and drought resistant genotypes might be costly (Birgas 2005), specific to certain species (MacLachlan et al. 2017) or require tools like genomic selection (Beaulieu et al.  119  2014). Thus, it could be argued that it is as important to focus on drought resilience as it is on growth in order for improved planting stock to be financially attractive to the forest industry. Although the Q3 model developed and used in this study linked localized forest management decisions and macroscale outcomes, the ability to realistically simulate the macroscale adoptions of improved planting stocks was limited by a series of issues. First, to simplify the analyses, a number of important future forest-level changes were not simulated such as the effects of: i) interactions between productivity and various climate variables (Crookston et al. 2010; Jiang et al. 2016); ii) regulatory obligations encompassing non-timber values (e.g., visual quality, old growth areas, etc.); iii) increased emphasis on conservation constraints (Mathey et al. 2008); and iv) future disturbance agents including forest fires (Gauthier et al. 2015b). These factors would reduce the productive forest area (PFA) leading to further limits on harvest flows, but it could also increase the financial attractiveness of improved planting stocks strategies, particularly close to manufacturing facilities. Under an extreme climate scenario (RCP +8.5 W m-2), the vulnerability of fibre supply to forest fires would lead to large reductions in forest stocks throughout the planning horizon, but this might be mitigated through increased yields in unburned areas along with post-burn yields via improved stocks (Gauthier et al. 2015b). Second, although drought vulnerability is a very important abiotic stressor for forests under climate changes, other stressors including temperature shifts, and interactions with biotic stressors (e.g., insects and disease) would lead to additional forest stocks losses and additional costs to the forestry industry (Spittlehouse 2005; Schwab 2008; Chen et al. 2016; Boucher et al. 2018). Third, the adaptive capacity of the forestry sector was confined to planting improved stocks following clearcutting; maintaining a level of crown closure may help to reduce drought stress and increase the survival of planted seedlings (Kabzems et al. 2015). Refining the drought  120  exposure and sensitivity maps used in this research chapter to reflect the drought vulnerability conditional on crown closure (Arx et al. 2013) would support an evaluation of partial harvesting systems including continuous cover forestry (Pommerening and Murphy 2004), potentially resulting in a greater adaptive capacity of the forestry industry. Fourth, the scenarios developed used either the adoption of all local stocks or all improved stocks rather than a mixture for a given planting effort. Allowing for variations in stocks for a particular planting effort might result in greater adaptive capacity and financial returns, and help maintain genetic diversity over the macroscale to mitigate unknown future abiotic and biotic stressors. Fifth, and finally, this analysis did not examine the benefits of improved stocks on carbon markets (Yemshanov et al. 2005; Smyth et al. 2014) or considered the emerging forest product markets (Yemshanov and McKenney 2008; Hurmekoski and Hetemaki 2013) to obtain economically attractive strategies that enhance forest yields. Forest management reforestation strategies and objectives can be very complex and consider a host of additional factors beyond just planting improved stocks to respond to expected changes in climate (Linder 2000). In this research I developed a mechanism for examining how climate changes between 2010 and 2040 could impact the adoption of improved stock across the macroscale of Canada’s western boreal, and applied this for drought vulnerability in particular. High-resolution forest attributes information and a growth and yield meta-model supported a bottom-up vulnerability assessment that was linked with top-down macroscale price scenarios and climate models. This linkage facilitates the evaluation of how future development paths of the forestry industry could increase or decrease vulnerability to potential future changes in climate regimes outside of the drought sensitivity examined in this study. As new datasets and the scalability of modelling efforts increases (Boucher et al. 2018), other climate change stressors and emerging markets are  121  expected to be incorporated into the Q3 framework in order to work towards a more complete profitability analysis of improved planting stock.  In conclusion, large-scale changes to forest conditions and dynamics require solutions that account for climate driven threats when implementing a response strategy. Finding appropriate human intervention responses to these events, which are both ecologically and economically rational, requires a macro-systems perspective beyond a stand to landscape-level thinking. The ecological and economic dimensions of this system require information at all spatial scales from the local or stand-level, to the landscape-level and then to the macroscale level. Q3 demonstrates an approach for providing this link. This research indicates that a reliance on an ‘extensive’ forestry strategy with a reactive view to climate change will be more costly under future outlooks of climate change relative to a planned macroscale strategy that adopts improved planting stock. Planting improved stock can be a financially attractive forest management strategy, especially when considering stand-establishment constraints, which can further reduce the drought vulnerability in the western boreal forest in Canada.    