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Stand structure classification, succession, and mapping using LiDAR Moss, Ian 2012

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STAND STRUCTURE CLASSIFICATION, SUCCESSION, AND MAPPING USING LIDAR by IAN MOSS BSF, The University of British Columbia, 1979 MSc, The University of Georgia, 1988  A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Forestry)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) April 2012 © Ian Moss, 2012  Abstract In this dissertation, a consistent, reasonably precise, verifiable system of stand structure classification was developed and demonstrated. The goal was to provide a foundation for better communication amongst forest management professionals. A novel distance metric and classification algorithm were introduced. The distance metric was based on similarity in reversed cumulative stems and basal area per ha by diameter (DBH; 1.3 m above ground). This distance metric: (1) uses commonly available information; (2) avoids the separation of data into arbitrary DBH classes; and (3) represents a broad range of simple to complex stand structures. Using 421 plots established across a range of Interior Douglas-fir (Pseudotsuga menziesii var. glauca (Beissn.) Franco) and lodgepole pine (Pinus contorta var. latifolia (Engelm.) Critchfield) stands in the Cariboo region of British Columbia, Canada, a 17-class system of classification was constructed. Whole stand statistics, cumulative distributions, and stand structure/distribution indices were used to evaluate the results. The classes were reasonably precise, with meaningful partitions separating single layered versus complex stands. The utility of the classification system was investigated for diagnosing potential patterns of succession. Over 100 simulated stand structure progressions were simulated using plot data input into an individual-tree growth model. Similar progressions in stand structure classes were assigned common pathways. Four general patterns of succession were observed: (1) a high density single layered pathway; (2) a moderate density single layered pathway; (3) a moderate density complex pathway; and (4) a moderate density, mixed complex-single layered pathway. Lastly, the feasibility of using aerial Light Detection and Ranging (LiDAR) for stand structure classification in forest inventory was assessed. LiDAR was reasonably effective in distinguishing structural classes on the basis of cumulative distributions in basal area or gross volume with respect to DBH, but it was less successful when the distributions in numbers of stems per ha were included. Further study using additional LiDAR metrics beyond those used in this study are needed to improve the use of LiDAR for stand structure classification. This stand structure classification system has potential for a wide variety of forest management applications, including improvement of linkages between strategic and tactical planning and implementation.  ii  Preface Chapters 1 and 5 were completed by me, with recommendations from my research committee members (Drs. Valerie LeMay (research supervisor), Peter Marshall, Bruce Larson, and Gary Bradfield). Versions of Chapters 2, 3, and 4 of this dissertation have been prepared as papers for submission. However, none have been published as of yet. The research in Chapter 2 was completed by me (95%), with the following contributions: (1) the permanent plot procedures were developed by D.R. Systems Inc., of Nanaimo, British Columbia (BC), Canada; (2) I designed the temporary plot establishment and measurement procedures, and supervised field crews who did the actual data collection (carried out under contract with Lignum Limited, BC); and (3) compilation of field data into a normalized database was done by me with contributions by Mishtu Banerjee of Scientificals Consulting, BC. Recommendations by committee members on the research and on the dissertation, and by reviewers of a draft paper submitted to the Canadian Journal of Forest Research were incorporated into the chapter.  The background conceptual ideas for Chapters 3 and 4 were jointly conceived with Dr. Valerie LeMay. However, all research in terms of the design, implementation and analysis of the data were completed by me. Dr. LeMay provided substantial editorial recommendations on both Chapters 3 and 4, along with some suggestions for background literature. Recommendations by other committee members were also incorporated into the chapters. Overall, my contribution to these chapters was 90%. Appendix A refers to applications of the research described in Chapters 2 and 3. I had significant involvement (over 75%) in designing, implementing, and reporting on the three projects highlighted therein. Contributions by other consultants and/or forest practitioners are noted in that Appendix.  iii  Table of Contents Abstract .................................................................................................................................... ii Preface ..................................................................................................................................... iii Table of Contents ................................................................................................................... iv List of Tables ........................................................................................................................ viii List of Figures ......................................................................................................................... xi Acknowledgements .............................................................................................................. xiii Dedication .............................................................................................................................. xv Chapter 1:  Introduction ..................................................................................................... 1  1.1  Why Classify ......................................................................................................................... 3  1.2  Approaches to Classification in Forestry .............................................................................. 4  1.3  Seral Stage Development and Classification ........................................................................ 7  1.4  Mapping Stand Structure Classes ....................................................................................... 11  1.5  Systems of Classification: Desirable Features .................................................................... 12  1.6  Objectives of Dissertation ................................................................................................... 13  Chapter 2:  A Quantitative Technique for Stand Structure Classification ................. 14  2.1  Introduction ......................................................................................................................... 14  2.2  Description of the Stand Structure Classification Algorithm.............................................. 17  2.2.1  Distance Metric............................................................................................................... 19  2.2.2  Number of Classes .......................................................................................................... 20  2.2.3  Separation of Observations into Classes......................................................................... 21  2.2.4  Validation and Efficacy of the Resulting Classification ................................................. 22  2.2.5  Assessment of the Classification Algorithm Relative to Desired Criteria ...................... 23  2.3  Application to a Forest Area ............................................................................................... 24  2.3.1  Forest Area Description .................................................................................................. 24  2.3.2  Data Description ............................................................................................................. 25  2.3.3  Stand Structure Classes................................................................................................... 26  2.4  Discussion ........................................................................................................................... 32  2.5  Conclusions ......................................................................................................................... 37  iv  Chapter 3:  Using Stand Structure Classes to Predict Ecological Succession Pathways ........................................................................................................ 39  3.1  Introduction ......................................................................................................................... 39  3.2  Material and Methods ......................................................................................................... 43  3.2.1  Study Area Description................................................................................................... 43  3.2.2  Data and Stand Structure Progressions ........................................................................... 45  3.2.2.1  Permanent Sample Plot Data.................................................................................. 45  3.2.2.2  Initial Stand Structure Classes ............................................................................... 45  3.2.2.3  Forecasts of Plot Data and Assigning Stand Structure Classes .............................. 47  3.2.2.4  Potential Succession Pathways and Cluster Analysis ............................................ 47  3.2.2.5  Examining Pathways for Differences .................................................................... 48  3.3  Results ................................................................................................................................. 48  3.3.1  Plot Data ......................................................................................................................... 48  3.3.2  Potential Succession Pathways ....................................................................................... 48  3.3.3  Cluster Analysis .............................................................................................................. 52  3.3.4  Detailed Examination of Succession Pathways .............................................................. 54  3.3.4.1  SSC 4 ..................................................................................................................... 54  3.3.4.2  SSC 3 ..................................................................................................................... 56  3.3.4.3  Overall Observation ............................................................................................... 58  3.3.5  Stand Structure, Growth and Yield ................................................................................. 59  3.4  Discussion ........................................................................................................................... 62  3.5  Conclusions ......................................................................................................................... 67  Chapter 4:  Stand Structure Classification Using Airborne LiDAR Data ................... 69  4.1  Introduction ......................................................................................................................... 69  4.2  Materials and Methods ........................................................................................................ 71  4.2.1  Study Area Description................................................................................................... 71  4.2.2  Data................................................................................................................................. 72  4.2.2.1  Ground Data ........................................................................................................... 72  4.2.2.2  LiDAR Data ........................................................................................................... 73  4.2.3  Data Compilation ............................................................................................................ 74  4.2.3.1  Ground Data ........................................................................................................... 74  4.2.3.2  LiDAR Data ........................................................................................................... 76  4.2.4  Statistical Analyses ......................................................................................................... 77 v  4.2.4.1  Correlations Between LiDAR and Ground Variables ............................................ 77  4.2.4.2  Variation of LiDAR Variables by Stand Structure Class....................................... 78  4.2.4.3  Stand Structure Classes Using Cluster Analysis of LiDAR Data .......................... 78  4.2.4.4  Predicting Ground Stand Structure Classes Using LiDAR Variables.................... 79  4.2.4.5  Influence of Different Numbers of Classes on Classification Success Rate .......... 80  4.3  Results ................................................................................................................................. 81  4.3.1  Ground Data ................................................................................................................... 81  4.3.2  Correlations Between LiDAR and Ground Variables .................................................... 81  4.3.3  Variation in LiDAR Variables by Stand Structure Class ............................................... 87  4.3.4  Stand Structure Classes Using Clustering of LiDAR Data ............................................. 87  4.3.5  Predicting Stand Structure Classes Using Ground Calibrated LiDAR ........................... 90  Variables ...................................................................................................................................... 90 4.3.6  Influence of Different Numbers of Classes .................................................................... 98  4.4  Discussion ........................................................................................................................... 99  4.5  Conclusions ....................................................................................................................... 105  Chapter 5: 5.1  Conclusions .................................................................................................. 106  Contributions to Knowledge ............................................................................................. 106  5.1.1  Summary ....................................................................................................................... 106  5.1.2  Chapter 2 Synopsis: Research Conclusions and Implications ...................................... 106  5.1.3  Chapter 3 Synopsis: Research Conclusions and Implications ...................................... 110  5.1.4  Chapter 4 Synopsis: Research Conclusions and Implications ...................................... 113  5.2  Project Strengths and Limitations ..................................................................................... 115  5.2.1  Primary Strengths of Project ......................................................................................... 115  5.2.2  Project Scope and Limitations ...................................................................................... 116  5.3  Future Research and Development ................................................................................... 117  5.3.1  Development of Classification Support Tools .............................................................. 117  5.3.2  Incorporating Tree Species into the System of Classification ...................................... 118  5.3.3  Spatial Considerations .................................................................................................. 119  5.3.4  Rescaling Classification Variables ............................................................................... 120  5.3.5  Additional Research Topics .......................................................................................... 121  5.4  Concluding Remarks ......................................................................................................... 121  References ............................................................................................................................ 123  vi  Appendices ........................................................................................................................... 144 Appendix A A Graphical Summary of 17 Stand Structure Classes ............................................... 144 Appendix B Applications of Stand Structure Classification in Forest Resources Management .... 153  vii  List of Tables Table 2.1. Study area summary statistics for quadratic mean diameter (QMD), Lorey’s mean height (LMH), number of stems per ha (SPH), basal area per ha (G) and volume per ha (VPH) (n=421 plots). .............................................................................................................. 26  Table 2.2. Number of plots, stems per ha, and basal area per ha by stand structure class using the new stand structure classification system. ............................................................... 27  Table 2.3. Number of plots, stems per ha, and basal area per ha by stand structure class using the k-means clustering. ........................................................................................................... 33  Table 3.1. Number of measurements (N1), number of plots (N2), and plot statistics (minimum (Min), mean (Mean) and maximum (Max)) for stems per ha (SPH > 0 cm DBH), basal area per ha (G; m2 ha-1) and Lorey’s mean tree height (HT; m) by initial stand structure class (SSC). ............................................................................................................................. 49  Table 3.2. Number of plots by initial stand structure class and succession pathway (SP). Stand structure classes generally represent: single-layered stands (1 to 11); multi-layered or complex stands (13 to 17); and intermediate structures (12). ................................................. 53  Table 3.3. Plots and associated successional pathways (SP) that started in or passed through stand structure class 4 in the PrognosisBC simulations, and the number of years that each plot stayed in each stand structure class before proceeding to the next class to the right. Stand structure classes generally represent: single-layered stands (1 to 11); multi-layered or complex stands (13 to 17); and intermediate structures (12). ................................................. 55 Table 3.4. Mean (and standard deviation) for basal area (G; m2ha-1) and stems per ha (SPH; ha-1), and number of simulated growth cycles (5-yr projections, N) in stand structure class 4 by succession pathway (SP 3 or 4) and by species (FD=Douglas-fir PL=lodgepole pine (PL), and Other=other species).. ...................................................................................................... 56  viii  Table 3.5. Average number of years and proportion of plots (1.00 represents all plots, also shown in bold, and a blank indicates no plots) by stand structure class (SSC) and succession pathway (SP) for plots (N) starting or passing through as stand structure class 3. ................. 57  Table 4.1. Summary statistics for pine (P), spruce/fir (S), and deciduous (D) species groups, where: H6 is Lorey’s mean tree height (m) for all stems  6 cm dbh; N6 is the stems ha-1; G6 is basal area (m2 ha-1); DG6 is quadratic mean diameter (cm); VG is total volume (m3 ha-1); and VM is merchantable volume (m3 ha-1). (n=189 ground plots). ........................................ 82  Table 4.2. Numbers of plots by stand structure class (SSCLASS) for pine (P), spruce/fir (S), deciduous (D) and all species combined. ................................................................................ 83  Table 4.3. Pearson correlations (r) between ground variables, including the ranked transformed basal area (RG6) and stems (RN6) per ha above 6 cm DBH (see Table 1 for a description of remaining variables) versus LiDAR variables: percent of total first (PF2) and last (PL2) returns  2 m, and area under the distribution for first (AF2) and last (AL2) returns  2 m. ...................................................................................................................................... 85  Table 4.4. Log-log models for ground variables predicted from LiDAR variables (ns= not significant at α=0.05), and associated sample based summary statistics. ............................... 86  Table 4.5. A ground plot approximation of a LiDAR-based system of stand structure classification.. ......................................................................................................................... 89  Table 4.6. Means and standard errors for ground plot and LiDAR statistics for 5 LiDAR classes defined by cumulative distributions of AFx and ALx. ................................................ 