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Modelling the decay patterns and harvested wood product pools of residential houses Xie, Sheng H. 2015

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MODELLING THE DECAY PATTERNS AND HARVESTED WOOD PRODUCT POOLS OF RESIDENTIAL HOUSES  by  Sheng H. Xie  B.Sc., The University of British Columbia, 2013  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF  THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE  in  The Faculty of Graduate and Postdoctoral Studies  (Forestry)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  February 2015  © Sheng H. Xie, 2015  Abstract The harvested wood products (HWP) in use carbon pool plays a beneficial but frequently unrecognized role in climate change mitigation by storing carbon that has been removed from the atmosphere and providing services that can substitute for emission intensive products. Countries with a culture of building houses with wood use a majority of HWP for structural purposes and, due to the long-lived nature of houses, the structural HWP within these dwellings can last for a long time. Long-lived products have the potential to make a major contribution to the HWP in use pool and accurate quantification of this pool is an important topic worthy of detailed investigation. This study reviewed published HWP decay models and developed a “regression-aggregation-fit” methodology to accurately model the inverse sigmoidal decay patterns of houses at the national level. Using this method, the end-use half-lives of U.S. single-family and multi-family houses, U.S. mobile homes, Canadian residential houses and Norwegian residential houses were estimated to be 137 years, 44 years, 92 years and 146 years, respectively. For comparison, the default product half-lives recommended by the IPCC are 35 years for sawnwood and 25 years for wood-based panels. The direct application of these default product half-lives to quantify the HWP pool in houses is likely to result in substantial underestimation of this carbon pool. The Gamma distribution model was shown to be the most applicable generalized model for describing the country-specific decay pattern of houses. It adequately modelled housing data sets from three different countries and it was the best of the six models evaluated. This model was used to quantify the structural HWP pool in U.S. single-family and multi-family houses and in 2009 this pool was 668 Tg C, which was about 20% larger than published estimates. A constant mass input scenario indicated that this pool may act as a sink for about 750 years with a saturation value of about 1.2 Pg C.  This methods developed in this thesis should improve the accuracy of national greenhouse gas inventory reporting for countries with extensive forests and a tradition of building with wood.     ii  Preface I hereby declare that this thesis is the product my original work and that, to the best of my knowledge and belief, this thesis contains no material previously published or written by another person, except where due reference is made in the text of the thesis. The core theme of this thesis is to model the decay patterns and harvested wood product pools of residential houses. I, Sheng H. Xie, was the main author in the conception and design, acquisition, analysis and interpretation of data, writing and revision of all chapters contained in this thesis up to the approval of the final draft. My supervisor, Dr. Paul McFarlane, provided substantial contribution to the conception and design, interpretation, writing and revision of all chapters contained in this thesis up to the approval of the final draft. The thesis, and the research to which it refers, contains no material which has been accepted for the award of any other degree or diploma at any university or equivalent institution. Revised versions of this thesis will be submitted for publication.   iii  Table of Contents Abstract ............................................................................................................................................................................... ii Preface ................................................................................................................................................................................ iii Table of Contents ............................................................................................................................................................ iv List of Tables ................................................................................................................................................................... viii List of Figures ................................................................................................................................................................... ix List of Abbreviations....................................................................................................................................................... xi Acknowledgements ....................................................................................................................................................... xii Chapter 1 Introduction .................................................................................................................................................... 1 Chapter 2 Literature review .......................................................................................................................................... 7 2.1 Introduction ............................................................................................................................................................ 7 2.2 Most commonly used quantification models and half-life values ....................................................... 7 2.2.1 First order decay (FOD) model ................................................................................................................. 8 2.2.2 Product half-life vs. end-use half-life ..................................................................................................... 9 2.2.3 Long-lived products versus short-lived products ............................................................................ 10 2.3 Current state of knowledge on the half-life of US residential houses ............................................... 11 2.3.1 Winistorfer et al. (2005) ............................................................................................................................. 13 2.3.2 Skog (2008)................................................................................................................................................... 14 2.4 Current state of knowledge on the HWP pool size of US residential houses ................................ 14 2.5 Other proposed models and half-lives ....................................................................................................... 15 2.5.1 “Instantaneous oxidation” model ........................................................................................................... 15 2.5.2 Instant decay model .................................................................................................................................. 16 2.5.3 Linear decay model ................................................................................................................................... 16 2.5.4 Logistic decay model ................................................................................................................................ 19 2.5.5 Three-segment decay model ................................................................................................................. 21 2.5.6 Gamma distribution model .................................................................................................................... 22 2.5.7 Miner’s (2006) Country-specific model .............................................................................................. 22 2.5.8 Comparison of HWP decay models .................................................................................................... 24 2.6 Research objectives .......................................................................................................................................... 25 iv  Chapter 3 Determination of the decay pattern of US single-family and multi-family houses ............ 26 3.1 Introduction ......................................................................................................................................................... 26 3.2 Methods ............................................................................................................................................................... 26 3.2.1 Raw Data ....................................................................................................................................................... 29 3.2.2 Determination of apparent half-lives .................................................................................................. 32 3.2.3 Age of houses ............................................................................................................................................. 32 3.2.4 Aggregated first order decay curve (AggFOD) ............................................................................... 32 3.2.5 Decay models fitted to the AggFOD curve ....................................................................................... 33 3.2.6 Assumptions ................................................................................................................................................ 34 3.3 Results ................................................................................................................................................................... 35 3.3.1 Determination of half-lives using the first order decay model ................................................... 35 3.3.2 Aggregated first order decay curve (AggFOD) ................................................................................ 37 3.4 Discussion ............................................................................................................................................................ 39 3.5 Conclusions ......................................................................................................................................................... 44 Chapter 4 Application of the decay estimation methodology to US mobile homes and Canadian and Norwegian residential houses .......................................................................................................................... 45 4.1 Introduction ......................................................................................................................................................... 45 4.2 Methods ............................................................................................................................................................... 45 4.2.1 US mobile homes ....................................................................................................................................... 45 4.2.2 Canadian residential houses .................................................................................................................. 46 4.2.3 Norwegian residential houses ................................................................................................................ 51 4.2.4 Apparent half-life estimations, aggregated first order decay (AggFOD) curve and decay models fitted to the AggFOD curve .............................................................................................................. 53 4.2.5 Assumptions ................................................................................................................................................ 55 4.3 Results ................................................................................................................................................................... 55 4.3.1 US mobile homes ....................................................................................................................................... 55 4.3.2 Canadian residential houses ................................................................................................................... 57 4.3.3 Norwegian residential houses ................................................................................................................ 61 4.4 Discussion ............................................................................................................................................................ 63 4.4.1 US mobile homes ....................................................................................................................................... 63 v  4.4.2 Comparison of houses in Canada, US and Norway ....................................................................... 64 4.5 Conclusion ............................................................................................................................................................ 67 Chapter 5 Quantification of the pool of structural HWP in US residential houses ................................. 68 5.1 Introduction ......................................................................................................................................................... 68 5.2 Methods ............................................................................................................................................................... 68 5.2.1 Quantification of HWP pools ................................................................................................................. 68 5.2.2 Constant mass input scenario analysis ................................................................................................ 72 5.2.3 Validation methods .................................................................................................................................... 72 5.2.4 Assumptions ................................................................................................................................................ 74 5.3 Results .................................................................................................................................................................... 75 5.3.1 Structural HWP pool of US single-family and multi-family houses ............................................ 75 5.3.2 Structural HWP pool of US mobile homes ......................................................................................... 76 5.3.3 Constant mass input scenario ................................................................................................................ 76 5.4 Discussion ............................................................................................................................................................. 78 5.4.1 Structural HWP pool size estimated for US single-family and multi-family houses ............. 78 5.4.2 Structural HWP pool size estimated for US mobile homes .......................................................... 79 5.4.3 Constant mass input scenario ............................................................................................................... 80 5.4.4 Comparison of models for the US single-family and multi-family houses ............................ 82 5.4.5 Validation of the HWP pool size estimates for US single-family and multi-family houses85 5.5 Conclusions ......................................................................................................................................................... 86 Chapter 6 Conclusions and future research ......................................................................................................... 88 6.1 Conclusions .......................................................................................................................................................... 88 6.2 Strengths and Weaknesses ............................................................................................................................ 89 6.3 Future research .................................................................................................................................................. 90 References ....................................................................................................................................................................... 92 Appendices..................................................................................................................................................................... 100 Appendix A Housing units remaining by period of construction data used in this paper .............. 100 A.1 US single-family and multi-family houses (Surveys 1985~2013) .................................................. 100 A.2 US mobile homes (Surveys 1985~2013) ............................................................................................... 101 A.3 Canadian residential houses (Surveys 1971~2011) ............................................................................ 102 vi  A.4 Norwegian residential houses (Survey 1980~2011) .......................................................................... 106 Appendix B Detailed analyses of HWP carbon pool size in single-family and multi-family houses estimated by previous publications ................................................................................................................... 107 B.1 Wilson (2006) ................................................................................................................................................. 107 B.2 Skog (2008) .................................................................................................................................................... 108 Appendix C Validation of Skog’s (2008) housing pool size estimation of 682 Tg C versus US EPA’s (2013) HWP in use pool size estimation of 1395 Tg C ................................................................................. 110 C.1 Introduction ................................................................................................................................................... 110 C.2 Conversion to a common approach ..................................................................................................... 110 C.3 Accounting for a comparable component of the HWP in use pool ............................................ 111 C.4 Comparison of values ................................................................................................................................ 114   vii  List of Tables Table 2-1 Default product half-lives for the Tier 2 method provided by the IPCC (2014) ....................... 9 Table 2-2 End-use half-lives uses by US EPA (2013) .......................................................................................... 10 Table 2-3 Half-life values used by previous literature ....................................................................................... 12 Table 3-1 Comparison of the period of construction categories used in Survey 1973 to 1983 and Survey 1985 or later. ............................................................................................................................................... 29 Table 3-2 Age of US single- and multi-family houses represented by the periods of construction in American Housing Surveys .................................................................................................................................. 33 Table 3-3 Comparison of the sum of squared errors of decay models when fitted to the AggFOD curve ............................................................................................................................................................................. 37 Table 3-4 Comparison of the areas under the curves of decay models under the constant mass input scenario of 1 Tg C/ year over the 300 years ....................................................................................... 39 Table 4-1 Sources and profiles of available housing units data by periods of construction ................ 47 Table 4-2 Comparison of the division of periods of construction categories of each Canadian Survey.......................................................................................................................................................................... 48 Table 4-3 Age of Canadian residential houses represented by the periods of construction ............... 51 Table 4-4 Comparison of the division of periods of construction categories of each Norwegian Survey.......................................................................................................................................................................... 52 Table 4-5 Age of Norwegian residential houses represented by the periods of construction ........... 53 Table 4-6 Summary of half-lives and 95% decay under different scenarios for Canadian residential houses ......................................................................................................................................................................... 59 Table 4-7 Comparison of the SSE and parameter(s) of the decay models under each scenario ....... 59 Table 5-1 Calculation methodology to determine the amounts of carbon remaining by initial input and the pool sizes at the end of each year for models other than FOD ............................................... 71 Table 5-2 The size of the carbon pool of structural HWP in US single-family and multi-family houses in 2001, 2003, 2005 and 2009 determined by the six decay models plus the default IPCC Tier 2 method ............................................................................................................................................................ 76 Table 5-3 A summary of the saturation pool sizes and sink durations calculated by the different decay models under a constant input scenario in Figure 5-55-5a and the relationship between the constant input scenario to the actual HWP consumption data ........................................................ 81 Table 5-4 A comparison of decay models for the US single-family and multi-family houses ............ 83 Table 5-5 A summary of the previously published estimates of HWP in use pool for the US and those estimated in this study .............................................................................................................................. 85 Table 5-6 A comparison of the HWP carbon pools in 2003 estimated by Wilson (2006) and this study’s Gamma (SF+MF, 2.07, 80.2) model .................................................................................................... 86   viii  List of Figures Figure 1-1 Forest carbon cycle and major carbon pools in the forestry sector ........................................... 2 Figure 1-2 Linkage of the IPCC HWP categories to roundwood harvest and finished products ........... 3 Figure 2-1 Schematic representation of the carbon flows of HWP in use pool .......................................... 7 Figure 2-2 Constant annual input of 1 Tg C scenario for solid wood in single-family houses and in all the other end uses .............................................................................................................................................. 11 Figure 2-3 Decay curves of instant decay, linear decay and FOD models with half-lives of 35 years. ........................................................................................................................................................................................ 17 Figure 2-4 Decay curves for construction lumber, other lumber, pulp and paper and HWP in landfills using the models of Kurz et al. (1992) ............................................................................................... 19 Figure 2-5 Decay curves of logistic decay with a half-life of 149 years, three-segment decay with a half-life of 138 years,  Gamma distribution with α=2.07 and β=80.2, and Miner’s (2006) country-specific model. .......................................................................................................................................................... 21 Figure 2-6 Fraction of houses removed annually in each age group and the cumulative decay curve (Miner, 2006) ............................................................................................................................................................. 23 Figure 3-1 Quantification method for the carbon pool of HWP in houses ................................................. 27 Figure 3-2 Comparison of housing units remaining data reported in “Surveys 1973~1983” and “Survey 1985 or later” ............................................................................................................................................. 30 Figure 3-3 Unexpected low values from Surveys 1987~2003 for houses built in 1975~1979 ............... 31 Figure 3-4 FOD curves fitted to the housing unit remaining data from AHS with estimated apparent half-lives and r2 values ........................................................................................................................................... 35 Figure 3-5 Estimated apparent half-lives of houses at different age stages .............................................. 37 Figure 3-6 Aggregated first order decay (AggFOD) curve.............................................................................. 38 Figure 3-7 Decay models fitted to the AggFOD curve of the US single- and multi-family houses ... 38 Figure 3-8 Comparison between Miner's (2006) model and the AggFOD curve. ................................... 42 Figure 4-1 Canadian housing units remaining by period of construction .................................................. 50 Figure 4-2 Norwegian housing units remaining by period of construction .............................................. 53 Figure 4-3 Estimated apparent half-lives of US mobile homes as a function of housing age ............ 56 Figure 4-4 AggFOD curve-US mobile homes ..................................................................................................... 56 Figure 4-5 Decay models fitted to the AggFOD curve of US mobile homes ............................................. 57 Figure 4-6 Estimated half-lives of Canadian residential houses as a function of housing age ........... 58 Figure 4-7 Aggregated first order decay (AggFOD) curves-Canadian residential houses ................... 58 Figure 4-8 Decay models fitted to the AggFOD curve of Canadian residential houses (a ~ d) ......... 60 Figure 4-9 Estimated apparent half-lives of Norwegian residential houses as a function of housing age ............................................................................................................................................................................... 62 Figure 4-10 AggFOD curve-Norwegian residential houses ............................................................................. 62 Figure 4-11 Decay models fitted to the AggFOD curve of Norwegian residential houses ................... 63 ix  Figure 4-12 A comparison of the apparent half-life estimations of Canadian residential houses to the ones of US single-family and multi-family houses and Norwegian residential houses ........... 64 Figure 4-13 A comparison of the AggFOD curve of Canadian residential houses to the AggFOD curves of US single-family and multi-family houses and Norwegian residential houses ................ 65 Figure 5-1 Product categories and subcategories of HWP in houses reported by McKeever and Howard (2011) ........................................................................................................................................................... 69 Figure 5-2 The hierarchical breakdown of the HWP in use pool ................................................................... 73 Figure 5-3 Carbon pool sizes of structural HWP in US single-family and multi-family houses from 1900 to 2009 determined using the six decay models plus the default IPCC Tier 2 method ......... 75 Figure 5-4 Carbon pool size of structural HWP in US mobile homes aggregated from 1950 to 2009 determined by the six decay models plus the IPCC Tier 2 method ........................................................ 77 Figure 5-5 Stock of structural HWP versus time for US single-family (SF) and multi-family (MF) houses and mobile homes (MH) assuming a constant mass input scenario of 7 Tg C/year .......... 77    x  List of Abbreviations AggFOD Aggregated first order decay AHS American Housing Survey CHASS Computing in the Humanities and Social Sciences CO2 Carbon dioxide CH4 Methane EFI European Forest Institute FOD First order decay GHG Greenhouse gas(es) Glulam Glue-laminated timber HWP Harvested wood products IPCC Intergovernmental Panel on Climate Change KP Supplement 2013 Revised Supplementary Methods and Good Practice Guidance Arising from the Kyoto Protocol  LVL Laminated veneer lumber MF Multi-family MH Mobile homes NHS National Household Survey NIR National Inventory Report OSB Oriented strand board OSL Oriented strand lumber Paralam Parallel strand lumber PUMF Public Use Microdata Files SF Single-family SSE Sum of squared errors SWDS Solid waste disposal sites UNFCCC United Nations Framework Convention on Climate Change US EPA US Environmental Protection Agency USDOC US Department of Commerce    xi  Acknowledgements I would like to express the deepest appreciation to my supervisor Dr. Paul McFarlane, whose wisdom, professionalism and passion inspired and motivated me through the wonderful journey of my Master’s study. His mentorship, guidance and encouragement on both my research and career have been priceless. I am especially thankful for his patience with my unconstrained ideas, my awkward writing skills and endless questions. I would also like to thank Dr. Werner Kurz, for serving as one of my committee members and the persistent support and advice he has provided. A special thanks to my supervisory committee members Dr. Robert Kozak and Ms. Jennifer O’Connor for their time and support they have dedicated to me in seeing through the completion of this work. I am extremely grateful to my parents, Mrs. Ping Li and Mr. Huai Yong Xie, my wife, Sheryn Lu, and my new born daughter, Janie Xie. I would like to tell them that my family is my greatest power source. This research was funded by the Pacific Institute for Climate Solutions (PICS).   xii  Chapter 1 Introduction When the industrial revolution began around 1750, the atmospheric concentration of carbon dioxide (CO2) was about 280 ppm (IPCC, 2007a). By 2011, this concentration had increased to 391 ppm (IPCC, 2013). Over the same time frame, the concentrations of other greenhouse gases (GHG) also increased. For example, the atmospheric concentration of methane (CH4) increased from 715 ppb in 1750 to 1803 ppb in 2011 (IPCC, 2007a; IPCC, 2013). The higher concentrations of GHG in the atmosphere have resulted in increased radiative forcing (RF) which has resulted in greater surface warming (IPCC, 2013). It is now considered with very high confidence that the higher global surface temperature has been predominantly caused by the anthropogenic increase in GHG concentrations (IPCC, 2013). Carbon dioxide is the most important GHG and the radiative forcing associated with the atmospheric CO2 concentration was estimated to be 2.03 W∙m-2 in 2011 compared to 1.33 W∙m-2 in 1750. For comparison, in 2011 the radiative forcing associated with the atmospheric CH4 concentration and solar irradiance were estimated to be 1.20 W m-2 and 0.10 W∙m-2, respectively (IPCC, 2013). Efforts to ameliorate climatic impacts have focussed on two major strategies: reducing GHG emissions and increasing net carbon sequestration (Lemprière et al., 2013). For example, preventing deforestation is one way of reducing carbon emissions and afforestation can enhance carbon sequestration. The forestry sector plays an important role in the global carbon cycle and it influences climate change because of its ability to act as a carbon source or sink. Over recent decades, the world’s forestry sector has sequestered approximately 2.4 Pg C year-1 which is equivalent to about 25% of the annual global CO2 emissions and about the same magnitude as carbon sink of the oceans (Pan et al., 2011; Peters et al., 2011; Bellassen and Luyssaert, 2014). However, about half of the annual mass of carbon sequestered by the forestry sector has been released back into the atmosphere due to land-use change, deforestation and degradation (Pan et al., 2011; Helin et al., 2013). There are three major carbon pools within this sector: forests, harvested wood products (HWP) in use and HWP in landfills (Figure 1-1). HWP are defined by the United Nations Framework Convention on Climate Change (UNFCCC) as: “wood-based materials harvested from forests, which are used for the production of commodities such as furniture, plywood, paper and paper-like products, or for energy” (UNFCCC, 2003, p. 5). The term “harvested” is used to emphasize that HWP originate from forest harvesting operations. However, other fibre products made, for example, from rattan or bamboo can also be considered to be HWP (UNFCCC, 2003). Woody biomass that is left in the forest and decays on the harvest site is not categorized as HWP (Pingoud et al., 2003; Green et al., 2006; Milakovsky, Frey and James, 2012). In other words, HWP are any lignocellulosic materials produced, used and disposed by human society. Forests absorb CO2 from the atmosphere through photosynthesis and can create a carbon pool by storing carbon (Figure 1-1). The production of wood and paper products after harvesting 1  incorporates much of this carbon into the HWP consumed by society, as represented by the HWP in use and HWP in landfill pools in Figure 1-1. When such forests are managed sustainably, a steady flow of harvested roundwood flows from the forests to meet society’s needs for energy and materials (Eliasson et al., 2013). For many centuries, human society has used wood and other lignocellulosic materials to meet its needs for energy, shelter, furniture, communication, information recording, packaging and hygiene (McFarlane and Sands, 2013). In the latest version of its 2013 Revised Supplementary Methods and Good Practice Guidelines Arising from the Kyoto Protocol (KP Supplement), the Intergovernmental Panel on Climate Change (IPCC) has aggregated the broad range of individual wood and fibre products used by society into the following three overarching HWP categories: sawnwood, wood-based panels and paper (IPCC, 2014). These three HWP categories are linked to the roundwood harvest and finished products as shown in Figure 1-2.  