122  5 Conclusion 5.1 Contributions to Knowledge 5.1.1 Overall Importance In this dissertation, I investigated modelling approaches to provide macroscale ecological and economic information that has high spatial and temporal resolution. This information was then used in a newly developed macroscale decision support system that assists in the evaluation of macroscale alternative forest management strategies. Given the multijurisdictional context of this decision support system, the information needed for its parameterization and calibration is multivariate and thus, a large matrix. Generating this matrix requires linking multiple sources of data and models that span both spatial and temporal scales, as well as academic disciplines. I focused on methods that:  1. Provide stand-level forest attributes information to macroscales(Chapter 2);  2. Provide price volatility information to macroscale price scenarios (Chapter 3); and  3. Link economic-ecological information for studying forest management decisions at macroscales (Chapter 4).  These methods support a bottom-up, top-down, and combination of these perspectives to study the macrosystem. Methods for providing stand-level forest attributes information are useful for: supporting a bottom-up perspective of macroscale forest management, assessing and mapping the initial state of the forest; providing a linkage to empirical growth and yield models needed to project the initial state through time and remaining relevant to a forest manager who will actually implement forest management strategies. Further, high spatial resolution (e.g., 90 m) forest  123  attributes maps in Canada are either outdated (e.g., circa 2000) or lack variables needed for forest management decision making (e.g., age and height). Methods for providing price information are useful for supporting a top-down perspective of the macro-drivers of the economy. Prices are important determinants of investments and for evaluating the economic feasibility of alternative forest management strategies. These decisions help drive the evolution of the forest into future states. Methods that generate high temporal resolution prices have not been linked with scenarios driven by global changes in prices. Lastly, improvements to macroscale forecasting tools are needed given uncertainties surrounding the impacts of climate change and the role of the forestry sector in responding to these changes. The ability to link bottom-up stand-level information that is relevant to a forest manager with top-down price information that is consistent with global land use scenarios is essential for assessing forestry sector responses to climate change. I have argued throughout the thesis that the methods to provide and link ecological and economic data and models across macroscales must be: i) logically consistent conserving the multivariate dependencies of variables, ii) accurate across variables, and temporal and spatial scales, and iii) computationally relatively simple in order to be used in macroscale decision support systems. Failing to be logically consistent, accurate, and computationally simple would result in the generation of an implausible decision space that is not consistent with ecological and economic conditions (Stage 2003). The inability to overcome issues related to scaling data and models across space, time, and disciplines severely limits our understanding of the macro-system (Cumming et al. 2006; Seidl et al. 2013; Becknell et al. 2015; Kleindl et al. 2018).  Macroscale forest management analysis is necessary to respond to global changes (Heffernan et al. 2014; Bull et al. 2018; Kleindl et al. 2018). There is also a need to create forest and  124  environmental policies at the macroscales. These analyses are subject to cumulative management decisions with the localized, or stand-level, attributes influencing land use decisions (i.e., forest attributes information from Chapter 2). Further, the information selected for analysis needs to be consistent with scenarios of global change (price scenarios in Chapter 3) and climate change vulnerability (Chapter 4). Through this research, I gained a number of insights on linking data and models for macroscale problems relative to the characteristics necessary for constructing a plausible decision space for the forestry sector, as follows:  1. Trade-offs exists between accuracy, logical consistency and simplicity resulting from using multivariate estimation methods that predicted forest attributes (i.e., crown closure (CC), average height (Ht) and age, volume per ha (Vol), species percentages in this dissertation) across the boreal forest of Canada. In particular, I found that failing to achieve logical consistency among forest attributes would result in underestimating areas of both very low and very high productivity forests and estimated species compositions that included more species.  2. Logical consistency with the multivariate estimation methods requires: i) a smaller number of nearest neighbours in VSNN but this adversely affected the accuracy, or ii) a careful consideration of the designing of the SNLM was needed which took considerable time to develop.  3. A SNLM based on biological relationships can be easily discussed and improved by researchers. Further, these relationships can be exploited to provide an assessment of accuracy that is competitive with VSNN methods. 4. Allowing the parameters of the SNLM to vary spatially (KED method) resulted in greatest accuracy while achieving logical consistency. This method was used to provide  125  maps of boreal forest attributes in forest management areas where forest companies operate. These Canadian boreal forest maps represented the most up to date source of high resolution (90 m x 90 m) forest attributes information. 5. Forest product commodity prices have historically had smaller price volatility relative to fossil fuel based commodities. In particular, the volatility in fossil fuel prices positively influences price volatility in woody based biomass markets. 