91 Table 4.7. Contingency tables for the LiDAR Analogue and MDA classifications versus the 5-class ground based system of classification using the cumulative distributions of VGx with respect to diameter class. ........................................................................................................ 94  ix  Table 4.8. Contingency tables for the LiDAR Analogue and MDA classifications versus the 5-class ground based system of classification using the cumulative distributions of RGx and RNx with respect to diameter class. ........................................................................................ 95 Table 4.9. Means and standard errors for ground plot and LiDAR statistics for 5 ground based classes defined by cumulative distributions of RGx and RNx. ...................................... 96 Table 4.10. Maximum correlation coefficients for selected height of LiDAR return variables and corresponding DBH thresholds associated with RGx or RNx. ......................................... 97  x  List of Figures Figure 2.1. A flow chart describing the cluster algorithm. ..................................................... 18  Figure 2.2. Box plots by stand structure class for: basal area per ha (top left), stems per ha top right), quadratic mean diameter (bottom left), and volume per ha (bottom right).. ......... 28  Figure 2.3. Boxplots of the Gini Index (left) and the Stand Variance Index (STVI, right) by stand structure class. ............................................................................................................... 29 Figure 2.4. Average reverse cumulative distributions of basal area per ha (m2ha-1) versus DBH by stand structure class. ................................................................................................. 31 Figure 2.5. Average reverse cumulative distributions of stems per ha (m2ha-1) versus DBH by stand structure class. ............................................................................................................... 31  Figure 3.1. Potential succession pathways. ............................................................................ 50  Figure 3.2. Examples of different succession pathways based on individual plots. .............. 60 Figure 3.3. Changes stems per ha (top left), basal area per ha (top right; m2ha-1), Lorey’s mean height (middle left; m), live crown ratio (middle right) and in stand structure succession (bottom), versus year (in 5-year increments). ....................................................... 61 Figure 4.1. Box plots for stems per ha (N), basal area per ha (G), Lorey’s mean tree height (H), quadratic mean diameter (DG), and gross (VG) and merchantable (VM) volume per ha by stand structure class (n=189 plots)..................................................................................... 84  Figure 4.2. Box plots for percents of first (PF2) and last (PL2) returns above 2 m in height and areas under first (AF2) and last returns (AL2) above 2 m in height by ground-stand structure class. ......................................................................................................................... 88  xi  Figure 4.3. Box plots of N, G, H and VG with respect to LiDAR classes derived from the log-transform variable set. ...................................................................................................... 92  Figure 4.4. The change in KHAT with an increasing number classes. .................................. 99  xii  Acknowledgements This dissertation is the result of dedication and work by many. The work began under the Lignum Limited Innovative Forest Practices Agreement (IFPA) located in the CaribooChilcotin area of British Columbia. The following people in particular were involved in the initial development and application of this work: Dave Affleck, PhD; Mishtu (Satindranath) Banerjee, Bill Bourgeois, PhD; Steve Capling; Dave Conly; Tracy Earle; Craig Farnden, PhD; Kristi Iverson; John Liscomb, Shawn Meisner; Dwayne Payne; Don Reimer, PhD; Guillaume Therrien, PhD; and Carmen Wong. They contributed to every aspect of this work, from obtaining funding, organizing contracts, collecting data, helping with different kinds of analyses, and with considerations of how to best integrate this work within the practices of forest inventory, growth and yield, silviculture, and ecology. The idea for this dissertation was spawned and initially developed in one of the most progressive and rewarding working environments I have had the privilege to engage in, and in no small part it was due to the involvement of these individuals. In terms of funding, the initial work was supported by Forest Renewal BC with over a million dollars invested in the establishment of growth and yield and stand structure plots. Without these plot data and all of the organization that went into collecting them this dissertation would not have been possible. Secondly the decision to return to University would not have been made without the initial support of the Science Council of British Columbia. They contributed 40 thousand dollars, allowing me to support my family while attending classes for the first two years at UBC. Finally, there are three University of British Columbia Professors that I wish to give special thanks to. The first is Dr. Gordon Weetman whose engagement in my career began in my undergraduate years and continued regardless of where I moved to next. I will always be his student whether attending the Silviculture Institute of BC, engaging in the McGregor Model Forest, or engaging in discussions about BC and Canadian Forest Policy in his office. Gordon was instrumental in my decision to obtain a Master of Science degree from the University of Georgia in the mid 80’s, and he was instrumental in my decision to return once again to UBC.  xiii  The second professor is Dr. Peter Marshall. I first got to know Dr. Marshall after he reviewed my work for the Cariboo Lumber Manufacturers. This work explored a newly proposed BC silviculture policy requiring licensees to produce plantations below a maximum density, before qualifying as “free growing”. I received a passing grade. Our association and friendship continued to grow afterwards through encounters as part of the Chief Forester’s Forest Productivity Council for reviewing matters of growth and yield, and also through engagement in the Association of BC Forest Professional’s Board of Examiners over a 10 year period. Dr. Marshall also encouraged me to return to University and he was my first Ph.D. advisor. I have often sought Peter’s opinion and he has always provided fair and objective assessments in return. Without this guidance I might never have found my way to writing this dissertation. Finally, thanks go to my advisor, Dr. Valerie LeMay. Dr. LeMay encouraged me to continue when I had my doubts. She provided time and made considerable efforts to redirect and focus my work on “what needs to be done”. With Dr. LeMay’s unwavering support I overcame many obstacles toward completion in accordance with the standard that must be met. I didn’t know what that standard was until it was pointed out to me; of course that is one of the main reasons for pursuing a Ph.D. in the first place. A tremendous feeling of gratitude goes to Dr. LeMay and to all those Professors like her who help graduate students like me to get through the process and in so doing, learn something of great value along the way. Thank you, Dr. LeMay.  xiv  Dedication This dissertation is dedicated to my wife, Karen Diane Hoskyn; son, Bevan Hoskyn Moss; and daughter, Jocelyn Brianna Moss, all of whom gave me the encouragement, support and time to pursue my interests, and enabled me to do it in the company of those who could guide the way. It is also dedicated to my father, Alan Moss, who was my primary inspiration for becoming a forester, and to my mother, Rhoda Moss, who has always been generous with her advice and support while in pursuit of my dreams.  xv  Chapter 1: Introduction Stand structure has traditionally been defined in terms of a vertical component consisting of stems per ha by size class (e.g., tree diameters and/or heights), a horizontal component consisting of the spatial distribution of trees, and a third component consisting of measures of species abundance (Mueller-Dombois and Ellenberg 1974). Stand structure, or more generally the “structure of the plant community” has been defined by Kimmins (2004) as, “The vertical arrangement of canopy layers and plants of different life form or the horizontal variation in canopy closure and canopy layers or both. Community structure also includes standing dead trees (snags) and decomposing logs on the forest floor (coarse woody debris).” Smith et al. (1997) defined the internal structure of a stand as being “… determined by considerations such as the variation in species and age classes (or lack of it), the arrangement of different layers or stories of vegetation (usually differing as to species), and the distribution of diameter classes.” Structure is central to the process of forest management. According to O’Neil et al. (2001), structure “… is what a central manager can manipulate to achieve various objectives.” Their focus was on wildlife habitat assessment and management. Smith et al. (1997) described the practice of silviculture as “ … a kind of process engineering or forest architecture aimed at creating structures or developmental sequences that will serve intended purposes, be in harmony with the environment, and withstand loads imposed by environmental influences.” Lindenmayer et al. (2006) commented, in reference to the stand scale, that “The internal structure and composition of harvested units can have a significant influence on the degree to which a managed forest can sustain biodiversity and maintain ecosystem processes,” and made similar comments with reference to forest scale structure. In reviewing forest fire behavior in boreal ecosystems, Ryan (2002) stated that, “Structure defines the total amount of biomass that can be burned, and therefore the total energy that can be released in a fire. The size distribution of the structural components defines the rate at which energy will be released during favorable burning conditions.” One of the challenges in the practice of forestry has been the development of a wide variety of structural classifications for specific purposes, including: assessing wildlife habitat 1  (O’Neil et al. 2001); indicating biodiversity (Smith et al. 2008); defining stages of stand development (Oliver 1981; O’Hara et al. 1996); defining forest fire fuel types (Fernandes 2009); supporting nature-based forest management (Larsen and Nielson 2007) and diversityoriented silviculture (Lähde et al. 1999); describing idealized silvicultural systems (Smith et al. 1997); characterizing differences in natural disturbance regimes (Franklin et al. 2002); and establishing stand or timber types for the purpose of summarizing national forest inventories (Reque and Bravo 2008). These classifications characterize differences in stand structure through different lenses, and with various degrees of abstraction and levels of precision. However, in the final analysis, it is the same objects that are being classified from different perspectives. All of these objects have one thing in common: the vertical and horizontal distributions of trees with respect to both tree species and size distributions (diameter or height; Mueller-Dombois and Ellenberg 1974). Of these four dimensions commonly used, namely species, height, diameter, and distribution of trees across space, the distribution with respect to tree size (diameter and/or height) is perhaps the easiest and the most generally applied. In this dissertation, I propose the overall premise that stand structure classifications should be built on a common foundation to facilitate interdisciplinary communications amongst forestry professionals and others, particularly at a high level. Further, this classification system could be modified for lower levels in the classification hierarchy and/or modified to accommodate additional stand structure measures for specific end uses. The rationale for this kind of system is that all of the classifications introduced previously have been oriented towards classifying the same objects (stand structure) based on a common subset of attributes. The broad outline of this dissertation, including this chapter, is: 1. A review of systems of forest classification and opportunities to utilize a more systematic approach to stand structure classification, and statement of dissertation objectives (Chapter 1). 2. Development, implementation and evaluation of a new method for producing systems of stand structure classification using ground data (Chapter 2).  2  3. Evaluation of the potential to extend the stand structure classification for the purpose of mapping patterns of forest stand succession (Chapter 3). 4. Assessment of airborne light detection and ranging (LiDAR) sensor data for the purpose of inventorying different stand structures within a forested landscape, with and without the use of ground data (Chapter 4). 5. Overall discussion of chapters 2 through 4, a summary of related work involving the operational development and use of the system of stand structure classification, and dissertation conclusions (Chapter 5). To further establish the context for this work, Section 1.1 addresses the question: Why Classify? In Section 1.2, specific classification systems commonly used in forestry are referenced and the structural aspects of those systems involving vegetation classification are highlighted. The systems of classification specifically related to patterns of seral stage development or change with time are discussed in Section 1.3. Section 1.4 introduces the concept of mapping the locations and extents of stand structure classes within large forested landscapes. Section 1.5 describes some desirable features or properties of effective and efficient systems of classification, particularly with reference to their use in forestry. Section 1.6 then lays out the specific objectives for this dissertation.  1.1  Why Classify  There are two primary reasons for building systems of classifications: 1. To organize knowledge of relationships or identify patterns amongst different processes or objects in space and/or time (Duda et al. 2001); and 2. To produce consistent, parsimonious, precise, and structured language about the nature of similar kinds of objects as a foundation for communication and the building of common understanding. In the context of science, new knowledge can be created simply by (re)categorizing objects or processes in a way that leads to different realizations of certain relationships or causal chains of events. Einstein’s (1916) re-categorization of time and space as being relativistic instead of absolute is one such example. The first challenge is to find a method or way of 3  categorizing things that will facilitate an advance. The second challenge is to demonstrate that the new categories produce new insights and knowledge. The third challenge is to make the methods and categories available to others so that the knowledge gained can be shared and deployed to good effect within a broader community, and so that further advances in new knowledge and understanding can be made.  1.2  Approaches to Classification in Forestry  Systems of classification have been developed for numerous applications in forestry, including characterization of the following:   climate (e.g., Kottek et al. 2006; Pojar et al. 1987);    soil (e.g., Soil Survey Staff 1975; Soil Classification Working Group 1998);    streams (Rosgen 1994), riparian areas (e.g., British Columbia (BC) Ministry of Forests and Range 1995) and wetlands (National Wetlands Working Group 1988);    potential climax vegetation (e.g., Daubenmire 1952; Pojar et al. 1987)    wildlife habitat (e.g., O’Neil and Johnson 2001);    natural vegetation (e.g., Barbour and Billings 2000; Grossman et al. 1998) and seminatural and highly cultured vegetation (e.g., Barbati and Marchetti 2004);    land use (e.g., Anderson et al. 1976) and land cover (e.g., Natural Resources Canada 2011);    grasslands (e.g., Wikeem and Wikeem 2004);    forest fire fuel types (e.g., Taylor et al. 1996);    timber types based primarily on species composition (e.g., Alig and Butler 2004) and differences in site productivity (Edwards and Christie 1981), and so too differences in size (e.g., seedling, sapling, pole, sawtimber) and/or age (e.g., juvenile, immature, mature, old growth; BC Ministry of Environment, Lands, and Parks 1998), stocking or crown closure and sometimes complexity (e.g., single layered, multiple or two layered, complex; BC Ministry of Sustainable Resource Management 2003); and    silviculture systems based on overstory/understory requirements for successful regeneration, establishment and subsequent growth of trees with desired species composition and of sufficient number and spatial distribution to constitute adequate stocking (e.g., Smith et al. 1997). 4  All of the classification systems that include some component of vegetation have structural elements beyond species composition that attempt to capture specific aspects of structural variation, usually with respect to height, but also with respect to diameter, which are two commonly measured dimensions of tree size that are well correlated. The BiogeoclimaticEcosystem classification (BEC) system developed for use in British Columbia (BC), Canada (Pojar et al. 1987) refers to different tree (> 10 m tall), shrub (2 –10 m tall), herb, and moss layers (BC Ministry of Environment, Lands, and Parks 1998). The naming of each of the ecosystem associations utilizes these definitions by identifying the dominant tree species in the upper layer, followed by dominant shrub, herb and moss species depending on their relative frequencies, range in percent cover, and their value as indicators for distinguishing between associations. The designation of forest fire fuel types is primarily associated with differences in tree species (especially hardwoods versus conifers). However, the kind (fine versus coarse), amount of fuel, and fuel vertical distribution (particularly as it relates to ground surface fuels), canopy base height, canopy bulk density, and canopy fuel load, are also critical components for estimating fire behavior characteristics (Cruz et al. 2003). O’Neil and Johnson’s (2001) wildlife habitat classification involves forest structural features related to average tree diameter, canopy cover and numbers of canopy layers. These are used to identify 26 different classes. The probable occurrences of particular habitat elements and their geographic distributions, such as the occurrences of different dead standing trees of certain tree diameter and decay class, or the probable presence of tree cavities or the presence of trees with large live branches, are then related to different stand structure classes. The occurrences and relative frequencies of these structural classes are in turn related to 1 of 32 broadly defined habitat types (e.g., Eastside Mixed Conifer Forest; Chappell et al. 2001). Specific species uses or requirements are then identified according to all three scales (habitat type, stand structure class, habitat elements), thereby recognizing scale dependencies in wildlife-habitat relationships (O’Neil and Johnson 2001).  5  These vegetation systems of classification are all concerned with distributions of trees with respect to size. They frequently involve layers as a means of defining differences in the vertical distributions of trees. However there is no consistent definition of layers amongst the systems of classification (Parker and Brown 2000). Layers are defined either arbitrarily with respect to height classes, or with respect to minimum differences in the heights between two or more layers, or with respect to cohorts differentiated on the basis of age and timing of disturbances. Frequently, the assignment of trees to one layer versus another is not obvious in the field, in which case stands can be declared multi-storied or complex as opposed to single- or two-layered stands. Exactly where the line is drawn between these classes is often open to debate, because the concept of layers is difficult to consistently apply, except in the most obvious of situations (e.g., plantations following clear-cutting showing a clear twolayered structure). It is clear that the vertical distributions of trees are important for a number of reasons, but there may be better ways of estimating these distributions (e.g., Latham et al. 1998; Purves et al. 2007) and perhaps the concept of layers is simply best avoided in favour of other more reliable statistics such as diameter distributions (Parker and Brown 2000). Tree diameter distributions are commonly equated with the horizontal distributions of trees. For example, variation in the mean tree diameter from one plot to the next in a given stand has been used as an indicator of clumpiness, with a high variation constituting considerable clumpiness and low variation constituting a more or less uniform distribution across a small range of tree sizes. In this dissertation, a slightly different view is taken, in that tree diameter distributions are also used to indicate vertical distributions of tree sizes. The rationale behind this view is that diameters are strongly indicative of height, given the strong correlations in these two tree-size measures (exceptions occur, for example when considering only those trees in dominant and codominant crown positions, particularly in single cohort stands; B. Larson 2012, pers. comm., 13 Jan.). Further, diameter is usually easily measured with high precision (albeit this is not always the case, particularly in tropical and in old deciduous forests; West 2003). Heights above 5 m are more difficult to directly measure; therefore, heights are often indirectly measured using triangulation. In dense and/or in very tall stands of trees, especially on flat (0% slope) ground, height is particularly difficult to measure precisely. In this dissertation, the view is that the vertical distributions of trees can be 6  reasonably and much more conveniently estimated based on a knowledge of tree species and diameter as well as perhaps some other attributes such as stand density and basal area. Differences in vertical and horizontal distributions of trees can therefore be represented by differences in the distributions of trees by diameter and species composition with little loss of information. This discussion leads back to the main assertion of this dissertation which is that knowledge of the underlying diameter distribution of trees is fundamental to what is commonly meant by stand structure, both as it relates to vertical and horizontal distributions of trees and associated crown characteristics. Under this assertion, a single, common, high-level classification system could be developed and used for a number of purposes. This common system could then be later adapted to meet specific needs and would provide a starting point for improved interdisciplinary communication. To be useful, a classification of this kind should have some characteristics that would represent an improvement over existing classifications. The challenge is how to design a process for building a system of classification that will meet these criteria; this is addressed in Chapter 2.  