Figure 1-1 Forest carbon cycle and major carbon pools in the forestry sector (adapted from Luyssaert et al., 2010 and IPCC, 2007a) 2   Figure 1-2 Linkage of the IPCC HWP categories to roundwood harvest and finished products (adapted from IPCC, 2014) When the diverse range of individual products made from sawnwood, panels or paper are used by society, each product creates a carbon pool with a magnitude and a duration that reflects the use of that product by society. Carbon remains stored in these HWP pools for varying lengths of time and the conversion to GHG occurs at different rates and various points over a product’s life cycle. Material that is combusted is likely to enter the atmosphere in the year that it is harvested, paper products typically have a life cycle of less than five years and structural wood products have a use phase that has been estimated to be from 20 to more than 100 years (Pingoud et al., 2003; IPCC, 2006; Skog, 2008; Bache-Andreassen, 2009). This “delay” in the release of carbon creates the HWP in use pool. Retired harvested wood products are either recycled for alternative uses or sent to landfills. The carbon in the products sent to landfills does not degrade immediately and contributes to the HWP pool in landfills.  Historically, the quantity of carbon stored in HWP and their ability to sequester carbon has been considered to be relatively small compared to the mass of carbon within the forest (Green et al., 2006). Between 2000 and 2007, the HWP sink was estimated to be about 15% of the net forest sink at the global level (Pan et al., 2011). Between 1990 and 2005, the forest biomass sink of the 25 members of the European Union was calculated to be 80 Tg C year-1. In contrast the net HWP sink of these same nations was about 5 Tg C year-1, equivalent to 6% of the forest biomass sink (Luyssaert et al., 2010). A recent US national inventory report estimated that, in 2011, the US aboveground forest biomass was about 14.6 Pg C. The pools of carbon present in HWP in use and in landfills in the US were respectively estimated to be about 10% and 7% of the carbon pool associated with the aboveground forest biomass (US EPA, 2013). In Canada, the pool size of the 3  entire forest sector in 1989 was estimated to be 86.6 Pg C, with only 1% of this value being contributed by HWP in use (Apps et al., 1999). In summary, the net carbon sink associated with HWP has been reported to be within the range of 1~15% of the sink associated with forest biomass. Because of their smaller size and net sequestration amount, the HWP pools have received substantially less research focus than the forest carbon stock and there is substantial uncertainty over the accuracy of these HWP pool size estimates.  The annual increase in the HWP pools may be determined from a knowledge of the yearly input flux and the rate at which carbon is removed from the pool each year. In this thesis, the rate of carbon removal from the pool is termed the decay rate and it may be modelled in several different ways. The IPCC KP Supplement recommended that the decay rate was quantified using the term “half-life” (IPCC, 2014) which is defined as “the number of years it takes to lose one-half of the material currently in the pool” (IPCC, 2006, p. 12.11). The concept of decay in this sense is therefore closely aligned with that of radioactive decay (Rutherford, 1900) and electromagnetic decay (Wilson, 1968).  Carbon leaving the HWP in use pool may be transferred to the atmosphere (e.g. by combustion or microbial decay) or to landfills (e.g. as demolition materials or waste paper) (Figure 1-1). At present the true decay patterns of HWP in use and in landfills are rather uncertain with the greater uncertainty associated with HWP in landfills. Due to this high level of uncertainty, the IPCC has recommended that the impact of the carbon stock in landfills is ignored (IPCC, 2014).  This study followed this IPCC recommendation and focussed on quantifying an important component of the HWP in use pool. Unless stated otherwise, the HWP pool referred to in this thesis is the HWP in use pool. Several papers have highlighted that current quantification methods may underestimate the size of the HWP in use pool (Row and Phelps, 1996; Eggers, 2002; Wilson, 2006; Marland, Stellar and Marland, 2010). In addition, more precise quantification of the parameters that influence the magnitude of these pools is important as an improved understanding may aid the development of useful policies to help mitigate climate change (Pingoud et al., 2003; IPCC, 2006; Skog, 2008). In addition, the IPCC recommended that nations should be transparent about their methods for collecting and using data and that the data should be verifiable (IPCC, 2014). However, much of the data and many of the estimation processes used to date have not been published in a transparent manner, which makes validating the results very difficult. In the HWP topic area, the IPCC itself has used expert knowledge based approaches together with decay models and half-lives that have not been supported by transparent and verifiable data. The approach adopted by the IPCC reflects the present state of knowledge of this field and, due to these knowledge gaps, several nations struggle to effectively model the HWP pools. Also, it is difficult to develop scientifically informed policies regarding the use of HWP in the absence of adequate models and scientifically based analytical frameworks. 4  Improved quantification of the HWP in use pools may reveal that continuous long term sequestration can be provided by increasing the use of wood products and this may have substantial impact on the climate mitigation policies. Over a long time span, a given forest area under uniform management conditions without other natural disturbances is often considered to be carbon neutral (Perez-Garcia et al., 2005; Lippke et al., 2011). If the forests that produce these HWP are sustainably managed, meaning that the harvest volume is less than the mean annual increment over the long term, then this forest-HWP-in-use system will be capable of creating stocks of carbon with the annual net carbon sequestration equalling the net annual increase in the size of the HWP in use pools. As long as the inflow to the HWP in use pools exceeds the outflow from the HWP in use pools, these pools will act as carbon sinks and pools with long term carbon inputs that are greater than the outputs have the potential to act as long term carbon sinks.  Another important policy outcome is the observation that HWP have the potential to substitute for fossil fuels and materials with greater climate impacts (Figure 1-1) (Sathre and O’Connor, 2010). Comprehensive life-cycle analyses have indicated that HWP require lower amounts of energy to produce than comparable products and much of the energy used to manufacture HWP is generated from biomass (Perez-Garcia et al., 2005; Lippke et al., 2011; Malmsheimer et al., 2011). Burning biomass returns carbon, which was absorbed by the forests, to the atmosphere. This process results no net increase of the atmospheric carbon as long as the forest inventories are stably managed, whereas burning fossil fuels creates a one way flow of carbon to the atmosphere because the process of retuning the carbon to fossil fuel reserves functions on a geological time scale (Bowyer et al., 2011). In North America, one-half to two thirds of the energy used in wood products manufacturing industry is bioenergy (Malmsheimer et al., 2011). Using HWP in place of fossil fuels and other energy intensive materials (e.g. steel, aluminum, concrete and plastic products) can effectively reduce carbon emissions. For example, the manufacture of wood framing has been assessed to consume one-half or less of the total energy and one-fifth to one-fourth of the fossil energy compared to steel framing for construction (Malmsheimer et al., 2011). Furthermore, the substitution will also increase the use of HWP which is likely to enhance the HWP pool sizes. However, many of these the life-cycle assessments are based on models and half-lives that have been estimated hastily or in a manner that is difficult to replicate and validate. Improved modelling of the HWP decay patterns and pools may therefore lay a foundation that increases the reliability of other research assessments and improves the scientific underpinnings of policy development and decision making. This study seeks to develop improved methodologies for modelling the decay patterns and quantifying the HWP pools in residential houses. Chapter 2 of this thesis reviews the significant published literature on the quantification of HWP in use pools and explains why the focal point of this thesis should be the carbon in structural HWP of residential houses in North America. The research objectives of this study are delineated after the literature review. In Chapter 3, the decay 5  pattern of single-family and multi-family houses in the US is modelled in a transparent manner and a standard methodology for developing these models is proposed. The decay patterns of mobile homes in the US and residential houses in Canada and Norway are then modelled in Chapter 4 using the state-of-the art methodology developed in Chapter 3. In Chapter 5, the carbon stocks of single- and multi-family houses and mobile homes in the US are quantified to demonstrate the potential for the structural HWP used in houses to act as a long term carbon sink. The results are validated using previously published values. Six different decay models are assessed and the most suitable model is recommended. Chapter 6 presents the conclusions of this study, outlines its strengths and weaknesses, and discusses future research opportunities.   6  Chapter 2 Literature review 2.1 Introduction This chapter reviews the most significant published literature on the quantification of HWP in use pool and presents the research objectives developed. Specifically, Section 2.2 introduces the most commonly used models for quantifying HWP in use. It also explains why the half-life is an important factor and why the focal point of this thesis should be the structural HWP carbon stored in residential houses in North America, with an emphasis on the United States (US). Section 2.3 reviews the half-life values of US houses estimated by previously published literature. Section 2.4 summarizes the current state of knowledge on the size of the HWP pool in US residential houses. Section 2.5 introduces some previously proposed models and Section 2.6 outlines the research objectives based on the literature review. 2.2 Most commonly used quantification models and half-life values Countries are interested in developing an accurate HWP accounting mechanism because those nations with an increasing HWP carbon stock can use this to offset its carbon emissions. A schematic representation of the flow of carbon into and out of the HWP in use pool is presented in Figure 2-1. The annual HWP production and consumption amount is usually reported by the national statistics department in most countries. However, information on the decay of HWP is difficult to collect because the retirement of HWP from use is usually not reported by individuals or monitored closely by national authorities.  Figure 2-1 Schematic representation of the carbon flows of HWP in use pool To be conservative, the IPCC originally suggested that HWP contribution should be ignored and therefore effectively considered that instantaneous oxidation of the carbon in the roundwood occurred once the tree was harvested (IPCC, 1997). This approach is still referred to as the default approach or Tier 1 method (IPCC, 2014). The detail of this method is discussed in Section 2.5.1. However, as mentioned in Chapter 1, carbon stored in HWP is often not emitted to the atmosphere immediately. Since 2006, the IPCC Guidelines have recommended that the first order decay (FOD) model is used to describe the decay patterns of HWP and the default half-life values for different 7  wood products are given (IPCC, 2006). This method is referred to as the Tier 2 method in the 2013 Revised Supplementary Methods and Good Practice Guidance Arising from the Kyoto Protocol (KP Supplement) (IPCC, 2014). Although the FOD model is recommended as the Tier 1 methodology, the IPCC has not provided a detailed and transparent explanation of why the decay of HWP follows this model. Previous publications have largely focussed on applying the FOD model to HWP consumption data, rather than challenging the assumption that the FOD model is the most appropriate method for characterizing the decay of HWP (Pingoud and Wagner, 2006). The details of the FOD model and the concept of a half-life are presented in Section 2.2.1. Section 2.2.2 then considers the differences between a product half-life and an end-use half-life. Subsequently section 2.2.3 then discusses the behaviours of products with long half-lives and those HWP with short half-lives. Being aware of the difficulties of developing a globally unified methodology, the IPCC allows Parties to use a Tier 3 method which involves country-specific half-lives and/or methodologies, as long as the methodologies are at least demonstrated to be as detailed and accurate as the Tier 2 method and adequate data are provided to support them (IPCC, 2014). Various Tier 3 models have also been proposed in previous publications. Most of them are generalized empirical models that can be represented by one or a series of formulas and may be applied to other systems. The details of these models are discussed in Section 2.5. 2.2.1 First order decay (FOD) model First order decay is also known as exponential decay. It was first formulated by Ernest Rutherford around 1900 to calculate the decay of radioactive substances (Rutherford, 1900). The exponential decay law was later proven to be widely applicable to natural sciences. An FOD model is usually described by a decay constant or half-life, which is defined as the time taken for a quantity to decay to half of its original amount (Equation 2-1~2-3). An FOD curve with a half-life of 35 years is presented in Figure 2-3.  𝑁𝑁𝑡𝑡 = 𝑁𝑁0𝑒𝑒−𝜆𝜆𝑡𝑡 Equation 2-1  𝑙𝑙𝑙𝑙𝑁𝑁𝑡𝑡 = 𝑙𝑙𝑙𝑙𝑁𝑁0 − 𝜆𝜆𝜆𝜆 Equation 2-2  𝜆𝜆1/2 = 𝑙𝑙𝑙𝑙(𝑁𝑁0/𝑁𝑁𝑡𝑡1/2)/𝜆𝜆 = 𝑙𝑙𝑙𝑙2/𝜆𝜆 Equation 2-3 where 𝑁𝑁𝑡𝑡  𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑙𝑙𝜆𝜆 𝑎𝑎𝜆𝜆 𝜆𝜆𝑖𝑖𝑎𝑎𝑒𝑒 𝜆𝜆   𝑁𝑁0 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑖𝑖𝑙𝑙𝑖𝑖𝜆𝜆𝑖𝑖𝑎𝑎𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑙𝑙𝜆𝜆   𝑁𝑁𝑡𝑡1/2 = 0.5𝑁𝑁0 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑙𝑙𝜆𝜆 𝑎𝑎𝜆𝜆 𝜆𝜆ℎ𝑒𝑒 half-life   𝜆𝜆 = 𝑙𝑙𝑙𝑙2/𝜆𝜆1/2 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑑𝑑𝑒𝑒𝑑𝑑𝑎𝑎𝑑𝑑 𝑑𝑑𝑎𝑎𝑙𝑙𝑖𝑖𝜆𝜆𝑎𝑎𝑙𝑙𝜆𝜆   𝜆𝜆1/2 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 half-life  8   When the FOD equation applies, a quantity will decay at the same ratio for each equal time interval* (Equation 2-4).   𝑑𝑑𝑒𝑒𝑑𝑑𝑎𝑎𝑑𝑑 𝑟𝑟𝑎𝑎𝜆𝜆𝑖𝑖𝑎𝑎|𝑡𝑡1𝑡𝑡2 = 𝑒𝑒−𝜆𝜆(𝑡𝑡2−𝑡𝑡1) Equation 2-4 where 𝜆𝜆 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑑𝑑𝑒𝑒𝑑𝑑𝑎𝑎𝑑𝑑 𝑑𝑑𝑎𝑎𝑙𝑙𝑖𝑖𝜆𝜆𝑎𝑎𝑙𝑙𝜆𝜆   The FOD is one of the simplest models that is able to describe dynamic decay processes (Pingoud and Wagner, 2006) and due to its wide applicability and its simplicity, it is reasonable that the IPCC selected this model as the Tier 2 method.  2.2.2 Product half-life vs. end-use half-life The aggregated HWP in use pool consists of several different sub-pools. The IPCC Tier 2 method presently outlines methodology for quantifying the pool sizes for sawnwood, wood-based panels and pulp and paper products using an FOD model and provides the IPCC default half-lives for each product category (Table 2-1). These half-lives are categorized based on the products rather than then the end uses of the products and they are referred to as product half-lives. Table 2-1 Default product half-lives for the Tier 2 method provided by the IPCC (2014) Product Half-life (years) Sawnwood 35 Wood-based panels 25 Paper and paperboard 2  The IPCC has not provided a detailed validation of the FOD model, nor have they included a transparent estimation of how these half-life values have been determined and there has been more discussion of the applicability of the model rather than its accuracy. The IPCC itself is not confident of these half-life values and strongly encourages countries to calibrate them with their own direct inventories of HWP or relevant market information (IPCC, 2014). It is intuitively reasonable to expect the half-life of sawnwood used for construction to be longer than that for furniture manufacturing. Half-lives categorized by the end uses rather than the products are referred to as end-use half-lives. For example, the end-use half-lives that the US * Some of the previous literature confuses the FOD model (Equation 2-4) with the linear decay model (Equation 2-7). For example Miner (2006) mistook Hashimoto and Moriguchi’s (2004) decay model being a straight line (linear) decay model when they actually used an FOD model. 9                                                   Environment Protection Agency (US EPA) has used for GHG emission reporting are 78.0~85.9 years for solid wood in single-family houses, 47.6~52.4 years for solid wood in multi-family houses, 23.4~25.8 years for solid wood used for housing repair and remodeling, 38 years for solid wood in the other end uses and 2.53 years for paper in all end uses (US EPA, 2013) (Table 2-2). The US EPA used a range of half-life values because the half-life was considered to be influenced by the age of the houses, with older houses tending to have shorter half-lives (Skog, 2008; US EPA, 2013). Table 2-2 End-use half-lives uses by US EPA (2013) End use Half-life (years) Solid wood in single-family houses 78.0~85.9 Solid wood in multi-family houses 47.6~52.4 Solid wood in housing repair and remodeling 23.4~25.8 Solid wood in all the other end uses 38 Paper in all end uses 2.53  2.2.3 Long-lived products versus short-lived products HWP with higher half-life values are longer-lived products and the ones with lower half-live values are shorter-lived products. Some nations use a majority of HWP for structural purposes and the structural HWP in residential houses are considered to be one of the longest-lived products in use (Ingerson, 2009). In this thesis, the term structural HWP refers to any wood product that contributes to the structural integrity of single-family, multi-family or mobile homes. For example, lumber, engineered wood products, plywood and oriented strand board (OSB) are frequently used as structural HWP. These pools of long-lived HWP therefore become significant in nations with a tradition of building wood-framed houses. This is especially important in North America, where for example wood-framed construction accounts for about 90% of the residential houses in the United States (Bowyer et al., 2010). In the US, over half of the harvested roundwood is used for long-lived uses and about 76% of the long-lived products are used in construction (Ingerson, 2009). Long-lived products have the potential to make a dominant contribution to the HWP carbon pool, as shown in Figure 2-2. As an illustration of this point, the carbon pools as a function of time in this figure have been developed assuming that the decay of HWP follows an FOD model and a constant annual input of 1 Tg C takes place for both solid wood in single-family houses, with a half-life of 80 years, and solid wood in all the other end uses, with a half-life of 38 years. Under these conditions, the use of structural solid woods in single-family houses results in an equilibrium pool size more than twice that for solid wood in all the other end uses and a sink period about thrice as long (Figure 2-2). 10   Figure 2-2 Constant annual input of 1 Tg C scenario for solid wood in single-family houses and in all the other end uses, assuming solid wood in single-family houses has a half-life of 80 years and the one in all the other end uses of 38 years according to the US EPA (2013). Key: SF=single-family. As shown in Equation 2-4 , the FOD model is not age-related, which means it assumes that a quantity decays at the same ratio per unit time irrespective of its age. This is often not the case for long-lived HWP such as residential houses. Intuitively, older houses are likely to have a higher decay than younger houses, which means the decay ratio should not be the same at all ages. This phenomenon has been acknowledged by the US in its GHG emission reporting (Table 2-2), but the methodology used to calculate these values was very indirect (Skog, 2008). Since a large amount of harvested roundwood ends up in residential housing construction in North America and these structural HWP are long-lived products that may make a dominant contribution to the size of the HWP in use pool, it is therefore sensible to focus the initial efforts on improved age-related modelling of HWP in North America’s residential houses. This topic is considered in greater detail in the next section. 2.3 Current state of knowledge on the half-life of US residential houses There have been numerous studies that have presented half-lives for modelling HWP in use and two documents have summarized all the half-life or life-span values that had been used in HWP models up to 2002 (Sikkema, Schelhaas and Nabuurs, 2002; Pingoud et al., 2003). However, rather than being “based on any empirical findings”, these values were acknowledged as generally being “expert judgements” (Pingoud et al., 2003, p. B1) and there is a lack of detailed references that provide a transparent derivation of these values. Based on these expert judgements, several recent 0204060801001200 100 200 300 400 500 600Pool Size (Tg C)YearsSolid wood in SF houses, half-life=80 yrs- Equilibrium pool size: 115 Tg C, - Period to equilibrium: 600 yrsSolid wood in other end uses, half-life=38 yrs- Equilibrium pool size: 55 Tg C, - Period to equilibrium: 200 yrs11  studies have estimated the half-lives for housing constructed in different regions. A summary of the most relevant estimates for this study is presented in Table 2-3.  Table 2-3 Half-life values used by previous literature Product category Region Half-life (years) Reference Sawnwood Global 35 (IPCC, 2014) Wood-based panels Global 25 (IPCC, 2014) Single-family houses US 75 (Winistorfer et al., 2005) Single-family houses US 78.0~85.9 (Skog, 2008) Multi-family houses US 47.6~52.4 (Skog, 2008) Construction materials Europe 50 (Eggers, 2002) Single-family houses US 200 (Row and Phelps, 1996) Multi-family houses US 150 (Row and Phelps, 1996) Oak construction UK 167 (equivalent value)  (Marland, Stellar and Marland, 2010) Residential houses US >100 (Miner, 2006)  Half-life values vary among regions but even within the same region, there are large uncertainties. For example, the half-life used by various studies undertaken in the US range from 75 to 200 years. The half-life values used in Eggers (2002) are based more on judgement than detailed analysis and that study used the logistic decay model which is described in detail in Section 2.5.4. Row and Phelps’s (1996) estimation methodology and the three-segment decay model that they used are considered in Section 2.5.5. Marland, Stellar and Marland (2010) proposed a Gamma distribution and the half-life is an equivalent value estimated based on the UK’s oak construction data, which are discussed in Section 2.5.6. Miner (2006) used a country-specific model using US housing data and the details are further discussed in Section 2.5.7.  The half-life values presented in the first four rows of Table 2-3 were all based on the first order decay assumption. As mentioned earlier, the IPCC (2006; 2014) has not included a transparent description of how these half-life values were determined. The half-life estimations by Winistorfer et al. (2005) and Skog (2008) are discussed in this section because they provide the most transparent methodology and data relevant to US houses. All other studies, other than Marland, Stellar and Marland (2010), do not provide a clear set of raw data or transparent methodology and they are therefore very challenging to interpret. Marland, Stellar and Marland (2010) described the use of the Gamma distribution model in detail (see Section 2.5.6) which determined an equivalent 12  half-life of 167 years for oak construction in the UK. They did not provide clear raw oak construction data and because their study applied to the UK rather than the US, the half-lives in their publication will not be considered further in this thesis. 2.3.1 Winistorfer et al. (2005) Winistorfer et al. (2005) used historical data on the stock of housing units to estimate the housing half-life in the US. That study compared the housing unit numbers published in 1920, 1930 and 1940 by the US Census Bureau (USDOC, 1940) to the unit remaining data for houses built pre-1920, pre-1930 and pre-1940 that were reported in 2001 (i.e. about 60 to 80 years later) by the American Housing Survey (AHS) (USDOC, 2002). The preliminary inference was that about half of the houses built before 1930 were still in use after 70 years. However, by comparing housing starts to the survey data, they found that there were more units reported in the Survey than actual houses built during the comparable period. This indicated that the age of the houses in the Surveys were likely to be underestimated. Winistorfer et al. (2005) considered that the Survey overestimated by about 12 million units of houses built between 1960 and 1999 and that these houses should be moved to the older groups. This adjustment resulted an estimate of the housing half-life of well over 85 years. However, due to a lack of trust in the Survey data, Winistorfer et al. (2005) chose a conservative half-life estimate of 75 years for the US single-family houses. Compared to the IPCC default values, this half-life estimation has a solid data source. However, there are three major weaknesses of this half-life estimation method. First, the housing units were pooled together to conduct a simple comparison between two data points for each time period, which is not a comprehensive approach to accurately describe the decay of houses. Second, the American Housing Survey has been conducted biennially and in 2005 there were eleven Surveys available. However, Winistorfer et al. (2005) only conducted the analysis using Survey 2001. The American Housing Survey uses a survey-based data collection method, which means that there is a high likelihood of a sampling uncertainty being introduced. If multiple surveys were used to do the comparison, this level of uncertainty may be reduced. Given the amount of data that the American Housing Survey reports, a more comprehensive and reliable statistical analysis could be used to estimate the half-life. Third, the half-life determination was based more on expert judgment rather than on a statistical analysis. The housing units stock evaluated included single-family houses, multi-family houses and mobile homes. After the adjustment mentioned earlier, the half-life estimate for all these houses increased from 70 years to 85 years. Among these three types of houses, single-family houses are expected to have the longest half-life. So the half-life of single-family houses should be over 85 years and the selection of a half-life of 75 years for the US single-family houses is a conservative estimate that is not based on robust evidence. 13  2.3.2 Skog (2008) Skog (2008) estimated the half-lives of US single-family and multi-family houses by using half-lives elaborated from the studies of Winistorfer et al. (2005) and Athena Institute (2004) as starting values. These starting values were put into the US WOODCARB II model to estimate the carbon stocks of HWP in US houses. An individual estimation of the carbon stocks of HWP in US houses in 2001 were determined and the WOODCARB II model was forced to match this value by changing the half-lives. A detailed description of this approach is presented in Appendix B.2. Skog (2008) assumed that the half-lives of houses built in different periods are varied, with older houses having shorter half-lives than newer houses. This implies that the FOD model does not apply as a generalized decay pattern for all houses. Dynamic half-lives in some way reduce the errors resulting from using the FOD model to describe the decay pattern of long-lived products mentioned in Section 2.2.3. This topic is further discussed in Section 2.5. Skog (2008) estimated that the half-life of houses built prior to 1940 was 78 years and he increased this value by 1.98 years for each twenty year period of construction from 1940. His half-lives therefore ranged from 78 - 85.9 years (Table 2-3).   Although he determined the half-lives of US houses, Skog (2008) did not propose a generalized empirical model that may be applied to other HWP pools. Without a generalized model, the methodology for calculating the HWP pool is complex. In the absence of a generalized model, the carbon stocks of HWP in houses built in different periods must be quantified separately and then added together to determine the total stock size. This time consuming methodology has been adopted by the US in its National Inventory Report (US EPA, 2013). 2.4 Current state of knowledge on the HWP pool size of US residential houses The IPCC mentioned four approaches to quantify the emissions and stocks of HWP (IPCC, 2006), which are presented below. • The Stock Change Approach estimates the annual change of the HWP stock within the consuming country’s border (IPCC, 2006), regardless where wood is grown (Bache-Andreassen, 2009) • The Atmospheric Flow Approach estimates the amount of carbon flux from (or to) HWP to (or from) the atmosphere, which occurs during the reporting year and is within the national boundaries (IPCC, 2006). Like the Stock Change Approach, regardless of the country of origin of the wood, as long as the carbon emissions to the atmosphere occur within the border, the consuming country is responsible for the emission reporting. • The Production Approach estimates the annual stock change of HWP that are produced by domestically harvested wood or wood-based material, regardless of where they are 14  consumed (IPCC, 2006). The result includes exported HWP but excludes imports, thus the harvesting country can build up a stock beyond the national border (Bache-Andreassen, 2009). • The Simple Decay Approach estimates the amount of carbon flux from (or to) HWP that are produced by domestically harvested wood to (or from) the atmosphere during the reporting year (Ford-Robertson, 2003). Among these four approaches, the IPCC (2014) prefers the use of the Production Approach. However, historically the Stock Change Approach has been favoured for quantifying the HWP pool in residential houses, because the data on material consumption for house construction do not usually specify the origin of the wood products. For example, Wilson (2006) estimated the structural HWP pool in US single-family and multi-family houses to be 528 Tg C in 2003 using the Stock Change Approach. A detailed description of Wilson’s (2006) calculation method is presented in Appendix B.1. In addition, Skog (2008) calculated that the HWP pool in US single-family and multi-family houses was 682 Tg C in 2001 using the Stock Change Approach. A detailed description of Skog’s (2008) calculation method is presented in Appendix B.2. In contrast, the US EPA’s National Inventory Report reported that the pool of HWP in use was 1,472 Tg C in 2009 using the Production Approach (US EPA, 2013). 2.5 Other proposed models and half-lives In addition to a wide range of half-lives, a variety of models have been used to characterize the decay of HWP in use. This section summarizes the information published on this topic. 2.5.1 “Instantaneous oxidation” model Instantaneous oxidation is the IPCC Tier 1 or default method (UNFCCC, 2003; IPCC, 2014). Since 2006, the IPCC has recommended that only Parties with insufficient data or an insignificant change of HWP in use stocks utilise this approach. However, the IPCC encourages the use of Tier 2 methodology to judge whether the stock change is significant. The Tier 2 method is the FOD model with default values provided by the IPCC (Table 2-1). Instantaneous oxidation is the only method that is permitted by the IPCC for quantifying HWP produced from deforestation, stored in solid waste disposal sites (SWDS) or used for energy (IPCC, 2014). Under instantaneous oxidation, wood harvested from the forest is considered to be emitted to the atmosphere immediately and thus makes no contribution to the HWP in use carbon pools.  The instantaneous oxidation model ignores the potential role of HWP pools in climate change mitigation, which, if used directly without validation of the HWP stock change, gives incentives to policy makers to focus on reducing industrial emissions of GHG’s, decreasing forest harvests, and 15  increasing forest areas in order to sequester more atmospheric carbon rather than stimulating the production of long-lived HWP. 2.5.2 Instant decay model Ford-Robertson (2003) used an instant decay model that assumed all emissions happened at the end of the product’s life (Equation 2-5 and Equation 2-6). For example, if sawnwood had a product life of 35 years, all of the carbon associated with that sawnwood product would be emitted after 35 years and the decay pattern would be the grey curve shown in Figure 2-3. This model was used to compare with the linear decay and FOD models. Instant 𝑁𝑁𝑡𝑡 = 𝑁𝑁0, 𝜆𝜆 < 𝜆𝜆1/2 Equation 2-5  𝑁𝑁𝑡𝑡 = 0, 𝜆𝜆 ≥ 𝜆𝜆1/2 Equation 2-6 where 𝑁𝑁t 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑙𝑙𝜆𝜆 𝑎𝑎𝜆𝜆 𝜆𝜆𝑖𝑖𝑎𝑎𝑒𝑒 𝜆𝜆    𝑁𝑁0 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑖𝑖𝑙𝑙𝑖𝑖𝜆𝜆𝑖𝑖𝑎𝑎𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑙𝑙𝜆𝜆   2.5.3 Linear decay model The linear decay model assumes that a quantity decays the same amount for each equal time interval as presented in Equation 2-7. The half-life can be calculated using Equation 2-8. Linear 𝑁𝑁𝑡𝑡 = 𝑁𝑁0 − 𝑏𝑏𝜆𝜆 Equation 2-7  𝜆𝜆1/2 =𝑁𝑁0 − 𝑁𝑁𝑡𝑡1/2𝑏𝑏=𝑁𝑁02𝑏𝑏 Equation 2-8 where 𝑁𝑁t 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑙𝑙𝜆𝜆 𝑎𝑎𝜆𝜆 𝜆𝜆𝑖𝑖𝑎𝑎𝑒𝑒 𝜆𝜆    𝑁𝑁0 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑖𝑖𝑙𝑙𝑖𝑖𝜆𝜆𝑖𝑖𝑎𝑎𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑙𝑙𝜆𝜆   𝑁𝑁𝑡𝑡1/2 = 0.5𝑁𝑁0 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑙𝑙𝜆𝜆 𝑎𝑎𝜆𝜆 half-life   𝑏𝑏 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑑𝑑𝑒𝑒𝑑𝑑𝑎𝑎𝑑𝑑 𝑟𝑟𝑎𝑎𝜆𝜆𝑒𝑒   𝜆𝜆1/2 𝑖𝑖𝑖𝑖 the half-life   A linear decay curve with half-life of 35 years is represented by the orange curve shown in Figure 2-3. 