6. A price scenario generating method demonstrated logical consistency between global land use models and historical price data. Failing to maintain price volatility spillover effects in conjunction with global land use scenarios resulted in different rankings of alternative investment strategies. 7. The Q3 ( the Quantify, Queue, Query decision support system) links the research findings of Chapters 2 and 3 of this thesis with the western boreal forest of Canada to determine where, when and to what spatial extent will improved planting stock be adopted in the future (between 2010 to 2040). At the macroscale, Q3 shows that increasing the amount of planting effort (i.e., area planted) will alter the timber harvest level. At the local scale, the management units with the lower transportation costs, younger stand and lower percentages of conifer species were the areas to benefit most financially from planting improved stock. 8. The Q3 model results also show the replanting with improved planting stock should focus on areas with drought stress. My results indicate that approximately 12% of the western boreal forest harvest area would be affected by adopting this strategy.   126  9. Failing to link localized forest management decisions with macroscale outcomes would omit the costs of ‘extensive forestry’ and lead to suboptimal decisions for adopting the expansion in the use of improved planting stock. My interdisciplinary work contributes to identifying and evaluating methods for linking data and models across scales which would be used for assessing macroscale forests management strategies for multiple academic disciplines. Ecologists continue to understand linkages between patches, ecosystems, and biomes; economists between firms, industries, and economies; and forest managers between stand-level decisions, landscapes and macroscales. Improving the linkages between macroscale and microscale phenomena and processes can help these disciplines find common ground for forest management strategies. The need for cross-region assessments that capture both the within-region heterogeneity and the region-wide effects on forest ecosystems is well documented (Cumming et al. 2006; Puettmann and Tappeiner 2013; Seidl et al. 2013; Becknell et al. 2015; Kleindl et al. 2018). The methods developed in this dissertation improves our ability to assess macroscale forest management problems by linking forest attributes information and price scenarios in macroscale models. 5.1.2 Summary Chapter 2 A key challenge of using multivariate estimation methods to predict forest attributes is identifying which method(s) provides the greatest accuracy while maintaining logical consistency of the forest attributes that is required for decision-support systems. Although VSNN methods have been popular since they are model-free, the trade-off between accuracy and logical consistency was more noticeable. Accuracy can be improved by increasing k, but values above k  127  > 2 resulted in logical inconsistencies among forest attributes for our study area. I found evidence of unrealistic combinations of species and compressed ranges in Y-variables that occurred with larger k values, which would impact the usefulness of estimated information for supporting forest decision analyses. I found that accuracies obtained using SNLM and KED for a common suite of forest attributes were comparable to the VSNN method k-MSN for k ≤ 2 which was needed to meet logical consistency rules. While the SNLM took considerable time to develop, the resulting system of models can be easily discussed and improved by researchers. The SNLM can also be readily transferred for implementation in decision support models at all scales including macroscales. Although KED requires further steps over using SNLM, the increase in accuracy could justify the increased associated costs given the importance of decisions based on analyses using these data. Improved accuracy and logical consistency will result in our ability to provide macroscale forest attribute information for decision-making. 5.1.3 Summary Chapter 3 In this research chapter, I linked a land-use model (GLOBIOM) to a price volatility time series model in order to forecast high temporal resolution price scenarios. The development of these scenarios included the conditional correlation between the commodities which was found to be moderate in strength. In particular, the conditional correlation between crude oil and wood biomass for energy was found to be positive. Incorporating this type of information into scenario development is especially useful for assessing alternative energy sources and is one of the first attempts made with forest sector models. This work identifies a method for linking price trends and the multivariate dependencies of price volatility needed for assessing the sensitivity of price  128  changes on forest sector decision making. I conclude that future forest investment decision making must take price trends and price volatility into account. 