1.3  Seral Stage Development and Classification  The notion of ecological succession refers to the process of change after disturbance (Kimmins 2004). A sequence of changes is referred to as a sere and each stage in the sequence is referred to as a seral stage. Sources of change are typically identified as being autogenic (i.e., self-generating within a given stand, ecosystem or plant community), allogenic (i.e., induced by external climatic factors related to fire, wind, flooding, etc.), or biogenic (i.e., related to insects, disease, and invasions of non-native species for example). Knowledge of patterns of change in species composition, stand structure characteristics, and of factors affecting the rate of change is a prerequisite for determining costs and benefits of forest management activity impacts on ecosystem services. Even more challenging is the ability to actually apply this kind of knowledge to any particular local situation in the process of both forest and stand management decision-making on a routine basis. To facilitate this process, the most common approaches are predominantly heuristic based on the development  7  of a language describing categories of development, or predominantly quantitative based on the use of various kinds of metrics, indices, or some hybrids of the two. Heuristic approaches typically utilize one or more of the following concepts: (1) cohorts or waves of regeneration following different kinds and severities of disturbances creating single- versus multi-cohort stands (Oliver and Larson 1990; O’Hara et al. 1996) and evenversus uneven-aged stand conditions (Shorohova et al. 2009); (2) periods of increased mortality due to effects of competition by way of a stem exclusion phase (Oliver and Larson 1990), a thinning phase (Spies and Franklin, 1996), or competitive exclusion (Carey and Curtis 1996); (3) open versus closed canopy conditions (O’Hara et al. 1996); (4) amount of biomass accumulation (Bormann and Likens 1979; Franklin et al. 2002); (5) vertical and horizontal diversity (Franklin et al. 2002); (6) botanical diversity (Carey and Curtis 1996); (7) legacies from previous disturbances (Franklin et al. 2002); (8) levels of maturity (Oliver and Larson 1990; Spies and Franklin 1996; Franklin et al. 2002); (9) niche diversification (Carey and Curtis 1996); (10) notions of steady state (Bormann and Likens 1979) and dynamic equilibrium or shifting gap phase dynamics (Spies and Franklin 1996); (11) pioneer versus climatic climax species (BC Ministry of Environment, Lands, and Parks 1998) or compositional change (Shorohova et al. 2009); and/or (12) energy acquisition, conservation, release and reorganization (Holling and Gunderson 2002). Within a European context Mayer (1976) and Liebundgut (1993) developed a classification based on the following ordered stages of development: initial (regeneration in a large opening cleared of trees), optimum (mortality in middle and lower layers starts to increase), terminal (stand volume reaches a maximum or begins to decrease), decomposition (rapid decrease in volume due to age related mortality in the overstory), regeneration (a multilayered or unevenaged structure begins development) and finally plenter (distinctly uneven-aged). All of these classifications start by describing stages in a process of stand development through inductive reasoning that have generally been derived based on individual case studies. Rules are commonly developed to assist in a more standardized application of the classification to particular stand types and/or disturbance regimes in specific locations. Often the rules themselves may involve a considerable degree of subjective interpretation. For example, single- versus multi-cohort stands can be notoriously difficult to diagnose simply because trees in different size classes 8  may belong to the same age class, and trees of different age classes may belong to the same size classes. However, knowledge of process is important to understanding stand and ecosystem dynamics. Classifications of this kind help to communicate that knowledge, regardless of the challenges involved in trying to apply such information in practice. In contrast to heuristic approaches, quantitative approaches are used in plant population biology for describing seral stage development patterns along a continuum or with respect to discrete stages or classes of development (Keddy 1989; Grace and Tilman1990; Grover 1997; Case 2000; Silverton and Charlesworth 2007). Most of these methods rely implicitly or explicitly on some notion of density-dependent competition for above and/or below ground resources, including competition for light, water and nutrients, as influenced or mitigated by species (genetic), temperature, and soil interactions. Competition affects the rate of growth, survival, and potentially the reproduction of trees. This is notwithstanding the presence of numerous other kinds of interactions, including parasitism, mutualism, commensalism, and amensalism (Silverton and Charlesworth 2007), where interactions can be positive, negative, and/or neutral. In forestry, there has been a tendency to reduce the complexity of competitive interactions down to a minimum as an aid to decision-making in the field. The universe of stand dynamics for an individual species can be reduced to a knowledge of stand density and some indicator of average tree size including: mean tree diameter giving rise to Reineke’s (1933) Stand Density Index (SDI); dominant tree height giving rise to Wilson’s (1946) Spacing Factor (WSF); maximum crown width as derived from tree diameters to estimate a Crown Competition Factor (CCF; Krajicek et al. 1961); stand basal area per ha versus stand density to produce Gingrich (1967) stocking diagrams; quadratic mean tree diameter giving rise to the Curtis et al. (1981) Relative Density (RD); and mean tree volume giving rise to Relative Stand Density (RSD) as indicated by Drew and Flewelling (1979) in stand density management diagrams. Due to tree allometry, all of these relationships are essentially derived from the “minus 3/2 power law” or “self-thinning rule” hyper-dissertation that states that the maximum average biomass per individual plant is proportional to stand density to the power of minus 3/2 (Yoda et al. 1963), multiplied by some species and potentially site-specific 9  constant as means of indicating differences in carrying capacity. While these indices have facilitated increased understanding of forest and stand dynamics, they are based on a number of assumptions that do not really hold true, as noted for example by Reynolds and Ford (2005):   the plant population is adequately represented by the mean plant;    resource use remains constant throughout the process of self-thinning;    competition is a horizontal packing process; and    initial stand conditions affect the rate of competition, but not the process itself.  As a consequence, the use of this theoretical approach to reliably describe individual tree and stand dynamics is in fact limited to a relatively narrow effective range of conditions, in particular, even-aged, mono-species plantations. However, widespread use of this theory in both a growth modeling and forest management decision making context continues in spite of these deficiencies, including describing stand succession patterns, because it has been difficult to find effective alternatives. The idea of an index for describing succession along a continuum in state-space is extremely appealing. However, in the absence of a reliable index, and given the wide variety of diameter distributions and their potential for change with time, one alternative is to conceive of a more empirical approach to quantifying similarities and differences in stand or plot-level tree diameter distributions, and to use these quantities to classify different stand structures as they exist and subsequently as they might be observed or predicted to change with time. This is different from the heuristic approach because there is no intent to establish a system of classification in juxtaposition to some a priori understanding of stages within an identified process of development. This approach involves simply describing differences and similarities in diameter distributions empirically that can then be used to investigate patterns of stand development. This is also different from the use of whole stand-level indices for describing development patterns along a continuum. It avoids certain limitations as to where these kinds of indices can be reasonably applied within the broader range of different kinds of diameter distributions.  10  In this dissertation, the process of developing succession pathways is based on this quantitative approach in that the system of classification proposed is based on a narrow range of stand structure attributes that are easy to measure and then this system is used to investigate different patterns of succession. The question addressed in Chapter 3 is whether or not this alternative approach is feasible, and if so what might be gained or lost in the process relative to the kinds of classifications described in these references.  1.4  Mapping Stand Structure Classes  In addition to characterizing potential and observed changes in stand structure characteristics with time, there is also a forest inventory requirement to identify change in these same characteristics over space and to display these as maps. Commonly, the standard inventory procedure involves using remote sensing tools to obtain imagery, such as colour-infrared aerial photography, that covers the entire area of interest. Interpreters are then employed to delineate relatively homogeneous units into polygons and to label these units according to well-defined forest and non-forest attributes (e.g., species composition, dominant tree height, age, crown closure, harvested area, etc.). These attributes specifically or incidentally include stand structure measures or classes. The primary objective in the process is to produce a map that is accurate in terms of attribution (or accurate in terms of classification), with high spatial resolution (i.e., typically, polygons range from 1 to 20 ha in size), subject to funding limitations and expected applications of the maps. These forest inventory maps are used for many planning and management applications. For example, one application involves using specific polygon attributes as inputs into whole stand or individual tree growth and yield models to forecast changes in forest and stand characteristics over time. More recently, the development of small footprint LiDAR has been identified as a particularly useful remote sensing tool for inventorying stand structure attributes at comparatively high levels of spatial resolution (e.g., representing polygons that are 20 m2) across large landscape areas when compared with more traditional techniques (Hyyppä et al. 2009). The primary focus of Chapter 4 is to assess the potential of LiDAR as a tool for stand structure classification of a kind analogous to that produced in Chapter 2. The potential is  11  assessed both with and without the use of ground plot data as a means of calibrating the interpretation of LiDAR data for inventory purpose.  1.5  Systems of Classification: Desirable Features  Systems of classification should have a number of desirable properties to be effective. First, the number of classes should not be very large. As the number of classes increase, the probability of separating observations into the correct class decreases, since the differences in attributes between classes become smaller. At the other extreme, as the number of classes decreases toward zero, the system of classification becomes less precise and therefore becomes less useful for distinguishing amongst various objects. Second, where uncertainty or disagreement exists as to the correct classification of a given object, there should be an objective and definitive way to determine the class to which a given object belongs. To achieve this property, detailed measurements of attributes, preferably with a small degree of measurement error and with a minimum of effort, would be needed. These data would then be input into a computational process that definitively identifies the appropriate class with a high degree of certainty. These two procedures would result in consistency and verifiability in the way objects are classified and in the way the classes are interpreted among a variety of potential users. A third desirable property is that it should be possible to apply the designated classification system to multiple spatial scales. This would mean that the same class definitions could be used to classify plots, stands, or whole landscapes. This allows users flexibility in the way the classification can be applied; however, it comes at the cost of having to qualify any statements involving the use of the classification by indicating the scale of application. This is necessary because the interpretation of the classes for specific applications are scale dependent. Another desirable property is that the system of classification facilitates communication amongst practitioners from a wide variety of backgrounds. For stand structure classification, these practitioners would include silviculturists, as well as timber, recreation, habitat, water, 12  inventory, and growth and yield specialists. At least at a high level, the classification system should facilitate effective, efficient and verifiable interdisciplinary communication important for designing and implementing successful forest research and management practices. Finally, provisions should be included in the classification system to allow it to be modified with sub-classes for higher resolution and, as necessary, for specific applications, perhaps using attributes that are not as precisely measured or that require a higher degree of subjective assessment. Conversely, there may be circumstances when a more general system of classification may be warranted by way of aggregation of certain classes. Overall, the system of classification should have a clearly defined foundation for either aggregating upward or disaggregating downward for specific applications, resulting in a widely-held common language to facilitate the basis for clear understanding.  1.6  Objectives of Dissertation  The objectives of this dissertation are as follows: 1. to develop a high level system of stand structure classification that fulfills the criteria established in Section 1.5 and that can be verified as representing meaningful structural differences (Chapter 2); 2. to evaluate the system of classification for its potential as a tool for identifying and diagnosing potential stand succession pathways (Chapter 3); and 3. to evaluate the potential for linking the classification to a forest inventory, in this case, based on the use of LiDAR (i.e., airborne laser measures) first and last return distributions as indicators of structural similarities and differences relative to the ground-based metrics derived for use in Chapter 2 (Chapter 4). The overall rationale for following this line of investigation is that a high level system of classification would be useful to facilitate consistent, reliable, and verifiable communications amongst various researchers and forest practitioners regarding differences in stand structure, particularly as it relates to describing temporal and spatial differences in tree diameter distributions on various scales. Chapter 5 summarizes the main results of these three research objectives and places these in context of this overall rationale. 13  Chapter 2: A Quantitative Technique for Stand Structure Classification 2.1  Introduction  Stand structure is the vertical and horizontal diversity of trees in stands at one point in time. Trees dominate forest environments due to their large size, perennial growth habit, longevity, and their significant value for consumptive and non-consumptive purposes (Oliver and Larson 1990). Generally, structural components of ecosystems are important because of their function or roles in the process of inducing and reacting to changes with time (Kimmins 2004). As a result, stand structure information is fundamental for: (1) assessing the relative abundances and qualities of species habitats (e.g., O’Neil et al. 2001); (2) identifying succession stages in the course of stand development (e.g., O’Hara et al. 1996; Oliver and Larson 1990); (3) characterizing outcomes of silviculture systems (Smith et al. 1997); (4) assessing potential wood products values; and (5) other assessments including fire risk and water quality and quantity. Naturally regenerated forests are often structurally diverse. However, recent changes in management of plantations have also promoted greater structural diversity through planting mixed species and/or continuous cover or variable retention forestry. As a result, Pretzsch et al. (2006) noted an increased demand in Europe for individual tree and stand growth simulators over more traditional stand-level yield tables associated with even-aged, single species stands. Overall, stand structure diversity measures are critical for forest management. Common measures of stand structure diversity include the stems per unit area by size (e.g., diameters and heights), the spatial distribution of trees, and species abundance (MuellerDombois and Ellenberg 1974). A wider variety of ecological attributes may be directly used in defining stand structure or may be indirectly included via strong correlations with other structural measures (e.g., Gagnon and Bradfield 1986). For example, O’Neil et al. (2001) identified stand structure elements important for characterizing wildlife habitats, including amount and decay classes of downed wood (i.e., coarse woody debris, CWD) in riparian versus upland areas, numbers and sizes of snags, numbers of large live branches, as well as many other tree, shrub, herb, and ground cover characteristics. However, CWD is strongly  14  correlated with the numbers of large trees as the sources of CWD, since these tend to increase with stand age (Sturtevant et al. 1997). As an alternative to a wide array of stand structure measures, stand structure classes (or types) have been proposed. In his review of North American forest modeling approaches, Turland (2007, p 4) noted that “Classification of the forest areas into strata and capturing details on the structure and composition of stands is necessary for modeling future growth impacts of silviculture, and yield forecasts.” The inclusion of stand structure class in forest inventory strata attributes can provide critical information for linking individual tree growth models to forest inventory. For example, Larsen and Nielson (2007) defined forest development types based on knowledge of natural disturbances and their influence on stand dynamics. To be effective, stand structure classification systems should have a number of desirable properties. First, the number of classes should not be very large. If the number of classes is large, the differences among classes may be small resulting in difficulties in classifying new stands. At the other extreme, the classification would add little or no new information if there were only a few classes. Second, there should be an objective and definitive way to determine the class to which a given object belongs. A quantitative method that uses detailed measurements of attributes and identifies the