16   Figure 2-3 Decay curves of instant decay, linear decay and FOD models with half-lives of 35 years. Ford-Robertson (2003) compared the instant decay, linear decay and FOD models using the same or equivalent half-life values of 8 years and fictitious input data. The FOD curve showed in Figure 2 of Ford-Robertson’s (2003) paper has a half-life of 5 years but the publication stated that the half-life was 8 years. Because of this error, Ford-Robertson considered that the impacts of these three different models to the HWP stocks were approximately equal in magnitude. A similar approach to that used by Ford-Robertson (2003) was used to plot the instant decay, linear decay and FOD models with half-lives of 35 years (Figure 2-3). At time periods shorter than the half-life, the FOD model has the fastest decay rate, the linear decay model has a medium rate of decay and instant decay model does not decay at all. The three models intersect at the half-life, point (35, 0.5). At time periods longer than the half-life, the instant decay model decays most quickly. From this point, the decay rate of the FOD model becomes slower than the linear decay model and it continually decreases in rate with increasing time. Consequently, the FOD model would sequester carbon for the longest period. The linear decay model assumes an equal rate of decay occurs at any given time until the amount reaches zero. In reality, HWP may decay at a nearly constant rate over a short period, but they are unlikely to do so over a longer period. Therefore, rather than being used independently, the linear decay model is usually integrated with other models to form a hybrid model or it is used segmentally with different rates being applied to describe decay patterns over different sequential time periods. For example, Kurz et al. (1992) proposed segmental linear decay models for 00.10.20.30.40.50.60.70.80.910 50 100 150 200Remnant fractionYearsInstant decayLinear decayFOD17  construction lumber, other lumber, pulp and paper and landfills. For construction lumber, they assumed a three-segment linear decay model applied where 5% decay occurred at year 1 (Equation 2-9), 50% decay at year 60 (Equation 2-10) and 95% decay at year 100 (Equation 2-11).  𝑁𝑁𝑡𝑡 = (1− 5%)𝑁𝑁0,                                   0 < 𝜆𝜆 <  1 Equation 2-9  𝑁𝑁𝑡𝑡 = 𝑁𝑁0 �95%−50%− 5%60− 1(𝜆𝜆 − 1)� , 1 < 𝜆𝜆 ≤ 60 Equation 2-10  𝑁𝑁𝑡𝑡 = 𝑁𝑁0 �50%−95%− 50%100− 60(𝜆𝜆 − 60)� , 60 < 𝜆𝜆 ≤ 100 Equation 2-11 where 𝑁𝑁𝑡𝑡  𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑙𝑙𝜆𝜆 𝑎𝑎𝜆𝜆 𝜆𝜆𝑖𝑖𝑎𝑎𝑒𝑒 𝜆𝜆   𝑁𝑁0 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑖𝑖𝑙𝑙𝑖𝑖𝜆𝜆𝑖𝑖𝑎𝑎𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑙𝑙𝜆𝜆   For the “other lumber” category, they assumed that a three-segment linear decay process operated with 40% decay at year 1 (Equation 2-12), 95% decay at year 50 (Equation 2-13) and 100% at year 100 (Equation 2-14).  𝑁𝑁𝑡𝑡 = (1− 40%)𝑁𝑁0,                                   0 < 𝜆𝜆 <  1 Equation 2-12  𝑁𝑁𝑡𝑡 = 𝑁𝑁0 �60%−95%− 40%50− 1(𝜆𝜆 − 1)� , 1 < 𝜆𝜆 ≤  50 Equation 2-13  𝑁𝑁𝑡𝑡 = 𝑁𝑁0 �5%−100%− 95%100− 50(𝜆𝜆 − 50)� , 50 < 𝜆𝜆 ≤ 100 Equation 2-14  For pulp and paper, they assumed that a four-segment linear decay model occurred with 50% decay at year 1 (Equation 2-15), 85% at year 5 (Equation 2-16), 90% at year 10 (Equation 2-17) and 100% at year 100 (Equation 2-18).  𝑁𝑁𝑡𝑡 = (1− 50%)𝑁𝑁0,                                   0 < 𝜆𝜆 <  1 Equation 2-15  𝑁𝑁𝑡𝑡 = 𝑁𝑁0 �50%−85%− 50%5− 1(𝜆𝜆 − 1)� , 1 < 𝜆𝜆 ≤ 5 Equation 2-16  𝑁𝑁𝑡𝑡 = 𝑁𝑁0 �15%−90%− 85%10− 5(𝜆𝜆 − 5)� ,      5 < 𝜆𝜆 ≤ 10 Equation 2-17  𝑁𝑁𝑡𝑡 = 𝑁𝑁0 �10%−100%− 90%100 − 10(𝜆𝜆 − 10)� , 10 < 𝜆𝜆 ≤ 100 Equation 2-18  18  For HWP in landfills, they assumed a two-segment linear decay process functioned where 1-2% decay per year occurred until a decay of 80% (1% decay per year is used in Figure 2-4 for landfills) and then decay stopped (Equation 2-19 and Equation 2-20).  𝑁𝑁𝑡𝑡 = 𝑁𝑁0(1− 𝑎𝑎𝜆𝜆),   𝑎𝑎 = 1% 𝜆𝜆𝑎𝑎 2%,𝑤𝑤ℎ𝑒𝑒𝑙𝑙 𝑁𝑁𝑡𝑡 > 0.8𝑁𝑁0 Equation 2-19  𝑁𝑁𝑡𝑡 = (1− 80%)𝑁𝑁0, 𝑤𝑤ℎ𝑒𝑒𝑙𝑙 𝑁𝑁𝑡𝑡 ≤ 0.2𝑁𝑁0 Equation 2-20  The HWP decay curves for each model developed by Kurz et al. (1992) are shown in Figure 2-4.  Figure 2-4 Decay curves for construction lumber, other lumber, pulp and paper and HWP in landfills using the models of Kurz et al. (1992) This set of decay models were developed at the Carbon Budget Workshop in 1989 involving experts from several disciplines to provide a reasonable first approximation based on historical data and expert judgment (Kurz et al., 1992). However, the process and data underpinning these models are not transparent. 2.5.4 Logistic decay model Row and Phelps (1990) proposed a logistic decay function model (Equation 2-21) (Eggers, 2002). A logistic decay model has four parameters, which makes this model a very flexible model in shape but also a very complicated model to apply when data points are limited. Equation 2-22 is a 00.10.20.30.40.50.60.70.80.910 20 40 60 80 100RemnantYearsConstruction lumberLandfillsOther lumberPulp and paper19  simplified version of the logistic decay model, where a and b are equal to 1.2, c is equal to 2 divided by half-life (2/t1/2) and d is equal to 5. Logistic 𝑁𝑁𝑡𝑡 = 𝑁𝑁0(𝑑𝑑 −𝑎𝑎1 + 𝑏𝑏 × 𝑒𝑒−𝑐𝑐×𝑡𝑡) Equation 2-21 where 𝑁𝑁𝑡𝑡  𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑙𝑙𝜆𝜆 𝑎𝑎𝜆𝜆 𝜆𝜆𝑖𝑖𝑎𝑎𝑒𝑒 𝜆𝜆   𝑁𝑁0 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑖𝑖𝑙𝑙𝑖𝑖𝜆𝜆𝑖𝑖𝑎𝑎𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑙𝑙𝜆𝜆   a, b, c and d are decay parameters  Simplified logistic 𝑁𝑁𝑡𝑡 = 𝑁𝑁0(1.2−1.21 + 5 × 𝑒𝑒−2𝑡𝑡/𝑡𝑡1/2) Equation 2-22 where 𝑁𝑁𝑡𝑡  𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑙𝑙𝜆𝜆 𝑎𝑎𝜆𝜆 𝜆𝜆𝑖𝑖𝑎𝑎𝑒𝑒 𝜆𝜆   𝑁𝑁0 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑖𝑖𝑙𝑙𝑖𝑖𝜆𝜆𝑖𝑖𝑎𝑎𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑙𝑙𝜆𝜆   𝜆𝜆1/2 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 half-life   Eggers (2002) and Karjalainen, Kellomoki and Pussinen (1994) used this simplified version of logistic decay model to quantify the HWP in use pool in a number of European nations, so this model is sometimes also referred to as the European Forest Institute (EFI) 2002 decay model (Miner, 2006) or the Karjalainen model (Pingoud, 2006). Eggers (2002) used a half-life of 50 years for wood products used in construction in five European countries (Table 2-3). However, the processes used to develop the simplified model, and calculate the half-lives are not stated transparently. In Figure 2-5, a logistic decay curve with a half-life of 149 years is compared to four other models described in Sections 2.5.5-2.5.7. The half-life value estimated in Section 3.3 is used here. A comparison with other decay models is addressed later in Section 2.5.7. 20   Figure 2-5 Decay curves of logistic decay with a half-life of 149 years, three-segment decay with a half-life of 138 years,  Gamma distribution with α=2.07 and β=80.2, and Miner’s (2006) country-specific model. 2.5.5 Three-segment decay model Row and Phelps (1996) also proposed a three-segment decay model. They considered that the rate of HWP decay should initially be constant until the quarter-life, then increase gradually to reach a maximum rate at the half-life and slow down thereafter. The formulas for the three-segment decay model are shown in Equation 2-23, Equation 2-24 and Equation 2-25. three-segment 𝑁𝑁𝑡𝑡 = 𝑁𝑁0 − �𝑁𝑁0 − 𝑁𝑁𝑡𝑡1/4� ×𝜆𝜆𝜆𝜆1/4, 𝜆𝜆 < 𝜆𝜆1/4  Equation 2-23  𝑁𝑁𝑡𝑡 = 𝑁𝑁0 �1−0.51 + 2�ln�𝜆𝜆1/2� − ln(𝜆𝜆)�� , 𝜆𝜆1/4 ≤ 𝜆𝜆 ≤ 𝜆𝜆1/2 Equation 2-24  𝑁𝑁𝑡𝑡 = 𝑁𝑁0 ×0.51 + 2(ln(𝜆𝜆) − ln�𝜆𝜆1/2�), 𝜆𝜆 > 𝜆𝜆1/2 Equation 2-25 where 𝑁𝑁𝑡𝑡  𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑙𝑙𝜆𝜆 𝑎𝑎𝜆𝜆 𝜆𝜆𝑖𝑖𝑎𝑎𝑒𝑒 𝜆𝜆  𝑁𝑁𝑡𝑡1/4  𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑙𝑙𝜆𝜆 𝑎𝑎𝜆𝜆 𝜆𝜆𝑖𝑖𝑎𝑎𝑒𝑒 𝜆𝜆1/4 and is calculated using Equation 2-24  𝜆𝜆1/4 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑞𝑞𝑎𝑎𝑎𝑎𝑟𝑟𝜆𝜆𝑒𝑒𝑟𝑟 𝑙𝑙𝑖𝑖𝑙𝑙𝑒𝑒,𝑤𝑤ℎ𝑖𝑖𝑑𝑑ℎ 𝑖𝑖𝑖𝑖 0.5𝜆𝜆1/2  𝜆𝜆1/2 𝑖𝑖𝑖𝑖 the half-life  00.10.20.30.40.50.60.70.80.910 50 100 150 200 250 300Remnant fractionYearsGamma3-segmentLogisticMiner21  This model was used to conduct half-life estimations and report the US national GHG inventory before the IPCC recommended the FOD as the Tier 2 method (US EPA, 2004). Row and Phelps (1996) estimated the half-lives of US single-family and multi-family houses to be 200 and 150 years, respectively, using this decay model (Table 2-3). However, the process of the model and half-life developments and the data used are not stated transparently. In order to represent the shape of this model, a three-segment decay curve with half-life of 138 years is plotted in Figure 2-5. The half-life value estimated in Section 3.3 is used here. A comparison with other decay models is addressed later in Section 2.5.7. 2.5.6 Gamma distribution model When studying Row and Phelps’s three-segment decay model (1996), Marland and Marland (2003) noticed that a cumulative Gamma distribution curve could be closely fitted to the three-segment decay curve. The formula for the Gamma distribution model is presented in Equation 2-26. Gamma 𝑁𝑁𝑡𝑡 = 𝑁𝑁0 × (1− 𝐺𝐺𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎(𝛼𝛼,𝛽𝛽, 𝜆𝜆)) Equation 2-26 where 𝑁𝑁𝑡𝑡  𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑙𝑙𝜆𝜆 𝑎𝑎𝜆𝜆 𝜆𝜆𝑖𝑖𝑎𝑎𝑒𝑒 𝜆𝜆   𝑁𝑁0 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑖𝑖𝑙𝑙𝑖𝑖𝜆𝜆𝑖𝑖𝑎𝑎𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑙𝑙𝜆𝜆   𝐺𝐺𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 (𝛼𝛼,𝛽𝛽, 𝜆𝜆) 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑟𝑟𝑒𝑒𝑎𝑎𝑙𝑙𝑎𝑎𝑙𝑙𝜆𝜆 𝑙𝑙𝑟𝑟𝑎𝑎𝑑𝑑𝜆𝜆𝑖𝑖𝑎𝑎𝑙𝑙 𝑎𝑎𝜆𝜆 𝑑𝑑𝑒𝑒𝑎𝑎𝑟𝑟 𝜆𝜆 𝑟𝑟𝑒𝑒𝑟𝑟𝑟𝑟𝑒𝑒𝑖𝑖𝑒𝑒𝑙𝑙𝜆𝜆𝑒𝑒𝑑𝑑 𝑏𝑏𝑑𝑑  𝜆𝜆ℎ𝑒𝑒 𝑑𝑑𝑎𝑎𝑎𝑎𝑎𝑎𝑙𝑙𝑎𝑎𝜆𝜆𝑖𝑖𝑐𝑐𝑒𝑒 𝐺𝐺𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑑𝑑𝑖𝑖𝑖𝑖𝜆𝜆𝑟𝑟𝑖𝑖𝑏𝑏𝑎𝑎𝜆𝜆𝑖𝑖𝑎𝑎𝑙𝑙 𝑤𝑤𝑖𝑖𝜆𝜆ℎ 𝛼𝛼, 𝜆𝜆ℎ𝑒𝑒 𝑖𝑖ℎ𝑎𝑎𝑟𝑟𝑒𝑒 𝑟𝑟𝑎𝑎𝑟𝑟𝑎𝑎𝑎𝑎𝑒𝑒𝜆𝜆𝑒𝑒𝑟𝑟,  𝑎𝑎𝑙𝑙𝑑𝑑 𝛽𝛽, 𝜆𝜆ℎ𝑒𝑒 𝑖𝑖𝑑𝑑𝑎𝑎𝑙𝑙𝑒𝑒 𝑟𝑟𝑎𝑎𝑟𝑟𝑎𝑎𝑎𝑎𝑒𝑒𝜆𝜆𝑒𝑒𝑟𝑟    Marland, Stellar and Marland (2010) developed this concept further by applying a Gamma distribution to oak construction data from Forest Research UK and they estimated α and β values to be 6.74 and 26.1, respectively. The equivalent half-life of a Gamma distribution with α and β values to be 6.74 and 26.1 is 167 years (Table 2-3). However, Marland, Stellar and Marland (2010) did not provide specific details on the oak construction data they used, nor did the Forest Research UK made those data available to this study. The adequacy of their model therefore could not be readily validated. A Gamma distribution curve with α equal to 2.07 and β equal to 80.2 (equivalent to a half-life of 140 years) is plotted in Figure 2-5. The α and β values estimated in Section 3.3 are used here. A comparison with other decay models is addressed later in Section 2.5.7. Because the Gamma distribution model has two parameters, it is a more flexible model than most of the models presented earlier. When making α equal to 1, a Gamma distribution model is converted to a first order decay model with a half-life of ln (2) multiplied by the β value. 2.5.7 Miner’s (2006) Country-specific model Decay models proposed in previous literature were generally not validated by transparent historical data. However for some countries, there are historical data available to develop an empirical 22  distribution. For example, Miner (2006) used the biannual housing units data from 1985 to 2003 (i.e. 10 reports) provided by the American Housing Survey (AHS) to plot a distribution curve of the fraction of original housing remaining (USDOC, 2004). The data were divided into five age groups: houses built in 1990-2003, 1970-1989, 1950-1969, 1930-1949 and before 1930.  Several assumptions were made for this model: • Except for age group 1990-2003, houses in the same age group decayed at the same ratio every year. The average fraction of houses removed annually was used to determine this decay ratio. • The decay ratio of houses in the age group 1990-2003 changed linearly every year from 0 to the average decay ratio of the previous age group (i.e. 1970-1989) (Figure 2-6). The approach was used because no data were available for the age group 1990-2003. • The decay of houses in each age group represented the decay of all houses of a similar age. This assumption allowed cumulative decay curve of houses to be developed. The decay ratio (i.e. fractional removal per year) for each age group and the cumulative decay curves are shown in Figure 2-6.  Figure 2-6 Fraction of houses removed annually in each age group and the cumulative decay curve (Miner, 2006) The first and second assumptions are not robust and further analysis is required to validate them. For example, the variance of the housing unit data for the age group 1970-1989 reported by the AHS is high and the average fraction of houses removed annually may not be a suitable 00.0010.0020.0030.0040.0050.0060.0070.650.70.750.80.850.90.9510 20 40 60 80 100Fraction of houses removed per yearRemnant fractionYearsAge group1990-2003Age group1970-1989Age group1950-1969 Age group1930-1949Age groupbefore 193023  representation of the decay ratio for this period. In addition, there are less data available for the age group 1990-2003 than for previous age groups used, so the initial part of the cumulative decay curve is more uncertain than later components of the curve. Furthermore, the average fraction of houses removed for the age group before 1930 may be skewed by the presence of even older houses and this phenomenon may explain the sudden change in removal ratio seen after 73 years (Figure 2-6). Compared to Winistorfer et al.’s (2005) half-life estimation based on the comparison of two data points, the average fraction removal approach used by Miner (2006) is more robust. However, Miner (2006) did not estimate a half-life and his analysis only goes to about 0.7 remnant fraction. If the decay curve was extrapolated to 0.5 remnant fraction, the half-life would be 148 years. However, given the amount of data that the American Housing Survey reports, a more reliable statistical analysis should be used to determine the half-life. Chapter 3 of this thesis presents a methodology developed using updated American Housing Survey data and the least squared estimates of half-lives are calculated. Overall, country-specific models should be more accurate than general models provided that they are developed using historical data. However, these models may also be more complex. Figure 2-5 shows a comparison of four model curves that are calibrated to have the same half-life value. The shapes and trends of the four curves are similar. 2.5.8 Comparison of HWP decay models The suitability of each model in describing the decay pattern of houses was evaluated using the following criteria: • Shape. Residential houses are long-lived assets and they are expected to remain functional for a prolonged period. Therefore, intuitively, new houses should not have a faster average decay rate than houses that have been used for a long time. In addition, the fastest decay rate should occur around the expected service life of the houses. The housing decay pattern should therefore conceptually have an inverse sigmoidal shape. • Ease of use. The ease of use depends on the complexity of the decay model. Generally, a linear model is simpler than a nonlinear model. A nonlinear model that can be transformed into a linear model is simpler than a model that cannot be transformed. A model with fewer parameters is simpler than a model with more variables. A model with fewer segments, meaning lower number of formulas, is simpler than a model with more segments. • Size of the data required. Data scarcity is the major constraint for accurately estimating the decay pattern. The ability of a model to be calibrated precisely using a small data set is therefore a substantial advantage. • Flexibility. A model is considered to be more flexible when the shape and scale of the curves plotted using different model parameters can change flexibly. More specifically, the model can be converted to other models by making the parameters equal to special values. 24  The first order decay model, linear decay model and instant decay model are the simplest models that are easy to use and require a minimum amount of data. However, these models do not provide an inverse sigmoidal shape and are not flexible. The three-segment decay model can provide an inverse sigmoidal shape and does not require a large data size, but it has more complicated formulas and is not flexible. The logistic decay model and the Gamma distribution model can provide an inverse sigmoidal shape and are more flexible models, but they are more complicated to use and require large data sets in order to be adequately calibrated. As shown in Figure 2-6, the country-specific model developed by Miner (2006) for US houses displayed a shape that was quite different to that of the first order decay model. A flexible model such as the Gamma distribution model may be able to adequately describe the decay pattern like this. 2.6 Research objectives Based on the literature reviewed in this chapter, the remainder of this thesis addresses the following three hypotheses: • the first order decay model does not provide the most precise estimation of the decay of HWP in houses; • the Gamma distribution model provides one of the best descriptions of the decay pattern of houses at the national level; • the previous estimations of the HWP in use pool may be substantially underestimated by several nations.  25  Chapter 3 Determination of the decay pattern of US single-family and multi-family houses 3.1 Introduction In Chapter 2, the decay models and half-lives proposed by previous publications were reviewed and the comprehensiveness and transparency of them were discussed. As mentioned, a large quantity of harvested wood products (HWP) is consumed for the construction of residential houses in North America. These HWP can last for a long time and long-lived HWP make the dominant contribution to the carbon stock size (Section 2.2.3). It is therefore logical to focus the initial efforts on improving the modelling of structural HWP in North American’s residential houses and quantify this structural HWP pool prior to assessing the size of the other HWP pools with shorter half-lives.  However, the paucity of Canadian housing data prevented this study from investigating North America as a whole. The limitations and uncertainties of the Canadian data are presented in Section 4.2.2 and discussed in Section 4.4. To our knowledge, the US provides the largest and most accessible publicly available historical data for single-family and multi-family houses. This thesis therefore used the best available data (i.e. US single- and multi-family houses) to initially develop and assess the applicability of the methodology. Once the methodology was developed, it could be applied to other countries (i.e. Canada in this case) to estimate the country-specific parameters. This is the same approach adopted by the IPCC in the Good Practice Guidance (IPCC, 2014). The IPCC recommends the FOD model proposed by Pingoud and Wagner (2006) and provides default half-lives but strongly encourages countries to calibrate the half-lives using their own country-specific data, where these exist. This Chapter outlines the data available from the American Housing Survey and its constraints, develops a novel methodology to model the decay pattern of US single-family (SF) and multi-family (MF) houses, uses this methodology to determine the end-use half-life of the HWP in these buildings, and compares the results to previously published information. This method is aimed to be applicable to other countries that have the similar data. Unless stated otherwise, the term “houses” in this chapter is referring to US single-family and multi-family houses. 3.2 Methods The net annual change in the structural HWP pool of houses can be calculated by subtracting the HWP carbon removed from the pool each year in demolished houses from HWP carbon added to the pool annually in newly built houses (Figure 3-1 and Equation 3-1). This study assumed that the structural HWP have the same half-life as houses. The structural HWP usually remain in the house 26  until it is demolished. Non-structural HWP, on the other hand, are used mainly as interior decorative materials and are unlikely to last as long as the structural components of the houses. Therefore, non-structural HWP have been assumed to have a different, and shorter, half-live than houses. This Assumption is further discussed in Assumption 5-1.  Figure 3-1 Quantification method for the carbon pool of HWP in houses This study also assumed that the carbon in HWP used for repairing and remodelling single- and multi-family houses was approximately equal to the carbon in those HWP being replaced (Assumption 3-1). This implies that annual change in the structural HWP pool associated with renovations is negligible. In reality, renovations may include an increase of the floor area of a house, which means that the carbon inputs may be higher than the outputs. Ignoring this higher input due to renovations may lead to a conservative estimation of the size of structural HWP pool in US single- and multi-family houses. Skog (2008) addressed the potentially higher input due to renovations by multiplying the estimated stock size by the ratio of the average recent floor area to the average floor area when houses were originally constructed. This ratio of floor areas is discussed further in Appendix B.2. However, only about 4.06% of the households that existed in 2011 undertook renovations that involved an increase in floor area (U.S. Census Bureau, 2010). In this thesis, it has been assumed that only those renovations that changed the floor area contributed to the HWP in use pool. Renovations and remodelling activities that did not change the floor area were assumed to have a balanced annual input and output of HWP and were assumed not to make a net contribution to the size of HWP pool. Also, because less than 5% of all renovations added to the floor area it was assumed that this variation falls within the uncertainty present in the house stock data available from the American Housing Survey. Therefore, this study assumed that renovations made a negligible contribution to the structural HWP pool (Assumption 3-1). The structural HWP pool in new houses can be estimated using the number of new houses built multiplied by the average mass of structural HWP carbon consumed per house (Equation 3-2). The structural HWP in demolished houses can be estimated using the number of houses demolished multiplied by the average mass of structural HWP carbon consumed per house (Equation 3-3). These data are usually collected or estimated on an annual basis which enables the annual net pool size change to be calculated and aggregated over the longer term to estimate the pool of structural HWP in houses. 27  McKeever and Howard (2011) estimated HWP consumption for houses, average floor area and housing starts in the US annually from 1950 to 2009. Sianchuk, Ackom and McFarlane (2012) estimated annual HWP consumptions, annual average floor areas and housing starts for the US single-family homes from 1900 to 2010. As a result, long term annual data are available for both 𝑁𝑁𝑛𝑛𝑛𝑛𝑛𝑛 ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑛𝑛 and 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑜𝑜𝑡𝑡𝑠𝑠 𝑛𝑛𝑜𝑜𝑜𝑜𝑤𝑤 𝐶𝐶/ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑛𝑛. However, to our knowledge, values for 𝑁𝑁𝑤𝑤𝑛𝑛𝑑𝑑𝑜𝑜𝑑𝑑𝑑𝑑𝑜𝑜ℎ𝑛𝑛𝑤𝑤 ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑛𝑛𝑜𝑜 have not been reported publicly or estimated comprehensively. In order to determine this variable, the decay kinetics of houses need to be modelled and this approach is used in this thesis, as outlined below.  A review of decay patterns proposed by previous literature has been presented in Chapter 2. Data scarcity has prevented many countries from developing country-specific methodologies. However, the IPCC’s default methodology and half-lives are not based on robust data or detailed kinetic analysis. They may also underestimate the size of the actual HWP pool, thereby providing an incentive for countries to develop more precise national models. To our knowledge, the American Housing Survey (AHS) has the most detailed long-term housing data that are publicly available. Using these data, this paper proposes a method to model the decay pattern of US residential houses. This method is expected to be applicable to other countries provided adequate data are available.  𝛥𝛥𝑃𝑃𝑡𝑡 = 𝐶𝐶𝑆𝑆𝑡𝑡𝑠𝑠 𝐻𝐻𝐻𝐻𝐻𝐻 𝑑𝑑𝑛𝑛 𝑛𝑛𝑛𝑛𝑛𝑛 ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑛𝑛𝑜𝑜,𝑡𝑡 − 𝐶𝐶𝑆𝑆𝑡𝑡𝑠𝑠 𝐻𝐻𝐻𝐻𝐻𝐻 𝑑𝑑𝑛𝑛 𝑤𝑤𝑛𝑛𝑑𝑑𝑜𝑜𝑑𝑑𝑑𝑑𝑜𝑜ℎ𝑛𝑛𝑤𝑤 ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑛𝑛𝑜𝑜,𝑡𝑡 Equation 3-1  𝐶𝐶𝑆𝑆𝑡𝑡𝑠𝑠 𝐻𝐻𝐻𝐻𝐻𝐻 𝑑𝑑𝑛𝑛 𝑛𝑛𝑛𝑛𝑛𝑛 ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑛𝑛𝑜𝑜,𝑡𝑡 ≈ 𝑁𝑁𝑛𝑛𝑛𝑛𝑛𝑛 ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑛𝑛𝑜𝑜,𝑡𝑡 ×𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎  𝑜𝑜𝑡𝑡𝑠𝑠 𝑛𝑛𝑜𝑜𝑜𝑜𝑤𝑤 𝐶𝐶/ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑛𝑛,𝑡𝑡 Equation 3-2  𝐶𝐶𝑆𝑆𝑡𝑡𝑠𝑠 𝐻𝐻𝐻𝐻𝐻𝐻 𝑑𝑑𝑛𝑛 𝑤𝑤𝑛𝑛𝑑𝑑𝑜𝑜𝑑𝑑𝑑𝑑𝑜𝑜ℎ𝑛𝑛𝑤𝑤 ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑛𝑛𝑜𝑜,𝑡𝑡≈ 𝑁𝑁𝑤𝑤𝑛𝑛𝑑𝑑𝑜𝑜𝑑𝑑𝑑𝑑𝑜𝑜ℎ𝑛𝑛𝑤𝑤 ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑛𝑛𝑜𝑜,𝑡𝑡 ×𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎  𝑜𝑜𝑡𝑡𝑠𝑠 𝑛𝑛𝑜𝑜𝑜𝑜𝑤𝑤 𝐶𝐶/ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑛𝑛,𝑡𝑡𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 Equation 3-3  𝑃𝑃𝑡𝑡1𝑡𝑡2 = �Δ𝑃𝑃𝑡𝑡𝑡𝑡2𝑡𝑡=𝑡𝑡1 Equation 3-4 where 𝛥𝛥𝑃𝑃𝑡𝑡  𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑙𝑙𝑒𝑒𝜆𝜆 𝑑𝑑𝑎𝑎𝑟𝑟𝑏𝑏𝑎𝑎𝑙𝑙 𝑖𝑖𝜆𝜆𝑎𝑎𝑑𝑑𝑠𝑠 𝑑𝑑ℎ𝑎𝑎𝑙𝑙𝑎𝑎𝑒𝑒 𝑎𝑎𝑙𝑙 𝐻𝐻𝐻𝐻𝑃𝑃 𝑖𝑖𝑙𝑙 ℎ𝑎𝑎𝑎𝑎𝑖𝑖𝑒𝑒𝑖𝑖 𝑎𝑎𝑙𝑙 𝑑𝑑𝑒𝑒𝑎𝑎𝑟𝑟 𝜆𝜆   𝐶𝐶𝑆𝑆𝑡𝑡𝑠𝑠 𝐻𝐻𝐻𝐻𝐻𝐻 𝑑𝑑𝑛𝑛 𝑛𝑛𝑛𝑛𝑛𝑛 ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑛𝑛𝑜𝑜,𝑡𝑡 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑖𝑖𝜆𝜆𝑟𝑟𝑎𝑎𝑑𝑑𝜆𝜆𝑎𝑎𝑟𝑟𝑎𝑎𝑙𝑙 𝐻𝐻𝐻𝐻𝑃𝑃 𝑑𝑑𝑎𝑎𝑟𝑟𝑏𝑏𝑎𝑎𝑙𝑙 𝑖𝑖𝑙𝑙 𝑙𝑙𝑒𝑒𝑤𝑤 ℎ𝑎𝑎𝑎𝑎𝑖𝑖𝑒𝑒𝑖𝑖 𝑖𝑖𝑙𝑙 𝑑𝑑𝑒𝑒𝑎𝑎𝑟𝑟 𝜆𝜆  𝐶𝐶𝑆𝑆𝑡𝑡𝑠𝑠 𝐻𝐻𝐻𝐻𝐻𝐻 𝑑𝑑𝑛𝑛 𝑤𝑤𝑛𝑛𝑑𝑑𝑜𝑜𝑑𝑑𝑑𝑑𝑜𝑜ℎ𝑛𝑛𝑤𝑤 ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑛𝑛𝑜𝑜,𝑡𝑡 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑖𝑖𝜆𝜆𝑟𝑟𝑎𝑎𝑑𝑑𝜆𝜆𝑎𝑎𝑟𝑟𝑎𝑎𝑙𝑙 𝐻𝐻𝐻𝐻𝑃𝑃 𝑑𝑑𝑎𝑎𝑟𝑟𝑏𝑏𝑎𝑎𝑙𝑙 𝑖𝑖𝑙𝑙 𝑑𝑑𝑒𝑒𝑎𝑎𝑎𝑎𝑙𝑙𝑖𝑖𝑖𝑖ℎ𝑒𝑒𝑑𝑑 ℎ𝑎𝑎𝑎𝑎𝑖𝑖𝑒𝑒𝑖𝑖 𝑖𝑖𝑙𝑙 𝑑𝑑𝑒𝑒𝑎𝑎𝑟𝑟 𝜆𝜆  𝑁𝑁𝑛𝑛𝑛𝑛𝑛𝑛 ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑛𝑛𝑜𝑜,𝑡𝑡  𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑙𝑙𝑎𝑎𝑎𝑎𝑏𝑏𝑒𝑒𝑟𝑟 𝑎𝑎𝑙𝑙 𝑙𝑙𝑒𝑒𝑤𝑤 ℎ𝑎𝑎𝑎𝑎𝑖𝑖𝑒𝑒𝑖𝑖 𝑏𝑏𝑎𝑎𝑖𝑖𝑙𝑙𝜆𝜆 𝑖𝑖𝑙𝑙 𝑑𝑑𝑒𝑒𝑎𝑎𝑟𝑟 𝜆𝜆   𝑁𝑁𝑤𝑤𝑛𝑛𝑑𝑑𝑜𝑜𝑑𝑑𝑑𝑑𝑜𝑜ℎ𝑛𝑛𝑤𝑤 ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑛𝑛𝑜𝑜,𝑡𝑡  𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑙𝑙𝑎𝑎𝑎𝑎𝑏𝑏𝑒𝑒𝑟𝑟 𝑎𝑎𝑙𝑙 ℎ𝑎𝑎𝑎𝑎𝑖𝑖𝑒𝑒𝑖𝑖 𝑑𝑑𝑒𝑒𝑎𝑎𝑎𝑎𝑙𝑙𝑖𝑖𝑖𝑖ℎ𝑒𝑒𝑑𝑑 𝑖𝑖𝑙𝑙 𝑑𝑑𝑒𝑒𝑎𝑎𝑟𝑟 𝜆𝜆   𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑜𝑜𝑡𝑡𝑠𝑠 𝑛𝑛𝑜𝑜𝑜𝑜𝑤𝑤 𝐶𝐶/ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑛𝑛,𝑡𝑡𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜  𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑎𝑎𝑐𝑐𝑒𝑒𝑟𝑟𝑎𝑎𝑎𝑎𝑒𝑒 𝑎𝑎𝑎𝑎𝑖𝑖𝑖𝑖 𝑎𝑎𝑙𝑙 𝑖𝑖𝜆𝜆𝑟𝑟𝑎𝑎𝑑𝑑𝜆𝜆𝑎𝑎𝑟𝑟𝑎𝑎𝑙𝑙 𝑤𝑤𝑎𝑎𝑎𝑎𝑑𝑑 𝑑𝑑𝑎𝑎𝑟𝑟𝑏𝑏𝑎𝑎𝑙𝑙 𝑟𝑟𝑒𝑒𝑟𝑟 ℎ𝑎𝑎𝑎𝑎𝑖𝑖𝑒𝑒 𝑤𝑤ℎ𝑒𝑒𝑙𝑙 𝑎𝑎𝑟𝑟𝑖𝑖𝑎𝑎𝑖𝑖𝑙𝑙𝑎𝑎𝑙𝑙𝑙𝑙𝑑𝑑 𝑏𝑏𝑎𝑎𝑙𝑙𝜆𝜆  𝑃𝑃𝑡𝑡1𝑡𝑡2  𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑑𝑑𝑎𝑎𝑎𝑎𝑎𝑎𝑙𝑙𝑎𝑎𝜆𝜆𝑖𝑖𝑐𝑐𝑒𝑒 𝑑𝑑𝑎𝑎𝑟𝑟𝑏𝑏𝑎𝑎𝑙𝑙 𝑟𝑟𝑎𝑎𝑎𝑎𝑙𝑙 𝑖𝑖𝑖𝑖𝑠𝑠𝑒𝑒 𝑑𝑑ℎ𝑎𝑎𝑙𝑙𝑎𝑎𝑒𝑒 𝑎𝑎𝑙𝑙 𝐻𝐻𝐻𝐻𝑃𝑃 𝑖𝑖𝑙𝑙 ℎ𝑎𝑎𝑎𝑎𝑖𝑖𝑒𝑒𝑖𝑖 𝑏𝑏𝑎𝑎𝑖𝑖𝑙𝑙𝜆𝜆 𝑏𝑏𝑒𝑒𝜆𝜆𝑤𝑤𝑒𝑒𝑒𝑒𝑙𝑙  𝑑𝑑𝑒𝑒𝑎𝑎𝑟𝑟 𝜆𝜆1 𝑎𝑎𝑙𝑙𝑑𝑑 𝜆𝜆2 28  3.2.1 Raw Data The AHS has published housing unit remaining data of single-family and multi-family houses by the decade of construction. These data enable analyses of individual housing cohorts, with ages ranging from approximately 0 to about 100 years. The earliest publicly available survey was conducted in 1973. From 1973 to 1981, the surveys were conducted annually then changed to biennially due to budget constraints (USDOC, 2014). In 1985, the sample, questionnaire and weighting procedures were redesigned and caution is required when comparing data after 1985 (Survey series II) to those from 1973 to 1983 (Survey series I) (USDOC, 1988). In addition, the periods of construction used in each survey series vary, which requires some periods of construction to be aggregated so that the survey series can be compared (Table 3-1). Table 3-1 Comparison of the period of construction categories used in Survey 1973 to 1983 and Survey 1985 or later. Surveys 1973 to 1983 (series I) Survey 1985 or later (series II) Period of construction (year) Period of construction (year) 1939 or earlier 1919 or earlier 1920~1929 1930~1939 1940~1949 1940~1949 1950~1959 1950~1959 1960~1964 1960~1969 1965~March 1970 April 1970 or later 1970~1974 1975~1979 1980~1984  1985~1989  1990~1994  1995~1999  2000~2004  2005~2009  2010~2014 29   Data can be pooled together to harmonize the categories. For example, categories “1919 or earlier”, “1920~1929” and “1930~1939” in series II could be pooled together to represent the category “1930 or earlier” in series I. Once the categories were harmonized, data in series I and II could be compared and the plot of data is presented in Figure 3-2. There was general uniformity within each series. However, at the connection of series I and II indicated by the vertical black dash line in Figure 3-2, sudden changes were observed. As noted by the AHS, the data in series I and II may be incomparable and it is reasonable to assume that data collected in series II are more accurate than series I due to the improved survey methodology used by the AHS (Assumption 3-2).  Consequently, data prior to the Survey 1985 were not used in this analysis.  There was a type of data needed to be discarded due to incompleteness. For instance, Surveys 1991 and 1993 reports housing units remaining of houses built in period 1990~1994. However, since 1991 and 1993 are within the period 1990~1994, the housing data were incomplete and the number would keep increasing until the end of 1994. As a result, data of houses built in period 1990~1994 reported in Surveys 1991 and 1993 were discarded. The first valid data point of this period was the one reported by Survey 1995.  Figure 3-2 Comparison of housing units remaining data reported in “Surveys 1973~1983” and “Survey 1985 or later” 681012141618201970 1975 1980 1985 1990 1995 2000 2005 2010Housing units remaining (millions)Survey yearsHouses Built in 1940~1949Houses Built in 1950~1959Houses Built in 1960~196930  The raw AHS data were collected from survey questionnaires in sample cities, and then used to estimate the housing-related information for the whole country (USDOC 2002). Although this approach results in some data uncertainty, to our knowledge, this data set provides the oldest historical record and the most frequently collected data. The data demonstrate the general decay trends of US houses.  Because the numbers are estimates, unexpected variability and uncertainty exist within the data. For example, houses built in 1975~1979 display unit remaining numbers in Surveys 1987 to 2003 that are substantially lower than those reported in Survey 1985 and Surveys 2005 to 2013 (Figure 3-3). It is physically infeasible for housing numbers constructed in a given decade to increase in number once that decade has finished. Therefore, using the general assumption that data reported in later periods are more accurate than earlier periods due to improved AHS methodologies (Assumption 3-2), the numbers reported in Surveys 1987~2003 were discarded for houses constructed in 1975~1979.  Figure 3-3 Unexpected low values from Surveys 1987~2003 for houses built in 1975~1979 Houses built in 2005~2009 were also excluded from the analysis. Only two data points from Surveys 2011 and 2013 were available for this period, and based on the variability shown by the other data in this data set, high uncertainty would have resulted from using only these two data points to determine the decay pattern.  The full data set used in this analysis is presented in Appendix A.1.  1011121314151985 1990 1995 2000 2005 2010Housing unit remaining (millions)Survey yearsHouses built in 1975~1979data useddata discarded31  3.2.2 Determination of apparent half-lives As discussed in Chapter 2 (Section 2.2 and 2.5), several models have been proposed to model the decay pattern of HWP in houses. According to the IPCC, first order decay is recommended as the Tier 2 method (Equation 2-1). Equation 2-1 can be represented by a linear model by using log transformation (Equation 2-2). As a first approximation, linear regressions were used to fit the FOD curves to the log transformed US housing remaining data by period of construction and unbiased least squares estimates of λ were acquired using the statistical package SAS® 9.4 and Microsoft® Excel. By definition, the half-life is the time that a quantity takes to decay to half of its initial amount. The half-lives of houses built in different periods were calculated using Equation 2-3. These half-lives are referred to as “apparent half-lives” because they were estimated using regression analysis, assuming the decay follows FOD. 3.2.3 Age of houses At the time the analysis was conducted, the latest American Housing Survey available to the public was Survey 2013. The age intervals of houses were calculated by subtracting their periods of construction from 2013. For example, houses built between 1980 and 1984, which was one of the construction periods used in the surveys, were considered to be 29 (2013 minus 1984) to 33 (2013 minus 1980) years old. Using this approach, fifteen continuous age groups were then used to represent houses built in different periods of construction reported by the surveys. Each group covered a 5- or 10-year period, apart from the pre-1919 group (Table 3-2). 