5.1.4 Summary Chapter 4 Designing and assessing forestry sector strategies requires systems capable of linking multi-source ecological and economic information from local to macroscales. This includes product prices and cost schedules to evaluate alternatives, growth and yield models to forecast future forests, and forest inventory data that characterize the variability of the initial state of the forest. In this chapter, I developed a decision support system to combine bottom-up drought vulnerability assessments with top-down price scenario and climate models. This approach alleviated some of the simplifying assumptions frequently made during the scaling and model linking processes, providing a means to evaluate the forestry sectors decision space for prioritizing improved planting stocks. Using this approach, I identified where, when and to what extent local forest management decisions involving harvesting and reforestation would be vulnerable to drought stress in Canada’s western boreal for the years from 2010 to 2040. In particular, FMUs that had low transportation costs, younger stand ages and lower percentages of conifer species were the most profitable and likely area for adopting improved stock. Results indicated as much as 12% of the regenerating forest following harvesting (i.e., using natural regeneration or local stocks) would be susceptible to drought events. To achieve a macroscale adoption of improved stock a coherent macroscale forest management strategy would be needed; conditional on the vulnerability of reforestation strategies to drought, improved planting stock can be an effective cost minimization strategy given stand establishment constraints. This  129  information helps support reforestation policies and tree improvement researchers in their efforts towards adopting mitigation strategies in response to climate change impacts on forests.  5.2 Limitations 5.2.1 Data  Overall, I used the best available accessible data. However, for the forest attribute information, I used forest attribute information from interpreted large-scale photo-plots rather than ground data in building models. In applying the forest attribute models to the macroscale, I used available Landsat coverages. Given the large spatial scale, these data had been extracted from a range of 10 years around 2010 (i.e., the start of the 30-year planning horizon), avoiding areas with great cloud cover, and other poor quality images. I would also have preferred using higher resolution price information, whereas only quarterly data were available. These limitations are common for macroscale problems, but may have implications. The large number of large-scale photo-plots measured over the extensive forest area of Canada’s boreal forest used in this study provided large ranges of forest attributes in the reference dataset linked to Landsat data (and other map data) needed for the multivariate estimation methods used in this dissertation. However, using photo-plots limited the particular forest attributes that could be used in the study, since some forest attributes can only be measured on ground plots. For example, diameters at breast heights (DBHs) can be measured for each tree in ground plots and can be summarized to obtain basal area per ha, diameter distributions, and other metrics. In photo-plots, these must be estimated by having a subset of photo-plots that are ground-measured and modelling the relationship between ground-measured DBH and photo-measured height and  130  crown area. Other variables such as age are very difficult to measure even on ground plots in forest areas with well-defined seasons as in the boreal forest. Also, age can be highly variable among trees in a stand, making it difficult to use one age to define a ground or photo-plot. I used the photo-interpreted stand age in this study. Using photo-plots, average age can be inferred using other photo-measured variables as well as other information available to highly-skilled photo-interpreters. Magnussen and Russo (2012) noted that photo-interpreted variables on photo-plots can be large contributors to sources of error in Canada’s NFI. However, given the extensive land area of a macroscale, and the extremely limited accessibility of much of Canada’s forests, photo-plots provide a viable option for providing the forest attribute information needed in decision support systems. Relying on Landsat data (along with other map data) to estimate the forest attributes in the modelling approaches tested in Chapter 2 also presents some limitations for providing information at macroscales. The forest attributes modelling approach selected in Chapter 2 was applied to the boreal forest landscape where forest companies operate; however, the acquisition of high quality Landsat images were from multiple dates spanning 10 years for some regions. This 10-year time interval was needed to create a composite image for the study area given clouds, smoke and other factors reducing image quality. However, this was the best available data, and similar data have been used in other macroscale research and in professional application. In Chapter 3, quarterly price information was used to parameterize mGARCH models of price volatility. This information represents the highest resolution that I could source, with woody residue markets being the most limiting. The implications of using quarterly prices were that the  131  mGARCH model requires many parameters and reducing the number of observations increases the risk of over fitting the model. To overcome this issue, a model selection approach was used which effectively reduced the number of parameter in the mGARCH model. 5.2.2 Models The specific modelling approaches evaluated and then applied for the macroscale analysis in this research used multi-source data specific to the study area of the western boreal forest of Canada. State-of-the art methods were included in all evaluations and development of models in Chapters 2 and 3.  For Chapter 2, not all possible approaches were evaluated, as noted in that chapter. Also, models are affected by available data as previously described. One of the challenges was selection of X variables to be used. I followed a logical approach to selecting variables, based on prior research. However, given the many possible sets of X variables, it is possible that I did not obtain the optimal sets of X variables for the forest attributes.  