structure class would be more likely to achieve this property, than a qualitative classification system. Together, these two properties (appropriate number of classes, objective classification) would result in consistency in stand classification by different practitioners. A third desirable property is that it should be possible to apply the classification system to multiple spatial scales. This would mean that the same class definitions could be used to classify plots, stands, or whole landscapes. However, this would not mean that the classification system would be scale invariant in application; the use of resulting stand structure classes would need to be consistent with the development (e.g., if developed using stand measures, it must be applied using stand measures). Fourth, the system should be easily applied using commonly measured attributes. Including a large number of stand structural elements would increase the cost of applying the system, while perhaps not increasing the usefulness, since stand structure measures are often 15  moderately to strongly correlated. Fifth, the system should facilitate communication amongst practitioners assessing and managing forest resources, including foresters, hydrologists, and biologists. Finally, the classification system should be flexible in that it could be modified to include other stand structure attributes where needed for specific applications. There are several quantitative methods that have been commonly used for constructing systems of classification with no a priori class definitions (e.g., Duda et al. 2001; Fahim et al. 2006). “Top down” methods include ordination methods (e.g., principal components analysis), classification and regression trees (CART), and divisive clustering methods which can be used to separate the observations into classes. “Bottom-up” processes include agglomerative clustering, which starts with a matrix of similarities or differences amongst all pairs of objects according to predetermined attributes (variable space; Manly 2005). Objects are then successively classed together. The objectives in these clustering algorithms are to obtain homogeneity within classes and/or heterogeneity between classes. Another alternative for developing a stand structure classification system is to have practitioners define a priori classes based on subjective criteria. Quantitative methods could subsequently be used to associate these a priori classes with particular attributes, leading to insights about the a priori classes that may then be used to modify the initial classes and/or to increase consistency in applying the classes. For example, Ejrnæs et al. (2002) used sample scores related to characteristics such as species richness along with other ordination variables to train a neural network to rank habitat conservation areas. Although a priori specifications may be intuitively appealing, quantitative approaches have the advantages of: (1) consistency in classification that can result in more effective communication among practitioners; and (2) the availability of associated measures of the precision allowing for an objective verification of the classification system. There are several unresolved issues in using available analytical methods for classifying stand structures. First, many attributes used to classify structures are continuous, and, therefore, may have no natural tendency toward discrete classes. The analytical method 16  employed should allow for this continuum, where classes can be subdivided for particular applications, and combined for others. Second, clustering methods may result in a few classes each with a large number of observations, along with a large number of classes each with few observations. In the field of pattern recognition, this has been referred to as a “class imbalance problem” associated with the occurrence of rare events (e.g., Barandela et al. 2002). For stand structure, classes with many observations may include important differences in stand structure that were not distinguished by the applied clustering method. Further, classes with few observations may represent excessively small domains; the differences between these classes may have little practical meaning. A third problem of classifying stand structures using conventional clustering methods is that these methods may exhibit path dependencies; often, there is no opportunity to reconfigure the assignments once they are made. As a result, the final system of classification may not minimize within class variation. K-means classification, using a vector of means for all attributes (centroids), may overcome the path dependencies (Fahim et al. 2006); however, the problem of class imbalances remains. The objective of this research was to develop an analytical method to classify stand structures that meets the stated desirable properties of classification, while avoiding class imbalances and path dependencies. This was motivated by the importance of stand structure in forest management. A top-down approach was developed that divides plots into stand structure classes and which: (1) does not rely on any a priori subjective assignment of classes; (2) relies on plot attributes that can be readily and reliably measured in the field; (3) explicitly accounts for greater balance of observations among classes; and (4) does not exhibit obvious path dependencies. A new distance metric that represents stand structure and an objective function based on this distance metric were included in this classification algorithm. In this paper, this new stand structure classification method is described and demonstrated for a forest area of British Columbia (BC), Canada.  2.2  Description of the Stand Structure Classification Algorithm  Most top-down classification methods involve four steps: (1) a distance matrix is chosen to reflect the dissimilarity among classes and the matrix is calculated for the sample data; (2) 17  the number of desired classes is selected; (3) the best arrangement of observations amongst the classes is obtained; and( 4) results are validated, often using a “leave-one-out” validation. In this section, each of these steps is described for the new stand structure classification method (Figure 2.1). Following this, a discussion of the stand structure classification method relative to the stated desired criteria is given.  Plot Data  Specify m classes in system  Compile plot SPH & BPH RCFDs  START  Initialize plot assignments, each to 1 of m Classes  Compile Plot Distance Matrix  Program Data  Calculate Between Group Differences Dijl For Each Plot  Calculate Within Group Differences Dijk For Each Plot  Calculate the within-to-between ratio, Rikl, for each potential move of plot i from group k to group l where l is not equal to k  Find the plot - group move combination with the minimum Rikl. .  Move plot plot i with minimum Rikl to group l. Update program data.  NO  Is minimum Rikl >= 1?  YES  STOP  Figure 2.1. A flow chart describing the cluster algorithm. All symbols are referred to in the text. 18  2.2.1  Distance Metric  For this new stand structure classification method, a new distance metric was developed that reflects the differences in stand structure among observations, which can be sample plots or stands. The matrix of distances between observations (hereafter considered to be sample plots) is calculated using the following steps. 1.  Reverse cumulative frequency distributions (RCFDs) are calculated based on stems and basal area per ha for each plot. For the stems per ha (SPH), the reverse cumulative frequency is the numbers of trees per ha ≥ a diameter threshold, starting with the minimum DBH (diameter outside bark at breast height of 1.3 m above ground) of all plots in the dataset, rounded to the nearest cm, and then increasing the DBH by 1 cm increments to the maximum DBH of all observations in the dataset. A similar process is followed to obtain the reverse cumulative frequency for basal area per ha (G).  2.  Each reverse cumulative distribution is standardized over the plot database by: i)  ranking plots from smallest to largest based on the SPH of all trees;;  ii)  obtaining a relative rank for each plot by dividing the plot rank by the maximum rank (i.e., the total number of observations); and  iii)  using the list of ranks for each SPH obtained, the SPH for the reverse cumulative distributions of step 1 were replaced by the equivalent rank (i.e., rank-standardized SPH).  This rank transformation was repeated for the reverse cumulative distributions for G. 3.  The distance between each pair of observations is computed by: i)  calculating the sum of the absolute differences in the rankstandardized SPH across the range of 1cm diameter thresholds is calculated;  ii)  calculating the sum is similarly calculated for rank-standardized G;  iii)  squaring each of these two sums and adding them together; and  iv)  computing the square root of this sum as the distance metric. 19  4.  These distances are then summarized into a symmetric distance matrix.  Since both small and large trees are important for stand structure, the reverse cumulative distributions were based both on SPH, which gives greater weight to small trees that are often more numerous, and on G, which gives greater weight to large trees. Other approaches have been based on SPH or G alone. For example, Staudhammer and LeMay (2001) used the variance of G across DBHs, heights, and species in their measure of structural diversity. Using variances in their index removed the need for arbitrary DBH and height class boundaries. As with their approach, the classification in this dissertation removes the need for arbitrary class boundaries. However, cumulative distributions over DBH are used instead, since this approach better emphasizes differences in the distributions than using variance alone. Unlike other approaches (e.g., Nagel et al. 2007; Fortin and Bedard 2007), empirical distributions were used instead of a theoretical distribution, such as the Weibull (1951) distribution, resulting in a distribution-free classification method. Although species may be important for stand structure, species was not used in calculating the distance matrix, nor were separate distance matrices calculated for each species. Where there are many species, species and DBH are often confounded. As a result, distributions by DBH likely also reflect distributions by species and DBH. Where there are fewer species, distributions by DBH and species could be used and the distance metric changed accordingly. However, using distributions only by DBH allows the classification to be applied across species mixtures. Further, only live trees were used in the application example presented in this chapter. For some applications, the numbers of dead trees might be important, and, as with species, the distance metric could be changed to reflect both live and dead trees.  2.2.2  Number of Classes  For this stand structure classification algorithm, the number of classes must be selected a priori. The goal in choosing the number of classes in clustering is to balance within versus between cluster variability. With a small number of classes, there would be large variability between class centroids, in this case SPH and G distributions, but also larger within class 20  variability. A large number of classes would reduce the within class variability, but result in greater difficulty in assigning a plot (or stand) to a stand structure class since there would be a number of classes with similar class centroids (i.e., similar stand structures). Rather than explicitly building this trade-off into the classification algorithm using a measure of within versus between class variability, a range of the number of classes that might be practically useful is recommended. The classification results for each number of classes specified should then be compared and one system selected for use.  2.2.3  Separation of Observations into Classes  Using the distance matrix and the specified number of classes, the algorithm follows a series of steps to separate the observations as follows: 1. Each observation (plot or stand) is randomly assigned to one of the stand structure classes. 2. Then, the operation proceeds for each observation by: i)  moving the observation to one of the other classes;  ii)  calculating the ratio, R, as:  nl  Rikl   D j 1 nk  D j 1  ijl  (1)  ijk  where Rikl is the ratio associated with the movement of observation i from class k to class l, subject to the constraint that l  k; Dijl is the distance from observation i to observation j, where i is in class k and j is in class l; Dijk is the distance from observation i to observation j, where i and j are in class k; and nl is the number of observations in class l; nk is the number of observations in class k. iii)  moving the observation to each of the other classes, and calculating Rikl for each move; and  21  iv)  determining the minimum of these ratios, Rmini, associated with a move of the observation to a given class l.  3. Using these ratios, an observation is selected and moved by: i)  identifying the observation that has the move with the lowest Rmini across all i observations; set MINR equal to this value; and  ii)  moving that observation, provided that the class from which it is being removed has at least two other observations; or  iii)  selecting the next best plot (next lowest Rmini) and moving that observation instead.  4. Steps 2 and 3 are repeated while the resultant MINR < 1. The ratio (Eq. 1) represents the relative decrease (or increase, if > 1) in the within class differences obtained by moving observation i from class k to class l. Therefore, as long as MINR<1, the process continues. Since the process begins with a random assignment of observations to classes, the algorithm is run several times and the run that minimizes the sum of the within-class distances across all classes is selected as the final classification.  2.2.4  Validation and Efficacy of the Resulting Classification  Once the classification is completed, the results can be assessed by introducing each observation originally used to construct the classification as if it were a new observation (i.e., re-substitution). The observation is then assigned to the class based on the minimum of the distance metric and compared to the original assignment. The classification system should have a high proportion of occasions where the class assigned to each of the observations is consistent with the original class. Comparisons to alternative classification algorithms can also provide insights on the accuracy of the new classification system. For example, k-means clustering using plot-level variables could be considered for stand structure classification. Results of k-means could then be compared to results using the new classification system.  22  As well as this validation method and comparison to an alternative algorithm, large differences in the reverse cumulative distributions centroids across classes indicate greater efficacy of class separation. Within and between class variances in plot-level variables (or stand-level variables if observations were stands) can further indicate the efficacy of the stand structure classification system; large between class differences and small within class variances indicate better classification. Commonly used indices of stand structure can also indicate the success of stand structure classification. In particular, the Gini index is based on the proportions of SPH being uniformly distributed over the range of DBH within a given plot when the index is equal to zero (e.g., Lexerød and Eid 2006). The stand structure variance index (STVI) by Staudhammer and LeMay (2001) is based on variance of G over DBH relative to a uniform distribution from the smallest to largest DBH amongst all plots (called maximally diverse in their paper) can be calculated for each observation and within and between class variances examined. Finally, the stand structure classification system should be assessed by forest practitioners. The classes should indicate stand structure differences that might affect management practice and should be considered useful and easy to use by a range of forest practitioners.  2.2.5  Assessment of the Classification Algorithm Relative to Desired Criteria  Since a quantitative algorithm is used, the resulting stand structure classes are more likely to be useful for a wide variety of forest management applications, since no a priori decisions are made regarding what each stand structure class should represent. As noted, a common system would facilitate communication among forest practitioners. Second, the classification uses SPH and G distributions by DBH that are commonly measured in sample plots (or summarized for stands). These directly measure horizontal variation and indicate vertical variation via the strong correlations between DBH and height measures. As noted, species could be easily added to the system, but there may only be a narrow range of DBHs for each species when there are many species. Third, path dependencies are minimized by: (1) using an iterative procedure where observations are free to move between classes at any time during the process; and (2) repeating the classification a number of times with varying random assignments initiating the algorithm and selecting the best of these runs. Fourth, 23  class imbalances are explicitly reduced. Although a minimum of two observations per class is arbitrary, specifying a minimum class membership removes the possibility of single-class observations. Further, there is an explicit trade-off between the numbers of observations assigned to any class and the proportion of the variance in the SPH and G distributions represented by that class. A particular class becomes less “attractive” as more observations are added, since R increases, thereby further reducing class imbalances. Lastly, the ranking procedure helps to reduce distances amongst outliers and increase distances where there are a larger number of plots with similar distributions, and in this way tends to also promote a more even distribution of plots amongst the various classes.  2.3 2.3.1  Application to a Forest Area Forest Area Description  The application area encompassed 600,000 ha of the former Lignum Innovative Forest Practices Agreement Area (Wong and Iverson 2004) within the Cariboo region of BC, centered around Williams Lake (52o 7’ 29.56” N, 122o 7’ 52.9” W, 575 m elevation), and located predominantly in the Interior Douglas Fir (IDF), Sub-boreal Pine Spruce (SBPS), Sub-boreal Spruce (SBS) biogeoclimatic ecological classification zones (Steen and Coupe 1997). The forests were dominated by lodgepole pine (Pinus contorta var. latifolia (Engelm.) Critchfield), interior Douglas-fir (Pseudotsuga menziesii var. glauca (Beissn.) Franco), and by lesser amounts of hybrid Engelmann and white spruce (Picea glauca (Moench) Voss x Picea engelmannii Parry ex Engelm.), subalpine fir (Abies lasiocarpa (Hook.) Nutt.), trembling aspen (Populus tremuloides Michx.) and paper birch (Betula papyrifera Marsh.). Douglas-fir dominated stands occurred predominantly in the IDF, were frequently mixed with lesser amounts of lodgepole pine, and were generally considered to be “complex” with a wide range of DBHs up to 140 cm. These stands developed under frequent standmaintaining disturbances and infrequent stand initiating disturbances (Hoffos et al. 2001; Wong and Iverson 2004). Natural disturbances were predominantly caused by fire. As a result of many years of fire suppression, these stands have tended to become increasingly dense when compared with conditions under the historical fire regime (Daigle 1996; Wong 24  and Iverson 2004). In more recent times, human disturbance by logging using single tree selection has occurred in many of these stands. Lodgepole-pine dominated stands are most commonly thought to have been disturbed by more intense stand destroying fires (Hoffos at al. 2005). Since lodgepole pine trees have serotinous cones, regeneration following fire has resulted in stands with a wide range of densities but tending to be more even-aged. Alternatively, lodgepole pine stands can also be affected by low intensity fires and/or insect attack (e.g., mountain pine beetle, Dendroctonus ponderosae Hopk.) that initiate partial stand replacement and understory regeneration and growth response (Agee 1993), resulting in higher structural diversity than stands disturbed by intense fires.  