3.2.4 Aggregated first order decay curve (AggFOD) By assuming that the apparent half-life of houses in each age group represents the apparent half-life of all houses with the same age (Assumption 3-3), the estimated apparent half-lives were used to quantify the decay patterns of houses with different ages (Table 3-2). Since age groups 0~3 years and 4~8 years were either incomplete or discarded, the apparent half-life of houses aged 0~8 years was assumed to be the same as the apparent half-life of houses aged 9~13 years (Assumption 3-4). The apparent half-life of houses aged 94 years or older was assumed to apply to all houses in the US older than 94 years (Assumption 3-5). This assumption agreed with previous publications that the tail of the decay curve of long-lived HWP follows a first order decay curve with one half-life (Pingoud and Wagner, 2006; Marland, Stellar and Marland, 2010). These decay patterns were then aggregated to develop a cumulative decay curve for US single-family and multi-family houses by using the end point of the previous decay curve as the start point of the next. For example, if the decay of houses aged 0~13 years were assumed to have the same apparent half-life of 356 years, then from time 0~13 years, all houses built at time 0 would decay follow a FOD model with the half-life of 356 years. The remnant fraction of these houses would decrease from 1 to 0.975 during year 0 to year 13. If the decay of houses aged 14~18 years were assumed to have the same apparent half-life of 540 years, then from time 14~18 years, all the 32  houses remaining at year 13 would decay following a FOD model with the half-life of 540 years. The remnant fraction of these houses would decrease from 0.975 to 0.969 during year 14 to year 18. The decay of houses in the rest of the age groups was determined in the same fashion. The decay of all houses aged beyond 94 years was extrapolated based on Assumption 3-5.  Table 3-2 Age of US single- and multi-family houses represented by the periods of construction in American Housing Surveys Period of construction (year) Age groups (years old) 1919 or earlier 94 or older 1920~1929 84~93 1930~1939 74~83 1940~1949 64~73 1950~1959 54~63 1960~1969 44~53 1970~1974 39~43 1975~1979 34~38 1980~1984 29~33 1985~1989 24~28 1990~1994 19~23 1995~1999 14~18 2000~2004 9~13 2005~2009 4~8 2010~2013 0~3  This cumulative decay curve is referred to as the aggregated first order decay (AggFOD) curve and it specified the fraction of houses remaining at different ages.  3.2.5 Decay models fitted to the AggFOD curve As mentioned in Chapter 2, several models have been proposed to describe the decay pattern of HWP in use. The benefit of using a formulated model is that, if it is sufficiently robust, it may be generalized and applied to other systems, especially to systems that only have limited data 33  available. An effectively formulated decay model can therefore help understand the decay pattern, improve the accuracy of half-live estimation and HWP pool calculations, and facilitate scenario analysis. The decay pattern of HWP in houses, as an example of long-lived products, is age-related with younger houses being reported to decay more slowly than older houses (Pingoud and Wagner, 2006; Marland, Stellar and Marland, 2010). Logistic decay model (Row and Phelps, 1990), three-segment decay model (Row and Phelps, 1996) and Gamma distribution model (Marland, Stellar and Marland, 2010) were proposed based on this consideration. The AggFOD curve developed based on the US housing remaining data was expected to provide a realistic representation of the actual decay pattern of US houses. Hence, the logistic decay model (Equation 2-22), the three-segment decay model (Equation 2-23, Equation 2-24 and Equation 2-25) and the Gamma distribution model (Equation 2-26) were fitted to the AggFOD curve using the statistical package SAS® 9.4 and Microsoft® Excel 2013 and a comparative analysis among these three models was conducted. Due to the curved shape of the FOD model (Equation 2-1), it was apparent that statistically fitting the linear decay model (Equation 2-7) and the instant decay model (Equation 2-5) to the AggFOD curve would not provide meaningful results. The “equivalent” half-life of the AggFOD curve was therefore used to calculate and plot the FOD, linear decay and instant decay curves. These results were then compare with the fitted logistic decay, three-segment decay and Gamma distribution curves. 3.2.6 Assumptions Five key assumptions were made in the development of these models: Assumption 3-1: the carbon in HWP used for repairing and remodelling in single- and multi-family houses is approximately equal to the carbon in those HWP being replaced, which means the contribution of renovations to the HWP pool was ignored in this study. Assumption 3-2: data reported in later periods are more accurate than data from earlier periods due to improved methodology of the AHS Survey. Assumption 3-3: the apparent half-life of houses in each age group adequately represents the apparent half-life of all houses of the same age. Assumption 3-4: the apparent half-life of houses aged between 0~8 years was the same as the apparent half-life of houses aged between 9~13 years. Assumption 3-5: the apparent half-life of the oldest existing houses is adequately represented by the last age group in the AHS survey (94 years or older). 34  3.3 Results 3.3.1 Determination of half-lives using the first order decay model The number of houses remaining for each decade or five-year construction period Table 3-2 underwent a logarithmic transformation and the best-fit FOD model was determined using linear regression. The back-transformed regression lines over a 100 year period, the estimated λ values, the apparent half-lives and the r2 values for each curve are presented in Figure 3-4.    Figure 3-4 FOD curves fitted to the housing unit remaining data from AHS with estimated apparent half-lives and r2 values. The time periods associated with the letters “a” to “d” represent the period of construction of the housing cohort.  R² = 0.9664R² = 0.885505101520251900 1950 2000 2050 2100Housing unit remaining (millions)Survey yearsa. 1919 or earlier and 1920~1929Houses built 1919 or earlier?̂?𝜆 = 0.00799 𝑑𝑑𝑟𝑟𝑖𝑖−1?̂?𝜆1/2 = 86.7 𝑑𝑑𝑟𝑟𝑖𝑖1920~1929?̂?𝜆 = 0.00546?̂?𝜆1/2 = 127 𝑑𝑑𝑟𝑟𝑖𝑖R² = 0.8908R² = 0.9310246810121935 1985 2035 2085 2135Housing unit remaining (millions)Survey yearsb. 1930~1939 and 1940~19491940~1949?̂?𝜆 = 0.00499?̂?𝜆1/2 = 139 𝑑𝑑𝑟𝑟𝑖𝑖1930~1939?̂?𝜆 = 0.00803?̂?𝜆1/2 = 86.4 𝑑𝑑𝑟𝑟𝑖𝑖R² = 0.5726R² = 0.852051015201955 2005 2055 2105 2155Housing unit remaining (millions)Survey yearsc. 1950~1959 and 1960~19691960~1969?̂?𝜆 = 0.00342 𝑑𝑑𝑟𝑟𝑖𝑖−1?̂?𝜆1/2 = 203 𝑑𝑑𝑟𝑟𝑖𝑖1950~1959?̂?𝜆 = 0.00238 𝑑𝑑𝑟𝑟𝑖𝑖−1?̂?𝜆1/2 = 292 𝑑𝑑𝑟𝑟𝑖𝑖R² = 0.7309R² = 0.3773051015201972 2022 2072 2122 2172Housing unit remaining (millions)Survey yearsd. 1970~1974 and 1975~19791970~1974?̂?𝜆 = 0.00314 𝑑𝑑𝑟𝑟𝑖𝑖−1?̂?𝜆1/2 = 221 𝑑𝑑𝑟𝑟𝑖𝑖1975~1979?̂?𝜆 = 0.00160 𝑑𝑑𝑟𝑟𝑖𝑖−1?̂?𝜆1/2 = 433 𝑑𝑑𝑟𝑟𝑖𝑖35    Figure 3-4 cont.: FOD curves fitted to the housing unit remaining data from AHS with estimated apparent half-lives and r2 values. The time periods associated with the letters “e” to “d” represent the period of construction of the housing cohort. In general, the FOD model had an adequate fit to the raw data. Regression lines fitted to older housing cohorts had higher r2 values than those for younger houses, presumably because older housing cohorts had more data points and lower apparent half-lives. Lower apparent half-lives mean that the curves have a higher declining slope and thus a stronger correlation between the response variable (housing units remaining) and the explanatory variable (housing age). The apparent half-lives of houses at different age stages are plotted in Figure 3-5. Assumption 3-3, Assumption 3-4 and Assumption 3-5 have been applied to the development of this Figure. While the apparent half-lives vary by age, younger houses generally had higher apparent half-lives than older houses and the variability decreased as age of the houses increased. These points are discussed in greater detail in Section 3.4. R² = 0.8018R² = 0.38760246810121982 2032 2082 2132 2182Housing unit remaining (millions)Survey yearse. 1980~1984 and 1985~19891980~1984?̂?𝜆 = 0.00452 𝑑𝑑𝑟𝑟𝑖𝑖−1?̂?𝜆1/2 = 153 𝑑𝑑𝑟𝑟𝑖𝑖1985~1989?̂?𝜆 = 0.00102 𝑑𝑑𝑟𝑟𝑖𝑖−1?̂?𝜆1/2 = 680 𝑑𝑑𝑟𝑟𝑖𝑖R² = 0.5929R² = 0.21810246810121992 2042 2092 2142 2192Housing unit remaining (millions)Survey yearsf. 1990~1994 and 1995~19991990~1994?̂?𝜆 = 0.00300 𝑑𝑑𝑟𝑟𝑖𝑖−1?̂?𝜆1/2 = 231 𝑑𝑑𝑟𝑟𝑖𝑖1995~1999?̂?𝜆 = 0.00128 𝑑𝑑𝑟𝑟𝑖𝑖−1?̂?𝜆1/2 = 541 𝑑𝑑𝑟𝑟𝑖𝑖R² = 0.28070246810122002 2052 2102 2152 2202Housing unit remaining (millions)Survey yearsg. 2000~20042000~2004?̂?𝜆 = 0.00195 𝑑𝑑𝑟𝑟𝑖𝑖−1?̂?𝜆1/2 = 356 𝑑𝑑𝑟𝑟𝑖𝑖36   Figure 3-5 Estimated apparent half-lives of houses at different age stages 3.3.2 Aggregated first order decay curve (AggFOD) The data in Figure 3-5 were used to plot the AggFOD (Figure 3-6). The inverse sigmoidal shape of this curve indicated that the decay rate was initially relatively slow, increased to a maximum at a point and, beyond this point, decreased with increasing housing age. The curve revealed that the US houses had a half-life of 137 years, and that 95% of the houses would have decayed in 425 years. The Gamma distribution model, the logistic decay model and the three-segment decay model were fitted to the AggFOD curve (Figure 3-7a). When the time scale was set at 300 years, the Gamma distribution curve had the smallest sum of squared errors (SSE) of 0.0363. The comparison of the SSEs of these three decay models are presented in Table 3-3. Figure 3-7b shows the comparisons among the FOD model, the linear decay model and the instant decay model, each with an equivalent half-life of 137 years of the AggFOD curve. Table 3-3 Comparison of the sum of squared errors of decay models when fitted to the AggFOD curve  Parameters SSE Gamma distribution model α=2.07, β=80.2; equivalent t1/2 = 140 years, t95% = 390 years 0.0363 Logistic decay model t1/2 = 149 years 0.154 Three-segment decay model t1/2 = 138 years 0.265 01002003004005006007008000 20 40 60 80 100Apparent half-life (years)Age of houses (years)1919 or earlier1920-19291930-19391940-19491950-19591960-19691970-19741975-19791980-19841985-19892000-20041990-19941995-199937    Figure 3-6 Aggregated first order decay (AggFOD) curve  Figure 3-7 Decay models fitted to the AggFOD curve of the US single- and multi-family houses 00.10.20.30.40.50.60.70.80.910 50 100 150 200 250 300Remnant fractionTime after construction (years)13700.10.20.30.40.50.60.70.80.910 100 200 300Remnant fractionTime after construction (years)a. Decay models fit to AggFODAggFODGammaLogistic3-segment00.10.20.30.40.50.60.70.80.910 100 200 300Remnant fractionTime after construction (years)b. Models with an equivalent half-lifeAggFODFODLinearInstant38  If a constant mass input scenario of 1 Tg C/year was assumed, similar to the assumption used in Figure 2-2, which means the y-axis in Figure 3-7 would be the carbon amount remaining, the areas under the curves would actually indicate the carbon stock size over 300 years. At the 300 year-time scale under the constant input scenario, model 1~5 had similar values (153.4~154.9 Tg) while the results of linear and instant decay model were lower (Table 3-4). Except the linear and instant decay models, the other models all achieved similar stock size to the AggFOD curve. The linear and instant decay model had the worst fit to the AggFOD as Figure 3-7b shows. However, this only shows the stock size under the constant mass input scenario of 1 Tg C/year over 300 years. The magnitude may be more different if actual stock numbers were added. More discussion on this will be presented in Chapter 5 when the pool size of HWP in US houses is quantified. Table 3-4 Comparison of the areas under the curves of decay models under the constant mass input scenario of 1 Tg C/ year over the 300 years  Area under the curve, 0~300 years, assuming 1 Tg C/year constant input (Tg) AggFOD curve 154.7 Gamma distribution model 154.7 Logistic decay model 153.4 Three-segment decay model 154.6 FOD model 154.9 Linear decay model 137.0 Instant decay model 137.0  3.4 Discussion This thesis used FOD as the initial methodology for modelling the decay of US single- and multi-family houses for the following reasons: • the FOD model is the Tier 2 methodology recommended by the IPCC (IPCC, 2014).  • the FOD model is one of the simplest and most widely applied decay models • The non-linear FOD model can be represented by a linear model when the data are subject to a log transformation so that a linear regression analysis is possible. • Previous publications have indicated that the tail of the housing decay pattern follows FOD (Pingoud and Wagner, 2006; Marland, Stellar and Marland, 2010). A linear decay model was also fitted to the raw data and then aggregated to develop a cumulative decay curve similar to the AggFOD. The FOD model had a slightly better fit to the raw data than 39  the linear decay model (only 0.007 higher in total r2 values) because the FOD model fits the decay pattern of older houses better than the linear decay model, which validates the observations made by previous literature. However, rather than using the apparent half-lives to represent the decay rate of houses in each age group, is preferable to use the apparent decay rate (Equation 2-7) because the linear decay model requires that estimates of both the number of housing starts (𝑁𝑁�0) and the decay rate (𝑏𝑏�) are used in order to determine the half-life (Equation 2-8). This approach involves defining “age zero” (i.e. the year that a house was built) so that the age of the houses for a given period of construction can be determined. The mid-point of the period can be used to estimate the age but uncertainty and inaccuracy exist because the housing starts in the first half of the period are unlikely to be the same as the housing starts in the second half. Taking houses built in 1950~1959 for example, the mid-point of 1950~1959 is January 1, 1955. Hence, for houses built in the 1950s, Survey 1985 reported the number of housing units remaining for houses that were 30 years old (i.e. 1985 - 1955 = 30), Survey 1987 reported units remaining for 32 year-old houses and so on until the latest Survey 2013. Using linear regression, the estimated decay rate 𝑏𝑏� was 32.5 units/year and the estimated number of housing starts 𝑁𝑁�0 was 15057 units. The half-life can then be calculated using Equation 2-8 to be 232 years. In contrast, the FOD model only requires an estimate of λ to calculate half-lives (Equation 2-3) and the age group concept is more accurate than the mid-point approach outlined above. For example, houses built between 1950 and 1959 have an age range of 54 (i.e. 2013 – 1959 = 54) to 63 (i.e. 2013 – 1959 = 63) years old and they have a half-life of 292 years. This half-life is attributed to all houses aged 54-63 years old. Since the Gamma distribution model has the lowest SSE as presented in Table 3-3, it was also tried to be fit to the raw data. However, when fitting a non-linear model that cannot be transformed into a linear model, a large number of data is required. There was only a maximum of 15 data points of the number of housing units remaining for each age group and the statistical package SAS® 9.4 or Microsoft® Excel 2013 cannot find a solution within suitable time. In addition, unlike the other decay models that only have one parameter to be estimated, the Gamma distribution model has two parameters, which added complexity to the regression analysis. The regression analysis using the FOD model revealed that US houses constructed in various periods have different apparent half-lives (Figure 2-5). Houses built prior to 1950 exhibited an average apparent half-life of about 100 years whereas those built between 1950 and 1974 had an apparent half-life range of 203-291 years. Houses constructed after 1975 exhibited a highly uncertain apparent half-life in the range of 153-680 years. The half-life estimates of younger houses exhibited higher uncertainties than those of older houses because there were fewer data available. The r2 values of the regressions for the houses built before 1974 were also higher than those constructed after 1975 (Figure 3-4). These factors reflect both the variability within the data and the fact that older houses have more extensive data sets. The major implication of this high variance is that the FOD model does not describe the early phase of the housing decay process as 40  well as it describes the later phase. As mentioned by several earlier publications, the “tail” of the true housing decay pattern may be accurately described the FOD model, while the “head” may not (Row and Phelps, 1990; Marland and Marland, 2003; Pingoud and Wagner, 2006). This study acknowledged this and introduced a concept of apparent half-lives that allowed the FOD model results to be used sequentially to construct the AggFOD curve and, in this way, to try minimise the influence of a relatively poor description of the early decay phase. Whether the half-lives shown in Figure 3-5 are statistically different to each other requires that a statistical analysis is undertaken. Since the American Housing Survey (AHS) collected and reported housing units remaining data biennially, these data are likely to involve autocorrelation. First- to tenth-order autocorrelations were investigated but they were unable to describe the time series pattern observed in this study. For this reason, confidence intervals about each half-life value could not be developed and other statistical inferences regarding the statistical significance of the data could not be conducted. That being said, the least sum of squared estimates of half-lives for the logarithm transformed FOD models are still unbiased because the assumption of linearity was met, as confirmed by visually checking the residual plots in the statistical package SAS® 9.4. The results presented in Figure 3-5 support the conclusion that older houses generally exhibited shorter half-lives and younger houses had longer half-lives, which is in agreement with the statement by Winistorfer et al.’s (2005) observation that the US houses built before 1950s lacked many of the functions possessed by those built after that date. Winistorfer et al. (2005) and Skog (2008) both used dynamic half-lives for houses built in different periods when estimating the HWP pool size. Although the half-life values were not calculated, the decay curves presented in Kurz et al. (1992), Karjalainen, Kellomoki and Pussinen (1994), Row and Phelps (1996), Eggers (2002), Miner (2006) and Marland, Stellar and Marland (2010) also suggest that younger houses have longer half-lives than older houses. This methodology was inspired by Miner’s (2006) country-specific model. Miner’s model is described in Chapter 2. The differences in the approach used in this thesis and Miner’s model are presented below. • Data sources. Both approaches use data from the American Housing Survey (AHS). Miner’s (2006) model used data from Survey 1985 to 2003, whereas the model in this paper used data from Surveys 1985 to 2013 (i.e. 5 more Surveys). • Assumptions. Miner’s (2006) model assumed that the fractional removal of houses in the latest age group (i.e. 1990~2003) changed linearly every year from 0 to the average fractional removal of the age group 1970~1989. In contrast, the models evaluated in this thesis assumed that the apparent half-life for houses aged 0~8 years was the same as the decay pattern for houses aged 9~13 years (Assumption 3-4). The detailed assumptions used for Miner’s (2006) model have been presented in Chapter 2 Section 2.5.7. 41  • Accuracy of the analysis.  o Miner’s (2006) model used housing unit remaining data in adjacent Surveys to calculate the fractional removal. For example, the fractional removal of houses built between 1950 and 1969 from the 1985 and 1987 AHS surveys was calculated using the housing unit remaining data in Survey 1985 minus the one in Survey 1987 and this difference was then divided by the number of houses remaining in Survey 1985. The calculated fraction removals were averaged to represent the fraction removal of houses in that age group. The fraction removal of all age groups was calculated and aggregated to develop the cumulative decay curve. In contrast, the model used in this thesis applied linear regression to estimate the apparent half-lives and these unbiased estimates of apparent half-lives were then used to develop the cumulative decay curve.  o Miner (2006) divided the houses into five age groups, whereas the approach used in this thesis used 13 age groups (age groups 0~3 and 4~8 were pooled together with 9~13 according to Assumption 3-4). Consequently, when aggregating the decay rates of the different age groups to develop the cumulative decay curve, our age increments were smaller than Miner’s. A comparison between Miner’s (2006) model and the AggFOD curve is presented in Figure 3-8.   Figure 3-8 Comparison between Miner's (2006) model and the AggFOD curve. 00.10.20.30.40.50.60.70.80.910 50 100 150 200 250 300Remnant fractionTime after construction (years)AggFODMiner's (2006) model14813742  Miner (2006) did not calculate the equivalent half-life of his model. As shown in Figure 2-6, he only extended his analysis to 93 years at which point 71% of the original houses were forecast to remain in the housing stock. Using Assumption 3-5, the decay curve calculated using Miner’s (2006) model was extrapolated to 300 years based on the fractional removal rate of the oldest age group. The resultant decay curve is represented by the red dashed curve in Figure 3-8. Using this approach, Miner’s (2006) model estimated an equivalent half-life of 148 years, which is 11 years longer than the equivalent half-life of the AggFOD curve. The Gamma distribution curve, logistic decay curve and three-segment decay curve have a better fit to the AggFOD than the FOD curve, linear decay curve and instant decay curve (Figure 3-7). Among the three most sophisticated models, the Gamma distribution model had the lowest sum of squared errors (SSE) of 0.0363, which is 0.118 smaller than the SSE of the logistic decay model and 0.228 smaller than the SSE of the three-segment decay model. The Gamma distribution has a shape parameter, α, and a scale parameter, β, whereas the logistic decay model or the three-segment decay model only have one parameter, which is the half-life. The Gamma distribution model should therefore be more adaptable and have a wider applicability than the other two. Another benefit of the Gamma distribution model is that when the shape parameter α equals 1, the Gamma distribution is simplified to be FOD. Under these conditions, the scale parameter β equals the half-life of the FOD divided by ln2. This flexibility, combined with its good fit to the data, makes the Gamma distribution the most suitable model to describe the decay pattern of the US single- and multi-family houses. As mentioned in Chapter 2, several previous publications have estimated the half-lives of US single-family and multi-family houses (Table 2-3). Winistorfer et al. (2005) chose a conservative half-life estimate of 75 years despite presenting evidence that a more realistic value was probably in excess of 85 years. In a similar manner to this study, Skog (2008) noted that older houses had shorter apparent half-lives than older houses and he used a half-life range of 78-85.9 years (Table 2-3).  Although Miner (2006) did not determine a specific half-life, by applying the assumptions and methodology used in this thesis to his data, an equivalent half-live of 148 years was estimated (Figure 2-8). Miner’s (2006) results indicate that the half-life of US single-family and multi-family houses are probably higher than estimated by Winistorfer et al. (2005) and Skog (2008). The results obtained in this thesis also showed that older houses had shorter half-lives than newer houses and that a half-life of 137 years was determined from the AggFOD curve. These results also show that Row and Phelps’s (1996) half-live value for single family homes of 200 years is too high. All of these values are substantially longer than the IPCC default values of 35 years for sawnwood and 25 years for wood-based panels (IPCC, 2014). The IPCC default product half-lives may therefore be interpreted as being highly conservative, which provides an incentive for nations with large HWP in use pools to apply Tier 3 methodology. 43  3.5 Conclusions A single first order decay model cannot adequately describe the decay pattern of US single- and multi-family houses because younger houses decay slower than older houses. The IPCC default methodology, which recommends the use of a first order decay model, is unlikely to be able to adequately describe the decay pattern of this housing stock. However, the first order decay model can be used to estimate the apparent half-lives of houses constructed over a series of relatively short time periods and these apparent half-lives vary with the age of the houses. Older houses have shorter apparent half-lives than newer houses.  These apparent half-lives can then be used to develop an aggregated first order decay (AggFOD) curve which is considered to adequately represent to the actual decay pattern of US single- and multi-family houses.  The Gamma distribution model with α equal to 2.07 and β equal to 80.2 (i.e. an equivalent half-life of 140 years and the 95% decay point of 390 years) achieved the lowest sum of squared errors of 0.063 when fitted to the AggFOD curve over a time period of 300 years. The Gamma distribution model is therefore recommended for estimating the decay pattern of US single- and multi-family houses. This model estimated an equivalent end-use half-life of 137 years for houses, which is longer than most of the previously published half-lives for US family homes and substantially greater than the IPCC default product half-life values for sawnwood and wood-based panels. This longer half-life is likely to impact on the accuracy of previous estimates of the US HWP in use pool. Such long half-lives will also incentivize nations with large HWP in use pools to apply Tier 3 methodology for the estimation of their carbon dynamics.   44  Chapter 4 Application of the decay estimation methodology to US mobile homes and Canadian and Norwegian residential houses 4.1 Introduction As mentioned in Chapter 3, this study focuses on improving the modelling of structural HWP in North American’s residential houses because they make the dominant contribution to the wood products carbon pools in use in that region. In Chapter 3, US single-family and multi-family houses were chosen to develop the “regression-aggregation-fit” methodology because, to our knowledge, the US provides the largest and most readily accessed publicly available historical data for single-family and multi-family houses. In this Chapter, the “regression-aggregation-fit” methodology is used on publicly available data for US mobile homes (MH) and Canadian residential houses to demonstrate the applicability of this methodology to the other North American residential houses. To further test the applicability of the methodology, one European or Asian country with a tradition of building wooden houses and with robust and readily accessible data in English was sought using these criteria. Norway was included in this study to further examine the international applicability of the “regression-aggregation-fit” methodology. 4.2 Methods The methodology used to estimate the housing decay kinetics in Chapter 3 (see Section 3.2) was applied to data sets for US mobile homes, Canadian residential houses and Norwegian residential houses. Each data set had its unique format and was treated slightly differently. The details on how the data were utilized are presented in Sections 4.2.1 to 4.2.3. 4.2.1 US mobile homes The American Housing Survey has published data on the units remaining by period of construction for mobile homes since Survey 1985. The period of construction categories used were identical to those for single-family and multi-family houses presented in Table 3-1. No mobile homes were reported prior to 1930 and substantial numbers were not constructed annually until the 1950s (Appendix A.2). The mobile home numbers for the “1930~1939” and “1940~1949” categories increased from Surveys 1985 to 2013. It is physically infeasible for housing numbers constructed in a given period to increase once that period has finished. The increasing number reported for these age categories is probably due to incomplete data, as explained by the AHS (e.g. USDOC 2002). Consequently, the data reported for mobile houses constructed in “1930~1939” and “1940~1949” were excluded from this analysis. Mobile home numbers from surveys that reported incomplete data for a period of construction were also discarded. For instance, Surveys 1991 and 1993 reported the units remaining of mobile 45  homes built in the period 1990~1994. However, since 1991 and 1993 are within the period 1990~1994, the data were incomplete and the number would keep increasing until the end of 1994. As a result, data were included starting from Survey 1995.  After the incomplete data were discarded, only Surveys 2011 and 2013 reported data for mobile homes built in “2005~2009” and only Survey 2013 reported data for “2010~2014”. These data were also discarded due to insufficient data points for a regression analysis. The full data set of US mobile homes used in this analysis is presented in Appendix A.2. The age range of the mobile homes for each period of construction was the same as the age ranges allocated to single-family and multi-family houses used in Chapter 3 (Table 3-2). 4.2.2 Canadian residential houses 4.2.2.1 Data sources Until 2011, Statistics Canada conducted a census every five years that reported the number of residential housing units by period of construction. After this time, the National Household Survey (NHS), a voluntary survey, replaced the census long form and reported the housing data (Statistics Canada, 2013).  In this survey, residential houses include single-family and multi-family houses and mobile homes. For convenience, the housing units by period of construction are referred to as the Survey data and the corresponding year is referred to as the Survey year. Housing data included in Survey 2011 were obtained from Statistics Canada-NHS (Statistics Canada, 2013). Data in Surveys 1996 to 2006 were available from Statistics Canada-Census (Statistics Canada, 1998; 2002; 2007). Data in Survey 1991 were acquired from BC Stats-1991 Census of Canada (BC Stats, 1991). Links to archived Census profiles before 1991 were not provided by Statistics Canada nor provincial statistical websites.  The Computing in the Humanities and Social Sciences (CHASS) Data Centre of the University of Toronto has archived Census profiles from 1961 to 2011, NHS 2011 and Public Use Microdata Files (PUMF) from 1971 to 2006 (CHASS, 2013; 2014). However, CHASS-Census from 1961 to 1996 did not have aggregated national level data and PUMF 2006 did not have housing data.  Therefore, relevant housing data available from CHASS were obtained from Census 2001 to 2006, NHS 2011 and PUMF 1971 to 2001. No national housing data prior to 1971 could be obtained from publicly available sources. Table 4-1 summarizes the sources for the housing units by periods of construction data used in this study. Irrespective of the source, the housing data reported by the Census and NHS used the same numbers whereas the numbers reported by PUMF differed slightly from the Census values. The data source that had more divisions in the period of construction category was selected, because 46  more divisions provided smaller increments in the cumulative decay curve (Section 3.4). For example, CHASS-NHS 2011 pooled all houses built before 1945 into a “1945 or earlier” category whereas Statistics Canada-NHS separated them into categories for houses built in “1920 or earlier” and between “1921~1945”. Therefore, Statistics Canada-NHS data were used for this analysis.  Data for Survey 1991 to 2001 were both available from Census and PUMF (Table 4-1). The numbers reported by PUMF were slightly different from those reported by the Census but the differences were less than 0.75%. Therefore, data from PUMF were considered to be consistent with the Census. However, when both Census and PUMF data were available for a given construction period, Census data were used because Census data were from a national or provincial government’s official website. Since data for Survey years 1971, 1981 and 1986 were only available from PUMF (Table 4-1), they were used in the analysis. The bold font in Table 4-1 indicates the sources of data for each Survey year that were actually used in the analysis. Table 4-1 Sources and profiles of available housing units data by periods of construction (bold font indicates the sources of data that were actually used in the analysis) Sources Statistics Canada BC Stats CHASS Reports NHS Census Census NHS Census PUMF Survey years of available data      1971      1981      1986   1991   1991  1996    1996  2001   2001 2001  2006   2006  2011   2011    4.2.2.2 Determination of period of construction Unfortunately, the data analysis was complicated by the variation in the division of the periods of construction categories used by the various Surveys. This complexity required that periods of construction be either split or aggregated in order to compare the numbers of housing units in each survey (Table 4-2).  The oldest period of construction category of Surveys 1991 and 1996 was “1945 or earlier” whereas in the others, this period was reported as two categories, namely “1920 or earlier” and “1921~1945”. Fortunately, these two surveys were also available from PUMF and this source reported the data in the following two categories: “1920 or earlier” and “1927~1945”. Because numbers reported in PUMF were slightly different from Census, to keep the data source as consistent as possible, PUMF data were only used to split the “1945 or earlier” into “1920 or earlier” and “1921~1945” (Equation 4-1). 47  Table 4-2 Comparison of the division of periods of construction categories of each Canadian Survey. 