In Chapter 3, I demonstrated a method to link price trend scenarios forecasted using a partial equilibrium model (PEM) with historical price volatility. The PEM makes coarse assumptions concerning timber supply including potentials of future yield in forest products and the demand for these products. However, the linkage between Q3 in Chapter 4 and the PEM in Chapter 3 was based on the price information; whereas production capacity could also have been linked. The reasoning behind using price as a link between Q3 and the PEM was based on the assumption that forestry firms are price takers, individual firms have a small market share, and buyers have  132  information of future markets. However, including an industrial production capacity constraint in Q3 would help to provide a more consistent link between Q3 and PEM. Information on these capacities is however, difficult to disaggregate at a forest management unit level, given the diversity of products and conversion factors between products (Ghafghazi et al. 2017).  Lastly, in the macroscale analysis used in Chapter 4, I developed and used a stand-level meta-model based on growth and yield outputs from the individual tree model, MGM. Although other GY models could have been used, MGM was selected since it has been validated and calibrated for the western boreal as in this study. Given the absence of fine-scale information (i.e., tree lists) inputs needed for MGM, this stand-level meta-model was needed to obtain future-forests for the different management scenarios. An alternative approach would have been to estimate tree-lists for each stand in Chapter 2, but this would be computationally extremely challenging for a macroscale analysis. Another alternative was using process-based models to obtain biome-level growth and yields, but this would have reduced the spatial acuity in this study. Further, process-based models have not been generally applied by governments nor industry in Canada in projecting timber supply, since they generally have not been specifically validated for accuracy of yield estimates over time. 5.3 Future work While the future demand for more and higher resolution information seems to be insatiable for supporting decisions, it is also important to question how this information can be linked and used within decision support systems. Thus, the future of macroscale modelling and its usefulness for assessing forest management alternatives will depend on i) the accessibility of data and models  133  and ii) the methods providing the linkages between data sources and models. In particular, the following lists focus areas for future research. 1. Link data measured on the ground to remote sensing information or other remote sensing information (e.g., RapidEye, Satellite Pour l'Observation de la Terre (SPOT)) as an alternative to the freely available photo-plot data and Landsat data used in Chapter 2. Ground-based measurements, while costly, would provide forest attribute information that could not be achieved with photo-interpretation (i.e., diameters). This would help support decisions concerning future timber harvesting profiles and provide a linkage to disaggregated timber product prices (i.e., by lumber grade) and product manufacturing in the forestry sector (Ghafghazi et al. 2017). Higher resolution imagery is currently more costly to acquire; however, this information may be useful relative to Landsat imagery (30m). Thus, it could be hypothesized that this information may provide greater accuracy in determining information for decision support because smaller pixels will have less occurrence of ‘pixel mixing’ where the spectral signature may include two contrasting objects (i.e., road and dense forest). 2. Develop price scenario generating models that consider higher resolution price data that considers a greater diversity of forest products including emerging products (i.e., bioeconomy) or non-commercial timber values (i.e., carbon). In Chapter 3, forest products prices were confined to the outputs from GLOBIOM and US Energy Information Administration (2010); however, emerging forest products and carbon markets are also of interest to macroscale policy makers. In the decision support system (Q3), the inclusion of these markets is likely to impact the financial attractiveness of the forestry industry and thus, impact the future development paths of the forestry industry.  134  3. Simulate impacts of climate changes on stand-level growth. Although regeneration success (or failures) were simulated using Q3 in Chapter 4, along with changes in growth and yield of improved stocks, changes in climates may directly impact growth rates of both natural and improved stocks. Empirical growth and yield models that alter growth and yield under future climates (e.g., Crookston et al. 2010) would permit analyses of how these changes may alter management strategies priorities.  4. Include other macroscale disturbance agents (e.g., wildfire), additional global land use scenarios, and a greater consideration for forest management objectives other than timber into macroscale models that evaluate forest management. The cumulative impacts and sensitivity from these macroscale changes may have a greater impact on industry financial attractiveness and ability to adopt climate strategies relative to simplified scenarios that omit these processes (i.e., focused on value streams generated purely by timber procurement).  135  References  Adamowicz, W.L., Armstrong, G.W., Messmer, M.J. 2003. The economics of boreal forest management. In Towards sustainable management of the boreal forest. Edited by Burton, P. J., Messier, C., Smith, D. W., Adamowicz, W.L. NRC Research Press, Ottawa. pp. 181–211. Ahmed, S. 2016. Impacts of tree improvement programs on yields of white spruce and hybrid spruce in the Canadian boreal forest (PhD Thesis). University of British Columbia. Accessed (June 24th, 2018) online from <https://open.library.ubc.ca/cIRcle/ collections/24/items/1.0319209 >  Ahtikoski, A., Haapanen, M., Hynynen, J., Karhu, J., Kärkkäinen, K. 2018. 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