2.3.2  Data Description  A total of 421 plots were established over a wide variety of stand structures and sites throughout the application area. Of these, 174 plots (41%) were 0.10 ha square plots, with an average of 258, and a range of 13 to 846 trees per plot. The remaining 247 plots (59%) were nested plots with a variable radius plot for larger trees (DBH ≥ 12.5 cm) and a fixed area plot for smaller trees (4 cm ≤ DBH < 12.5 cm) at the same sample point. The basal area factors for the variable radius plots ranged from 3 to 12 m2 ha-1 based on the objective of measuring 10 or more large trees per plot. The fixed area plots ranged from 1.78 to 17.84 m radius in size based on the objective of measuring 10 or more small trees per plot. On average, there were 27 trees measured per point, with a range of 10 to 58 trees per plot. For all plots, tree species and DBH were recorded for each tree, along with tree status as alive or dead. Heights were measured for a sample of trees in each plot and remaining heights were estimated for the 0.10 ha plots; all heights were measured for the nested plots. Merchantable volume per tree from 30 cm above ground to a 10 cm top diameter inside bark were estimated using Kozak’s (1988) taper functions with coefficients provided by the BC Ministry of Forests (2000). Plots were then summarized to obtain merchantable volume per ha (VPH; m3 ha-1), quadratic mean diameter (i.e., diameter equivalent to the mean basal area per tree, QMD; cm), Lorey’s height (i.e., height weighted by basal area, LMH; m), basal area per ha (G; m2 ha-1), and stems per ha (SPH; Table 2.1). As well, the reverse cumulative 25  distributions of SPH and G by DBH were also calculated and used in the distance metric described earlier. Table 2.1. Study area summary statistics for quadratic mean diameter (QMD), Lorey’s mean height (LMH), number of stems per ha (SPH), basal area per ha (G) and volume per ha (VPH) (n=421 plots).  QMD  LMH  SPH  G  VPH  (cm)  (m)  ( stems ha )  (m ha )  (m3ha-1)  Minimum  0.8  2.2  90  0.1  0  Median  11.4  16.1  2699  31.6  115.2  Maximum  32.6  37.6  39642  94.4  726.6  2.3.3  -1  2  -1  Stand Structure Classes  For this study area, the number of stand structure classes was varied in preliminary analyses and then was set to 17 based on the objective of having enough classes to represent the variety of stand structures, while still being able to interpret the resulting classes. The algorithm was run a number of times varying the initial random assignment of plots to the 17 classes, and the final classification was selected based on the smallest sum of the within-class distances across all classes. The resulting stand structure classes were numbered sequentially, roughly by increasing average basal area per ha; however, average tree size and other factors were considered as well (Table 2.2). The number of plots in a class ranged from 14 (3.4 % of all the observations; class 17) to 34 (6% of all the observations; class 1) with an average of 25. Using re-substitution to evaluate the consistency of classification results, only 1 of the 421 plots was misclassified resulting in a success rate of greater than 99%. In terms of plot SPH, stand structure class 9 had the smallest range (1530 stems ha-1 to 4339 stems ha-1), followed by classes 7, 3, 5 and 12 (Table 2.2). Relative to all 421 plots, these ranges were narrow indicating that the stand structure classes separate plots by plot SPH distribution. In terms of plot G, stand structure classes 1 to 5, 13 and 14 had G values less than the overall average of 31.7 m2 ha-1 for all plots. Stand structure classes 3, 6, 7, and 12 had ranges in plot G that were narrower than the range across the remaining classes. 26  Boxplots of plot G and SPH, variables that were used in classification, along with volume per ha (m3/ha) and quadratic mean DBH (cm), variables not specifically used in classification, showed reasonably clear differentiation among classes for all four variables (Figure 2.2). Within class variation was higher for some classes than for others, and there was some overlap in the ranges of these four variables among classes. Table 2.2. Number of plots, stems per ha, and basal area per ha by stand structure class using the new stand structure classification system.  Stand Structure Class  Number  Stems Per Ha  Basal Area Per Ha  of Plots Minimum Mean Maximum Minimum Mean Maximum  1  34  90  2565  18090  0.1  4.5  11.3  2  31  3260  9392  18289  5.8  16.9  27.4  3  32  813  2065  4672  10.3  16.3  20.8  4  33  2430  6652  21161  20.2  29.0  44.4  5  31  1443  2202  5711  21.5  25.7  31.4  6  29  897  1890  9456  30.4  33.6  38.4  7  27  1990  3472  5513  31.5  35.9  39.0  8  22  2290  6724  13258  39.9  49.4  67.9  9  21  1530  2480  4339  43.2  50.7  64.1  10  23  890  2261  8672  44.9  53.3  76.9  11  19  680  2037  5679  41.1  53.4  94.4  12  22  670  2460  5510  34.7  40.8  44.3  13  22  303  8408  39642  9.5  18.2  33.2  14  23  410  3256  21201  19.1  24.3  30.5  15  19  660  7170  22660  27.2  35.2  42.8  16  19  600  5684  16303  32.5  43.4  55.5  17  14  1510  5483  35320  42.2  51.5  65.6  All  421  90  4291  39642  0.1  31.7  94.4  27  100  25000 -1 SPH (stems SPHSPH (# ha-1) ha )  90 80 2 G (mG ha-1)  70 60 50 40  20000 15000 10000  30  5000  20 10 0  0  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  Stand Structure Class  40  800  30  600  VPH  VPH (m3ha-1)  (cm) QMDQMD  Stand Structure Class  20  10  0  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  Stand Structure Class  400  200  0  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  Stand Structure Class  Stand Structure Class  Figure 2.2. Box plots by stand structure class for: basal area per ha (top left), stems per ha top right), quadratic mean diameter (bottom left), and volume per ha (bottom right). (Box plots: Central line is the median, the top of the box is the 75 percentile, the base of the box is the 25% percentile, whiskers indicate 95% and 5% percentiles, and asterisks and circles indicate outliers.)  The means of the Gini Index and the SDVI increased with the stand structure class (Figure 2.3). Using SDVI for DBH alone provides a value of 1 for stands with a uniform distribution of G over the DBH range (i.e., greater diversity), which was from 0 to 140 cm for this example. An STVI of 0 indicates a unimodal (i.e., narrow range of DBH) distribution with the lowest diversity, whereas values near 0 indicate low diversity, either close to a unimodal distribution or alternatively, close to a maximally bimodal distribution with trees at the 28  extremes of the DBH range only. Classes 13 to 17 tended to SDVI values closer to 1 indicating higher complexity compared with the remaining classes. Classes 1 and 2 indicated low complexity, since these classes included plots with small trees and limited size diversity. There were wide variances in STVI within some classes, likely partly due to STVI being defined by distribution of basal area only. Overall, there was generally clear differentiation in these plot-level variables among stand structure classes resulting in high between class and  1.0 1.0  1.0  0.8 0.8  0.8  0.6 0.6  0.6  STVI STVI  Gini Index  Index Gini Gini Index  low within class variation.  0.4 0.4 0.2 0.2  0.4 0.2  0.0 0.00  0 11 22 33 44 55 66 77 88 99 10 1011 1112 1213 1314 1415 1516 1617 1718 18  0.0  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  Stand Class StandStructure Structure Class Stand Structure Class  Stand Structure Class  Figure 2.3. Boxplots of the Gini Index (left) and the Stand Variance Index (STVI, right) by stand structure class. (See Fig. 2 for description of box plots.)  The interpretation of the Gini Index is less straight forward because it is scaled relative to the mean tree DBH for each plot. Hence a stand with a small average tree diameter and proportionately large range of diameters can be ranked similarly to a stand with a large average tree diameter and also a large range of diameters. For the Gini Index to increase above 0, the distributions of trees must become increasingly skewed toward smaller or larger trees relative to the mean, but exactly which direction is ambiguous.  29  Using the classification results and average reverse cumulative distributions by class (i.e., class centroids), differences between stand structure classes are quite apparent (Figures 2.4 and 2.5). Stand structures that are often referred to as single-layered with most trees in a limited range of DBHs versus complex with a wide range of DBHs were clearly differentiated (Figure 2.4). The complex stands can be readily identified in terms of cumulative distributions of basal area per ha that decline gently over the entire range of diameters and this is most apparent where the range in diameters is large, i.e. classes 13 to 17. Stands with basal area concentrated within a smaller range of diameters are indicated by cumulative distributions of basal area that are relatively flat at either end and steep in the middle, unlike the distributions for classes 13 to 17. Note that Figure 2.4 is truncated at 12cm DBH and therefore does not show the flat portion of the curve as diameter decreases toward zero. The steep slope indicates a predominance of trees in a layer contained in portions where the slope is steep. However, these correspondences are approximate, based on average trends. There is some within class variation, but the trends in cumulative basal area with respect to increasing diameter tended to be precise across the range of diameters, particularly in steep portions of the curve, when observing data from individual plots versus the average for the associated classes. Some classes (i.e., 2, 4, 8, 13, 15, 16, and 17) were distinguished by many small trees resulting in a steep descent for the reverse cumulative SPH distribution (Figure 2.5). Classes 1 to 11 represented relatively narrow ranges of DBH in plots (Figures 2.4 and 2.5), classes 13 to 17 represented wide ranges, and class 12 was intermediate.  30  60  50  G (m2ha-1)  G (m2 ha-1)  10  11  9  40  30  8 6 7  17 20  5 16  12  3  14  10  15  13 4 2 1  0  12  16  20  24  28  32  36  40  44  48  52  56  60  64  68  72  76  80  84  88  92  96 100  DBH (cm) DBH (cm)  Figure 2.4. Average reverse cumulative distributions of basal area per ha (m2ha-1) versus DBH by stand structure class. (Solid lines indicate classes commonly described as “even-aged”; dashed lines indicate “uneven-aged” stands).  10000 9000 2 8000  SPH # ha-1  SPH (stems ha-1)  13 7000  15  6000 16  5000  17 4000 8 7  3000  4  14 5 12  2000  9 10 3  1000  6 11 1  0 0  1  2  3  4  5  6  7  8  9  10  11  12  DBH (cm)  DBH (cm)  Figure 2.5. Average reverse cumulative distributions of stems per ha (m2ha-1) versus DBH by stand structure class. (Solid lines indicate classes commonly described as “even-aged”; dashed lines indicate “uneven-aged” stands). 31  As noted, comparison with an alternative method for classification can be helpful in assessing the new stand structure classification method. In this case, plot-level statistics representing Lorey’s mean tree height, SPH, G, and quadratic mean diameter were used in calculating Euclidean distances and a k-means cluster algorithm (Systat Software Inc. 2004) was used to separate the 421 plots into 17 classes. The tendency of k-means clustering to produce an unequal distribution of plots amongst classes was observed with nine classes having seven or less observations per class (i.e., less than 1.7 % of the observations in each case) (Table 2.3). One class contained 111 cases or 26 % of all observations. In contrast, the number of observations per class in this study ranged from 14 (3.4 % of all the observations) to 34 (6% of all the observations). The classes clearly differed in terms of stems per ha as can be seen from the non-overlapping ranges; they were specifically ordered in terms of numbering to highlight this fact. Overall, the new stand structure classification system, which used a distance metric that better reflects stand structure and an algorithm that reduces class imbalances, better reflected structural differences among classes than the k-means approach. Consequently, it led to better stand structure classes. As noted previously, another important assessment of a stand structure classification system is whether it provides classes that are useful for forest management. The results for this study area were provided to forest practitioners as a field guide with illustrations and photographs for each stand structure class (Farnden et al. 2003). Initial indications were that the resulting classes could be identified in the field and were useful for stand description/management purposes. 2.4  Discussion  The new stand structure classification system using the new distance metric described and illustrated in this paper has a number of advantages over other available classification methods. It subdivides the continuum of stand structure measures into a desired number of classes without any a priori descriptions of class membership, is nonparametric, uses commonly measured attributes, and avoids class imbalances. 32  Table 2.3. Number of plots, stems per ha, and basal area per ha by stand structure class using the kmeans clustering.  Stand Structure Class  Number  Stems Per Ha  Basal Area Per Ha  of Plots Minimum  Mean  Maximum Minimum  Mean  Maximum  1  67  90  968  1380  0.1  30.2  62.6  2  111  1393  1797  2311  0.8  30.5  94.4  3  84  2335  2847  3480  3.5  33.0  65.6  4  55  3502  4126  4813  1.6  33.0  76.9  5  30  4940  5583  6240  6.3  36.9  91.2  6  20  6451  7137  7705  15.4  32.4  67.9  7  14  8182  8937  9744  6.6  24.9  62.9  8  11  9980  10770  11628  7.7  32.6  57.6  9  7  12243  12719  13258  12.4  31.7  58.9  10  4  14380  14533  14616  33.2  38.4  42.8  11  5  15300  15889  16303  13.4  28.1  43.6  12  4  17429  18010  18289  1.0  15.9  36.5  13  2  19573  19857  20141  38.5  41.3  44.1  14  3  21161  21207  21259  25.7  33.9  44.4  15  2  22639  22650  22660  25.4  31.1  36.8  16  1  35320  35320  35320  58.2  58.2  58.2  17  1  39642  39642  39642  18.4  18.4  18.4  All  421  90  4291  39642  0.1  31.7  94.4  Empirical cumulative distributions of stems and basal area per ha by DBH were used in the classification resulting in a distribution-free approach, avoiding the constraint of assuming theoretical distributions. This avoided the censoring of actual distributions that can result from the inherent limits of theoretical distributions. Nagel et al. (2007) examined five different distributions (negative exponential, rotated sigmoid, increasing-q, unimodal and binomial) in both managed and unmanaged northern hardwood stands in the western Upper Peninsula of Michigan. They found that managed stands could be well represented by an 33  increasing q-distribution 44% of the time, and that these were independent of spatial scale. In unmanaged stands, rotated sigmoid shapes were effective 50% of the time, but the preferred choice of distribution varied significantly with scale. They noted that an appropriate theoretical distribution needed to represent a given condition may be affected by differences in the scale of observation. The new stand structure classification system would avoid these difficulties. Using cumulative distributions of basal area and stems per ha by DBH that represent both small trees, which tend to have high numbers of stems per ha, and large trees, which tend to have high basal area per ha, results in more meaningful structural distinctions. The rankings of the distributions are used to standardize the two scales of measurement for the application data. Ranks are also normalized to values between zero and one to facilitate tracking of the progress of the algorithm with each iteration using the within and between class differences. The reverse cumulative distributions are used in the distance metric, R (Eq. 1). At each iteration, observations are moved based on providing the smallest R, subject to the constraint that this minimum R must be < 1. This criterion is equal to the marginal change in the sum of within class differences (based on the class to which a plot is being reassigned) divided by the marginal change in the sum of between class differences (based on the class from which the plot is being reassigned). The distance matrix is calculated in advance for each pair of observations rather than in the process of running the cluster algorithm. This reduces computational difficulties by reducing the number of variables retained, as well as removing the need to recalculate mean values and sums of squares for each step in the clustering process. The constraint of R <1 used in this algorithm does not remove the problem of the algorithm becoming trapped in local optima, a common problem with clustering procedures. In another version of this algorithm, the constraint that the ratio must be <1 was replaced by the criterion that the routine stops when a single plot cycles between two classes (i.e., it is moved from one class to another, and then moved back to the same class). The change in the stopping rule improved the quality of solutions as indicated by further decreases in the sum 34  of within class differences and increases in the sum of between class differences, but did not achieve the objective of avoiding local optima. Likely such local traps are the result of moving one plot at a time, when two or more simultaneous moves may be required to obtain further gains. To systematically search for optimal moves of this kind would be expensive in terms of processing time. A compromise might be to allow a larger number of simultaneous moves at the beginning, subject to the constraint that the moves involve R values ≤ 1. Simulated annealing (Duda et al. 2001) might also be applied in an effort to restrict solutions to global optima. However, there appears to be no universal solution to this kind of a problem (Duda et al. 2001). The decision was made for this clustering algorithm to repeat the clustering process a number of times with different starting conditions, and to select the solution with the minimum sum of within class differences. In monitoring the behavior of the algorithm toward a final solution in applications of this algorithm, the reduction in the sum of within class differences at each iteration was observed to be a smooth progression, asymptotic and convex. The increase in the sum of between class differences was also a smooth progression and asymptotic, but concave. This suggests that the objective function produces results that would be similar to minimizing the sum of pairwise differences within each class or alternatively, to maximizing the pairwise differences between classes. Similar results are also likely when minimizing the within class sum of squared errors (Duda et al. 2001). One of the goals in developing the algorithm was to separate the stand structure continuum into classes with a reasonably even distribution of observations amongst the classes. Several factors contributed to reaching this goal. First, ranking and normalizing observations based on stems and basal area per ha before calculating R ensures that outliers are more closely aligned with their nearest neighbours. Second, the use of R that measures the change in the sum of within class differences from a given observation to all other observations within a class ensures that R increases as the number of observations within a target class goes up. The result is that the attractiveness of the target class decreases relative to the attractiveness of the remaining classes. This is in contrast to what would occur if movement of observations from one class to the next was based on the change in mean instead of total differences. In 35  the example provided, there was a relatively even distribution of plots among the 17 stand structure classes. However, the class membership still reflected the number of samples in a given structure class. For example, Classes 1 to 5, with lower basal areas per ha had higher than the average numbers of samples (i.e., 25 plots) as these stand structures were better represented in the dataset. This stand structure classification system resulted in classes that provide distinct differences in stand structure measures (Figure 2.2), as shown for the example provided. As an alternative to stand structure classes, other approaches to characterizing stands have involved the use of structural indices. The STVI by Staudhammer and LeMay (2001) presented a combined structural index that could be used for basal area distributions by DBH and/or height, where species is incorporated by calculating separate indices by species and summing over all species. However, the STVI was explicitly derived to provide a continuous measure of structural diversity relative to a standard of a most diverse stand (i.e., uniform distribution of G by DBH and/or by height). Although STVI is related to the stand structure classification system described in this paper, as shown in the application example, the stand structure classes do not relate to a standard. Rather, the continuum of stand structure differences is divided into classes with the intent that these classes can then be described and illustrated based on commonly measured attributes for use by a variety of practitioners. The application of this stand structure classification system was illustrated by classifying 421 plots of a study area into classes that exhibited between-class differences and within-class similarities in terms of both empirical distributions of SPH and G by DBH and average stand statistics. For this application, species was not used; all live trees were pooled in the stems per ha and basal area per ha DBH distributions. In another application of this algorithm (results not shown), separate cumulative distributions by species for each plot were used. Absolute differences between plots were then summed across all species to derive the distance matrix. However, separation by species required many more classes to reasonably represent all possible combinations of species and size class distributions resulting in a system that is too complex and consequently not useful. Further, a rare species would be difficult to represent in this system, and, where there are many species, there may be a 36  confluence of species and DBH. Where species composition is important for application, Staudhammer and LeMay (2001) recommended separation of species into guilds. The addition of species guilds could be used in this stand structure classification system and this might provide useful stand structure classes. As with species, additional attributes could be represented in the stand structure classification system. For example, distributions of snags and coarse woody debris have been shown to be important for a number of wildlife species (see O’Neil et al. 2001). However, since many habitat elements are the result of live trees, the use of stems and basal area per ha distributions by DBH may already indicate these structural differences. For example, the occurrence of large diameter living trees indicates a greater potential for the occurrence of large diameter dead trees. Although the distance metric and the algorithm described and illustrated in this paper could be modified to include additional stand structure attributes, the stand structure classification system illustrated has a number of desirable characteristics. Changes to the algorithm may provide additional benefits, but these may be at the cost of some of the desired characteristics of a stand structure classification system. Fundamentally, the resulting classes must be useful. Based on the application to the study area described in this paper, this system does provide useful stand structure classes that could be used by a variety of forest practitioners.  