1971 (PUMF) 1981 (PUMF) 1986 (PUMF) 1991 (Census) 1996 (Census) 2001 (Census) 2006 (Census) 2011 (NHS) 1920 or earlier 1920 or earlier 1920 or earlier 1945 or earlier 1945 or earlier 1920 or earlier 1920 or earlier 1920 or earlier 1921~1945 1921~1945 1921~1945 1921~1945 1921~1945 1921~1945 1946~1950 1946~1960 1946~1960 1946~1960 1946~1960 1946~1960 1946~1960 1946~1960 1951~1960 1961~1965 1961~1970 1961~1970 1961~1970 1961~1970 1961~1970 1961~1970 1961~1970 1966~1968 1969 1970 1971 1971~1975 1971~1975 1971~1980 1971~1980 1971~1980 1971~1980 1971~1980   1976~1979 1976~1980 1980~1981 1981~1986 1981~1991 1981~1990 1981~1985 1981~1985 1981~1990     1986~1990 1986~1990 1991~1996 1991~1995 1991~1995 1991~1995   1996~2001 1996~2000 1996~2000   2001~2006 2001~2005   2006~2011   key: dash lines indicate that the sizes of the cells are not adjusted to the relative lengths of the periods. 48  𝑁𝑁1920 𝑜𝑜𝑠𝑠 𝑛𝑛𝑎𝑎𝑠𝑠𝑑𝑑𝑑𝑑𝑛𝑛𝑠𝑠 = 𝑁𝑁𝐶𝐶𝑛𝑛𝑛𝑛𝑜𝑜𝑜𝑜𝑜𝑜,1945 𝑜𝑜𝑠𝑠 𝑛𝑛𝑎𝑎𝑠𝑠𝑑𝑑𝑑𝑑𝑛𝑛𝑠𝑠 ×𝑁𝑁𝐻𝐻𝑃𝑃𝑃𝑃𝑃𝑃,1920 𝑜𝑜𝑠𝑠 𝑛𝑛𝑎𝑎𝑠𝑠𝑑𝑑𝑑𝑑𝑛𝑛𝑠𝑠𝑁𝑁𝐻𝐻𝑃𝑃𝑃𝑃𝑃𝑃,1920 𝑜𝑜𝑠𝑠 𝑛𝑛𝑎𝑎𝑠𝑠𝑑𝑑𝑑𝑑𝑛𝑛𝑠𝑠 + 𝑁𝑁𝐻𝐻𝑃𝑃𝑃𝑃𝑃𝑃,1921~1945 Equation 4-1 where 𝑁𝑁 𝑖𝑖𝑖𝑖 ℎ𝑎𝑎𝑎𝑎𝑖𝑖𝑖𝑖𝑙𝑙𝑎𝑎 𝑎𝑎𝑙𝑙𝑖𝑖𝜆𝜆𝑖𝑖 𝑟𝑟𝑒𝑒𝑎𝑎𝑎𝑎𝑖𝑖𝑙𝑙𝑖𝑖𝑙𝑙𝑎𝑎,  𝜆𝜆ℎ𝑒𝑒 𝑖𝑖𝑎𝑎𝑏𝑏𝑖𝑖𝑑𝑑𝑟𝑟𝑖𝑖𝑟𝑟𝜆𝜆𝑖𝑖 𝑖𝑖𝑙𝑙𝑑𝑑𝑖𝑖𝑑𝑑𝑎𝑎𝜆𝜆𝑒𝑒 𝜆𝜆ℎ𝑒𝑒 𝑖𝑖𝑎𝑎𝑎𝑎𝑟𝑟𝑑𝑑𝑒𝑒 𝑎𝑎𝑙𝑙𝑑𝑑 𝑟𝑟𝑒𝑒𝑟𝑟𝑖𝑖𝑎𝑎𝑑𝑑 𝑎𝑎𝑙𝑙 𝑑𝑑𝑎𝑎𝑙𝑙𝑖𝑖𝜆𝜆𝑟𝑟𝑎𝑎𝑑𝑑𝜆𝜆𝑖𝑖𝑎𝑎𝑙𝑙   Surveys 2001 and 2006 reported data for “1981~1985” and “1986~1990”. Since all other Surveys reported data for “1981~1990”, the two periods used for the 1980’s data in Survey 2001 and 2006 were added together to create an equivalent “1981~1990” category. Most categories ended with the final year or the middle year of a decade. For example, the second category of Survey 2011 ended with 1945 and the third category finished with 1960. However, the last categories did not follow this rule. Most of the more recent categories included the year when the Survey was conducted. For example, “1981~1985” and “1986” should be two separate categories, but in Survey 1986, they were reported as “1981~1986”. These categories cannot be split or aggregated and therefore they added a complication to the process of unifying periods of construction across all surveys. Consequently, the housing data in periods that did not end in the middle or end of a decade were all discarded. As Table 4-2 shows, only Surveys 2006 and 2011 had periods “1996~2000” and “2001~2005”, and only Survey 2011 had the period “2006~2011”. Data in these period categories were also discarded due to insufficient data points for regression analysis. 4.2.2.3 Analytical Scenarios Variations existed in the Canadian data set in a similar manner to those noted in Chapter 3 for the US housing data. The Canadian data were analyzed under four scenarios. Scenario 1: a plot of the data set indicated that housing units reported in Survey 1971 were substantially lower than the numbers in Surveys 1981 and 1986 (Figure 4-1). According to Assumption 4-1 and principle of conservatism, data in Survey 1971 were discarded. In this case, conservatism means that if discarding some questionable data would result a faster decay, in order not to underestimate the emission (i.e. overestimate the pool size), then that discard is justified.  Scenario 2: The housing data for 1981 and 1986 could be interpreted as being anomalously high (Figure 4-1). In this scenario, the data in Surveys 1981 and 1986 were discarded. Under this scenario, the number of houses built in 1961~1970 reported in Survey 1971, also needed to be discarded because that number was too low and would cause a positive trend line in the housing decay rate. Scenario 3: a third analytical alternative was to discard all data sourced from PUMF and only use data in Surveys 1991~2011. Under this scenario, the number reported in Survey 1991 for houses built 49  in 1946~1960 was anomalously low so it was discarded. The housing numbers were nearly unchanged from survey to survey (Figure 4-1) which would result in high apparent half-lives. Scenario 4: this final scenario used all data presented in Figure 4-1. As discussed, some data for the US and Norway (Section 4.2.3) were discarded because they presented positive trends in the decay pattern or there were insufficient data available for the regression analysis. A positive data trend is an error because it is physically impossible for the housing number constructed in a given period to increase once the period has ended. In contrast, the Canadian data could actually be used in the regression analyses without further discarding, which is the case of Scenario 4.  However, because the number of Canadian data points was limited, the regression estimation for the apparent half-life was very sensitive to each number reported. Because the impact of each number could not be ignored, the accuracy of every data point was an important factor. This was the reason why a scenario analysis was conducted only on Canadian data but not on the other data sets. The results of these four scenarios are compared and discussed in Sections 4.3.2 and 4.4. The full Canadian housing data set used in this analysis is presented in Appendix A.3.  Figure 4-1 Canadian housing units remaining by period of construction 4.2.2.4 Age of houses The housing age for each period of construction was calculated using the same approach as for US houses in Section 3.2.3. The latest survey available was Survey 2011. Therefore, houses built in the period 1981~1990 had an age range from 21 (2011 minus 1990) to 30 (2011 minus 1981) years old. 00.511.522.533.541970 1980 1990 2000 2010Housing units remaining (millions)Survey years1920 or earlier1921-19451946-19601961-19701971-19801981-19901991-199550  Ten continuous age groups were than used to represent houses built in different periods (Table 4-3 and Assumption 4-2). Table 4-3 Age of Canadian residential houses represented by the periods of construction Period of construction (year) Age groups (years old) 1920 or earlier 91 or older 1921~1945 66~90 1946~1960 51~65 1961~1970 41~50 1971~1980 31~40 1981~1990 21~30 1991~1995 16~20 1996~2000 11~15 2001~2005 6~10 2006~2011 0~5  4.2.3 Norwegian residential houses Statistics Norway has reported residential housing numbers in 1980, 1990, 2001 and 2011 by period of construction (Statistics Norway, 2005, 2013). In order to use consistent terminology, these years will be referred to as Survey years.  The periods of construction categories varied from one Survey year to another, which required periods of construction to be either split or aggregated in order to compare the numbers of housing units in each survey (Table 4-4). No data were available to split the categories “1920 or earlier” and “1921~1945” in Survey 2011 so that they would align with the categories in the earlier surveys. Therefore, data for the “1900 or earlier” and “1901~1920” categories in Surveys 1980, 1990 and 2001 were pooled together and termed “1920 or earlier”. Data for “1921~1940” and “1941~1945” were aggregated in the same fashion and named “1921~1945”. As shown in Table 4-4, only Surveys 2001 and 2011 had periods “1991~2001” and only Survey 2011 had the period “2002~2012”. Data in these categories were discarded due to insufficient data points for regression analysis. 51  As observed with the US and Canadian housing data (Chapter 3 and Section 4.2.2 respectively), variations and data uncertainty exist in the Norwegian data set. A plot of the data set indicated that housing units reported for the periods “1971~1980” and “1980~1990” increased with time (Figure 4-2). This is realistically impossible and the data for houses built in these two periods of construction were discarded. Table 4-4 Comparison of the division of periods of construction categories of each Norwegian Survey. Surveys 1980, 1990, 2001 Survey 2001 Survey 2011 1900 or earlier 1900 or earlier 1920 or earlier 1901~1920 1901~1920 1921~1940 1921~1940 1921~1945 1941~1945 1941~1945 1946~1960 1946~1960 1946~1960 1961~1970 1961~1970 1961~1970 1971~1980 1971~1980 1971~1980 1981~1990 1981~1990 1981~1990  1991~2001 1991~2001  2002~2012  The remnant number of houses built in 1961~1970 reported in Survey 1980 were unexpectedly lower than the numbers reported in the other three surveys, causing a positive trend line for these data (Figure 4-2). The remnant number of houses built in 1920 or earlier reported in Survey 2011 was unexpectedly higher, leading to an abnormally slow decay trend (blue line with diamond markers in Figure 4-2). These two data points were discarded to ensure realistic and conservative estimations of the decay patterns. The full Norwegian housing data set used in this analysis is presented in Appendix A.4. The housing age of each period of construction represented was calculated the same way as for the US houses in Section 3.2.3. The latest survey available was Survey 2011 and the age categories used are presented in Table 4-5. 52   Figure 4-2 Norwegian housing units remaining by period of construction  Table 4-5 Age of Norwegian residential houses represented by the periods of construction Period of construction (year) Age group (years old) 1920 or earlier 91 or older 1921~1945 66~90 1946~1960 51~65 1961~1970 41~50 1971~1980 31~40 1981~1990 21~30 1991~2001 10~20 2002~2012 0~9  4.2.4 Apparent half-life estimations, aggregated first order decay (AggFOD) curve and decay models fitted to the AggFOD curve As described in Chapter 3 (Section 3.2.2), the FOD model was used to provide a first approximation of the decay pattern. The FOD was converted to a linear model using log transformation (Equation 1351852352853353851980 1990 2000 2010Housing units remaining (thousands)Survey years1920 or earlier1921~19451946~19601961~19701971~19801981~1990discarded data53  2-2). Linear regressions were conducted using the housing units remaining data by period of construction for the US mobile homes and Canadian and Norwegian residential houses and unbiased least squares estimates of λ were acquired using the statistical packages SAS® 9.4 and Microsoft® Excel 2013. The Apparent half-lives of houses built in different periods were calculated using the estimated λ values (Equation 2-3). The definition of apparent half-lives is presented in Section 3.2.2. The apparent half-life or decay constant λ specifies the decay ratio. These apparent half-lives were then attributed to all houses with the same age (Assumption 4-2) using the age groups presented in Table 3-2, Table 4-3 and Table 4-5. The decay patterns of houses at different ages were then quantified. These decay patterns were subsequently aggregated to develop aggregated first order decay (AggFOD) curves for US mobile homes and Canadian and Norwegian residential houses using the methodology described in Chapter 3 (Section 3.2.4). The AggFOD curves specified the fraction of houses remaining at different ages. Since the data for US mobile homes aged 0~8 years old, Canadian residential houses aged 0~15 years old and Norwegian residential houses aged 0~40 years old were discarded, the apparent half-life of these mobile homes or houses were assumed to be the same of the next age groups (Assumption 4-3). Specifically, the apparent half-life of US mobile homes aged 0~8 years old was assumed to be the same as that of the mobile homes aged 9~13 years old; the apparent half-life of Canadian residential houses aged 0~15 years old was assumed to be the same as that of the houses aged 16~20 years old; and the apparent half-life of Norwegian residential houses aged 0~40 years old was assumed to be the same as that of houses aged 41~50 years old. The apparent half-life of the oldest age groups in Table 3-2, Table 4-3 and Table 4-5 were assumed to apply to all mobile homes or houses older than that age category (Assumption 4-4). Specifically, the apparent half-life of US mobile homes aged 94 years or older was assumed to apply to all mobile houses older than 94 years; the apparent half-life of Canadian residential houses aged 91 years or older was assumed to apply to all houses older than 91 years; and the apparent half-life of Norwegian residential houses aged 91 years or older was assumed to apply to all houses older than 91 years. The methodology used to develop each AggFOD curve is presented in Section 3.2.4. In Chapter 3, six decay models were used to evaluate the AggFOD curve of US single-family and multi-family houses using parameters either estimated by fitting to the AggFOD curve or equivalent half-lives developed from the AggFOD curve. These formulated models are generalized empirical models that have the benefit of being readily applied to other systems, especially systems with limited data. A formulated decay model can simplify the applicability and help understand the decay pattern. 54  The Gamma distribution provided the lowest sum of squared errors in Chapter 3, which meant that it was the best model to describe the decay pattern of US single-family and multi-family houses (Section 3.4). The six decay models evaluated in Chapter 3 were also compared to the AggFOD curves of US mobile homes, Canadian and Norwegian residential houses using SAS® 9.4 and Microsoft® Excel 2013 to determine which model provided the best description of the decay pattern of these houses.  4.2.5 Assumptions The assumptions made in the development of the AggFOD curves for these data sets were generally the same as those used in Chapter 3 (Section 3.2.6), with only small differences in some details as outlined below. Assumption 4-1: data reported in later periods were more accurate than earlier periods due to improved Survey methodologies. Assumption 4-2: the apparent half-life of houses in each age group represented the apparent half-life of all houses of the same age. Assumption 4-3: the apparent half-life of US mobile homes aged 0~8 years old was the same as the apparent half-life of mobile homes aged 9~13 years old; the apparent half-life of Canadian residential houses aged 0~15 years old was the same as the apparent half-life of houses aged 16~20 years old; and the apparent half-life of Norwegian residential houses aged 0~40 years old was the same as the apparent half-life of houses aged 41~50 years old. Assumption 4-4: the apparent half-life of US mobile homes aged 94 years or older was applied to all mobile homes older than 94 years; the apparent half-life of Canadian residential houses aged 91 years or older was applied to all houses older than 91 years; and the apparent half-life of Norwegian residential houses aged 91 years or older was applied to all houses older than 91 years. 4.3 Results 4.3.1 US mobile homes The estimated apparent half-lives of US mobile homes as a function of housing age are presented in Figure 4-3. Younger houses displayed longer apparent half-lives than older houses which is consistent with observations made for US single- and multi-family houses in Chapter 3 (Section 3.3.1). The apparent half-lives presented in Figure 4-3 were used to plot the AggFOD curve (Figure 4-4), which revealed that US mobile homes had a half-life of 44 years and the 95% decay point was 98 years. 55   Figure 4-3 Estimated apparent half-lives of US mobile homes as a function of housing age  Figure 4-4 AggFOD curve-US mobile homes A Gamma distribution model, a logistic decay model and a three-segment decay model were fitted to the AggFOD curve and the outputs were compared in Figure 4-5a with the time scale set at 300 years. The logistic decay curve achieved the lowest SSE of 0.110 when the half-life was 42 years. In 0102030405060700 20 40 60 80 100 120Apparent half-life (years)Age of houses (years)00.10.20.30.40.50.60.70.80.910 50 100 150 200 250 300Remnant fractionTime after construction (years)4456  contrast, the best-fit Gamma distribution curve exhibited an SSE of 0.217 when α was 1.95 and β was 23.7. The three-segment decay curve obtained an SSE of 3.14 with a half-life of 35 years (Figure 4-5a). Figure 4-5b compares the outputs of the FOD model, the linear decay model and the instant decay model with an equivalent half-life of 44 years to the AggFOD curve.  Figure 4-5 Decay models fitted to the AggFOD curve of US mobile homes 4.3.2 Canadian residential houses Four scenarios, based on the inclusion or exclusion of data, were used to analyze the Canadian housing data (Section 4.2.2). The apparent half-lives of Canadian residential houses as a function of housing age under each scenario are presented in Figure 4-6. As noted earlier, for US single- and multi-family houses in Chapter 3 (Section 3.3.1), younger houses generally displayed longer apparent half-lives than older houses. The exception to this observation was Scenario 3 where the oldest houses displayed the longest apparent half-life. The apparent half-lives for houses aged 0~30 years were estimated to be the same across all four scenarios because they used the same data and assumption (Assumption 4-3). The inclusion or exclusion of data only applied to Surveys 1971~1986 so data for Surveys 1991~2011 were not affected. Scenario 1 and Scenario 4 had an overlap for houses aged 31~40 (period 1971~1980) because they both included the same data for Survey 1986. Scenario 2 and Scenario 3 had an overlap for houses aged 31~50 because they both discarded Surveys 1981~1986. The differences between these scenarios was that Scenario 2 discarded the data of Survey 1971 for houses aged 41~50 (period 1961~1970) whereas Scenario 3 discarded all data from Survey 1971. The apparent half-lives presented in Figure 4-6 were used to plot the AggFOD curves 00.20.40.60.810 100 200 300Remnant fractionTime after construction (years)a. Decay models fit to AggFODAggFODGammaLogistic3-segment00.20.40.60.810 100 200 300Remnant fractionTime after construction (years)b. Models with an equivalent half-lifeAggFODFODLinearInstant57  (Figure 4-7). The half-lives and 95% decay values determined under the different scenarios are summarized in Table 4-6.  Figure 4-6 Estimated half-lives of Canadian residential houses as a function of housing age  Figure 4-7 Aggregated first order decay (AggFOD) curves-Canadian residential houses 010020030040050060070080090010000 20 40 60 80 100 120Apparent half-life (years)Age of houses (years)Scenario 1 Scenario 2 Scenario 3 Scenario 400.10.20.30.40.50.60.70.80.910 50 100 150 200 250 300Remnant fractionTime after construction (years)Scenario 1Scenario 3Scenario 2Scenario 458  A Gamma distribution model, a logistic decay model and a three-segment decay model were fitted to each AggFOD curve and the outputs are compared in Figure 4-8 a, c, e and g with the time scale set at 300 years. The Gamma distribution model achieved the lowest sum of squared errors (SSE) for all four scenarios (Table 4-7). Figure 4-8 b, d, f and h compare the outputs of the FOD model, the linear decay model and the instant decay model with an equivalent half-life to the AggFOD curve. Although these models are the simplest models, none of them provide an adequate fit to the AggFOD curve. Table 4-6 Summary of half-lives and 95% decay under different scenarios for Canadian residential houses Scenarios Scenario 1 Scenario 2 Scenario 3 Scenario 4 half-life (t1/2) 75 years 122 years 374 years 92 years 95% decay (t95%) 222 years 338 years 3266 years 260 years  Table 4-7 Comparison of the SSE and parameter(s) of the decay models under each scenario  Scenario 1 Scenario 2 Scenario 3 Scenario 4 parameter(s) SSE parameter(s) SSE parameter(s) SSE parameter(s) SSE Gamma α=2.71, β=32.9 0.198 α=2.83, β=50.6 0.106 α=0.708, β=652 1.12 α=2.54, β=43.2 0.0657 Logistic t1/2=81 0.469 t1/2=131 0.453 t1/2=246 3.42 t1/2=100 0.250 three-segment t1/2=72 1.99 t1/2=121 1.06 t1/2=245 4.15 t1/2=89 1.53    59      Figure 4-8 Decay models fitted to the AggFOD curve of Canadian residential houses (a ~ d)   00.20.40.60.810 100 200 300Remnant fractionTime after construction (years)a. Decay models-Scenario 1AggFODGammaLogistic3-segment00.20.40.60.810 100 200 300Remnant fractionTime after construction (years)b. Simple models-Scenario 1AggFODFODLinearInstant00.20.40.60.810 100 200 300Remnant fractionTime after construction (years)c. Decay models-Scenario 2AggFODGammaLogistic3-segment00.20.40.60.810 100 200 300Remnant fractionTime after construction (years)d. Simple models-Scenario 2AggFODFODLinearInstant60    Figure 4-8 cont.: Decay models fitted to the AggFOD curve of Canadian residential houses (e ~ h) 4.3.3 Norwegian residential houses The estimated apparent half-lives of Norwegian residential houses as a function of housing age are presented in Figure 4-9. As for other assessments, younger houses generally displayed longer apparent half-lives than older houses (Sections 3.3.1, 4.3.1 and 4.3.2). 00.20.40.60.810 100 200 300Remnant fractionTime after construction (years)e. Decay models-Scenario 3AggFODGammaLogistic3-segment00.20.40.60.810 100 200 300Remnant fractionTime after construction (years)f. Simple models-Scenario 3AggFODFODLinearInstant00.20.40.60.810 100 200 300Remnant fractionTime after construction (years)g. Decay models-Scenario 4AggFODGammaLogistic3-segment00.20.40.60.810 100 200 300Remnant fractionTime after construction (years)h. Simple models-Scenario 4AggFODFODLinearInstant61   Figure 4-9 Estimated apparent half-lives of Norwegian residential houses as a function of housing age The apparent half-lives presented in Figure 4-9 were used to plot the AggFOD curve (Figure 4-10). The curve indicated that the Norwegian residential houses had a half-life of 146 years and the 95% of decay happened at year 481.  Figure 4-10 AggFOD curve-Norwegian residential houses 0501001502002503003500 20 40 60 80 100 120Half-life (years)Age of houses (years)00.10.20.30.40.50.60.70.80.910 50 100 150 200 250 300Remnant fractionTime after construction (years)14662  A Gamma distribution model, a logistic decay model and a three-segment decay model were fitted to the AggFOD curve and the outputs are compared in Figure 4-11a with the time scale set at 300 years. The Gamma distribution curve achieved the lowest SSE of 0.0400 when α equaled to 1.80 and β equaled to 101. In contrast, the logistic decay curve exhibited an SSE of 0.169 and a half-life of 160 years. The three-segment decay curve obtained an SSE of 0.177 and a half-life of 148 years. Figure 4-11b compares the outputs of the FOD model, the linear decay model and the instant decay model with an equivalent half-life of 146 years to the AggFOD curve.  Figure 4-11 Decay models fitted to the AggFOD curve of Norwegian residential houses 4.4 Discussion 4.4.1 US mobile homes In contrast to US single- and multi-family homes, relatively new US mobile homes (i.e. those aged between 0 and 15 years old) appear to decay faster than those aged 20 to 35 years old (Figure 4-5). While it is uncertain why mobile homes exhibit this decay pattern, three possible reasons are presented below: • there were data collection errors for mobile homes in the American Housing Survey; • more recently constructed mobile homes were not build as well as older ones;  • the Global Financial Crisis (DPAD, 2013) resulted in an increased removal, or reduced occupancy, of recently constructed mobile homes. This  decay curve for US mobile homes (Figure 4-3) displays a different pattern to that observed for US single and multi-family homes (Figure 3-6). It does not display the lag in decay seen for the 00.20.40.60.810 100 200 300Remnant fractionTime after construction (years)a. Decay models fit to AggFODAggFODGammaLogistic3-segment00.20.40.60.810 100 200 300Remnant fractionTime after construction (years)b. Models with an equivalent half-lifeAggFODFODLinearInstant63  single- and multi-family decay curve and it decays in a more linear manner until it reaches the half-life. The absence of a slow initial decay may explain why the logistic decay model fits this decay curve slightly better than the Gamma distribution model. However, the Gamma distribution model was still considered to provide an adequate description of the decay curve of US mobile homes. 4.4.2 Comparison of houses in Canada, US and Norway The results of the Canadian data under each scenario may be viewed as a range to indicate the response of the AggFOD and the models to the uncertainties inherent in the data. The range of outcomes may be compared to the apparent half-life estimations obtained for US single-family and multi-family houses and Norwegian residential houses (Figure 4-12a). The ranges observed among the scenarios indicate that the regression estimation method developed in Chapter 3 and used in this chapter is sensitive to and constrained by the raw data sets. Scenario 3 excluded PUMF data and resulted in anomalously high numbers in apparent half-life estimations, especially for houses aged 91 years or older. Figure 4-12b shows the comparative half-life data for the US, Norway and Canada excluding the results from Scenario 3.  Figure 4-12 A comparison of the apparent half-life estimations of Canadian residential houses to the ones of US single-family and multi-family houses and Norwegian residential houses Figure 4-7 shows the Canadian AggFOD curves under each scenario. Four scenarios were adopted to study the Canadian data. Data were discarded based either on conservatism and assumption (Scenario 1), reasonableness and judgment (Scenario 2) or data source (Scenario 3). Scenario 4 used all the available data. All Canadian scenarios indicated slow initial and final decay rates and a more rapid decay rate near the 50% remnant fraction (Figure 4-13a). However, Scenario 3 may be considered to have too few data (a maximum of 5 data points were used for each regression analysis) and a too narrow range of data (only a 20-year survey range could be used). In contrast, 0 20 40 60 80 100 12001002003004005006007008009001000Age of houses (years)Half-life (years)a. including Scenario 3Canada US Norway0 20 40 60 80 100 1200100200300400500600700800Age of houses (years)Half-life (years)b. excluding Scenario 3Canada US Norway64  Scenario 1 had 7 data points and a 30-year survey range; Scenario 2 had 6 data points and a 40-year survey range; and Scenario 4 had 8 data points and a 40-year survey range. Scenario 3 was therefore excluded from further consideration. Figure 4-13 shows the curves excluding Scenario 3 as an estimation range with the comparison to US and Norwegian houses. The data for US single- and multi-family houses and mobile homes were added together using the number of units in each category to develop the AggFOD curve of US residential houses.  Figure 4-13 A comparison of the AggFOD curve of Canadian residential houses to the AggFOD curves of US single-family and multi-family houses and Norwegian residential houses If Scenario 3 was excluded, the mid-point half-life of the decay curve range of Canadian residential houses was about 98 years and the 95% decay mid-point was around 280 years (Table 4-6 and Figure 4-13). If the probability of each scenario is considered to be equal, then the mid-point of the range may be used to represent the decay pattern. Both of these values are about 7% higher than those of Scenario 4, which are 92 and 260 years respectively. In addition, it is difficult to determine whether it was preferable to discard either Survey 1971 or Surveys 1981 and 1986. Scenario 4 used the full data set. Based on these reasons, this study recommends using Scenario 4 (i.e. no data discarding) to determine the decay pattern of Canadian residential houses. Using Scenario 4, the half-life and the 95% decay point of Canadian residential houses are shorter than the equivalent values of US single- and multi-family houses (137 and 425 years), US residential 0 50 100 150 200 250 30000.10.20.30.40.50.60.70.80.91Time after construction (years)Remnant fractionCanadaNorwayUS SF+MFUS SF+MF+MH65  houses (i.e. SF+MF+MH) (128 and 416 years) and Norwegian residential houses (146 and 481 years). While younger Canadian houses seem to decay more slowly than US and Norwegian houses (Figure 4-13b), the highly uncertain decay pattern for younger houses due to the lack of data is a common problem to every method, not just this “regression-aggregation-fit” method. The Norwegian decay pattern is highly uncertain from 0 to 40 years due to discarding of unusable data (Section 4.2.3). The Canadian estimations are uncertain from 0 to 15 years and the US estimations are uncertain from 0 to 8 years due to incomplete data. The apparent half-life of houses in these periods was assumed to be the same as the apparent half-life of the next available age group (Assumption 3-4 and Assumption 4-3). The uncertainties and limitations of the Canadian data are clearly revealed in Figure 4-12 and Figure 4-13. A major weakness of the “regression-aggregation-fit” method, as for any regression analysis, is the need for a suitably large data sample. Assumption 4-3 attributed the earliest known apparent half-life to all younger houses and Assumption 4-4 extrapolated the last known apparent half-life to all older houses. Therefore, the “regression-aggregation-fit” method has additional limitations in adequately dealing with houses that were built recently or long ago. Moreover, the housing units remaining data were collected from one survey period to the next in a temporal sequence, so these results may be autocorrelated. First- to tenth-order autocorrelations were investigated but they were unable to describe the time series pattern observed in this study. Autocorrelation was therefore not included in this thesis with the consequence that it was not possible to conduct uncertainty analyses because the estimates of the standard deviation of the coefficient (i.e. decay constant λ) was biased. Although time series are involved, the least squares approach still provides unbiased estimates of the apparent half-lives because the linearity assumption of the model was met. In addition, the scenario analysis of the Canadian data provides a preliminary indication of the uncertainty analysis. Intuitively, the apparent half-lives for younger houses should be longer than older houses. This does not mean that an individual house that was built recently will last longer than an individual house that was built a long time ago. The apparent half-life is estimated by assuming that houses follow a first order decay pattern over a decadal period, which may not be the true half-life of the houses. However, the half-life of AggFOD curve is considered to be a realistic estimate of the true half-life. The model described in this paper is an age-related dynamic model, which is likely to change under different structural, societal and catastrophic circumstances. The apparent half-lives and the parameters of the decay models should be re-calibrated at regular intervals, and especially after each housing survey has been conducted and additional data become available. The fitted Gamma distribution models had the lowest sum of squared errors among all decay models for the US single- and multi-family houses and Canadian and Norwegian residential 66  houses. The best model for the US mobile homes was the logistic decay model, although the Gamma distribution model was also considered to provide an adequate fit, with the respective SSEs being 0.110 and 0.217. Therefore, the Gamma distribution is recommended as the most appropriate generalized model for describing the decay pattern of houses. The selection of the most appropriate model is further discussed in Chapter 5 (Section 5.4.4). 4.5 Conclusion The “regression-aggregation-fit” method developed using the US single-family and multi-family housing units remaining data may be applied to other countries and other data sets, as demonstrated by its use for US mobile homes and Canadian and Norwegian residential houses. Uncertainties and limitations exist in Canadian data and the “regression-aggregation-fit” method is very sensitive when the data size is small. Ideally, large data sets containing accurate and temporally consistent information should be used. The half-life and 95% decay point of US mobile homes were determined to be 44 and 98 years, respectively. For Canadian residential houses, the equivalent values were 92 and 260 years and for Norwegian residential houses, they were 146 and 481 years. In contrast, the half-life and 95% decay point of US single- and multi-family houses were 137 and 425 years respectively (Chapter 3, Section 3.3.2). While the decay rates and patterns of US single- and multi-family houses and Norwegian residential houses were similar, the decay rate of Canadian residential houses was more rapid than in both of these nations, although it followed a similar shape. The Gamma distribution model provided a good description of the decay pattern of Canadian and Norwegian residential houses. The logistic decay model had the best fit to the decay curve for US mobile homes. However, the Gamma distribution model was considered to provide an adequate description of this decay curve and it was therefore recommended as the most appropriate generalized model for describing the decay pattern of houses.   67  Chapter 5 Quantification of the pool of structural HWP in US residential houses 5.1 Introduction As discussed in Section 2.2, countries can benefit from increasing the HWP pool to offset their carbon emissions. In order to include this stock in national carbon accounts, it is important to “neither over- nor under-estimate” the pool size and its rate of change (UNFCCC, 2003). Structural HWP in single-family and multi-family houses are one of the major end uses of wood products in some countries and this application is one of the longest-lived uses of HWP (Winistorfer et al., 2005; McKeever and Howard, 2011). Long-lived HWP tend to form carbon pools that have larger pool sizes and longer sink durations than those with shorter half-lives (Section 2.2.3). Therefore, it is necessary to first accurately quantify the structural HWP in single-family and multi-family houses when developing emissions estimates for the HWP sector.  In previous chapters, the apparent half-lives and the cumulative decay curves (AggFOD) of US single-family and multi-family houses and mobile homes were determined. Six decay models were then fitted to the AggFOD curve to determine the model that best described the decay pattern. This chapter uses these six decay models to estimate the pool size of structural HWP in US single-family and multi-family houses and US mobile homes. The results are validated by comparison with published values. The sensitivity of the pool size estimation to the choice of the half-life and the model is also assessed and a preferred model is selected. 5.2 Methods 5.2.1 Quantification of HWP pools  The relationship between the annual carbon fluxes and the carbon pool size of structural HWP in houses is shown in Figure 3-1. The annual stock change was calculated using Equation 3-1 and the pool size was estimated by aggregating the annual stock changes (Equation 3-4). The annual consumption of HWP for housing construction (i.e. the annual input flux) for each year between 1950 and 2009 has been reported by the United States Forest Service (McKeever and Howard, 2011). The hierarchical arrangement of product categories and subcategories of HWP consumed in the construction of houses is shown in Figure 5-1. Only the structural materials that are used in construction were assumed to have the same half-life as houses (Assumption 5-1). Non-structural HWP were excluded from the carbon pools estimated in this paper. Further details related to this assumption are presented in Section 5.2.4. Between 1900 and 1950, the major structural HWP used for housing construction were softwood lumber and softwood plywood because more novel products, such as engineered wood products 68  and OSB, were yet to be introduced to the market. The consumption of softwood lumber and plywood in any given year was estimated using Equation 3-2. The earliest year in the dataset was chosen to be 1900 because that was the earliest year with publicly available estimates of housing starts.  The average consumption of structural HWP per house for each year between 1900 and 1950 was back-extrapolated by Sianchuk, Ackom and McFarlane (2012) and these data were used in this thesis. For simplicity, it was assumed that the annual HWP input entered the pool at the end of the year (Assumption 5-2), which implies that negligible decay of HWP occurred during the year. Additional details on this assumption are presented in Section 5.2.4.  Figure 5-1 Product categories and subcategories of HWP in houses reported by McKeever and Howard (2011) (Key: OSB=oriented strand board, Glulam=glue-laminated timber, LVL=structural laminated veneer lumber, Paralam=parallel strand lumber and OSL=oriented strand lumber) The pool size of HWP in houses at the end of the year was calculated by adding the new input at the end of the year being considered to the amount of carbon that remained from all previous inputs (Equation 5-1).  𝑃𝑃𝑡𝑡 = 𝐶𝐶𝑠𝑠𝑛𝑛𝑑𝑑𝑎𝑎𝑑𝑑𝑛𝑛𝑑𝑑𝑛𝑛𝑎𝑎,𝑡𝑡 + 𝐶𝐶0,𝑡𝑡 Equation 5-1 where 𝑃𝑃𝑡𝑡  𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑟𝑟𝑎𝑎𝑎𝑎𝑙𝑙 𝑖𝑖𝑖𝑖𝑠𝑠𝑒𝑒 𝑎𝑎𝜆𝜆 𝜆𝜆ℎ𝑒𝑒 𝑒𝑒𝑙𝑙𝑑𝑑 𝑎𝑎𝑙𝑙 𝜆𝜆ℎ𝑒𝑒 𝑑𝑑𝑒𝑒𝑎𝑎𝑟𝑟 𝜆𝜆, 𝜆𝜆 > 𝑖𝑖, 𝜆𝜆 > 1900   𝐶𝐶𝑠𝑠𝑛𝑛𝑑𝑑𝑎𝑎𝑑𝑑𝑛𝑛𝑑𝑑𝑛𝑛𝑎𝑎,𝑡𝑡  𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑑𝑑𝑎𝑎𝑟𝑟𝑏𝑏𝑎𝑎𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑙𝑙𝜆𝜆 𝜆𝜆ℎ𝑎𝑎𝜆𝜆 𝑟𝑟𝑒𝑒𝑎𝑎𝑎𝑎𝑖𝑖𝑙𝑙𝑒𝑒𝑑𝑑 𝑙𝑙𝑟𝑟𝑎𝑎𝑎𝑎 𝑟𝑟𝑟𝑟𝑒𝑒𝑐𝑐𝑖𝑖𝑎𝑎𝑎𝑎𝑖𝑖 𝑖𝑖𝑙𝑙𝑟𝑟𝑎𝑎𝜆𝜆 𝑖𝑖𝑙𝑙 𝑑𝑑𝑒𝑒𝑎𝑎𝑟𝑟 𝜆𝜆  𝐶𝐶0,𝑡𝑡 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑑𝑑𝑎𝑎𝑟𝑟𝑏𝑏𝑎𝑎𝑙𝑙 𝑖𝑖𝑙𝑙𝑟𝑟𝑎𝑎𝜆𝜆 𝑎𝑎𝑙𝑙 𝐻𝐻𝐻𝐻𝑃𝑃 𝑖𝑖𝑙𝑙 𝑙𝑙𝑒𝑒𝑤𝑤 ℎ𝑎𝑎𝑎𝑎𝑖𝑖𝑖𝑖𝑙𝑙𝑎𝑎 𝑑𝑑𝑎𝑎𝑙𝑙𝑖𝑖𝜆𝜆𝑟𝑟𝑎𝑎𝑑𝑑𝜆𝜆𝑖𝑖𝑎𝑎𝑙𝑙 𝑖𝑖𝑙𝑙 𝑑𝑑𝑒𝑒𝑎𝑎𝑟𝑟 𝜆𝜆  The amount of carbon that remained at the end of each year (𝐶𝐶𝑠𝑠𝑛𝑛𝑑𝑑𝑎𝑎𝑑𝑑𝑛𝑛𝑑𝑑𝑛𝑛𝑎𝑎,𝑡𝑡) was estimated using the six decay models described in Chapter 2 with the parameters or half-lives estimated in Chapter 3 for the US single-family and multi-family houses. Specifically, the six models and the parameters used were:  69  • the Gamma distribution model with α=2.07 and β=80.2, referred to as “Gamma (SF+MF, 2.07, 80.2)”;  • the logistic decay model with a half-life of 149 years, referred to as “Logistic (SF+MF, 149)”;  • the three-segment decay model with a half-life of 138 years, referred to as “three-segment (SF+MF, 138)”;  • the first order decay model with a half-life of 137 years, referred to as “FOD (SF+MF, 137)”;  • the linear decay model with a half-life of 137 years, referred to as “Linear (SF+MF, 137)”; and • the instant decay model with a half-life of 137 years, referred to as “Instant (SF+MF, 137)”. The half-life of 137 years used for the last three models listed above was obtained from the US AggFOD curve for single-family and multi-family houses presented in Section 3.3. The other half-lives or parameters were obtained by fitting the corresponding decay models to the US AggFOD curve (Table 3-3). The parameters or half-lives for the US mobile homes were estimated in Section 4.3.1. The six models and the parameters used were: • the Gamma distribution model with α=1.95 and β=23.7, referred to as “Gamma (MH, 1.95, 23.7)”;  • the logistic decay model with a half-life of 42 years, referred to as “Logistic (MH, 42)”;  • the three-segment decay model with a half-life of 35 years, referred to as “three-segment (MH, 35)”;  • the first order decay  model with a half-life of 44 years, referred to as “FOD (MH, 44)”;  • the linear decay model with a half-life of 44 years, referred to as “Linear (MH, 44)”; and • the instant decay model with a half-life of 44 years, referred to as “Instant (MH, 44)”. The FOD model is not age-related. If the half-life is the same from year to year, then the annual decay ratio is the same, as demonstrated by Equation 2-4. When t2-t1=1 year in this equation, the annual decay ratio is a constant value. Therefore, the amount of carbon remaining at the end of a given year was simply calculated using the pool size at the end of the previous year multiplied by the annual decay ratio irrespective of the initial carbon input (Equation 5-2).  𝑃𝑃𝑡𝑡 = 𝑃𝑃𝑡𝑡−1𝑒𝑒−𝑑𝑑𝑛𝑛2/𝑡𝑡1/2 + 𝐶𝐶0,𝑡𝑡 Equation 5-2 where 𝑃𝑃𝑡𝑡  𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑟𝑟𝑎𝑎𝑎𝑎𝑙𝑙 𝑖𝑖𝑖𝑖𝑠𝑠𝑒𝑒 𝑎𝑎𝜆𝜆 𝜆𝜆ℎ𝑒𝑒 𝑒𝑒𝑙𝑙𝑑𝑑 𝑎𝑎𝑙𝑙 𝜆𝜆ℎ𝑒𝑒 𝑑𝑑𝑒𝑒𝑎𝑎𝑟𝑟 t   𝐶𝐶0,𝑡𝑡 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑑𝑑𝑎𝑎𝑟𝑟𝑏𝑏𝑎𝑎𝑙𝑙 𝑖𝑖𝑙𝑙𝑟𝑟𝑎𝑎𝜆𝜆 𝑎𝑎𝑙𝑙 𝐻𝐻𝐻𝐻𝑃𝑃 𝑖𝑖𝑙𝑙 𝑙𝑙𝑒𝑒𝑤𝑤 ℎ𝑎𝑎𝑎𝑎𝑖𝑖𝑖𝑖𝑙𝑙𝑎𝑎 𝑑𝑑𝑎𝑎𝑙𝑙𝑖𝑖𝜆𝜆𝑟𝑟𝑎𝑎𝑑𝑑𝜆𝜆𝑖𝑖𝑎𝑎𝑙𝑙 𝑖𝑖𝑙𝑙 𝑑𝑑𝑒𝑒𝑎𝑎𝑟𝑟 𝜆𝜆  𝑒𝑒−𝑑𝑑𝑛𝑛2/𝑡𝑡1/2 = 0.995,𝑤𝑤ℎ𝑒𝑒𝑟𝑟𝑒𝑒 𝜆𝜆1/2 = 137 𝑑𝑑𝑒𝑒𝑎𝑎𝑟𝑟𝑖𝑖  For all the other models, the annual decay ratios are variables that relate to the length of time that carbon has remained in the pool. In these cases, the amount of carbon remaining was calculated 70  by using the initial carbon inputs for each year, multiplying this value by the corresponding remnant fraction and summing each annual carbon remnant together (Equation 5-3). The approach is demonstrated in Table 5-1. The remnant fraction of each model as a function of “time after construction” (i.e. age) was determined previously and is presented in Figure 3-7.  𝑃𝑃𝑡𝑡 = � 𝐶𝐶0,𝑑𝑑𝑅𝑅𝑅𝑅(𝜆𝜆 − 𝑖𝑖)𝑡𝑡−1𝑑𝑑=1900+ 𝐶𝐶0,𝑡𝑡 Equation 5-3 where 𝑃𝑃𝑡𝑡  𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑟𝑟𝑎𝑎𝑎𝑎𝑙𝑙 𝑖𝑖𝑖𝑖𝑠𝑠𝑒𝑒 𝑎𝑎𝜆𝜆 𝜆𝜆ℎ𝑒𝑒 𝑒𝑒𝑙𝑙𝑑𝑑 𝑎𝑎𝑙𝑙 𝜆𝜆ℎ𝑒𝑒 𝑑𝑑𝑒𝑒𝑎𝑎𝑟𝑟 𝜆𝜆, 𝜆𝜆 > 𝑖𝑖, 𝜆𝜆 > 1900   𝐶𝐶0,𝑑𝑑 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑑𝑑𝑎𝑎𝑟𝑟𝑏𝑏𝑎𝑎𝑙𝑙 𝑖𝑖𝑙𝑙𝑟𝑟𝑎𝑎𝜆𝜆 𝑎𝑎𝑙𝑙 𝐻𝐻𝐻𝐻𝑃𝑃 𝑖𝑖𝑙𝑙 𝑙𝑙𝑒𝑒𝑤𝑤 ℎ𝑎𝑎𝑎𝑎𝑖𝑖𝑖𝑖𝑙𝑙𝑎𝑎 𝑑𝑑𝑎𝑎𝑙𝑙𝑖𝑖𝜆𝜆𝑟𝑟𝑎𝑎𝑑𝑑𝜆𝜆𝑖𝑖𝑎𝑎𝑙𝑙 𝑖𝑖𝑙𝑙 𝑑𝑑𝑒𝑒𝑎𝑎𝑟𝑟 𝑖𝑖  𝑅𝑅𝑅𝑅(𝜆𝜆 − 𝑖𝑖)𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑟𝑟𝑒𝑒𝑎𝑎𝑙𝑙𝑎𝑎𝑙𝑙𝜆𝜆 𝑙𝑙𝑟𝑟𝑎𝑎𝑑𝑑𝜆𝜆𝑖𝑖𝑎𝑎𝑙𝑙 𝑎𝑎𝑙𝑙 𝜆𝜆ℎ𝑒𝑒 𝑖𝑖𝑙𝑙𝑖𝑖𝜆𝜆𝑖𝑖𝑎𝑎𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑙𝑙𝜆𝜆 𝑎𝑎𝜆𝜆 𝑎𝑎𝑎𝑎𝑒𝑒 (𝜆𝜆 − 𝑖𝑖)  The carbon pool sizes estimated using different decay models were compared to evaluate the sensitivity of the pool size to the decay model. In order to analyze the impact of using the IPCC Tier 2 method with default half-lives, the pool size was also determined using the FOD model with half-lives of 35 years for lumber and 25 years for panels (IPCC, 2014). These values are referred to as FOD (SF+MF, IPCC) and FOD (MH, IPCC) for the HWP pools of the single- and multi-family houses and mobile homes respectively. Table 5-1 Calculation methodology to determine the amounts of carbon remaining by initial input and the pool sizes at the end of each year for models other than FOD. 𝐶𝐶0,"𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦": carbon input of HWP in new housing constructions of year "yyyy". RF (n): remnant fraction of the initial amount at age n.  The year of initial carbon input Pool size 1900 1901 1902 … 2009  Initial input 𝐶𝐶0,1900 𝐶𝐶0,1901 𝐶𝐶0,1902 … 𝐶𝐶0,2009 The year of pool size estimation 1900 𝐶𝐶0,1900 - - … - 𝐶𝐶0,1900 1901 𝐶𝐶0,1900× 𝑅𝑅𝑅𝑅(1) 𝐶𝐶0,1901 - … - 𝐶𝐶0,1900 × 𝑅𝑅𝑅𝑅(1)+ 𝐶𝐶0,1901 1902 𝐶𝐶0,1900× 𝑅𝑅𝑅𝑅(2) 𝐶𝐶0,1901× 𝑅𝑅𝑅𝑅(1) 𝐶𝐶0,1902 … - 𝐶𝐶0,1900 × 𝑅𝑅𝑅𝑅(2)+ 𝐶𝐶0,1901 × 𝑅𝑅𝑅𝑅(1)+ 𝐶𝐶0,1902 … … … … … … … 2009 𝐶𝐶0,1900× 𝑅𝑅𝑅𝑅(109) 𝐶𝐶0,1901× 𝑅𝑅𝑅𝑅(108) 𝐶𝐶0,1902× 𝑅𝑅𝑅𝑅(107) … 𝐶𝐶0,2009 𝐶𝐶0,1900 × 𝑅𝑅𝑅𝑅(109)+ 𝐶𝐶0,1900 × 𝑅𝑅𝑅𝑅(109)+ 𝐶𝐶0,1902 × 𝑅𝑅𝑅𝑅(107)+⋯+ 𝐶𝐶0,2009  71  5.2.2 Constant mass input scenario analysis  The due to the long half-lives of structural HWP, the real differences among the various decay models are only revealed when they are run for a longer period. However, the relatively short time frame for the available housing data prevent such model runs from being conducted using real data. Therefore, a constant annual mass input scenario was used to reveal the longer-term differences in the carbon stocks for US single-family and multi-family houses. The average annual carbon inflow of structural HWP to the single-family and multi-family housing pool was approximately 7 Mg C/house and the average annual housing starts were about 1 million (McKeever and Howard, 2011). Therefore, the constant mass input scenario was assumed to have a fixed and equal annual input of 7 Tg C to the housing pool every year. The half-lives or decay parameters of US single- and multi-family houses determined in Section 3.3.2 and the IPCC default half-lives were used to estimate the pool sizes under a constant mass input scenario and the models were run over a period of a millennium. The same inputs of 7 Tg C year-1 were used for mobile homes to ensure that the stock difference between single- and multi-family housing pool and mobile home pool was not caused by a difference in inputs. Using this approach, the influence of the different half-life on each model could be demonstrated clearly. The half-lives or decay parameters of the US mobile homes determined in Section 4.3.1 were used to estimate the mobile home pool under this constant mass input scenario. 5.2.3 Validation methods Several estimates of the size of the United States HWP in use pool have been published. This thesis has calculated values for the pool of structural HWP in US single-family and multi-family houses. This pool includes both domestically produced HWP and imported HWP which are consumed in US houses. The calculation process used in this thesis is equivalent to the Stock Change Approach presented in the IPCC Guidelines (IPCC, 2014).  Wilson (2006) calculated the pool size of structural HWP in US single-family and multi-family houses in 2003 using Equation 5-4, which implies that Wilson’s calculation process is also equivalent to the Stock Change Approach. In addition, the target pool quantified by Wilson (2006) was structural HWP in houses, which is the same pool that has been quantified in this thesis. Therefore, our estimate is directly comparable to Wilson’s.   𝐶𝐶𝑆𝑆𝑃𝑃+𝑃𝑃𝑃𝑃,2003 = 𝑁𝑁𝑠𝑠𝑛𝑛𝑑𝑑𝑎𝑎𝑑𝑑𝑛𝑛𝑛𝑛𝑤𝑤,2003 × 𝐶𝐶𝑜𝑜𝑡𝑡𝑠𝑠𝑜𝑜𝑐𝑐𝑡𝑡𝑜𝑜𝑠𝑠𝑎𝑎𝑑𝑑 𝐻𝐻𝐻𝐻𝐻𝐻/ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑛𝑛 Equation 5-4 where 𝑁𝑁𝑠𝑠𝑛𝑛𝑑𝑑𝑎𝑎𝑑𝑑𝑛𝑛𝑛𝑛𝑤𝑤,2003 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝜆𝜆𝑎𝑎𝜆𝜆𝑎𝑎𝑙𝑙 𝑙𝑙𝑎𝑎𝑎𝑎𝑏𝑏𝑒𝑒𝑟𝑟 𝑎𝑎𝑙𝑙 ℎ𝑎𝑎𝑎𝑎𝑖𝑖𝑒𝑒𝑖𝑖 𝑟𝑟𝑒𝑒𝑎𝑎𝑎𝑎𝑖𝑖𝑙𝑙𝑒𝑒𝑑𝑑 𝑖𝑖𝜆𝜆𝑎𝑎𝑙𝑙𝑑𝑑𝑖𝑖𝑙𝑙𝑎𝑎 𝑖𝑖𝑙𝑙 2003  𝐶𝐶𝑜𝑜𝑡𝑡𝑠𝑠𝑜𝑜𝑐𝑐𝑡𝑡𝑜𝑜𝑠𝑠𝑎𝑎𝑑𝑑 𝐻𝐻𝐻𝐻𝐻𝐻/ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑛𝑛 𝑖𝑖𝑖𝑖 𝑎𝑎𝑐𝑐𝑎𝑎𝑒𝑒𝑟𝑟𝑎𝑎𝑎𝑎𝑒𝑒 𝑑𝑑𝑎𝑎𝑟𝑟𝑏𝑏𝑎𝑎𝑙𝑙  𝑎𝑎𝑎𝑎𝑖𝑖𝑖𝑖 𝑎𝑎𝑙𝑙 𝑖𝑖𝜆𝜆𝑟𝑟𝑎𝑎𝑑𝑑𝜆𝜆𝑎𝑎𝑟𝑟𝑎𝑎𝑙𝑙 𝐻𝐻𝐻𝐻𝑃𝑃 𝑟𝑟𝑒𝑒𝑟𝑟 ℎ𝑎𝑎𝑎𝑎𝑖𝑖𝑒𝑒  Unfortunately, several of the published studies have quantified different components of the HWP in use pool, which makes direct comparisons difficult. Skog (2008) estimated the carbon pool in 72  single-family and multi-family houses in the US in 2001 using a methodology equivalent to the Stock Change Approach. However, it appears that Skog (2008) did not distinguish between structural and non-structural HWP. Repair and remodelling also seem to be included in the estimate. A detailed analysis of Skog’s (2008) approach and why it is concluded that he calculated all solid wood in US single-family and multi-family houses, including structural and non-structural HWP and HWP for repair and remodeling is presented in Appendix B.2.  In order to compare Skog’s (2008) estimation to ours, non-structural HWP and HWP used for renovation need to be excluded. Figure 5-2 presents the breakdown of the HWP in use pool with a focus on the hierarchy of solid wood products used in houses. This conceptual breakdown was used to adjust the estimation of HWP pools via wood product allocation. The detailed adjustments made to Skog’s (2008) values are presented in Appendix B.2.  Figure 5-2 The hierarchical breakdown of the HWP in use pool Wilson’s (2006) estimate and Skog’s (2008) adjusted value were compared to our estimates and the differences are discussed in Section 5.4.5. The US Environmental Protection Agency (US EPA)’s National Inventory Report (NIR) (US EPA, 2013) used Skog (2008)’s estimate of the HWP pool size in 2001 to calibrate the WOODCARB II model and, using this methodology, it reported the pool of HWP in use using the Production Approach. Because the production and Stock Change Approaches account for exports and imports differently, this value may not be compared directly to the estimate determined in this thesis. Adjusting the result from a Production Approach to a value from a Stock Change Approach requires a knowledge of the raw import and export data which was not provided by the US EPA. Since the US EPA uses the same half-lives and WOODCARB II model as Skog (2008), it has been assumed here that a comparison between this study and Skog’s (2008) results may be used to indicate whether the HWP contribution reported by the US EPA is an under- or over-estimate. 73  5.2.4 Assumptions In order to conduct the analyses undertaken in this chapter, two assumptions were made and they are summarized below. The assumptions made earlier in this thesis to calculate the half-lives also apply to this chapter. Assumption 5-1: the structural HWP used in housing have the same half-life as houses.  The structural HWP usually remain in the house until it is demolished, so it has been assumed that the decay pattern of single-family and multi-family houses apples to the structural HWP used to build the houses. On the other hand, non-structural HWP such as hardwood lumber and non-structural panels are used mainly as interior decorative materials and are unlikely to last as long as the structural components of the houses. Therefore, non-structural HWP have been assumed to have a different, and shorter, half-live than houses.  Assumption 5-2: the annual HWP carbon input goes into the housing carbon pool at the end of each year. The annual input carbon fluxes to houses may be assumed to follow one of two patterns: continuous constant inflow or instantaneous inflow. The continuous constant inflow pattern assumes that the annual carbon input goes into the pool continuously and constantly throughout the year. The instantaneous inflow assumes that the carbon input occurs discretely at a single point of time, e.g. the beginning of the year, the middle of the year or the end of the year. The simplicity of the FOD model enables both discrete and continuous inflow patterns to be used. For example, the IPCC recommends the continuous constant inflow (Pingoud and Wagner, 2006; IPCC, 2014). In this case, the decay of new carbon input starts within the year and Equation 5-5 becomes:  𝑃𝑃𝑡𝑡 = 𝑃𝑃𝑡𝑡−1𝑒𝑒−𝑑𝑑𝑛𝑛2/𝑡𝑡1/2 + (� 𝐶𝐶0(𝜆𝜆′)𝑒𝑒−𝑑𝑑𝑛𝑛2/𝑡𝑡1/2×(1−𝑡𝑡′)𝑑𝑑𝜆𝜆′10) Equation 5-5  Equation 5-5 can be simplified to:  𝑃𝑃𝑡𝑡 = 𝑃𝑃𝑡𝑡−1𝑒𝑒−𝑑𝑑𝑛𝑛2/𝑡𝑡1/2 + 𝐶𝐶0,𝑡𝑡1− 𝑒𝑒−𝑑𝑑𝑛𝑛2/𝑡𝑡1/2𝑙𝑙𝑙𝑙2/𝜆𝜆1/2 Equation 5-6  However, the greater complexity of the other models used in this analysis makes it difficult to integrate the continuous constant inflow approach into a manageable equation. Therefore the instantaneous inflow assumption is more suitable as a first approximation.  The HWP consumption data have been reported annually and the values include the consumption for the whole year (McKeever and Howard, 2011). It has therefore been assumed that an instantaneous inflow that occurs at the end of the year based on the way that the consumption 74  data have been reported. This assumption implies that the decay of a new input during the year is negligible. As shown by the half-life estimation in Chapter 3, houses initially decay slowly and little change may be anticipated during the first year. This assumption was therefore not expected to significantly affect the accuracy of the housing HWP pool estimates. 5.3 Results 5.3.1 Structural HWP pool of US single-family and multi-family houses The structural HWP pools in US single-family and multi-family houses built from 1900 to 2009 calculated using the different housing decay models are presented in Figure 5-3. All curves, other than the grey line, were plotted using the six models mentioned in Section 5.2.1 with the parameters either fitted to the AggFOD or the half-life equivalent to the AggFOD. The grey curve describes the carbon stock arising from using the FOD model with the IPCC default half-lives (Tier 2 method).  Figure 5-3 Carbon pool sizes of structural HWP in US single-family and multi-family houses from 1900 to 2009 determined using the six decay models plus the default IPCC Tier 2 method The structural HWP pool sizes determined by each model in 2001, 2003 and 2009 are presented in Table 5-2. The pool sizes in 2001, 2003 and 2009 were also estimated in other published literature and, as part of the validation process, the values are compared in Section 5.4.5. The shapes of the curves presented in Figure 5-3 are discussed in Sections 5.4.1, 5.4.4 and 5.4.5. 01002003004005006007008001900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000Pool size (Tg C)YearGamma (SF+MF,2.07,80.2) Logistic (SF+MF,149)3-segment (SF+MF,138) FOD (SF+MF,137)Linear (SF+MF,137) Instant (SF+MF,137)FOD (SF+MF,IPCC)75  Table 5-2 The size of the carbon pool of structural HWP in US single-family and multi-family houses in 2001, 2003, 2005 and 2009 determined by the six decay models plus the default IPCC Tier 2 method  Carbon stock size by year (Tg C) Decay model used 2001 2003 2009 Gamma (SF+MF, 2.07, 80.2) 577 605 668 Logistic (SF+MF, 149) 565 593 655 three-segment (SF+MF, 138) 559 587 648 FOD (SF+MF, 137) 532 558 614 Linear (SF+MF, 137) 548 575 634 Instant (SF+MF, 137) 615 646 721 FOD (SF+MF, IPCC) 365 380 404  5.3.2 Structural HWP pool of US mobile homes The structural HWP pool in US mobile homes built from 1950 to 2009 determined by the different housing decay models are presented in Figure 5-4. Reliable data on mobile home starts prior to 1950 were not available. All curves, other than the grey line, were plotted using the six models mentioned in Section 5.2.1. The grey curve describes the carbon stock arising from using the FOD model with the default IPCC Tier 2 half-lives. The results presented in Figure 5-3 are discussed in Section 5.4.2. 5.3.3 Constant mass input scenario Figure 5-5a shows the HWP pool size for US single-family and multi-family houses under the constant input scenario assuming a fixed and equal annual input of 7 Tg C to the pool. The IPCC default half-life was used to plot the grey curve in Figure 5-5a. The other curves were plotted using the half-lives or decay parameters determined in Section 3.3.2. Figure 5-5b shows the HWP pool size for US mobile homes under the same constant input scenario of a fixed and equal annual input of 7 Tg C to the pool. The same annual inputs were used for Figure 5-5 a and b to ensure that the earlier separation of curves was not caused by a difference in inputs and therefore reflected the impacts of the models and the half-lives. The half-lives or decay parameters of the US mobile homes were determined in Section 4.3.1. The results presented in Figure 5-5 are discussed in Section 5.4.3. 76   Figure 5-4 Carbon pool size of structural HWP in US mobile homes aggregated from 1950 to 2009 determined by the six decay models plus the IPCC Tier 2 method  Figure 5-5 Stock of structural HWP versus time for US single-family (SF) and multi-family (MF) houses and mobile homes (MH) assuming a constant mass input scenario of 7 Tg C/year. The red vertical line in Figure 5-5a shows the 109-year study period of Figure 5-3. 051015202530351950 1960 1970 1980 1990 2000Pool size (Tg C)YearGamma (MH,1.95,23.7) Logistic (MH,42)3-segment (MH,35) FOD (MH,44)Linear (MH,44) Instant (MH,44)FOD (MH,IPCC)0200400600800100012001400160018000 200 400 600 800 1000Pool size (Tg C)Yeara. SF+MF, 7 Tg CGamma (SF+MF,2.07,80.2)Logistic (SF+MF,149)3-segment (SF+MF,138)FOD (SF+MF,137)Linear (SF+MF,137)Instant (SF+MF,137)FOD (SF+MF,IPCC)0200400600800100012001400160018000 200 400 600 800 1000Pool size (Tg C)Yearb. MH, 7 Tg CGamma (MH,1.95,23.7)Logistic (MH,42)3-segment (MH,35)FOD (MH,44)Linear (MH,44)Instant (MH,44)77  5.4 Discussion The results presented in Section 5.3 are discussed in the following sequence. Initially, the sizes and rates of increase in the HWP pools of single- and multi-family houses and mobile homes are considered. Sections 5.4.1 and 5.4.2, show that the HWP in use pools associated with US houses are still increasing in size and have not reached steady state conditions. In order to explore the potential HWP pool size and time to saturation under long term input conditions, a constant mass input scenario equivalent to the construction of about 1 million houses annually is evaluated. Finally, the most suitable models for assessing the HWP pool in single- and multi-family houses and mobile homes in the US are presented. The validation of the size of each of these pools is then considered. 5.4.1 Structural HWP pool size estimated for US single-family and multi-family houses The model outputs indicate that a substantial amount of carbon was retained in US single-family and multi-family houses and that this pool had been increasing since 1900 (Figure 5-3). Between 1900 and 1945, the pool increased steadily and slowly at the rate of about 1.55 Tg C/year. There was a clear change in the rate of increase in the pool after 1945, which marked the end of the World War II and the start of an economic boom in the US (French, 1997). The slope between 1945 and 2006 is about 10 Tg C/year, which is about a 6 fold increase in rate compared with the earlier period. The slope of the curves decreased after 2006 and the absolute pool size estimated by the FOD (SF+MF, IPCC) model decreased after 2007 because shorter half-lives were used. These do not necessarily mean that the pool has begun to saturate but is likely to be due to the recent Global Financial Crisis (DPAD, 2013). As the US economy recovers and the rate of house construction the slope may be expected to increase once again. The curves representing the seven models all reveal the same general shape (Figure 5-3). Except for the FOD (IPCC) model, the values for the six other models were relatively close to each other and they estimated the carbon stock in US single-family and multi-family houses to be about 668±53.4 Tg C. In this assessment, the FOD (SF+MF, IPCC) model resulted in HWP pool size estimate that was approximately 40% lower than the average of the other models, primarily due to the use of an inappropriately short half-life. The IPCC only provides average values for the half-lives of wood products in use. However, it is reasonable to expect that structural sawnwood and panels in houses have longer half-lives than the default average IPCC values. This study has indicated that half-life categorization based on the end uses of the products is likely to be more accurate than an approach based on generalized product half-lives. However, this study also acknowledges that it is challenging to acquire good data that enables the accurate determination half-lives of products based on end uses other than houses.  78  Among the six other models, the FOD (SF+MF, 137) model provided the most conservative assessment of the HWP pool, whereas the Instant (SF+MF, 137) model afforded the least conservative estimate (Figure 5-3). The results also demonstrated that over the 109 year period studied, the use of an accurate half-life is more important than the selection of the most suitable model, but note the discussion in Section 5.4.3 about the importance of model shape when exploring longer study periods. This point is demonstrated by considering the HWP pool sizes in 2009 estimated by the various models (Table 5-2). The FOD (SF+MF, IPCC) model determined a pool size of 404 Tg C which was 66% of the value of 614 Tg C estimated by the FOD (SF+MF, 137) model. In contrast, the pool size quantified by the FOD (SF+MF, 137) model was 8% less than the Gamma (SF+MF, 2.07, 80.2) model, which had an equivalent half-life of 140 years. In Section 5.4.4, it will be shown that the Gamma (SF+MF, 2.07, 80.2) model is the preferred choice for quantifying the HWP pool in single-family and multi-family houses in the US. If the IPCC default half-lives were closer to the real values, which may be the case for some HWP, it is possible that choosing the most suitable models is more important than selecting the more accurate half-life.  The use of the methodology developed in this thesis will help the Annex 1 countries to the Framework Convention on Climate Change more accurately complete their National Inventory Reports. Commencing in 2015, these countries are required to report their annual national GHG inventories from 1990 to the most recent year by quantifying the emissions and removals of direct GHGs from six sectors, including land-use, land-use change and forestry and waste (UNFCCC, 2006). It is likely that in the near future, HWP stock changes may be included in national inventory reports. The significance of using this approach may be highlighted by considering the data over the period 1990- 2013 in Figure 5-3. This time-frame represents the reporting period for an Annex 1 nation. Over this period, the stock change determined using the Gamma model (SF+MF, 2.07, 80.2) was 216 Tg C whereas the stock change estimated using the FOD model (SF+MF, IPCC) was 103 Tg C (Figure 5-3). Therefore, using the IPCC default product half-life and the first order decay model to directly estimate the stock change of structural HWP in residential houses may lead to a substantial underestimation. The substantial differences between these values is likely to incentivize Annex 1 countries with large HWP in-use pools to use the methodology developed in this study as a component of their annual national inventory reports.  5.4.2 Structural HWP pool size estimated for US mobile homes The pool size of structural HWP in mobile homes was estimated by most models to be within the range 22-26 Tg C in 2009 (Figure 5-4), which is approximately 4% of the value of single-family and multi-family houses in that year. The curves in Figure 5-4 increase relatively steadily. However, because the half-life of mobile homes are shorter than single-family and multi-family houses, the net sequestration rate is more influenced by the fluctuation in the annual consumption of HWP. A decrease in rate and, for some models, an absolute decrease in pool size also occurred around 2007 as a result of the Global Financial Crisis (Figure 5-4). As mentioned earlier, these results do 79  not necessarily mean that the pool has begun to saturate. As the US economy recovers, the rate of HWP deposition may be expected to increase once again. The average rate of increase between 1970 and 2007 was about 0.8 Tg C/year or 8% of that for single-family and multi-family houses. The previously published HWP pool estimates have usually quantified HWP in single-family and multi-family houses separately from other end uses and the HWP pool for mobile homes has usually been included in the “other end uses” category. The reason for this categorization is due to the half-life of mobile homes being much shorter than that for single-family and multi-family houses and it is reasonably close to the half-life of HWP for several other end uses. The IPCC default half-lives are 35 years for sawnwood and 25 years for panels (IPCC, 2014). The half-life of mobile homes estimated in this study is 44 years (Section 4.3.1). As shown in Figure 5-4, the difference between the estimates using the six decay models and that using the FOD (MH, IPCC) model is about 3.4 Tg C in 2009 or approximately 13% of the mobile home HWP pool. The US EPA’s calibrated half-life for solid wood in end uses other than single-family and multi-family construction is 38 years (Skog, 2008; US EPA, 2013). This value may be a blended value that includes HWP in mobile homes. Using this half-life value in an FOD model reduced the difference in 2009 to 2.2 Tg C or approximately 8% of the mobile home HWP pool. These results therefore justify that the grouping of the HWP pool in mobile homes with HWP in the other end uses category. A higher rate of increase indicates a faster net sequestration of carbon and thus a larger pool of HWP is created over the same time span. A steadily increasing carbon pool indicates the existence of continuous carbon sequestration and that the housing HWP carbon pool acts as an ongoing sink. However, the time spans of the available data constrained the analyses to 109 years for single-family and multi-family houses and 59 years for mobile homes. From scientific and policy perspectives, it is important to understand the longer term behaviour of these pools as sinks or sources of carbon. The limited time span of this study is further discussed in Section 5.4.3 and the analyses are extended beyond these periods using a scenario analysis to cover substantially longer periods in order to assess the long-term behaviour of these pools. 5.4.3 Constant mass input scenario The study periods of 109 years (from 1900 to 2009) for single-family and multi-family houses and a 59 year period (from 1950 to 2009) for mobile homes are relatively short time spans compared to their half-lives of 137 and 44 years respectively and, as mentioned earlier, there is little evidence that these HWP pools have reached equilibrium carbon storage. The ultimate differences among the various decay models are only revealed when they are run for a longer period. The curves in Figure 5-5 demonstrate that the structural HWP pool in houses is likely to sequester carbon for a period of several centuries and, if managed appropriately, it could serve as a substantial long-term carbon pool. The saturation size was estimated to be about 1.2 Pg C and the 80  sequestration duration approximately 750 years (Figure 5-5). These numbers vary when different decay models are used. A summary of the saturation size and sink duration calculated by different decay models under the constant input scenario used here is presented in the first two columns of Table 5-3. The pool sizes in year 105 under the constant input scenario and the pool sizes in 2005 using the actual HWP consumption data are also shown in the third and fourth columns of this table. The year 2005 is the point when the increase rate of the pool began to slow down due to the Global Financial Crisis. The ratios between the pool sizes estimated in 2005 in Figure 5-3 and pool sizes estimated by the constant input scenario in year 105 presented in the last column of Table 5-3. This ratio indicates the validity of the constant input assumption to the reality over the compared time span. As shown by the last column of Table 5-3, the ratios are all close to 1, which infers that the constant input assumption is valid over the time span of 105 years. In a qualitative sense, the constant input scenario may provide a useful indication of how these pools may function in the longer term. However, it should be noted that whether or when the pool will saturate in the future depends on how the net annual carbon input varies and on future changes in half-lives. Table 5-3 A summary of the saturation pool sizes and sink durations calculated by the different decay models under a constant input scenario in Figure 5-5a and the relationship between the constant input scenario to the actual HWP consumption data Decay models Approx. saturation size (Tg C) Approx. sequestration duration (years) A: HWP pool size in year 105 (Tg C) (Figure 5-5a) B: HWP pool size in 2005 (Tg C) (Figure 5-3) 𝐵𝐵𝐴𝐴 Gamma (SF+MF, 2.07, 80.2) 1165 755 636 637 1.00 Logistic (SF+MF, 149) 1125 693 628 624 1.00 three-segment (SF+MF, 138) >1715 >1000 624 618 0.990 FOD (SF+MF, 137) 1378 1000 576 588 1.02 Linear (SF+MF, 137) 963 273 600 605 1.01 Instant (SF+MF, 137) 959 137 742 682 0.919 FOD (SF+MF, IPCC) 337 338 300 398 1.32  This observation indicates that policies that increase the use of structural wood products, in place of more carbon intensive products, should be encouraged. If annual inputs of HWP to residential and non-residential buildings were maintained at a uniform rate, these pools could potentially to act as carbon sinks for centuries and, conceptually, if the annual HWP inputs could be steadily increased and the half-lives do not decrease, these pools may never saturate. 81  The previous study period of 109 years is represented by the red vertical line in Figure 5-5a.  