2.5  Conclusions  In this chapter, a quantitative stand structure classification system was proposed and demonstrated for one study area. The goal in the algorithm was to minimize within class differences of stems and basal area per ha distributions by DBH, while avoiding class imbalances. The application to the study area indicates that the resulting classes show differences in common stand structure measures that were not explicitly used in the algorithm, and preliminary results indicate that the resulting classes are useful to practitioners. Overall, this stand structure classification system provides an effective mechanism for assessing current as well as future states of forests important for reaching forest management objectives. The main strength of this development is in the deployment of 37  non-parametric cumulative distributions with equal weight given to the distributions in numbers of stems and to basal areas per hectare. The cluster algorithm succeeded in producing a reasonably balanced distribution of observations amongst the various classes, but path dependencies remain dependent on the initial assignment of observations to classes at the start of the algorithm. The main limitation is that differences in species composition with respect to diameter were not explicitly accounted for as part of the process in building a system of classification.  38  Chapter 3: Using Stand Structure Classes to Predict Ecological Succession Pathways 3.1  Introduction  Changes in stand structure of forest environments, specifically, species diversity, variation in tree sizes, and other elements, may follow a somewhat predictable path of ecological succession. Gomez-Pompa and Vazquez-Yanes (1981) distinguished five succession stages in evergreen rainforests of Mexico following a stand-replacing disturbance event, namely: 1) a short period of dominance by ephemeral herbs (a few weeks to months); 2) dominance by secondary shrubs that eliminate pioneer herbs by shading (6 to 18 months); 3) dominance by secondary trees of low stature (3 to 10 years); 4) dominance by taller secondary trees (10 to more than 40 years); and 5) dominance by tall primary trees (until a major disturbance occurs). Kimmins (2004, p. 33) characterized stand succession as early, mid, late and climax seral stage development, emphasizing time since disturbance. Perry et al. (2008) stated that the sequence described by Gomez-Pompa and Vazquez-Yanes (1981) represents succession in all forests although the number of stages and duration of each stage varies depending on the environment and total species pool. The general autogenic pattern of secondary ecological succession of tree species in temperate and northern forests proceeds with somewhat random processes involving the germination of seeds that either exist from previous disturbances or become newly established following disturbance. Beyond that an evolutionary process is followed whereby certain kinds of species are selected in terms preferred traits (e.g. shade intolerance) influencing survival and growth depending on the post disturbance environment and its development with time (Drury and Nisbet 1973; Whelan 1995; also see Oliver and Larson’s 1990 commentary on ”relay” versus “initial” floristics). A wide variety of succession pathways can be manifested contingent on the interactions between autogenic and allogenic processes and their influence on species establishment, survival, growth, and mortality. In the Canadian boreal forests, succession may start from shade-intolerant hardwoods, for example, aspen (Populus tremuloides Michx.) and proceed toward more tolerant conifers such as white spruce (Picea glauca (Moench) Voss) (Kabzems and Garcia 2004), perhaps as a result of regeneration immediately following disturbance or after some delay or both (Peters et al. 2006). In 39  temperate European forests, the general succession pattern may start with shade-intolerant conifer Scots pine (Pinus sylvestris L.) and proceed toward more tolerant hardwoods, such as oak (Quercus sp.) and beech (Fagus sylvatica L.) (Kint et al. 2006). Consequently, changes in stand structure have been used to characterize ecological succession in forests. This structural sequence is consistent with the notion of a final stage in succession or climax (after Clements 1916) that can be maintained for long time periods. For this stand structure to be maintained, the forest must be dominated by shade-tolerant species that can reproduce under their own canopy (typically with small gaps between the crowns of trees; see Oliver and Larson 1990, pp. 151-152.) and/or from large-tree senescence and small-spatial scale disturbances such as endemic pathogens and insect causing mortality of individual trees. Because stand structure is indicative of stages of succession, many authors have used stand structure attributes to characterize stand dynamics in forest environments. Oliver and Larson (1990, p. 142) labeled the stand development stages as stand initiation, stem exclusion, understory re-initiation, and old growth phases, emphasizing dominant processes. Mayer (1976) and Liebundgut (1993) identified six stages as follows: initial, optimum, decomposition, (complex) regeneration, and plenter. Shorohova et al. (2009) classified boreal forest dynamics based on time since disturbance along with prevailing disturbance regime, site type, and stand characteristics. They identified four stages: even-aged, compositional change development; even-aged, mono-dominant development; cohort dynamics; and fine-scale gap dynamics. Huber (2011a) developed a means of relating Mayer’s and Liebundgut’s stages to actual ground conditions, and then used these to characterize individual tree model (PrognAus) output (Huber 2011b). He compared the results with Mayer’s (1976) hypotheses, including the hypothesis that the steady state at the end of a long simulation would result in a Plenter forest, or uneven-aged condition; instead he found that it resulted in a terminal or decomposition stage according to his numerical manifestation of the Mayer and Liebundgut classification scheme.  40  As well as being used to describe ecological succession stage, stand structural elements are used to prescribe silvicultural interventions, to describe and manage for habitat requirements for species, and to assess forest environments with regards to a suite of social benefits from forests. Silviculture systems, including clearcut, seed tree, shelterwood, selection and coppice, are based on obtaining successful reproduction, survival and growth of trees of one or more desired species (Smith et al. 1997). O’Neil et al. (2001) defined 26 different stand structural types based on canopy cover (open, medium and closed), average tree size (seedlings, saplings, medium trees, large trees, and giant trees) and number of layers or canopy strata for habitat in Oregon and Washington, USA. Knoke (2010) indicated that stand structural classes were a necessary prerequisite for evaluating stand values including wildlife species habitat, watershed characteristics, recreation opportunities, fire hazards, and timber supply. In Chapter 2 of this dissertation, I developed an objective stand structure classification system as a means of separating commonly measured plot (or stand) information into distinct, homogeneous, stand structure classes without any preconceived notion as to what the classes should mean in terms of ecological processes, succession pathways, and stand dynamics. The goal of the classification algorithm was to produce a meaningful, classification system that would facilitate more consistent, reliable and verifiable communication of stand structure attributes across a wide variety of forest resource management disciplines. Briefly, the algorithm classifies plots (or stands) based on a new distance metric that quantifies similarities in the empirical reverse cumulative diameter at breast height (DBH, 1.3 m above ground) distributions of basal area and stems per ha (i.e., proportions of trees or basal area greater than a particular DBH) by species or for all species combined. The algorithm also includes a mechanism to avoid large class imbalances wherein some clusters have only a few observations and others represent most of the observations (e.g., Barandela et al. 2002). In this study, the question of whether knowledge of the stand structure class at the beginning of a projection period could be used to predict a likely ecological succession pathway was posed. In particular, the objective stand structure classification system developed in Chapter 41  2 was examined as a mechanism for examining consistencies and variations in ecological succession in stands of the Interior Douglas-Fir (IDF) Biogeoclimatic Zone of central British Columbia (BC), Canada (Steen and Coupe 1997). An improved understanding would improve communications regarding the stand conditions needed to manifest desired future forest conditions, particularly with regards to patterns of succession and the underlying changes in tree species composition and diameter distributions over time. The IDF stands examined in this study are primarily mixtures of interior Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco var. glauca (Beissn.) Franco) and lodgepole pine (Pinus contorta Dougl. Ex. Loud. var. latifolia (Engelm.) Critchf.). The 17-class stand structure system presented in Chapter 2 was also used in this study, and the specific questions addressed were: 1. Does a comprehensive pattern of succession emerge after observation of a wide variety of simulated stand conditions through time as evaluated through the lens of the 17 stand structure classes? 2. Does the number of alternative succession pathways become more limited depending upon the stand structure class identified at the start of any one projection period? 3. Related to question 2, is it possible to predict the succession pathway given the current stand structure class along with easily measured plot-level (or stand-level) variables? 4. Can differences among succession pathways be readily visualized in terms of species composition and the underlying diameter distributions? 5. Do differences in succession pathways result in consequences from a growth and yield perspective? A model-based approach was used to examine the succession of stand structure over a long time period. First, each fixed area permanent sample plot (PSP) in the available database was classed into one of the 17 stand structure classes previously determined for these forests. Each PSP was then used to initiate a forecast of tree and stand development at 5-year intervals for a 155 year period using an individual tree growth model. At the end of each 5year projection, the forecasted PSPs were reclassified into one of the structure classes. From 42  these data, patterns of stand structure progression were examined for consistency across all PSPs. The growth model used represents the specific ecological forest type and was specifically calibrated for use in this area. For this research, the model was assumed to be correct. It was also assumed that no new trees established as ingress during the projection period and that there were no natural or anthropogenic disturbances that would alter the development pattern, meaning that the stand followed an ideal progression toward a climax condition. These assumptions provided a basis for evaluating stands relative to the initial stand structure conditions. They provided a benchmark for identifying probable patterns of succession while avoiding confounding effects of various kinds of potential disturbance agents and associated responses. Although more realistic scenarios could have been used, the purpose behind these assumptions was to establish an initial point of reference. A number of factors including species composition are investigated as a means of explaining why specific pathways are taken through the 17-class system of classification and not others. In this concept, species composition both determines and is determined by structural features, but structural features come first by way of the design of the system of classification.  3.2 3.2.1  Material and Methods Study Area Description  The study area was located in the general vicinity of Williams Lake, BC (52o 7’ 29.56” N, 122o 7’ 52.9” W, 575 m elevation) in the Interior Douglas Fir, Dry Cool Subzone, Fraser Variant, in the Interior Douglas-fir, lodgepole pine, Pinegrass (Calamagrostis rubescens, Buckley) – Feathermoss (Pleurozium, schreberi (Brid.) Mitt.) site series (IDFdk3/01, Steen and Coupe 1997; Hope et al. 1991). The Fraser variant covers 8953 km2 and generally ranges from 750 to 1200 m in elevation. The mean annual precipitation is 433 mm with 207 mm occurring in summer months. Mean annual snowfall is 231 cm, and there are on average 151 frost-free days. Substantial growing season moisture deficits are common and frost can occur at any time (Hope et al. 1991). The soils associated with the Pinegrass-Feathermoss  43  site series are generally Orthic Gray Luvisols (Soil Classification Working Group 1988) capped by a Hemimor humus form (Green et al. 1993). As noted, the forests in this study area are dominated by interior Douglas-fir and lodgepole pine. Of the two species, interior Douglas-fir1 is more shade tolerant and generally thought to be shade demanding during the establishment phase on drier sites (USDA 1990), which are common in this study area. This species can persist under low light levels for relatively long periods of time by allocating more carbohydrates to lateral branch growth instead of height growth (Williams et al. 1999). Interior Douglas-fir responds well to release from overstory competition and may reach a height of 30 to 37 m with DBHs (measured at 1.3 m above ground-level) ranging between 38 and 102 cm in 200 to 300 years, or even larger over longer periods of time. The species develops thick bark with age, making it increasingly resistant to fire, with the result that two and three layered stands often develop naturally, particularly under frequent, lower-intensity fire regimes (Steinburg 2002). Such stands may persist without any disturbance other than natural senescence of overstory trees accompanied by regeneration in the understory (Tesch 1981). Successful establishment of interior Douglas-fir can be strongly inhibited in large openings due to increased exposure to the effects of frost or drought, as well as by an increased presence and vigour of grasses in these circumstances (Fleming et al. 1996; Harper et al. 2005). Cattle grazing and trampling, and natural or prescribed grass-land fires can also cause small tree mortality. Lodgepole pine is shade intolerant, and exhibits more aggressive height growth relative to diameter growth. The species can survive under partial shade, but does not respond well to release from overhead shade and most likely will not survive under these conditions (USDA 1990; Williams et al. 1999). Lodgepole pine grows rapidly in height except in very dense stands where height repression can occur. It can grow up to 30 m in height and 40 cm in DBH and rarely survives beyond 200 years. A combination of fire suppression and endemic  1  Coastal Douglas-fir or Pseudotsuga menziesii var. menziesii (Mirb.) Franko is generally considered to be  shade intolerant, whereas interior Douglas-fir is shade tolerant. 44  levels of mountain pine beetle (Dendroctonus ponderosae Hopkins; MPB) can facilitate the development and persistence of lodgepole pine in a complex stand type (Axelson et al. 2009). However, this same pattern may also be created as a result of frequent low intensity, stand maintaining ground fires (Hoffos et al. 2001; Wong and Iverson 2004), particularly in relatively open lodgepole pine stand conditions (Anderson 2003) or in open, relatively moist Douglas-fir – lodgepole pine conditions (Tesch 1981). Fire suppression in similar types in Western North America is generally believed to have resulted in higher stand densities in these dry Douglas-fir / lodgepole pine stands when compared with those prior to European settlement (Daigle 1996; Wong and Iverson 2004), but this general observation is not without considerable uncertainty (Klenner et al. 2008).  3.2.2 3.2.2.1  Data and Stand Structure Progressions Permanent Sample Plot Data  PSP data provided by the former BC Ministry of Forests and Range were used in this study since these plots are relatively large in size and improved quality control procedures were used to ensure reasonably precise measurements. PSPs occurring in the IDFdk3/01 site series (103 plots) were selected from the database. On average, there were 833 measured trees per plot, and plot sizes ranged from 0.04 to 0.10 ha with 94 of the 103 plots having a plot size of 0.10 ha. There were 140 records in total, with six PSPs each having three remeasurements (excluding the first measurement), and 19 PSPs each having one remeasurement. The PSPs were established between 1965 and 2001, with most of them (74 plots) established between 1999 and 2001. Although this forest area has recently experienced a mountain pine beetle epidemic, all of the plots measurements were prior to the epidemic. The PSPs were dominated by interior Douglas-fir and lodgepole pine, in pure species stands and in mixtures. Each PSP at a particular measurement time was treated as a single observation in this paper (herein referred to as a “plot”), since the main goal was to identify potential patterns of succession over an extended period of time.  3.2.2.2  Initial Stand Structure Classes  The initial reverse cumulative diameter distributions by stems and by basal area per ha (hereafter termed “basal area distribution” when basal area per ha was used, and “stems per 45  ha distribution” when stems per ha was used) were used to assign each of the 140 observations to one of the 17 stand structure classes (SSCs) previously established for these forests (Figures 2.4 and 2.5). As described in Chapter 2, SSCs 1 to 11 broadly represent single-layered stands from relatively low to high basal area per ha. Generally, the majority of basal area in these stands falls in a relatively narrow range of diameters. In contrast, SSCs 13 to 17 have much flatter cumulative basal area distributions, accompanied by considerable basal area in trees of relatively large diameters (i.e. > 50 cm DBH) that are more representative of complex stands. These classes were numbered to be consistent with a progression from low to high basal area. SSC 12 represents an intermediate structure class between single layered and complex stands. To some degree, the SSC classes can be differentiated on the basis of whole stand statistics (Figure 2.2). One important distinction is that SSCs 2, 4 and 8 represent stands with high stems per ha when compared with the rest. There was a considerable amount of variation in stems per ha within each stand structure class, but less variation in the basal area per ha. For each plot, the distance metric was calculated using the distributions of basal area and stems per ha, relative to the reference data distributions for all original plots used in Chapter 2 to develop the 17-class system. In calculating the distance for each plot, the distribution for basal area per ha was found by calculating the basal area greater than the DBH threshold, beginning with 140 cm DBH and then decreasing to 0 cm in 1 cm decrements. This process was repeated for the distribution in stems per ha. The two distributions were then rescaled to values between 0 and 1, based on the ranking of plots in the original reference dataset in Chapter 2, where 0 was equal to the minimum values (i.e. 0 basal area or stems per ha) and 1 was equal to the maximum rank. For each plot, the differences between the two ranked plot distributions and the reference plots in an SSC were calculated by 1 cm decrements. These differences were then summed, squared, and added, before finally taking the square root to obtain the distance for a plot from each of the reference plots in a given SSC. The most similar stand structure class was then selected based on the smallest distance to the reference plots.  