Comparing the relative closeness of the other curves to the grey curve on the left of the red line confirms that when dealing with a relatively short time frame, under these study conditions, the selection of an accurate half-life is more important than the choice of the best model. This point is demonstrated by considering the pool sizes in year 105 estimated by the various models (Table 5-3). The FOD (SF+MF, IPCC) model which used a half-life of 35 years for sawnwood and 25 years for panels determined a pool size of 300 Tg C which was 52% of the value of 576 Tg C estimated by the FOD (SF+MF, 137) model. In contrast, the pool size quantified by the FOD (SF+MF, 137) model was 9% less than the Gamma (SF+MF, 2.07, 80.2) model, which had an equivalent half-life of 140 years. Five of the six models studied only begin to diverge around 250 to 300 years or about twice the half-life of 137 years. The instant (SF+MF, 137) model begins to diverge from the others at an earlier point of about 0.5 of the half-life. When dealing with shorter-lived end-use HWP, such as mobile homes, this divergence happens earlier. The separation point in Figure 5-5b is around 80 to 120 years or 2.3 times the half-life of 44 years. This indicates that when dealing with a relatively greater time period under these study conditions, using the most appropriate decay model plays a more important role on both pool size and sink duration than the half-life. This point is demonstrated by considering the pool sizes estimated by the various models after a millennium (Table 5-3). The pool size predicted by the FOD (SF+MF, 137) model was 15% more than the Gamma (SF+MF, 2.07, 80.2) model, 18% more than the Logistic (SF+MF, 149) model, 20% less than the three-segment (SF+MF, 138) model, and 30% more than the Linear (SF+MF, 137) and Instant (SF+MF, 137) models. The term “relatively greater time period” means the time length of the study period compare to the length of half-life of the product studied. The longer the product half-life, the longer it takes for the divergence of the curves to occur. In the case of US single-family and multi-family houses and mobile homes, choosing the appropriate half-life plays a more important role when the time span is less than twice the half-life and selecting the best decay model plays a more important role when the time span is greater than twice the half-life. 5.4.4 Comparison of models for the US single-family and multi-family houses Seven different models were assessed under two different circumstances. First, the models were used to estimate the HWP pools in single- and multi-family houses and mobile homes using actual data. Second, due to the relatively short time period of this first assessment, each model was run using a long-term constant annual carbon mass input scenario. The suitability of each model was evaluated using the following criteria: • Adequacy of fit to the housing decay data presented in Chapter 3. • Conservatism. If two models had a similar adequacy of fit to the housing data, the model that provided the smaller estimation of the pool size or the faster decay rate was preferred 82  because it reduced the risk of overestimating the HWP pool size and thus underreporting HWP emissions. • Ease of use. The ease of use depends on the complexity of a decay model. Generally, a linear model is simpler than a nonlinear model. A nonlinear model that can be transformed into a linear model is simpler than a model that cannot. A model with fewer parameters is simpler than a model with more. A model with fewer segments, meaning lower number of formulas to describe, is simpler than a model with more. • Flexibility. A model is considered more flexible when the shape and scale of the curves plotted using different model parameters can change flexibly or, more specifically, the model can be converted to other models by making the parameters equal to specific values. A comparison of decay models for the US single-family and multi-family houses based on the criteria described above is presented in Table 5-4.  Table 5-4 A comparison of decay models for the US single-family and multi-family houses based on the criteria described in Section 5.4.4 Decay models Adequacy of fit Conservatism Ease of use Flexibility Final score FOD (SF+MF, 137) - +/- ++ -- - FOD (SF+MF, IPCC) -- ++ ++ -- +/- Instant (SF+MF, 137) - -/+ + - - Linear (SF+MF, 137) - ++ + - + Three-segment (SF+MF, 138) + - - - -- Logistic (SF+MF, 149) ++ + ---/+ ++/- ++ Gamma (SF+MF, 2.07, 80.2) +++ + -- + +++ Key: a minus sign means a negative assessment and a plus sign means a positive assessment. The number of signs indicates the level of negativity/positivity. The plus-minus or minus-plus sign means the negativity or positivity depends on the time span of study. The FOD (SF+MF, 137) and FOD (SF+MF, IPCC) did not adequately describe the decay pattern of US single-family and multi-family houses, as demonstrated in Section 3.4. When the time span considered was less than two times the half-life, the FOD (SF+MF, 137) model provided the most conservative estimate of the HWP pool size (Figure 5-3). However, when the time span was beyond 2 times the half-life, the FOD (SF+MF, 137) model no longer provided the most conservative assessment (Figure 5-5a). The FOD (SF+MF, IPCC) was conservative at all times but substantially underestimated the potential HWP pool in single-family and multi-family houses. The first order decay model is one of the simplest decay models but it is also less flexible, as demonstrated in Chapter 2. 83  The instant (SF+MF, 137) model did not provide an adequate fit, as demonstrated in Figure 3-7b, as it underestimated the ability of HWP in use to retain carbon at time periods longer than the half-life. It was not conservative at time periods less than the half-life because it assumes that no decay occurred prior to the half-life. It was one of the simplest decay models used but it was also less flexible, as demonstrated in Chapter 2. This model may be used when dealing with micro-situations such as a few houses. However, when conducting national-level estimation of the carbon pool, because the true service lives (half-lives) of houses vary with time, this model is inappropriate. The linear (SF+MF, 137) model did not provide an adequate fit, as demonstrated in Figure 3-7b, because it underestimated the ability of HWP to retain carbon in the long term. It provided conservative estimates (Figure 5-3 and Figure 5-5) and was one of the simplest decay models, as demonstrated in Chapter 2. The model itself was not flexible but if combined to form a hybrid model, like the one presented in Figure 2-4, it may be able to provide an acceptable estimation of HWP pool sizes. However, a hybrid model will compromise the ease of use of this model to some extent. The three-segment (SF+MF, 138) model provided an acceptable fit, as demonstrated in Figure 3-7a. However, it did not provide a conservative estimation of the HWP pool size when the model was run for longer time periods (Figure 5-5a). This was because the decay rate calculated using the third segment formula was too slow. In addition, this model was not easy to use due to the complexity and number of formulas and it is not a flexible model, as demonstrated in Chapter 2. The logistic (SF+MF, 149) model provided excellent fit to the housing data (Figure 3-7a). The model also provided fair conservatism when estimating the pool size (Figure 5-3 and Figure 5-5). The logistic decay model has four parameters but usually three of them act as constants. When only one parameter is used, the model is less flexible but it was still better than most of the other decay models evaluated. When all four parameters were used, this model was the most flexible of the seven decay models assessed in this study, but under these conditions the ease of use was compromised. The logistic decay model could also be converted to a near-FOD or a near-linear model when making the parameters equal to specific values. The Gamma (SF+MF, 2.07, 80.7) model provided the best fit to the housing data (Figure 3-7a). This model also provided reasonable conservatism when estimating the pool size (Figure 5-3 and Figure 5-5). The Gamma distribution model has two parameters and was one of the most flexible decay models evaluated. The Gamma model can be converted to a FOD or a near-linear decay model when making the parameters equal to specific values. The model is relatively complex compared to the other models discussed in this study. However, the Gamma distribution model was considered to be the best overall model, as presented by the final score in the last column of Table 5-4, and it is therefore recommended to be used when estimating the HWP pool in US single-family and multi-family houses. 84  5.4.5 Validation of the HWP pool size estimates for US single-family and multi-family houses As described in Section 5.2.3, several estimates of the HWP in use pool size for the US have been published. A summary of three previously published values of HWP in use pools and the approaches they used are presented in Table 5-5.  The sections below compare the results of these three investigations with the findings of our study. This thesis has calculated values for the pool of structural HWP in US single-family and multi-family houses. These values therefore include both domestically produced HWP and imported HWP which are consumed in US houses. This methodology is equivalent to the Stock Change Approach presented in the IPCC Guidelines (IPCC, 2014). In Section 5.4.4, the Gamma (SF+MF, 2.07, 80.7) model was selected as the preferred choice for quantifying the HWP pool in single-family and multi-family houses in the US. The findings of our study therefore will use the results estimated by the Gamma (SF+MF, 2.07, 80.7) model. Table 5-5 A summary of the published estimates of HWP in use pool for the US and those estimated in this study Study Pool quantified Approach Half-life (years) Year Estimated stock size (Tg C) Wilson, 2006 Structural HWP Stock change 80 2003 528 Skog, 2008 (WOODCARB II) Structural + non-structural HWP + repair and remodeling Stock change SF: 78.0~85.9* MF: 47.6~52.4 2001 682 (415)† US EPA, 2013 HWP in use (domestic + export) Production approach SF: 78.0~85.9 MF: 47.6~52.4 2001 1395 This thesis (Gamma) Structural HWP Stock change 140 (equivalent) 2001 577 2003 605 _______________________________ * Skog (2008) and US EPA (2013) used variable half-lives for houses built in different periods because older houses exhibited shorter half-lives than younger houses (see Section 3.4). † The number in the brackets is the stock size excluding non-structural HWP and repair and remodeling. The detailed adjustment method is described in Appendix B.2.  Wilson (2006) reported that the structural HWP pool in single-family and multi-family houses in 2003 was 528 Tg C which is 13% smaller than our estimation (Table 5-5). He undertook a quick estimation of this HWP pool by multiplying the number of single-family and multi-family houses by the average HWP carbon content per house.  A detailed description of Wilson’s (2006) calculation method is presented in Appendix B.1 and the key elements are compared in Table 5-6. The major variation between the two studies is due to the use of different data inputs. Wilson (2006) did not 85  specify how he obtained his structural HWP carbon content per house. He used the American Housing Survey data to estimate the number of houses remaining. The American Housing Survey provides a projected national value based on survey answers that were collected from a restricted sampling of selected cities and the numbers obtained are considered to be less accurate than those derived from housing starts determined by the US Census Bureau (Appendix B.1). The data sources used in this thesis are highly transparent and are considered to be more reliable. Issues relating to data source reliability and transparency are further discussed in Appendix B.1. Skog (2008)’s estimation using the US WOODCARB II model includes non-structural HWP and HWP used for repair and remodeling and his value must be adjusted in order to compare with the results presented in this thesis. The detailed adjustment method is described in Section 5.2.3 and Appendix B.2. Skog (2008)’s pool size of 415 Tg C of structural HWP used in single-family and multi-family houses after the adjustment is 28% smaller than our estimation (Table 5-5). This difference is primarily due to the difference in half-life estimations with the half-lives estimated by Skog (2008) being about 40% less than the Gamma (SF+MF, 2.07, 80.7) model values used in this thesis. If combining the results of Wilson (2006) and Skog (2008), our estimation is about 20% larger. Table 5-6 A comparison of the HWP carbon pools in 2003 estimated by Wilson (2006) and this study’s Gamma (SF+MF, 2.07, 80.2) model  Wilson (2006) This thesis, Gamma (SF+MF, 2.07, 80.2) Pool size (Tg C) 528 605 Housing stock, 2003 120.6 million 96.8 million Carbon content/house (kg C/house) 4380 6245  The US Environmental Protection Agency (US EPA)’s National Inventory Report (US EPA, 2013) reported the pool of HWP in use using Production Approach to be 1,395 Tg C (Table 5-5). This value may not be compared directly to our estimate as indicated in Section 5.2.3. However, since the US EPA uses the same half-lives and decay model as Skog (2008) and the half-life value calculated in this thesis was about 40% is higher than the adjusted half-life values of Skog (2008), it is likely that the HWP contribution reported by the US EPA is an underestimate of the actual value. A detailed comparison of the results of Skog (2008) and US EPA (2013) is presented in Appendix C. 5.5 Conclusions The structural HWP in houses can retain a significant amount of carbon for a substantial period and, in the United States, the size of this HWP pool has been increasing steadily. The pool of structural HWP in US single-family and multi-family houses was estimated to be 668 Tg C in 2009 86  and, under constant input conditions, this pool was forecast to saturate in about 750 years and while this long-term estimate is conceptual and highly uncertain, it does demonstrate that with current rates of construction and half-lives the HWP pool in US houses could increase for many decades.  Structural HWP acting as long-term carbon sinks offers the potential to create policies that stimulate increased use of wood in buildings, to further enhance carbon storage in HWP pools for many decades into the future. When the carbon stock size estimation is for a relatively short period (i.e. less than 2 times the half-life in the case of US houses), an accurate estimation of the half-life is more important than choosing the best model. When dealing with a relatively longer time frame (i.e. beyond 2 times the half-life in the case of US houses), the accuracy of the decay model plays a more important role on the estimation of both the pool size and the sink duration.  The gamma distribution model is recommended as the best model to quantify the carbon pool of structural HWP in residential houses in the United States. A comparison of published estimates of the structural HWP in use pools in the US houses with the results presented in this thesis showed that the published estimates probably underestimated the true pool size by 20%.   87  Chapter 6 Conclusions and future research 6.1 Conclusions An analysis of the decay pattern of US single- and multi-family houses revealed that younger houses decayed more slowly than older houses and it is highly likely that the long-term decay pattern of these houses follows an inverse sigmoidal shape. A single first order decay model, which is the recommended IPCC default methodology, predicts that young houses exhibit a more rapid decay rate than older houses and it cannot therefore adequately describe the real decay pattern of US houses. A new method, termed “regression-aggregation-fit”, was developed to address this constraint. The first order decay model was used to estimate the apparent half-lives of houses constructed over a series of relatively short time periods. The apparent half-lives determined using linear regression varied with the age of the houses with older houses exhibiting shorter apparent half-lives than newer houses. These apparent half-lives were then be used to develop an aggregated first order decay (AggFOD) curve which adequately represented the actual decay pattern of US single- and multi-family houses. Using a sum of least squares method, the Gamma distribution model was shown to adequately describe the decay curve. The best fit for this distribution to the decay curve for US single- and multi-family houses over a time period of 300 years was achieved with α equal to 2.07 and β equal to 80.2. This model estimated an equivalent end-use half-life of 140 years for houses and the 95% decay point was 390 years. This end-use half-life is longer than most of the previously published half-lives for US family homes and substantially greater than the IPCC default product half-life values for sawnwood and wood-based panels. This longer half-life is likely to affect the accuracy of previous estimates of the US HWP in use pool. Such long half-lives will also incentivize nations with large HWP in use pools to apply Tier 3 methodology for the estimation of their carbon dynamics. The “regression-aggregation-fit” method was applied to other data sets, as demonstrated by its use for US mobile homes and Canadian and Norwegian residential houses. Uncertainties and limitations exist in Canadian data and the “regression-aggregation-fit” method is very sensitive with small data sets. Ideally, large amounts of data containing accurate and temporally consistent information should be used. The half-life and 95% decay point of US mobile homes were determined to be 44 and 98 years, respectively. For Canadian residential houses, the equivalent values were 92 and 260 years and for Norwegian residential houses, they were 146 and 481 years. While the decay rates and patterns of US single- and multi-family houses and Norwegian residential houses were similar, the decay rate of Canadian residential houses was more rapid than in both of these nations, although it followed a similar shape.  The Gamma distribution model also provided a good description of the decay pattern of Canadian and Norwegian residential houses. Although the logistic decay model had the best fit to the decay 88  curve for US mobile homes, the Gamma distribution model was considered to provide an adequate description of this decay curve. Taking into account the model’s adequacy, conservatism, ease of use and flexibility, the Gamma distribution was recommended as the most appropriate generalized model for describing the decay pattern of houses. The structural HWP in houses were shown to retain a significant amount of carbon for a substantial period. The structural HWP in US single-family and multi-family houses steadily increased between 1900 and 2009. By 2009, the pool of was estimated to have reached 668 Tg C and, under constant input conditions, this pool was forecast to saturate in about 750 years. Although this long-term estimate is conceptual and uncertain due to the constant input constraint, it does demonstrate that with current rates of construction, wood consumption rates per square metre and present half-lives, the HWP pool in US houses is likely to increase quite substantially for many decades.  This study showed that when modelling the decay of houses over a relatively short period (e.g. less than 2 times the half-life in the case of US houses), an accurate estimation of the half-life was more important than choosing the best model. In contract, when models were run over a longer time frame (e.g. beyond 2 times the half-life in the case of US houses), the accuracy of the decay model played a more important role in the estimation of both the pool size and the sink duration.  Since 2015, the 2006 IPCC Guidelines have come to effect and Annex 1 nations to the Framework Convention on Climate Change are now required to report on HWP emissions or contributions (IPCC, 2006; UNFCCC, 2006). This study has developed a methodology to more accurately quantify stock changes associated with the structural HWP in use pool and this approach should be of great interest to Annex 1 countries with substantial structural wood processing industries and a tradition of building wooden houses.  6.2 Strengths and Weaknesses A major strength of this research is that the decay pattern of houses was estimated in a transparent manner. The data used in the analyses are publicly available and the methodology used has been presented clearly. The approach developed in this thesis can be applied to any country that reports housing units remaining data by periods of construction. Using published, quantitative data that are verifiable, this study showed that the Gamma distribution provided an adequate description of the decay pattern of residential houses. However, as for any regression analysis, a major weakness of the “regression-aggregation-fit” methodology was the uncertainty that arose when handling the data for the youngest and oldest houses in the data sets. Assumptions were made to attribute the earliest known apparent half-life to all younger houses and to extrapolate the last known apparent half-life to all older houses. Therefore, this method has limitations in adequately dealing with houses that were built recently or long ago. Moreover, the housing units remaining data were collected from one survey period to 89  the next in a temporal sequence, so these results may be autocorrelated. First- to tenth-order autocorrelations were investigated but they were unable to describe the time series pattern observed in this study. Autocorrelation was not further investigated in this thesis with the consequence that uncertainty analyses could not be conducted. The Gamma distribution model was selected as the recommended model. However, the Gamma distribution model could not be directly fitted to the raw housing units remaining data by periods of construction to determine the apparent half-lives, as was done with the FOD model. This constraint arose because the Gamma distribution model has two parameters and it cannot be transformed into a linear model. A larger data set would be required to enable the statistical packages SAS® 9.4 or Microsoft® Excel 2013 to find a viable solution within a suitable time frame. 6.3 Future research The “regression-aggregate-fit” method developed in this study is a compromised approach. Ideally, as mentioned in Section 6.2, the Gamma distribution model should be fitted directly to the raw housing unit remaining data. However, this approach requires reliable historical data that preferably date back further than the half-life value. For example, in the case of US single- and multi-family houses, the half-life is about 140 years so ideally reliable survey information dating from 1875 should be available. Unfortunately, the oldest age category for US houses was for the period ‘1919 or earlier’ which created an effective age category of 94 years. For countries like Canada and Norway collected housing data more frequently would also considerably improve the accuracy of the estimation. In combination with more historical and frequently collected data, the ideal minimum number of data points for each period of construction was estimated to be 100.  The accuracy of the estimates could also be improved by using higher quality data. Survey data from, for example, the American Housing Survey and the National Household Survey in Canada, have the risk of perpetuating data collection errors such as incomplete data, incorrect values and sampling errors. In North America, municipalities usually keep records on the building and demolition permits issued within their jurisdiction as well as detailed property information. Although national-level statistics may not be available on demolition permits and the cost of compiling the records of all municipalities may be prohibitive, collecting data from several major cities and projecting the results to the national-level may be a possible sampling based solution. Due to confidentiality, privacy and security reasons, these data may not always be available to the public. However, it may still be possible for governments to acquire detailed and higher quality data and use these for national reporting. The models developed in this thesis utilised end-use half-lives rather than the product half-lives suggested by the IPCC. A product half-life is considered to be a weighted average blended value based on the production proportion of a series of end-use half-lives. However, it is uncertain whether a blended value will mathematically generate the same results as the separate end-use 90  values. Also, because the decay patterns of structural HWP in houses and HWP for other end uses are likely to be different, it seems unlikely that such a blended approach will adequately represent reality. Further research on the development of several end-use specific half-lives for important categories of wood products used by society is warranted.   When using the results of this study in national-level carbon accounting frameworks several other factors require further investigation, especially when using the Production Approach,. This approach requires that nations account for the decay of products that they export to other countries and, if Tier 3 methodology is used, adequate models for the decay of the major wood product categories would be needed. For example, Canada exports wood products to the US, Japan and China and other countries. Under the Production Approach, Canada is responsible for reporting the emissions and stocks of the exported wood and ideally the decay of these products should be modelled using transparent and verifiable methods. In order to accomplish this objective, suitable models, such as those outlined in this thesis, should be developed for the major wood product end uses in the major three or four nations that import Canadian wood products.  The HWP in use pool is a flow-through pool, meaning that much of the carbon does not go to the atmosphere directly. The carbon in the housing stock is transferred to other pools with a range of half-lives. For example, structural wood products removed from houses may be recycled, burned or sent to landfills. Understanding the fate of the carbon associated with each of these activities is also worthy of further investigation.    91  References Apps, M. J., Kurz, W. A., Beukema, S. J. and Bhatti, J. S. (1999) ‘Carbon budget of the Canadian forest product sector’, Environmental Science & Policy, 2(1), pp. 25-41. doi: 10.1016/S1462-9011(99)00006-4. The Athena Institute (2004) Minnesota Demolition Survey: Phase Two Report, Prepared for Forintek Canada Corp, 21 pp. Available at: http://www.athenasmi.org/wp-content/uploads/2012/01/Demolition_Survey.pdf (Accessed: March 20, 2013).  Bache-Andreassen, L. (2009) Harvested wood products in the context of climate change - A comparison of different models and approaches for the Norwegian greenhouse gas inventory. Oslo-Kongsvinger: Statistics Norway, 70 pp. Available at: https://www.etde.org/etdeweb/details_open.jsp?osti_id=967560 (Accessed: November 14, 2012). BC Stats (1991) 1991 Census of Population and Housing. Victoria, B.C: Statistics Canada. Available at: http://www.bcstats.gov.bc.ca/StatisticsBySubject/Census/1991Census.aspx (Accessed: March 20, 2013). Bellassen, V. and Luyssaert, S. (2014) ‘Managing forests in uncertain times’, Nature, 506(Febuary), pp. 153–158. doi: 10.1038/506153a. Bowyer, J., Bratkovich, S., Howe, J. and Fernholz, K. (2010) Recognition of Carbon Storage in Harvested Wood Products: A Post-Copenhagen Update. Minneapolis, USA: Dovetail Partners Inc., 19 pp. Bowyer, J., Bratkovich, S., Frank, M., Fernholz, K., Howe, J. and Stai, S. (2011) Managing Forests for Carbon Mitigation. Minneapolis, MN, 15 pp. Available at: http://www.dovetailinc.org/report_pdfs/2011/dovetailmanagingforestcarbon1011.pdf (Accessed: November 19, 2014). Computing in the Humanities and Social Sciences (CHASS) (2013) CHASS Data Centre/Census of Canada public use microdata. Available at: http://sda.chass.utoronto.ca/sdaweb/html/canpumf.htm (Accessed: November 19, 2014). Computing in the Humanities and Social Sciences (CHASS) (2014) CHASS DATA CENTER/Canadian Census Analyser. Available at: http://dc.chass.utoronto.ca/census/ (Accessed: November 20, 2014). Development Policy and Analysis Division (DPAD) (2013) World Economic Situation and Prospects 2013. Update as of Mid-2013. New York, NY: United Nations, Sales No. E.13.11.C.2, 17 pp. 92  Eggers, T. (2002) The impacts of manufacturing and utilisation of wood products on the European carbon budget. Jeonsuu, Finland: European Forest Institute, Internal Report 9, 89 pp. Available at: http://www.efi.int/files/attachments/publications/ir_09.pdf (Accessed: February 28, 2014). Eliasson, P., Svensson, M., Olsson, M. and Ågren, G. I. (2013) ‘Forest carbon balances at the landscape scale investigated with the Q model and the CoupModel - Responses to intensified harvests’, Forest Ecology and Management. Elsevier B.V., 290, pp. 67–78. doi: 10.1016/j.foreco.2012.09.007. Ford-Robertson, J. (2003) Implications of harvested wood products accounting: Analysis of issues raised by Parties to the UNFCCC and development of a simple decay approach. Wellington, New Zealand: Ministry of Agriculture and Forestry, 30 pp. Available at: http://maxa.maf.govt.nz/forestry/publications/harvested-wood-products-accounting/harvested-wood-products-accounting-technical-paper.pdf (Accessed: November 17, 2012). French, M. (1997) US Economic History Since 1945. Manchester, UK: Manchester University Press, 236 pp. Green, C., Avitabile, V., Farrell, E. P. and Byrne, K. A. (2006) ‘Reporting harvested wood products in national greenhouse gas inventories: Implications for Ireland’, Biomass and Bioenergy, 30(2), pp. 105–114. doi: 10.1016/j.biombioe.2005.11.001. Hashimoto, S. and Moriguchi, Y. (2004) Data Book: Material and Carbon Flow of Harvested Wood in Japan. Tsukuba, Ibaraki, Japan: the Center for Global Environmental Research, National Institute for Environmental Studies. ISSN 1341-4356. 40 pp. Available at: http://www-cger.nies.go.jp/ (Accessed: November 19, 2014). Helin, T., Sokka, L., Soimakallio, S., Pingoud, K. and Pajula, T. (2013) ‘Approaches for inclusion of forest carbon cycle in life cycle assessment - A review’, GCB Bioenergy. John Wiley & Sons Ltd, 5, pp. 475–486. doi: 10.1111/gcbb.12016. Ingerson, A. (2009) Wood Products and Carbon Storage: Can Increased Production Help Solve the Climate Crisis?. Washington, D.C.: The Wilderness Society, 47 pp. Available at: http://wilderness.org/content/wood-products-and-carbon-storage (Accessed: November 15, 2012). Intergovernmental Panel on Climate Change (IPCC) (1997) Chapter 5: Land-Use Change & Forestry, Reference Manual (Volume 3). Revised 1996 IPCC Guidelines for National Greenhouse Gas Inventories. Mexico City, 74 pp. Available at: http://www.ipcc-nggip.iges.or.jp/public/gl/invs1.html (Accessed: November 15, 2012). Intergovernmental Panel on Climate Change (IPCC) (2000) ‘Afforestation, Reforestation, and Deforestation (ARD) Activities’, in Watson, R. T., Noble, I. R., Bolin, B., Ravindranath, N. H., Verardo, D. J., and Dokken, D. J. (eds) Land Use, Land-Use Change and Forestry. Cambridge, UK: 93  Cambridge University Press, 375 pp. Available at: http://www.ipcc.ch/ipccreports/sres/land_use/index.php?idp=151 (Accessed: November 19, 2014). Intergovernmental Panel on Climate Change (IPCC) (2006) 2006 IPCC Guidelines for National Greenhouse Gas Inventories, Eggleston, S., Buendia, L., Miwa, K., Ngara, T., and Tanabe, K. (eds). Hayama, Japan: Institute for Global Environmental Strategies (IGES). Available at: http://www.ipcc-nggip.iges.or.jp/public/2006gl/ (Accessed: November 19, 2014). Intergovernmental Panel on Climate Change (IPCC) (2007a) Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K.B., Tignor, M., and Miller, H.L. (eds). Cambridge, United Kingdom and New York, NY, USA: Cambridge University Press, 996 pp. Intergovernmental Panel on Climate Change (IPCC) (2007b) Climate Change 2007: Mitigation. Contribution of Working Group III to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Metz, B., Davidson, O.R., Bosch, P.R., Dave, R., and Meyer, L.A. (eds), Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 851 pp. Intergovernmental Panel on Climate Change (IPCC) (2013) Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, Stocker, T.F., Qin., D., Plattner, G.-K., Tignor, M., Allen, S.K., Boschung, J., Nauels, A., Xia, Y., Bex, V. and Midgley, P.M. (eds). Cambridge, United Kingdom and New York, NY, USA: Cambridge University Press, 1535 pp. Intergovernmental Panel on Climate Change (IPCC) (2014) 2013 Revised Supplementary Methods and Good Practice Guidance Arising from the Kyoto Protocol, Hiraishi, T., Krug, T., Tanabe, K., Srivastava, N., Jamsranjav, B., Fukuda, M., and Troxler, T. G. (eds). Switzerland: IPCC. Available at: http://www.ipcc-nggip.iges.or.jp/public/kpsg/ (Accessed: November 19, 2014). Karjalainen, T., Kellomoki, S. and Pussinen, A. (1994) ‘Role of Wood-Based products in Absorbing Atmospheric Carbon’, Silva Fennica, 28(2), pp. 67–80. Kurz, W. A., Apps, M. J., Webb, T. M. and McNamee, P. J. (1992) The Carbon Budget of the Canadian Forest Sector: Phase I. Edmonton, AB: Canadian Forest Service, Northwest Region, Northern Forestry Centre, 93 pp. Information Report NOR-X-326, ISBN 0-662-19913-8. Lemprière, T. C., Kurz, W. a, Hogg, E. H., Schmoll, C., Rampley, G. J., Yemshanov, D., Mckenney, D. W., Gilsenan, R., Beatch, A., Blain, D., Bhatti, J. S. and Krcmar, E. (2013) ‘Canadian boreal forests and climate change mitigation’, Environmental Reviews, 21(4), pp. 293–321. doi: 10.1139/er-2013-0039. 94  Lippke, B., Oneil, E., Harrison, R., Skog, K., Gustavsson, L. and Sathre, R. (2011) ‘Life cycle impacts of forest management and wood utilization on carbon mitigation: knowns and unknowns’, Future Science: Carbon Management, 2(3), pp. 303–333. doi: 10.4155/cmt.11.24. Luyssaert, S., Ciais, P., Piao, S. L., Schulze, E. D., Jung, M., Zaehle, S., Schelhaas, M. J., Reichstein, M., Churkina, G., Papale, D., Abril, G., Beer, C., Grace, J., Loustau, D., Matteucci, G., Magnani, F., Nabuurs, G. J., Verbeeck, H., Sulkava, M., van der Werf, G. R. and Janssens, I. a. (2010) ‘The European carbon balance. Part 3: Forests’, Global Change Biology, 16, pp. 1429–1450. doi: 10.1111/j.1365-2486.2009.02056.x. McFarlane, P. and Sands, R. (2013) ‘Wood and paper products’, in Sands, R. (ed.) Forestry in a Global Context. 2nd edn. Wallingford, UK: CABI Publishing, pp. 77–97. Malmsheimer, R. W., Bowyer, J. L., Fried, J. S., Gee, E., Izlar, R. L., Miner, R. A., Munn, I. A., Oneil, E., Stewart, W. C. and ABSTRACT (2011) ‘Managing Forests because Carbon Matters: Integrating Energy, Products, and Land Management Policy’, Journal of Forestry, 109(7S), pp. S7–S50. Marland, E. and Marland, G. (2003) ‘The treatment of long-lived, carbon-containing products in inventories of carbon dioxide emissions to the atmosphere’, Environmental Science and Policy, pp. 139–152. doi: 10.1016/S1462-9011(03)00003-0. Marland, E. S., Stellar, K. and Marland, G. H. (2010) ‘A distributed approach to accounting for carbon in wood products’, Mitigation and Adaptation Strategies for Global Change, 15(1), pp. 71–91. doi: 10.1007/s11027-009-9205-6. McKeever, D. B. and Howard, J. L. (2011) Solid wood timber products consumption in major end uses in the United States, 1950 – 2009; A Technical Document Supporting the Forest Service 2010 RPA Assessment. General Technical Report FPL-GTR-199. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory, 41 pp. Milakovsky, B., Frey, B. and James, T. (2012) ‘Carbon Dynamics in the Boreal Forest’, in Mark S. Ashton, Mary L. Tyrrell, Deborah Spalding, B. G. (ed.) Managing Forest Carbon in a Changing Climate. Springer Netherlands, pp. 109–135. doi: 10.1007/978-94-007-2232-3. Miner, R. (2006) ‘The 100-Year Method for Forecasting Carbon Sequestration in Forest Products in Use’, Mitigation and Adaptation Strategies for Global Change. doi: 10.1007/s11027-006-4496-3. 20 pp. Pan, Y., Birdsey, R. A., Fang, J., Houghton, R., Kauppi, P. E., Kurz, W. A., Phillips, O. L., Shvidenko, A., Lewis, S. L., Canadell, J. G., Ciais, P., Jackson, R. B., Pacala, S. W., McGuire, A. D., Piao, S., Rautiainen, A., Sitch, S. and Hayes, D. (2011) ‘A large and persistent carbon sink in the world’s forests’, Science (New York, N.Y.), 333(August), pp. 988–993. doi: 10.1126/science.1201609. 95  Perez-Garcia, J., Lippke, B., Comnick, J. and Manriquez, C. (2005) ‘An assessment of carbon pools, storage, and wood products market substitution using life-cycle analysis results’, Wood and Fiber Science, 37(Corrim Special Issue), pp. 140–148. Available at: http://swst.metapress.com/index/V361873872VK17W3.pdf (Accessed: October 25, 2012). Peters, G. P., Marland, G., Le Quéré, C., Boden, T., Canadell, J. G. and Raupach, M. R. (2011) ‘Rapid growth in CO2 emissions after the 2008–2009 global financial crisis’, Nature Climate Change, pp. 2–4. doi: 10.1038/nclimate1332. Pingoud, K., Perälä, A., Soimakallio, S. and Pussinen, A. (2003) Greenhouse gas impacts of harvested wood products. Evaluation and development of methods, VTT RESEARCH NOTES 2189. VTT, Finland: VTT Technical Research Centre of Finland, 120 pp. +app. 16 pp. Available at: http://www.vtt.fi/inf/pdf/tiedotteet/2003/T2189.pdf (Accessed: November 14, 2012). Pingoud, K. and Wagner, F. (2006) ‘Methane emissions from landfills and carbon dynamics of harvested wood products: The first-order decay revisited’, Mitigation and Adaptation Strategies for Global Change, 11(5-6), pp. 961–978. doi: 10.1007/s11027-006-9029-6. Row, C. and Phelps, R. (1990) ‘Tracing the flow of carbon through the US forest products sector’, in Proceedings of the 19th World Congress of the International Union of Forest Research Organizations. 13 pp. Row, C. and Phelps, R. (1996) ‘Wood carbon flows and storage after timber harvest’, in Sampson, R. N. and Hair, D. (eds) Forests and Global Change: Vol. II. Forest Management Opportunities for Mitigating and Adapting to Climate Change. Washington, DC: American Forests, pp. 27–58. Rutherford, E. (1900) ‘A Radioactive Substance Emitted from Thorium Compounds’, Philosophical Magazine, 5(49), pp. 1–14. doi: 10.1080/14786440009463821. Available at: http://www.chemteam.info/Chem-History/Rutherford-half-life.html (Accessed: October 19, 2013). Sathre, R. and O’Connor, J. (2010) ‘Meta-analysis of greenhouse gas displacement factors of wood product substitution’, Environmental Science & Policy. Elsevier Ltd, 13(2), pp. 104–114. doi: 10.1016/j.envsci.2009.12.005.  Sianchuk, R., Ackom, E. and McFarlane, P. (2012) ‘Determining stocks and flows of structural wood products in single family homes in the United States between 1950 and 2010’, Forest Products Journal, 62(12), pp. 90–101. Sikkema, R., Schelhaas, M. J. and Nabuurs, G. J. (2002) International Carbon Accounting of Harvested Wood Products: Evaluation of two models for the quantification of wood product related emissions and removals. Contribution of the Netherlands to the International Collaborative Study. RIVM, National Institute of Public Health and the Environment, 83 pp. 96  Skog, K. E. (2008) ‘Sequestration of carbon in harvested wood products for the United States’, Forest Products Journal, 58(6), pp. 56–72. Available at: http://www.freepatentsonline.com/article/Forest-Products-Journal/181115599.html (Accessed: November 14, 2012). Statistics Canada (1998) 1996 Census of Canada: Electronic Area Profiles, 1996 Census. Available at: http://www12.statcan.gc.ca/english/census96/data/profiles/Rp-eng.cfm?LANG=E&APATH=3&DETAIL=0&DIM=0&FL=A&FREE=0&GC=0&GID=0&GK=0&GRP=1&PID=35782&PRID=0&PTYPE=3&S=0&SHOWALL=0&SUB=0&Temporal=1996&THEME=34&VID=0&VNAMEE=&VNAMEF= (Accessed: November 19, 2014). Statistics Canada (2002) 2001 Census of Canada: Topic-based tabulations, 2001 Census. Available at: http://www12.statcan.ca/english/census01/products/standard/themes/Rp-eng.cfm?LANG=E&APATH=3&DETAIL=0&DIM=0&FL=A&FREE=0&GC=0&GID=0&GK=0&GRP=1&PID=56035&PRID=0&PTYPE=55430,53293,55440,55496,71090&S=0&SHOWALL=0&SUB=0&Temporal=2001&THEME=40&VID=0&VNAMEE=&VNAM (Accessed: November 19, 2014). Statistics Canada (2007) 2006 Census of Canada: Topic-based tabulations, 2006 Census. Available at: http://www12.statcan.gc.ca/census-recensement/2006/dp-pd/tbt/Rp-eng.cfm?LANG=E&APATH=3&DETAIL=0&DIM=0&FL=A&FREE=0&GC=0&GID=0&GK=0&GRP=1&PID=89062&PRID=0&PTYPE=88971,97154&S=0&SHOWALL=0&SUB=0&Temporal=2006&THEME=69&VID=0&VNAMEE=&VNAMEF= (Accessed: November 19, 2014). Statistics Canada (2013) National Household Survey User Guide. Minister of Industry. Available at: http://www5.statcan.gc.ca/olc-cel/olc.action?ObjId=99-001-x2011001&ObjType=46&lang=en&limit=0 (Accessed: November 19, 2014). Statistics Norway (2005) Dwellings, by year of construction and type of building. Occupants and occupants per dwelling, by year of construction. 1980, 1990 and 2001. Available at: http://www.ssb.no/a/english/kortnavn/fobbolig_en/tab-2002-09-23-07-en.html (Accessed: November 20, 2014). Statistics Norway (2013) Population and housing census, dwellings, 19 November 2011, Table 7. Available at: http://www.ssb.no/en/befolkning/statistikker/fobbolig/hvert-10-aar/2013-02-26?fane=tabell#content (Accessed: November 20, 2014). United Nations Framework Convention on Climate Change (UNFCCC) (2003). Estimation, Reporting and Accounting of Harvested Wood Products. Technical paper. FCCC/TP/2003/7, 27 October. 44 pp. Available at: http://unfccc.int/resource/docs/tp/tp0307.pdf (Accessed: June 20, 2012).  United Nations Framework Convention on Climate Change (UNFCCC) (2006). Updated UNFCCC reporting guidelines on annual inventories following incorporation of the provisions of decision 14/CP.11. FCCC/SBSTA/2006/9. Twenty-fifth session Nairobi, 6-14 November. 93 pp. 97  U.S. Census Bureau (2010) Statistical Abstract of the United States: 2011. 130th ed. Washington, DC. Available at: http://www.census.gov/compendia/statab/2011/2011edition.html (Accessed: July 20, 2013). U.S. Department of Agriculture (USDA), Forest Service (2012) Future of America’s Forests and Rangelands-Forest Service 2010 Resources Planning Act Assessment. Gen. Tech. Rep. WO-87. Washington, D.C., 198 pp. U.S. Department of Commerce (USDOC) (1940) Census of Housing: 1940, 1950, 1960, 1970, 1980, Census of Housing. Available at: http://www.census.gov/housing/census/data/units.html (Accessed: January 08, 2015). U.S. Department of Commerce (USDOC) (1988) American Housing Survey for the United States in 1985. Washington, DC. Available at: http://www.census.gov/programs-surveys/ahs/data.1985.html (Accessed: January 20, 2013). U.S. Department of Commerce (USDOC) (2002) American Housing Survey for the United States : 2001. Washington, DC. Available at: http://www.census.gov/programs-surveys/ahs/data.2001.html (Accessed: January 20, 2013). U.S. Department of Commerce (USDOC) (2004) American Housing Survey for the United States: 2003. Washington, DC. Available at: http://www.census.gov/programs-surveys/ahs/data.2003.html (Accessed: January 20, 2013). U.S. Department of Commerce (USDOC) (2013) New Residential Construction, New Residential Construction. Available at: http://www.census.gov/const/www/newresconstindex.html (Accessed: October 26, 2014). U.S. Department of Commerce (USDOC) (2014) American Housing Survey (AHS)-About. Available at: http://www.census.gov/programs-surveys/ahs/about.html (Accessed: October 26, 2014). U.S. Environmental Protection Agency (US EPA) (2004) Inventory of U.S. Greenhouse Gas Emissions and Sinks: 1990-2002. Washinton D.C., 304 pp. Available at: http://www.epa.gov/climatechange/ghgemissions/usinventoryreport/archive.html (Accessed: October 15, 2014). U.S. Environmental Protection Agency (US EPA) (2013) Inventory of U.S. Greenhouse Gas Emissions and Sinks : 1990-2011. EPA 430-R-13-001. Washington, D.C., 505 pp. Available at: http://www.epa.gov/climatechange/ghgemissions/usinventoryreport/archive.html (Accessed: January 08, 2015). Wilson, F. L. (1968) ‘Fermi’s Theory of Beta Decay’, American Journal of Physics, pp. 1150-1160. doi: 10.1119/1.1974382. Available at: 98  http://scitation.aip.org/content/aapt/journal/ajp/36/12/10.1119/1.1974382 (Accessed: March 08, 2015). Wilson, J. (2006) ‘Using wood products to reduce global warming’, in Forests, Carbon and Climate Change: A Synthesis of Science Findings. Portland: Oregon Forest Resources Institute, pp. 116–129. Available at: http://www.oregon.gov/energy/GBLWRM/docs/forests_carbon_climate_change.pdf (Accessed: January 08, 2012). Winistorfer, P., Chen, Z., Lippke, B. and Stevens, N. (2005) ‘Energy consumption and greenhouse gas emissions related to the use, maintenance, and disposal of a residential structure’, Wood and Fiber Science, 37(Corrim Special Issue), pp. 128–139. Available at: http://swst.metapress.com/index/C1N040X565941T36.pdf (Accessed: March 20, 2013).   99  Appendices Appendix A Housing units remaining by period of construction data used in this paper A.1 US single-family and multi-family houses (Surveys 1985~2013)  US Single-family and multi-family houses, in thousands of standing units ######## discarded values Source: American Housing Survey http://www.census.gov/hhes/www/housing/ahs/nationaldata.html  1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 1919 or earlier 11073 10943 10896 10314 10252 10019 10057 10124 9827 9672 9364 9136 9235 8989 8789 1920-1929 6082 6149 5923 5677 5677 5545 5575 5564 5465 5479 5313 5357 5164 5323 5248 1930-1939 6879 7012 6976 6768 6747 6552 6710 6548 6593 6362 6009 5993 5840 5536 5731 1940-1949 8869 9038 8845 8607 8529 8400 8389 8334 8284 8152 7904 7916 7945 7836 7952 1950-1959 13974 14249 14256 13836 13633 13569 13852 13574 13779 13433 13003 12994 13222 13455 13595 1960-1969 16578 16768 16724 16161 16070 15806 15949 15810 15894 15482 15192 15292 15261 15405 15400 1970-1974 12023 12003 11907 11452 11559 11403 11592 11423 11520 11188 10741 10969 11068 11176 11147 1975-1979 14454 12822 12829 12146 11915 12314 11708 11757 12009 12314 14350 14404 13731 13579 14018 1980-1984 8480 8308 8182 8292 8143 8257 7735 7684 7664 7584 7517 7474 7478 7715 7563 1985-1989 1519 5360 9120 8951 8951 9033 8992 8873 8878 8865 8859 8811 8804 9014 8664 1990-1994  3 2389 5134 7573 7209 7203 7203 7155 7158 7028 7060 7206 6919 1995-1999  986 4591 8360 8883 8851 8830 8794 8821 8948 8613 2000-2004  3119 6237 9194 9152 9158 9250 8969 2005-2009  994 4882 7324 8267 7845 2010-2013  720 2379    100  A.2 US mobile homes (Surveys 1985~2013)  US Single-family and multi-family houses, in thousands of standing units ######## discarded values Source: American Housing Survey http://www.census.gov/hhes/www/housing/ahs/nationaldata.html  1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 1919 or earlier 2 5 0 0 0 0 0 0 0 0 0 0 0 0 0 1920-1929 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1930-1939 4 6 13 15 25 14 62 51 69 60 95 74 63 63 56 1940-1949 35 26 55 26 32 24 39 34 44 32 32 43 54 49 57 1950-1959 240 251 246 243 214 210 235 164 159 127 89 101 92 98 94 1960-1969 1229 1338 1287 1171 1169 1068 1028 891 845 790 663 609 630 631 578 1970-1974 1768 1822 1744 1675 1663 1575 1606 1407 1389 1366 1123 1138 1120 1062 945 1975-1979 1377 1479 1461 1490 1425 1363 1437 1318 1302 1245 1056 992 972 959 986 1980-1984 1249 1129 998 1099 919 1001 1025 1000 993 985 968 969 961 1013 618 1985-1989 193 632 1100 965 879 998 923 899 887 879 889 860 853 927 578 1990-1994     3 299 746 1249 1105 1091 1087 1084 1077 1082 1071 1090 843 1995-1999           146 841 1578 1687 1693 1683 1667 1657 1694 1304 2000-2004                 413 709 908 898 884 914 757 2005-2009                     47 272 413 528 454 2010-2013                           22 107    101  A.3 Canadian residential houses (Surveys 1971~2011) A.3.1 Scenario 1 Canadian residential houses, in standing units  ######## discarded     1971 1981 1986 1991 1996 2001 2006 2011 1920 or earlier 1188200 1279311 1035100 795167 780929 777940 775905 782015 1921-1945 1090300 1583385 1279600 981543 942816 883695 819415 734125 1946-1960 1991800 2659138 2289700 1766345 1,807,700 1819730 1812525 1756965 1961-1970 1676300 2638093 2240900 1837995 1,830,645 1833295 1753170 1757155 1971-1980   3459800 2473930 2,446,710 2460455 2421395 2395555 1981-1990    2163285 2,084,225 2080740 2084135 2112115 1991-1995      887255 894860 874850 1996-2000       820365 833025 2001-2005        1031020 2006-2011        1042425    102  A.3.2 Scenario 2 Canadian residential houses, in standing units  ######## discarded     1971 1981 1986 1991 1996 2001 2006 2011 1920 or earlier 1188200 1279311 1035100 795167 780929 777940 775905 782015 1921-1945 1090300 1583385 1279600 981543 942816 883695 819415 734125 1946-1960 1991800 2659138 2289700 1766345 1,807,700 1819730 1812525 1756965 1961-1970 1676300 2638093 2240900 1837995 1,830,645 1833295 1753170 1757155 1971-1980   3459800 2473930 2,446,710 2460455 2421395 2395555 1981-1990    2163285 2,084,225 2080740 2084135 2112115 1991-1995      887255 894860 874850 1996-2000       820365 833025 2001-2005        1031020 2006-2011        1042425    103  A.3.3 Scenario 3 Canadian residential houses, in standing units  ######## discarded     1971 1981 1986 1991 1996 2001 2006 2011 1920 or earlier 1188200 1279311 1035100 795167 780929 777940 775905 782015 1921-1945 1090300 1583385 1279600 981543 942816 883695 819415 734125 1946-1960 1991800 2659138 2289700 1766345 1,807,700 1819730 1812525 1756965 1961-1970 1676300 2638093 2240900 1837995 1,830,645 1833295 1753170 1757155 1971-1980   3459800 2473930 2,446,710 2460455 2421395 2395555 1981-1990    2163285 2,084,225 2080740 2084135 2112115 1991-1995      887255 894860 874850 1996-2000       820365 833025 2001-2005        1031020 2006-2011        1042425    104  A.3.4 Scenario 4 Canadian residential houses, in standing units  ######## discarded     1971 1981 1986 1991 1996 2001 2006 2011 1920 or earlier 1188200 1279311 1035100 795167 780929 777940 775905 782015 1921-1945 1090300 1583385 1279600 981543 942816 883695 819415 734125 1946-1960 1991800 2659138 2289700 1766345 1,807,700 1819730 1812525 1756965 1961-1970 1676300 2638093 2240900 1837995 1,830,645 1833295 1753170 1757155 1971-1980   3459800 2473930 2,446,710 2460455 2421395 2395555 1981-1990    2163285 2,084,225 2080740 2084135 2112115 1991-1995      887255 894860 874850 1996-2000       820365 833025 2001-2005        1031020 2006-2011        1042425  CHASS-PUMF: http://sda.chass.utoronto.ca/sdaweb/html/canpumf.htm CHASS-Census: http://dc.chass.utoronto.ca/census/ BCStats-Census: 1991: http://www.bcstats.gov.bc.ca/StatisticsBySubject/Census/1991Census/Profiles.aspx Statistics Canada-Census 1996: http://www12.statcan.gc.ca/english/census96/data/profiles/Rp-eng.cfm?LANG=E&APATH=3&DETAIL=0&DIM=0&FL=A&FREE=0&GC=0&GID=0&GK=0&GRP=1&PID=35782&PRID=0&PTYPE=3&S=0&SHOWALL=0&SUB=0&Temporal=1996&THEME=34&VID=0&VNAMEE=&VNAMEF= Statistics Canada-Census 2001: http://www12.statcan.ca/english/census01/products/standard/themes/Rp-eng.cfm?LANG=E&APATH=3&DETAIL=0&DIM=0&FL=A&FREE=0&GC=0&GID=0&GK=0&GRP=1&PID=56035&PRID=0&PTYPE=55430,53293,55440,55496,71090&S=0&SHOWALL=0&SUB=0&Temporal=2001&THEME=40&VID=0&VNAMEE=&VNAMEF= Statistics Canada-Census 2006: http://www12.statcan.gc.ca/census-recensement/2006/dp-pd/tbt/Rp-eng.cfm?LANG=E&APATH=3&DETAIL=0&DIM=0&FL=A&FREE=0&GC=0&GID=0&GK=0&GRP=1&PID=89062&PRID=0&PTYPE=88971,97154&S=0&SHOWALL=0&SUB=0&Temporal=20 Statistics Canada-NHS 2011: http://www12.statcan.gc.ca/nhs-enm/2011/dp-pd/dt-td/Rp-eng.cfm?LANG=E&APATH=3&DETAIL=0&DIM=0&FL=A&FREE=0&GC=0&GID=0&GK=0&GRP=0&PID=106699&PRID=0&PTYPE=105277&S=0&SHOWALL=0&SUB=0&Temporal=2013&THEME=98&VID=0&VNAMEE=&VNAMEF=  105  A.4 Norwegian residential houses (Survey 1980~2011)  Source: Statistics Norway. http://www.ssb.no/en/befolkning/statistikker/fobbolig/hvert-10-aar?fane=arkiv   1980 1990 2001 2011 1920 or earlier 246177 228206 212979 240781 1921-1945 188745 188257 170145 163960 1946-1960 346132 358209 335216 325890 1961-1970 286779 308485 296980 291095 1971-1980 345037 374190 377257 380846 1981-1990   294016 327133 330285 1991-2001     241838 256247 2002-2012       281730   106  Appendix B Detailed analyses of HWP carbon pool size in single-family and multi-family houses estimated by previous publications B.1 Wilson (2006) Wilson (2006) reported that the HWP pool in single-family and multi-family houses in 2003 was 528 Tg C. He calculated this value by using the average carbon mass of structural wood products per house (4,380 kg C/house) multiplied by the number of US houses that still existed in 2003 (120.6 million). In order to explain the difference between Wilson’s estimation and this study’s value, a detailed comparison between Wilson’s estimates and the results from the Gamma (SF+MF, 2.07, 80.2) model is presented in Table 5-6. Wilson (2006) did not provide the source for his use of 4,380 kg wood C/house. The 120.6 million houses remaining in use in 2003 was obtained from the U.S. Department of Housing and Urban Development (HUD), although the reference link provided by Wilson (2006) is outdated. However, it is likely that HUD used the housing number reported by the American Housing Survey 2003 because the data in Appendix A.1 of this thesis add up to the same number (USDOC, 2004). The estimates for HWP pool sizes in 2003 calculated by the seven models evaluated in this study are presented in the second column of Table 5-2. The American Housing Survey estimate of houses remaining is a projected national value based on survey answers that were collected from a restricted sampling of selected cities. Some of the housing remaining numbers for houses built during certain period reported by American Housing Survey were higher than the total housing starts reported of that period (USDOC, 2013). Housing starts reported by US Census are based on building permits issued and thus is more accurate. In contrast, our estimation of the number of houses remaining in 2003 is 96.8 million. This number was calculated from annual housing starts reported by US Census and by assuming that the decay of houses follows Gamma (SF+MF, 2.07, 80.2) model. It should be noted that the American Housing Survey data used in our analysis were only used to determine the decay pattern of houses (Chapter 3). The projection data may not be absolutely accurate, but a series of these projection data may be comparable so that they can be used for decay pattern determination. In addition, the American Housing Survey is the only public available source to our knowledge that reports housing remaining data by period of construction.  If using Wilson’s approach to estimate the pool size, our value of the average carbon content in structural HWP per house in 2003 is 6,245 Kg C/house, which is higher than Wilson’s 4,380 Kg C/house. It should be noted that this value is not the average carbon content per house of houses that constructed in 2003. It is the average of all houses in 2003, despite when they were built. While Wilson’s estimate had no source, our estimate was derived from the consumption and floor area data reported by McKeever and Howard (2011) and estimated by Sianchuk, Ackom and McFarlane (2012) which justifies that our estimation of the pool size is more reliable. 107  B.2 Skog (2008) Skog (2008) used Equation B-1 to estimate the carbon pool in single-family and multi-family houses in the US in 2001 in order to calibrate the half-lives in the US WOODCARB II model. The initial value of half-lives that Skog (2008) used were those estimated by Winistorfer et al. (2005). Based on the data source Skog (2008) cited, the HWP consumption for US housing construction data did not distinguish the material origin, whether imported or domestically harvested, which means that the estimate is equivalent to Stock Change Approach. The half-life calibrations were for “solidwood in single-family housing” and “multi-family housing” (Skog, 2008, pp. 61, 64). Therefore, it seems that non-structural HWP has been included in this pool estimation.  𝐶𝐶𝑆𝑆𝑃𝑃+𝑃𝑃𝑃𝑃,2001 =�(𝑁𝑁𝑑𝑑 × 𝐴𝐴𝑜𝑜𝑠𝑠𝑑𝑑𝑎𝑎𝑑𝑑𝑛𝑛𝑎𝑎𝑑𝑑,𝑑𝑑 ×𝐻𝐻 × 𝐶𝐶 ×𝐴𝐴2001𝐴𝐴𝑜𝑜𝑠𝑠𝑑𝑑𝑎𝑎𝑑𝑑𝑛𝑛𝑎𝑎𝑑𝑑,𝑑𝑑)𝑛𝑛𝑑𝑑=1 Equation B-1 where 𝑖𝑖 = 1 𝜆𝜆𝑎𝑎 𝑙𝑙, 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑎𝑎𝑎𝑎𝑒𝑒 𝑎𝑎𝑟𝑟𝑎𝑎𝑎𝑎𝑟𝑟 𝑑𝑑𝑎𝑎𝜆𝜆𝑒𝑒𝑎𝑎𝑎𝑎𝑟𝑟𝑑𝑑 𝑎𝑎𝑙𝑙 ℎ𝑎𝑎𝑎𝑎𝑖𝑖𝑒𝑒𝑖𝑖 𝑟𝑟𝑒𝑒𝑟𝑟𝑎𝑎𝑟𝑟𝜆𝜆𝑒𝑒𝑑𝑑 𝑖𝑖𝑙𝑙 𝐴𝐴𝐻𝐻𝐴𝐴 2001  𝑁𝑁𝑑𝑑  𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑙𝑙𝑎𝑎𝑎𝑎𝑏𝑏𝑒𝑒𝑟𝑟 𝑎𝑎𝑙𝑙 ℎ𝑎𝑎𝑎𝑎𝑖𝑖𝑒𝑒𝑖𝑖 𝑟𝑟𝑒𝑒𝑎𝑎𝑎𝑎𝑖𝑖𝑙𝑙𝑖𝑖𝑙𝑙𝑎𝑎 𝑙𝑙𝑎𝑎𝑟𝑟 ℎ𝑎𝑎𝑎𝑎𝑖𝑖𝑒𝑒𝑖𝑖 𝑖𝑖𝑙𝑙 𝑎𝑎𝑎𝑎𝑒𝑒 𝑎𝑎𝑟𝑟𝑎𝑎𝑎𝑎𝑟𝑟 𝑖𝑖.   𝐴𝐴 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑎𝑎𝑐𝑐𝑒𝑒𝑟𝑟𝑎𝑎𝑎𝑎𝑒𝑒 𝑙𝑙𝑙𝑙𝑎𝑎𝑎𝑎𝑟𝑟 𝑎𝑎𝑟𝑟𝑒𝑒𝑎𝑎. 𝐴𝐴𝑜𝑜𝑠𝑠𝑑𝑑𝑎𝑎𝑑𝑑𝑛𝑛𝑎𝑎𝑑𝑑  𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑎𝑎𝑐𝑐𝑒𝑒𝑟𝑟𝑎𝑎𝑎𝑎𝑒𝑒 𝑙𝑙𝑙𝑙𝑎𝑎𝑎𝑎𝑟𝑟 𝑎𝑎𝑟𝑟𝑒𝑒𝑎𝑎 𝑤𝑤ℎ𝑒𝑒𝑙𝑙 𝑎𝑎𝑟𝑟𝑖𝑖𝑎𝑎𝑖𝑖𝑙𝑙𝑎𝑎𝑙𝑙𝑙𝑙𝑑𝑑 𝑏𝑏𝑎𝑎𝑖𝑖𝑙𝑙𝜆𝜆, 𝐴𝐴2001 𝑖𝑖𝑖𝑖 𝜆𝜆ℎ𝑒𝑒 𝑎𝑎𝑐𝑐𝑒𝑒𝑟𝑟𝑎𝑎𝑎𝑎𝑒𝑒 𝑙𝑙𝑙𝑙𝑎𝑎𝑎𝑎𝑟𝑟 𝑎𝑎𝑟𝑟𝑒𝑒𝑎𝑎 𝑎𝑎𝑙𝑙 ℎ𝑎𝑎𝑎𝑎𝑖𝑖𝑒𝑒𝑖𝑖 𝑖𝑖𝑙𝑙 2001,   𝐻𝐻 𝑖𝑖𝑖𝑖 𝑎𝑎𝑟𝑟𝑖𝑖𝑎𝑎𝑖𝑖𝑙𝑙𝑎𝑎𝑙𝑙 𝑤𝑤𝑎𝑎𝑎𝑎𝑑𝑑 𝑎𝑎𝑖𝑖𝑒𝑒 𝑟𝑟𝑒𝑒𝑟𝑟 𝑙𝑙𝑙𝑙𝑎𝑎𝑎𝑎𝑟𝑟 𝑎𝑎𝑟𝑟𝑒𝑒𝑎𝑎 𝑎𝑎𝑙𝑙𝑖𝑖𝜆𝜆.   𝐶𝐶 𝑖𝑖𝑖𝑖 𝑑𝑑𝑎𝑎𝑟𝑟𝑏𝑏𝑎𝑎𝑙𝑙 𝑟𝑟𝑒𝑒𝑟𝑟 𝑎𝑎𝑙𝑙𝑖𝑖𝜆𝜆 𝑎𝑎𝑙𝑙 𝑤𝑤𝑎𝑎𝑎𝑎𝑑𝑑.   It is unclear why 𝐴𝐴2001𝐴𝐴𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜,𝑜𝑜 was included in Equation B-1. Skog (2008, p. 68) describes the calibration process as:  First, we took the count of houses standing in 2001 by age group and estimated carbon contained in them when they were first built (No. houses × original square meters per house × original wood use per square meter × carbon per unit of wood). Second, we adjusted to estimate of carbon content in 2001 by multiplying by the ratio of average m2 in the houses in 2001 to the average m2 in the houses at the time they were built. The result is an estimated 682 Tg carbon in single-family and multifamily houses in 2001. The WOODCARB II estimate of carbon in housing includes two parts. First, is the part of wood carbon in single-family and multifamily homes (standing in 2001) that was in the homes as originally constructed. Second, is the wood carbon used for residential repair and remodeling that is contained in those homes. These two carbon amounts present in homes in 2001 is influenced by the half-life of each type of home and by the half-life of wood carbon from repair and remodeling. 108  These half-lives were adjusted to have the WOODCARB II estimate match the 682 Tg C estimate using Census data. Since the WOODCARB II model includes wood carbon from repair and remodeling and the WOODCARB II model was forced to have the same results as the independent estimation 682 Tg C, we are guessing  𝐴𝐴2001𝐴𝐴𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜,𝑜𝑜 in Equation B-1 is to include repair and remodeling into the estimation by assuming that the repair and remodeling of houses built before 2001 is to increase the floor area from the average floor area when originally constructed to the average floor area in 2001. This assumption is actually valid as an approximation. Using the floor area data reported by McKeever and Howard (2011), the ratio of average floor area of houses built before 2001 (from 1950 to 2001) to the average floor area of houses built in 2001, ?̅?𝐴𝑏𝑏𝑏𝑏𝑏𝑏𝑜𝑜𝑜𝑜𝑏𝑏 2001𝐴𝐴2001, is 69.6%. The ratio of HWP volume used for single-family and multi-family housing construction to the sum of HWP volume used for single-family and multi-family housing construction and for repair and remodeling from 1950 to 2001, 𝑉𝑉𝑆𝑆𝑆𝑆+𝑀𝑀𝑆𝑆𝑉𝑉𝑆𝑆𝑆𝑆+𝑀𝑀𝑆𝑆+𝑉𝑉𝑜𝑜𝑏𝑏𝑟𝑟𝑜𝑜𝑜𝑜𝑜𝑜 𝑜𝑜𝑜𝑜𝑎𝑎 𝑜𝑜𝑏𝑏𝑟𝑟𝑜𝑜𝑎𝑎𝑏𝑏𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜, is 66.1%. Therefore, we believe that Skog quantified the carbon pool of all solid wood in the US single-family and multi-family houses, which includes structural HWP and non-structural HWP for original construction, and HWP for renovations afterwards. The above text quoted from Skog (2008, p. 68) also implies that the US WOODCARB II model using Stock Change Approach with the calibrated half-lives estimated the carbon pool size of all solid wood in single- and multi-family houses including structural HWP, non-structural HWP and HWP for repair and remodeling to be 682 Tg C in 2001.  In order to compare Skog’s (2008) estimation to ours, non-structural HWP and HWP used for renovation need to be excluded. We tried to re-establish Skog’s (2008) estimate by using the data sources cited in the publication. However, due to uncertainties about the actual raw values Skog (2008) used, we did not calculate out the same value. Figure 5-2 presents the breakdowns of the HWP in use pool with a focus on the hierarchy of solid wood products used in houses. Fortunately, this conceptual breakdown can be used to adjust the estimations via structural wood product allocation. The average proportion of structural and non-structural HWP consumed for new single-family and multi-family housing construction between 1950 and 2009 were 87.5% and 12.5% respectively, and the average proportion of new single-family and multi-family construction and renovation were 69.6% and 30.4% respectively (McKeever and Howard, 2011). Therefore, 682 Tg C was multiplied by 69.6% to exclude renovation and then multiplied by 88% to adjust for the proportion of structural HWP used in single-family and multi-family houses. These adjustments resulted in a stock size of 415 Tg C of structural HWP in 2001.   109  Appendix C Validation of Skog’s (2008) housing pool size estimation of 682 Tg C versus US EPA’s (2013) HWP in use pool size estimation of 1395 Tg C C.1 Introduction Using the Production Approach, the US EPA (2013) reported the cumulative stock size of HWP in use from 1900 to 2001 to be 1395 Tg C, however they did not report a value using the Stock Change Approach.  Skog (2008) estimated the cumulative carbon stock size of US houses from 1900 to 2001 to be 682 Tg C using the Stock Change Approach. In order to compare these numbers the following adjustments need to be made. • Conversion to a common approach:  In this case, the US EPA’s (2013) Production Approach value was converted to an equivalent Stock Change Approach by accounting for the net international trade in wood products. • Accounting for a comparable component of the HWP in use pool: The US EPA (2013) accounted for the entire HWP in use pool while Skog (2008) accounted for the HWP pool in US houses. In this comparison, Skog’s (2008) value was projected to the whole HWP in use pool by accounting for the consumption of all wood products and the half-life impacts on the subcomponents of the HWP in use pool. C.2 Conversion to a common approach The US EPA (2013) has reported the net annual carbon stock change of HWP using Stock Change Approach and Production Approach as part of their national inventory report  (Table C-1) (US EPA, 2013, p. A-354). By aggregating the annual net HWP carbon stock change, the HWP pool size increased by 2635 Tg CO2e between 1990 and 2011 using the Stock Change Approach and by 2287 Tg CO2e from 1990 to 2011 using the Production Approach. The Stock Change Approach estimated a pool size increase over the study period that was about 13% greater than that determined using the Production Approach. This implies that the US was a net importer of wood products from 1990 to 2011. The US EPA (2013) reported the cumulative stock size of HWP in use using the Production Approach from 1900 to 2001 to be 1395 Tg C, but did not report the result of the Stock Change Approach. As a first approximation, the USA EPA’s Production Approach value of 1395 Tg C was converted to an equivalent Stock Change Approach value, by multiplying by 1.13. The resulting estimate of the HWP in use pool using the Stock Change Approach was 1576 Tg C.    110  Table C-1 Net annual carbon stock change of HWP using Stock Change Approach and Production Approach (US EPA, 2013)  Stock Change Approach Production Approach Inventory year (Tg CO2e) (Tg CO2e) 1990 129.6 131.8 1991 116.3 123.8 1992 120 123.8 1993 126.8 120.7 1994 130 122.5 1995 126 118.4 1996 122.3 112.2 1997 131.4 117.3 1998 139.8 114.1 1999 149.4 119.1 2000 143.2 112.9 2001 128.3 93.4 2002 135.6 98.2 2003 134.6 94.8 2004 163 105.3 2005 161.4 105.4 2006 138.6 108.6 2007 115.4 103 2008 73.1 76.3 2009 42.4 54.3 2010 50.6 59.4 2011 57.4 71.7 pool size increase (1990-2011) 2635.2 2287  C.3 Accounting for a comparable component of the HWP in use pool Skog (2008) estimated the cumulative carbon stock size of US houses from 1900 to 2001 to be 682 Tg C using the Stock Change Approach. The HWP in use pool that US EPA quantified includes solid wood products and paper (US EPA, 2013). The solid wood products category used by the US EPA includes HWP in houses and other types of end use (e.g. non-residential construction and furniture). The US Forest Service reported that, in 2006, approximately 47% of the roundwood volume was used to manufacture solid wood 111  products and 53% was used to produce paper products (USDA, 2012). The solidwood products volume breakdown fractions for HWP in houses and other types of end use in the USA from 1950 to 2009 were approximately 53% and 47%, respectively (McKeever and Howard, 2011).  Figure C-1 Breakdown fractions for commodity production and solid wood product end uses in the United States (McKeever and Howard 2011; USDA, 2012) Although the volume breakdowns are known, these fractions cannot be used directly as the coefficient to project the stock size of HWP in houses into the stock size of HWP in use, because each type of the end uses has different half-lives and half-lives have greater impacts on the stock size. Section 5.4.3 has validated that the constant mass input scenario can be used as an indication of reality over the time span of 105 years for US houses. Therefore, the constant mass input scenario was used to provide ratios that quantitatively indicate the impacts of the half-lives on the stock size. The US EPA (2013) and Skog (2008) used the same decay model (i.e. first order decay) and half-life values for HWP. For single-family houses, the half-life was about 80 years; for multi-family houses, about 50 years (Table 2-3); and for renovations, about 25 years (Skog, 2008). Using McKeever and Howard’s (2011) HWP consumption values for single-family houses, multi-family houses and renovations, the blended half-life value for HWP in houses was estimated to be 44 years. The half-life value for other end uses in the models used by Skog (2008) and the US EPA (2013) was 38 years. Because the breakdown fractions of HWP in houses and other end uses were reported to be 53% and 47% respectively (McKeever and Howard, 2011), a constant mass input of 53 Tg C year-1 was 112  assumed for HWP in houses and a constant mass input of 47 Tg C year-1 was assumed for other end uses. To match the time period of 1900 to 2001 used by Skog (2008) and US EPA (2013), the time span of this validation was set as 101 years. The pool size ratio for “HWP in other end uses” divided by “HWP in houses” at 101 years is 0.81 (Figure C-2). Therefore, the estimated carbon stock size of “HWP in other end uses” is 553 Tg C (i.e. 682 Tg C multiply by 0.81) and the carbon stock size of solid wood products is 1235 Tg C (i.e. 682 Tg C plus 553 Tg C).  Figure C-2 Impacts on the pool sizes of different half-lives and consumptions of HWP in houses and other end uses The blended half-life value for HWP in houses is 44 years. The half-life value for other end use is 38 years (Skog, 2008). Using McKeever and Howard’s (2011) HWP consumption ratio for housing construction and other end uses, the blended half-life value for solid wood products (i.e. HWP in houses and HWP in other end uses combined) is 41 years. The half-life value for paper used by Skog (2008) and US EPA (2013) was 2.5 years. Because the breakdown fractions of solid wood products and paper are 47% and 53%, respectively, a constant mass input of 47 Tg C year-1 was assumed for solid wood products and a constant mass input of 53 Tg C year-1 was assumed for paper. The pool size ratio of “HWP in paper” over “HWP in solid wood products” at 101 years is 0.095 (Figure C-3). Therefore, the estimated carbon stock size of “paper” is 118 Tg C (i.e. 1235 Tg C 05001000150020002500300035000 20 40 60 80 100 120 140Pool Size (Tg C)Yearshalf-life = 44 yearsannual constant input = 53 Tg Chalf-life = 38 yearsannual constant input = 47 Tg CABA/B ≈ 0.81113  multiplied by 0.095) and the carbon stock size of HWP in use is 1353 Tg C (i.e. 1235 Tg C plus 118 Tg C).  Figure C.3 Impacts on the pool sizes of different half-lives and consumptions of solid wood products and paper C.4 Comparison of values  The calculations shown above are summarized in Table C-2. The difference between 1353 Tg C which is projected from Skog (2008) and 1576 Tg C which is converted from US EPA (2013) is only 14%. Considering the uncertainty of this validation approach, 14% difference is within the margin of error. US EPA (2013) and Skog (2008) both used the WOODCARB II model to estimate the stock size and the half-life values used are the same. It is reasonable to infer that the US EPA would calculate out the same estimation of 682 Tg C if the stock size of HWP in houses was estimated.  Skog’s (2008) estimation was adjusted to the stock size of structural HWP in houses to be 415 Tg C (Section 5.4.5 and Appendix B.2). The stock size of structural HWP in houses estimated in this thesis 05001000150020002500300035000 20 40 60 80 100 120 140Pool Size (Tg C)Yearshalf-life = 2.5 yearsannual constant input = 53 Tg Chalf-life = 41 yearsannual constant input = 47 Tg CABA/B ≈ 0.095114  is 577 Tg C which is higher than the adjusted value of Skog’s (2008), which implies that the stock size of HWP in use estimated by US EPA (2013) may also be an underestimation. Table C.2 Summary of conversion and projection steps and results  US EPA (2013) Skog (2008) Steps (Tg C) (Tg C) Initial value 1395 (Production Approach, HWP in use) 682 (Stock Change Approach, HWP in houses) Convert to Stock Change Approach 1576 (Stock Change Approach, HWP in use)  Project to solid wood product pool (i.e. add other end uses)  1235 (Stock Change Approach, solid wood products) Project to HWP in use pool (i.e. add paper)  1353 (Stock Change Approach, HWP in use) Comparable values 1576 (Stock Change Approach, HWP in use) 1353 (Stock Change Approach, HWP in use)  115  

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