46  3.2.2.3  Forecasts of Plot Data and Assigning Stand Structure Classes  PrognosisBC (v 3.01.001; BC Ministry of Forests 2008) calibrated for the IDFdk3/01 site series was used to grow individual trees in each plot and the Stand Visualization System (version 3.36; McGaughey 2002) was used to visualize the output. Growth and mortality was forecast for 155 years at 5-year intervals. While model uncertainty increases with projection length, a long trajectory was used to capture a potentially broad range of succession pathways, including those where presence or absence of smaller trees at the beginning of the projection period might be important to determining the pathway at later dates. As noted previously, no new trees were allowed to regenerate and no disturbance agents were introduced or accounted for in the simulations. This precluded the possibility of single-tree mortality causing regeneration into gaps. However, since lodgepole pine is shade intolerant and interior Douglas fir is only moderately shade tolerant on these sites, and since invasion by grasses may pre-empt successful regeneration, this assumption may be considered plausible for these forests. Each 5-year projection of each plot was then assigned to one of the 17 stand structure classes, following the same approach as for the initial plot measures.  3.2.2.4  Potential Succession Pathways and Cluster Analysis  Each plot followed a progression of stand structure classes. In order to address questions 1 and 2 posed in this study, all of the potential stand structure succession pathways were identified using these data. Each unique pair-wise combination of succession, from one stand structure class to the next, was identified and then mapped. The resulting diagram indicated all potential pathways starting in any given stand structure class. These stand class projections were then summarized by first calculating the time spent in each of the 17 classes for each of the plots, including 0 for no time spent in a class. Hierarchical clustering using SYSTAT (v. 11, Systat Software Inc. 2004) was applied to group these data into similar pathways using Euclidean distance. This process was used to identify the most common patterns of progression. The subsequent groups are termed succession pathways (SP’s) in this chapter.  47  3.2.2.5  Examining Pathways for Differences  Once the SPs were determined, questions 2 and 3 were addressed by investigating whether selected plot-level variables could be used to differentiate between SPs given the same initial SSC. In particular, two SSCs (3 and 4) were well represented in the projections and all SPs that included the two SSCs were identified. Variables such as the stems per ha and basal area per ha were then used in a multivariate discriminant analysis using SYSTAT (v. 11, Systat Software Inc. 2004) to examine whether the SP could be discriminated. Accurate discrimination results would indicate whether it is possible to predict the succession pathway given the current SSC using easily measured variables.  3.3 3.3.1  Results Plot Data  For the 140 plots, initial stand densities ranged from 190 to 16730 stems per ha, with a mean of 3179 trees greater than 0 cm DBH (i.e. more than 1.3 m tall) (Table 3.1). Basal area per ha ranged from 6 to 64 m2 ha-1 with a mean of 28. Lorey’s mean tree height (i.e., average height weighted by basal area per ha) ranged from 6 to 29 m, with a mean of 16. These statistics generally coincided with those in the reference data (data not shown) used to develop the 17 SSCs shown in Figure 2.2. Based on the initial plot data, the majority of plots were classed as SSCs 3 and 5, followed by SSCs 1, 6, and 7 (Table 3.1). The remaining classes were less well represented, but all SSCs had at least one plot.  3.3.2  Potential Succession Pathways  All pairs of progressions from one SSC to another were identified and diagrammed (Figure 3.1) resulting in potential succession pathways. Some distinct patterns were evident. The downward trend (solid lines) indicates a linear progression of stand structure classes. The pattern tends to be highly constrained at the beginning (SSCs 1 and 2) and at the end (SSC sequences 9 →10→11→ 16, 12→16, and 16→17) with the greatest range of potential succession pathways in the middle of the diagram. The SPs terminate in irregular stand structures represented by SSCs 16 and 17, consistent with the notion of progression from single to multi-layered stands. The SPs that moved from the lower to upper parts of the  48  diagram (dotted lines) were much less common, as were cyclical progressions (dotted lines marked with C).  Table 3.1. Number of measurements (N1), number of plots (N2), and plot statistics (minimum (Min), mean (Mean) and maximum (Max)) for stems per ha (SPH > 0 cm DBH), basal area per ha (G; m 2 ha-1) and Lorey’s mean tree height (HT; m) by initial stand structure class (SSC).  SPH  G  HT  SSC  N1  N2  Min  Mean  Max  Min  Mean  Max  Min Mean Max  1  10  10  280  860  2980  6  8  12  6  13  17  2  6  6  4225  10071  16730  17  23  28  6  7  9  3  33  18  280  2150  16630  9  17  30  9  14  19  4  5  5  6880  10358  15970  29  33  36  7  10  12  5  25  17  948  2413  8600  22  27  35  12  16  19  6  10  5  1370  2287  4430  29  35  40  15  18  20  7  12  9  1900  3932  6550  31  36  41  12  14  18  8  4  2  3104  4462  5530  44  49  55  14  16  17  9  1  1  1930  1930  1930  64  64  64  20  20  20  10  3  3  1030  1277  1490  51  52  53  21  23  25  11  3  3  680  1463  2370  42  48  51  23  25  26  12  1  1  2700  2700  2700  44  44  44  19  19  19  13  6  5  290  1764  4400  13  21  31  15  19  21  14  7  5  770  4002  8680  22  27  35  14  18  23  15  5  5  1420  3154  4940  31  34  37  18  21  25  16  8  7  190  4264  7680  31  42  53  23  25  29  17  1  1  3720  3720  3720  55  55  55  21  21  21  All  140  103  190  3179  16730  6  28  64  6  16  29  49  Single layer Moderate Density  1  Single layer High Density  2  3  Complex 13  4  5 14 7  15  6 C  8 12 9  <  11  10 C  C  17 C  16 C  Figure 3.1. Potential succession pathways, where: numbers indicate stand structure class (SSC); thin, solid straight lines indicate the succession pathways (SPs) with arrows indicating the direction of progression; thin, dotted straight lines indicate pathways in a direction that is opposite to the dominant; dashed lines marked with a “C” indicate a circular pattern that persisted throughout an entire simulation; arrows indicate the direction of travel along any one line; and a bridge indicates the two lines do not intersect. The heavy, curved lines indicate 4 generalized succession patterns: single layered, high density (  ); single layered, moderate density (  and mixed complex – single layered (  ); moderate density complex (  );  ).  50  The succession pathways can be vertically split with the irregular stand conditions tending to fall on the left hand side of Figure 3.1 (i.e., SSCs 13, 14 and 15), and single layered progressions tending toward the right (i.e. SSCs 8, 9 and others). The SSCs in the centre of Figure 3.1 (e.g., SSC 6) tend to be stands with a single canopy. The degree of heterogeneity of tree sizes generally affected whether stands progressed to the right, left or middle of Figure 3.1. Plots that appeared on the left side of the diagram (i.e., SSCs 13, 14, and 15) sometimes crossed over to the right mid way down the diagram, but crossing in the opposite direction only occurred at the bottom of the diagram toward stand structures 16 and 17. A single layered plot tended to proceed down the centre or toward the right hand side of the diagram. Also, if the canopy was more variable, then the direction of travel depended on whether the growth of the plot was dominated by small or large trees. Large tree growth domination drove the plot toward the left-hand side of Figure 3.1 to SSCs 13, 14, and 15; small tree growth domination pushed the plots to the middle or toward the right, particularly toward SSC 12. Based on the original 17-class system, SSC 12 was somewhat heterogeneous in terms of diameter or height differentiation, but was not as heterogeneous as SSCs 13 to 17. As a result, it was located on right of the diagram with SSCs 8, 9 and 10. Based on the projections of these plots, it was not unusual to find plots that were first dominated by large tree growth and later by small tree growth, driving the SSCs toward 14 and maybe 15 at the outset. This could then be followed by a change in direction to move toward the right hand side, typically following a path toward stand SSC 12 or 8, particularly if the understory at the start of the projection was dense. The seemingly cyclical patterns between stand structure classes occurred only occasionally. For example, there was one instance where the stand oscillated from SSC 12 where it persisted for 30 years to SSC 9 (5 years), then 12 (10 years), and then 9 (10 years) again before finally settling back in 12 where it persisted for 60 years. This indicates that the progression was following along a boundary between the two stand structure classes. Similar patterns occurred where a stand passed into a new SSC (e.g., from SSC 7 to 8), but stayed there only briefly (10 years) before moving to a third class (SSC 12), where it persisted for a 51  much longer period of time (95 years). These examples underline the importance of using the time spent in each class as a basis for establishing dominant patterns of succession.  3.3.3  Cluster Analysis  Using the 155 year forecasts by 5-year intervals from PrognosisBC , the time spent in each SSC, including 0 representing no time spent in a class, were calculated for each of the 140 plots (i.e., plot progressions). Hierarchical clustering was then used to group the plot progressions into SPs. Initially, 20 clusters were identified. However, one of the 20 clusters included 85 of the 140 plots. The 19 other clusters were retained, whereas the group of 85 plots was further divided into 15 clusters, resulting in 34 clusters overall (Table 3.2). Hence, these 15 clusters were more related in terms of time spent in each SSC (marked by * in Table 3.2), than the originally retained 19 clusters. All of the 17 SSCs were present in the dataset used to initialize the PrognosisBC simulations. However, SSCs 3 and 5 were best represented and, naturally, had considerable weight in the clustering process. Some of the clusters exhibited a staggered effect, beginning at a later point in the progression than others (i.e., started at the bottom of Figure 3.1) and tended to stay in one or two stand structure classes throughout the 155-year period. Therefore, these plot projections had very little overlap with those that started with much simpler stand structures (top of Figure 3.1). This may have contributed to a number of clusters having only one plot. Of course, at one extreme, every plot has a unique succession pathway and, at the other extreme, all plots follow one pathway. The decision of stopping at 34 clusters (succession pathways) seemed justified by the data and resulted in an acceptable degree of within pathway variation in progressions among stand structure classes.  52  Table 3.2. Number of plots by initial stand structure class and succession pathway (SP). Stand structure classes generally represent: single-layered stands (1 to 11); multi-layered or complex stands (13 to 17); and intermediate structures (12).  SP  1 7 1  2  3 6 6 2 1 8 8  4  Initial Stand Structure Class 5 7 6 8 9 10 11 12 13 14 3 1 13 4 1 2 6 1 3 1  15  16 17  Total  1 17 2* 25 3* 5 2 22 4* 1 3 5 5* 6 3 4 21 6 8 7 1 1 4 6 8 2 2 9 1 1 10* 1 1 11 2 1 3 12 1 1 13* 1 1 14* 1 1 15* 1 1 16* 1 1 17 1 1 18 1 1 19* 1 1 20* 2 2 21* 1 1 22* 1 1 23 2 2 24 2 2 25* 1 1 2 26 1 1 27 2 2 28 1 1 2 29 1 1 30 1 1 31 1 1 32 1 1 33 1 1 34 1 1 Total 10 6 33 5 25 12 10 4 1 3 3 1 6 7 5 8 1 140 * indicates further splitting of one class after reaching 20 classes in the clustering hierarchy.  53  3.3.4  Detailed Examination of Succession Pathways  As noted, Figure 3.1 was constructed by identifying all unique pairs of stand structure class progressions. As a result, the time spent in an SSC is not represented in the figure. For example, SSC 4 can progress to SSC 5, and beyond that it can seemingly radiate outward in many directions using Figure 3.1. A detailed examination of plot progressions for SSCs 3 and 4 was used to examine how time spent in a stand structure class related to clustering assignments to SPs, as well as to address questions 2 and 3 posed in the introduction.  3.3.4.1  SSC 4  Five plots were classed as SSC 4 (i.e., high density, single-story) at the time of initial measurement (i.e., the beginning of the 155-year forecast) (Table 3.3, plots C, D, J, L, and M), and eight additional plots progressed through SSC 4 (remainder of the plots in Table 3.3). These 13 plots were clustered into either SP 3 or 4. All of these plots passed through SSC 8 (i.e., high density, single story) and remained in that class for an extended period of time. The patterns of progression included SSCs 5 or 7 for some plots on the way to SSC 8. All of the plots that remained in SSC 8 for a long period of time (i.e., 120 to 125 years) were clustered into SP 4. The others moved to SSC 9 and some moved to SSC 10, and were clustered into SP 3. Based on this assessment, it appears that certain SSCs, such as SSC 6 for example, are not likely to be accessible from SSC 4, which is not evident from Figure 3.1. To investigate whether it is possible to predict whether a plot might be expected to follow a particular SP given the SSC and other measures at a particular time, the plot-level variables for the 13 plots over the time periods that they were classed as SSC 4 (55 time periods overall) were examined in an effort to explain the differences between those that followed SP 3 versus SP 4. Plots with higher stems per ha were more likely to progress as SP 3 than SP 4 (Table 3.4). Further, plots with higher lodgepole pine basal area per ha were more likely to follow the SP 3 progression. Using multivariate discriminate analysis and these two variables, 91 % of the 55 SSC 4 time periods were classified correctly as SP 3 versus SP 4 overall. In particular, the success rate for identifying SP 3 was 88% and for SP 4 was 93%. This examination of SSC 4 suggests that unique patterns of succession can be identified by exploiting within stand structure class variations. 54  Table 3.3. Plots and associated successional pathways (SP) that started in or passed through stand structure class 4 in the PrognosisBC simulations, and the number of years that each plot stayed in each stand structure class before proceeding to the next class to the right. Stand structure classes generally represent: single-layered stands (1 to 11); multi-layered or complex stands (13 to 17); and intermediate structures (12).  Stand Structure Class SP  Plot  1 2  3  A  3  B  10 10  3  C  3  D  3  E  3  5  3  4  14 7  6 15 8  12 9  10 11 16 17  5  10  30  50 45  10  20  25  60 20  10  10  80  55  15  15  70  55  10  15  10  45  55 20  F  10  20  65  55 5  3  G  5  25  95  30  3  H  10  25  85  35  4  I  15 15  4  J  30  125  4  K  30  120  4  L  35  120  4  M  35  120  5  10  13 5  5  120  55  Table 3.4. Mean (and standard deviation) for basal area (G; m2ha-1) and stems per ha (SPH; ha-1), and number of simulated growth cycles (5-yr projections, N) in stand structure class 4 by succession pathway (SP 3 or 4) and by species (FD=Douglas-fir PL=lodgepole pine (PL), and Other=other species). * indicates significant differences between SP 3 and 4 using a two sample t-test (p < 0.05).  Difference in Means Succession Pathway Variable  Species  3  4  All  Error)  26  29  55  55  All  36.0(6.1)  41.6 (4.2)  39.0 (5.2)  5.6(0.7)*  FD  32.9 (7.0)  20.6 (18.2)  26.4 (14.1)  12.3 (1.9)*  PL  1.5 (2.4)  19.8 (17.2)  11.2 (14.5)  18.3 (2.0)*  Other  1.3(1.2)  1.1 (1.6)  1.2 (1.4)  0.2 (0.2)  ALL  7618 (2900)  10410 (3125)  9090 (3021)  2792 (407)*  FD  7294 (3056)  6978 (5875)  7127 (4758)  316 (642)  PL  153 (274)  2926 (2700)  1615 (1972)  2773 (266)*  Other  171 (212)  505 (799)  348 (616)  334 (83)*  N G  SPH  3.3.4.2  (Standard  SSC 3  To further investigate whether succession pathways could be predicted starting from a particular stand structure class, plots that started or progressed through SSC 3 were examined. SSC 3 is similar to SSCs 1 and 2 and was located at approximately the same level in the succession hierarchy (Figure 3.1). Unlike SSC 4, plots that were SSC 3 at some point in the plot projections were clustered into a large number of SPs, specifically, SPs 1, 2, 3, 4, 5, 6, 9 and 10. Some of these plots started as SSC 1 and progressed to SSC 3. Four succession pathways had seven or more plots representing SSC 3: SPs 1, 2, 5, and 6 (Table 3.5). In terms of the plot projections classed as SSC 3, the following observations can be made: i) SPs 2 and 5 have more in common when compared with the other two groups - these two SPs were classified into the same group within the 20 original groups in the classification hierarchy (indicated with an asterisk in Table 3.2); ii) those plots classed as SP 56  5 remained in SSC 12 for a relatively long period of time (60 to 90 years, average 74 years) when compared with other SPs (averages of 18 to 51). For example, very few plots classed as SP 2 progressed to SSC 12 and then to SSC 10 and SSC 11.  Table 3.5. Average number of years and proportion of plots (1.00 represents all plots, also shown in bold, and a blank indicates no plots) by stand structure class (SSC) and succession pathway (SP) for plots (N) starting or passing through as stand structure class 3.  Average Number of Years by SP 5  Proportion of Plots by SP  SSC  1  2  6  1  8  5  20  14  15  19  5  13  18  6  14  1  2  5  6  0.54  0.14  1.00  1.00  1.00  1.00  55  0.86  1.00  1.00  21  73  1.00  1.00  1.00  15  5  0.50  0.13  2 3 4  7 8 9 10  20  16  0.14  1.00  11  41  10  1.00  0.25  51  74  1.00  1.00  0.57  0.25  12  38  18  0.23  13  6  14  27  15  25  16  48  22  1.00  0.43  17  19  25  1.00  0.14  N  13  7  13  7  0.38  0.54 14  5  1.00 1.00  8  8  8  8  There are other notable points regarding these succession pathways that started or passed through SSC 3. Based on these plot projections, those that passed through SSC 5 did not progress to SSC 11, indicating that perhaps this route is not possible given the starting stand 57  structure class. SP 1 was unique in that all plots classed as SP1 passed through SSC 15, whereas others did not; they also never passed through SSC 6, when all of the others did. This condition seemed to represent an extreme in terms of starting in SSC 3 and progressing through a multi-layered or complex stand condition. For those that passed through SSC 3 and were classed as SP 6, an exemplary point was that they took a very long time to proceed through SSC 5 (40 to 85 years) and SSC 6 (65 to 80 years), when compared with the rest (maximum 20 and 35 years for SPs 5 and 6 respectively), before sometimes reaching SSC 12. This coincided with a more single layered pattern of development when compared with the rest (see Figure 3.1). Also, SP 6 included plots that were 100% lodgepole pine and, as a result, they were unlikely to progress into any more complex structure beyond SSC 13.  Unlike the two extreme SPs 1 (single layered) versus 6 (complex), plots that passed through SSC 3 and were classed as SP 2 tended toward a complex pattern whereas those classed as SP 5 tended toward a single layered pattern of development. As with SSC 4, multivariate discriminant analysis of quadratic mean diameter, basal area per ha, the number of lodgepole pine stems per ha, and basal area weighted average live crown ratios for all plot progressions that passed through SSC 3 showed that the first axis accounted for 66% of the variation and also related to stand complexity. Using the analysis, the overall classification success rate was 81% with success rates by SP as follows: 83% for SP 1, 73% for SP 2, 80% for SP 5, and 100% for SP 6. Generally, with higher lodgepole pine density, and lower quadratic mean diameter, a plot classed as SSC 3 was more likely to remain as single layer stands (i.e., SSCs 5, 6, 7, 10, 11 and 12).  3.3.4.3  Overall Observation  Based on the examination of plot progressions that started or passed through SSCs 3 and 4, good success in predicting the likely succession pathway given the current SSC and easily measured variables is possible. 58  3.3.5  Stand Structure, Growth and Yield  Questions 4 and 5 asked whether the differences among succession pathways could be easily viewed based on species composition and the underlying diameter distributions at a given time, and whether differences in succession pathways resulted in differences in common stand-level variables over time. For this purpose, six simulations were selected from those classed as SSCs 3 and 4 at the start of the simulation, one each from SPs 1 to 6. The different succession pathways were examined in relation to starting conditions in SSC 3 or 4 (Figure 3.2) and changes in stand-level variables and stand structural class were compared over time (Figure 3.3). In general, it can be seen that the trend within SSCs 3 and 4 from single layered stand structure subclasses (SPs 4 and 6) to perhaps multi-layered (i.e., SPs 3 and 1) and then to complex stands (i.e. SPs 2 and 5) can be observed as a continuum (Figure 3.2). As noted, the entire scope of single layered to complex structures appeared to be encapsulated within SSC 3, resulting in different SP classes (i.e., 1, 2, 5, and 6). Species differences can cause differences in SPs in spite of the stand structure classes being initially derived without reference to species. For example, the plot classed as SP 3 in Figure 3.2 was a particularly interesting case because the trajectory followed a single layered pattern (i.e., SSC 4→8→9), but there were obviously two layers at the beginning (left-hand side figure). For this plot, the upper layer dominated by lodgepole pine seemed to contribute little or nothing to the growth of the stand. These scattered older trees are often identified as veterans implying that they were remnants from a previous disturbance and younger trees subsequently became established in the understory, growing up around the veterans. In reality, the lodgepole pine veterans would very likely die or blow over within the 155-year projection. In contrast, the understory was dominated by interior Douglas-fir and would be expected to develop in a more vigorous way, compared to single-storied stands of lodgepole pine with similar densities on similar kinds of sites.  59  Figure 3.2. Examples of different succession pathways based on individual plots. Initial stand structure (schematic on the left), initial stems per ha by DBH (cm) class (central graph), and initial basal area per ha by DBH class (graph on the right; m2ha-1) for several plots. The blue bars represent interior Douglasfir and the red bars indicate lodgepole pine. Each plot is labeled with a succession pathway (e.g. SP 4) followed by a “/” and then the stand structure class sequence with subscripts indicating the number of years spent in each class.  Stand structure classes and associated durations indicated in bold lettering  are good indicators of the associated pathways. 60  60  8000 3  50  Basal Area (m2/ha)  6000 Trees Per Hectare  3  4  4000  4  40  2 30  5 6 20  1 2000 5  2  10  6 1  0 0  0  25  50  75  100  125  0  150  50  25  50  75  100  125  150  100  125  150  80 1 1  30  60 Live Crown Ratio (%)  Lorey's Mean Tree Height (m)  40  2 5 6 3  20  4  6  5  2  40  3  4  20 10  0  0 25  50  75  Stand Structure Class  0  100  125  18 17 17 16 16 11 15 14 10 139 12 12 118 10 15 96 87 7 14 65 135 44 33 22 11 0  150  0  25  50  75  1 2 5 3  4  0  25  6  50  75  100  125  150  Figure 3.3. Changes stems per ha (top left), basal area per ha (top right; m2ha-1), Lorey’s mean height (middle left; m), live crown ratio (middle right) and in stand structure succession (bottom), versus year (in 5-year increments). The numbers used to label each line indicate stand structure pathway. 61  The differences in SPs for these six stands that all started as SSC 3 or 4 had stand-level growth and yield implications as shown by average height, basal area per ha, volume per ha, and stems per ha over time (Figure 3.3). SPs 3 and 4 that passed through SSC 4 had the highest basal area per ha values, along with the highest densities, and were accompanied by rapid mortality over time. They also had the lowest average height growth trajectories, and the lowest crown ratios. In contrast, the four trajectories that passed through SSC 3 (i.e., SPs 1, 2, 5, and 6) all had much lower densities at the beginning and over time. The density, basal area per ha, average height, and average live crown ratio projections for SPs 5 and 2 appeared to be almost identical, as expected, since they followed very similar succession pathways through stand structure classes, and had very similar starting diameter distributions (Figure 3.2). SP 6 was dominated by lodgepole pine and manifested a much flatter trajectory in basal area per ha and a lower average height trajectory. SP 1 represented an open-grown interior Douglas-fir stand with an exceptionally high average live crown ratio and height growth, suggesting that this succession pathway may produce some very large trees with time; this is consistent with the eventual progression through SSCs 14 and 15 to SSCs 16 and 17 that contain some very large trees for the area.  3.4  Discussion  A comprehensive pattern of succession emerged for these forests after observation of a wide variety of simulated stand conditions through time, as seen through the lens of the 17-classes. This pattern emerged without any need to predetermine the stages of succession using terms such as early, mid and late seral stage of development (Kimmins 2004), stem exclusion phase (Oliver and Larson 1990) or uneven-aged multi-cohort stand (O’Hara et al. 1996). However, such terminology remains helpful for explaining the dominant succession pathways down the left-hand side (multi-cohort), middle (relatively open, single-layered stands), or right-hand side (dense, single-layered stands) of Figure 3, as well as from the top to the bottom of the diagram (early, mid, and late seral stages). The primary advantage of the approach to stand structure classification used in this research was that it revealed other patterns that were perhaps not so obvious, including for example 62  stands that started in the centre of the diagram (e.g., SSC 3) and then moved toward the left while large trees dominated the growth pattern, sometimes followed by another move to the far right when smaller tree growth was dominant. Some of these shifts appeared to be species dependent. Where lodgepole pine dominated the overstory, the stand appeared to be unlikely to migrate into stand structure class 15, since this species rarely grows large enough in diameter. Other shifts occurred where there was a dense understory at the beginning of the simulations, but the trees were too small relative to the overstory to dominate the growth pattern in the early stages. Some time was required before such dominance was obtained. Shifts in stand development related to the dominance of small versus large trees have been observed in field studies in coastal Oregon (Binkley 2004) as well as in the Rocky Mountains of Colorado and Wyoming (Binkley et al. 2006). Doi et al. (2010) found that a 70 year old Eucalyptus saligna stand in Hawaii continued to manifest large tree dominance contrary to the expectation that there would be a shift in pattern at this late stage of development. They used this finding to suggest that such trees might still be capable of responding well to silviculture treatments such as thinning and fertilization, even at this late stage of development. Although Figure 3.1 is useful for summarizing the dominant direction and potential range of growth patterns, it was found that the potential number of pathways through this diagram were reduced when viewed from the starting position of a given stand structure class. For example, all stands starting in SSC 4 grew into SSC 8. A few stands in SSC 3 that were bordering on SSC 4 also progressed toward SSC 8. In the latter case, this involved passing through SSC 7 and, frequently SSC 5 on the way to SSC 8. At lower densities, SSC 4 also passed through SSC 7 on the way to SSC 8; this pathway did not occur for higher density initial conditions where a direct route from SSC 4 to SSC 8 occurred instead. There was some overlap in the succession pathways when approaching boundary conditions, but beyond these boundaries, there were distinctly different sets of pathways associated with each starting stand structure class.  63  The classification system would have been considerably less useful if the within-class structural differences could not have been used to discriminate when one succession pathway would be followed versus another. The fact that appropriate succession pathways could be identified, based on multivariate discriminant analyses, suggests that the empirical cumulative distributions in basal area per ha and stems per ha, independent of species, provided a firm foundation for determining similarities and differences in stand structure in both space and time. Accurate discriminations of succession pathways were obtained using species composition, basal area per ha, and stems per ha. However, it was also clear that the distributions of tree species with respect to size, particularly small versus large trees, were also important, along with variation in diameter and height distributions. These differences helped explain why one pathway was followed versus another even though species-bydiameter distributions were not explicitly accounted for in the system of classification, nor in the clustering process used to identify the general trends in succession. However, species differences become important when examining why a particular starting stand structure class was likely to follow a particular succession pathway. The original intent behind the use of cumulative distributions for the stand structure classification system was to develop a system that was independent of an arbitrary division into diameter classes. Also, these distributions have significance in growth and development of stands. Cumulative distributions of basal area greater than or equal to threshold diameter have been used as an indicator of competition for light in individual tree models such as PrognosisBC (Wykoff 1990; Vanclay 1994). Kohyama (1989, 1991, and 1992) undertook a series of investigations into the importance of these distributions as predictors of growth and mortality of trees with time. He worked with both primary (multi-cohort) and secondary (single-cohort) tropical foothill rain forests in Sumatra and warm temperate rain forests in Southern Japan. He observed that the allometric coefficient estimating leaf area as a function of diameter was generally close to a value of 2. This value corresponds with that of basal area in relation to tree diameter and, as a result, he asserted that the cumulative distribution should provide a good proxy for light attenuation through a canopy. Using this knowledge, he evaluated the use of basal area greater than or equal to a given threshold diameter, both with and without consideration of species composition, for predicting the change in a number 64  of stand attributes with time, including: small tree, density dependent mortality; variation in diameter growth; and the establishment of ingress. Kohyama found that it was important to include the large tree mortality independent of density to produce a steady state diameter distribution that was consistent with field observations. Finally, he observed that similar results were produced at the stand level when forecasts accounting for species differences were made, versus model simulations that describe changes in the diameter distribution as a whole without explicitly accounting for such species differences. On the basis of Kohyama’s work, the cumulative distribution approach to stand structure classification could reliably be used to map patterns of succession. This stand structure classification system reflects the important role of top-down asymmetric competition for light as a dominant factor both influencing and being influenced by individual tree rates of growth and mortality. Although this study did not include natural disturbances nor consider ingress, the approach used herein could be expanded to accommodate more wide-ranging influences of natural disturbances and regeneration patterns. The forecasts based on these assumptions could serve as a baseline for assessing differential effects of various agents and intensities of disturbance. The availability of model-based controls can be essential where experimental studies are difficult to establish in the field, or where the combinations of interest are difficult to find within the context of observational studies (e.g., Amoroso and Larson 2010). There were several limitations to this study in terms of broader applications. The focus was on a narrow range of sites, albeit a range of sites that are well represented within a large geographic region. This may not be a problem insofar as the order of succession from one stand structure to the next is likely to remain stable under the basic assumptions used to generate these results, but the speed with which plots are expected to proceed through these progressions would most certainly change. This fact would have to be integrated into the process of defining patterns of succession as a prerequisite for expanding the application of the classification system. This is not to suggest that site does not interact with autogenic processes to produce different patterns of succession, but rather that there are wide ranging circumstances where this may not be the case.  65  A second major limitation to the study was the lack of consideration given to the spatial distributions of trees. Different patterns of succession would likely emerge from the same diameter distributions with different spatial arrangements. Such an investigation might require an extension of the stand structure classification system to include differences in spatial arrangement. Prior work (data not shown) with this extended system was abandoned because of the need for extensive field measurements for spatial patterns. Ultimately, the spatial arrangements of trees are important for determining patterns of succession. Along with extending the stand classification system to include spatial patterns, the use of a distance dependent individual tree growth model would be needed to identify succession pathways based on spatial arrangements. Often these models are not available, as was the case for the forest used in this study. An investigation into this question might facilitate introducing spatial considerations into the definition of succession pathways, while retaining the generality of the non-spatial stand structure classification that was used in this study. A third limitation of this study relates to the process used to generate the dominant succession pathways. In reality two different plots may start in very different stand structure classes (e.g., SSC 3 versus 12) and yet belong to the same succession pathway. Using the criteria of time spent in each class, the small degree of overlap in the SP projections is likely to result in these two cases being assigned to separate pathways. This is a problem only insofar as it is desirable to reduce the data down to a minimal number of succession pathways. From a practical point of view it is perhaps of less of concern provided that there is enough data to represent the range of initial conditions within any given forest. The results of this work have also found practical application. People can be trained to identify species composition, stand structure classes, and associated succession pathways in the field as well as through aerial photo interpretation. These classifications facilitate the assignment of different growth and yield projections from an existing bank of plot data without having to establish an extensive set of plots to represent the same conditions. Furthermore, people can train themselves by establishing plots and compiling them using a computer program to verify their SSC and SP assignments. Such programs can also be used to identify plot conditions that are poorly represented within an existing plot database, and as 66  such, should be sampled more intensely as part of a growth and yield program. This process can then be used to underwrite forest estate planning and silviculture. Harvesting guidelines can be developed for specific combinations of species compositions, SSCs and SPs in specific landscapes that can be readily implemented in the field. The ability to recognize these features in the field in a consistent and reliable way can help to overcome deficiencies associated with photo interpreted inventories that are often imprecise at the scale of individual polygons. As a result of using a consistent language these tools can help to bridge a gap between developing strategic level plans using inventory sources of data, and the implementation of these same plans with the use of ground observations. 3.5  Conclusions  The system of stand structure classification developed in Chapter 2 and used in this study to classify stand structure over a 155 year projection period revealed a comprehensive pattern of succession. Differences in stand structure classes were found to be important in limiting the potential range of succession pathways. Distinct succession pathways were isolated according to differences in stand structure classes over time based on species proportions, diameter distributions, and dominance of large versus small tree growth patterns. This suggests that stand structures can be ordered in space and time using a combination of initial classification plus additional classes indicating relatively unique pathways of succession. This is particularly the case when initial assumptions are deployed to exclude ingress or allogenic disturbances in the process of defining alternative pathways. A given stand structure has the potential to be identified relative to a current stand condition, and additional classes can be identified as either preceding or following from the current state in the form of different dominant pathways of succession. This knowledge can then be expanded to further consider impacts of natural disturbance agents and the propensity of tree species to regenerate in the understory following such disturbances. The underlying reason this system of stand structure classification was successful in characterizing patterns of succession with a relatively high degree of precision was likely due to the use of cumulative distributions in basal area and stems per ha. These distributions characterize stand structure well, and can be used as a proxy for the attenuation of light. 67  However, the potential effect of differences in the spatial distributions of trees with respect to size is likely to be important and requires further investigation.  68  Chapter 4: Stand Structure Classification Using Airborne LiDAR Data 4.1  Introduction  Stand structure is the vertical and horizontal variation of trees in stands. Stand structure information is needed for assessing a number of forest values including wildlife habitat (e.g., bird abundance; DeGraaf at al. 1998; Diaz et al. 2005), timber value (Jackson and McQuillan 1979; Kennedy 1995), fire risk (Fernandes 2009), forest growth (Pretzsch et al. 2006; Weiner and Thomas 2001), and carbon sequestration (Gower et al. 1996; Binkley et al. 2002; Niinemets 2002; Berger et al. 2004). Overall, stand structure information is critical for a wide variety of management decisions. Collecting ground data can be expensive, particularly in remote areas with limited access, as with much of Canada’s forests. The process of classification would be enhanced if the data used for this purpose could be collected with a reasonably high level of accuracy and at high resolution (e.g. on a scale of 20 m2) over large landscape areas using remote sensing. Airborne Light Detection and Ranging (LiDAR) data may fulfill this data need, and provide an alternative or a supplement to ground data. The main research question addressed in this chapter is whether (LiDAR) data can be used effectively to represent stand structure defined by ground variables, particularly as it relates to distributions of stems and basal area per ha by DBH. LiDAR data have been researched as a means of assessing stand structure (e.g., Zimble et al. 2003; Coops et al. 2007; Frazer 2007; Falkowski et al. 2009), or more specifically to determine distributions of stems, basal area, or volume per ha with respect to diameter (Maltamo et al. 2004; Gobakken and Næsset 2005; Maltamo et al. 2006; Mehtätalo et al. 2007; Breidenbach et al. 2008; Thomas et al. 2008; Packalén and Maltamo 2008; Maltamo et al. 2009). These data have also been used to assess: wildlife habitat suitability (e.g., Coops et al. 2010), timber size and volume (Maltamo et al. 2004; Gobakken and Næsset 2005; Maltamo et al. 2006; Mehtätalo et al. 2007; Breidenbach et al. 2008; Thomas et al. 2008; Packalén and Maltamo 2008; Maltamo et al. 2009), fire risk (Riano et al. 2003), and forest growth and mortality (Yu et al. 2004). LiDAR has also been applied in a wide variety of forest types, including: primary and secondary neotropical forests in Costa Rica and Panama 69  (Drake et al. 2002, 2003); northern tolerant hardwoods in Ontario, Canada (Lim et al. 2003; Lim and Treitz 2004), tulip poplar (Liriodendron tulipifera L.) forest associations commonly found in the coastal plain of eastern US (Lefsky et al. 1999a); Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) and western hemlock (Tsuga heterophylla (Raf.) Sarg.) forests in the US Pacific Northwest (Lefsky et al. 1999b); and forest types commonly found in the European Nordic countries (e.g., Næsset 2007). Because of the importance of stand structure for forest land management and the increasing availability of LiDAR data, the use of airborne LiDAR data to represent stand structure is evaluated in this chapter. In particular, I examined the use of LiDAR data with relatively low point-densities (i.e., approximately 0.7 pulses per m2) for assigning a stand structure class, where the true structure class was defined by ground-measured distributions of stems and basal area per ha by DBH based on the classification system presented in Chapter 2. Cumulative distributions in other variables are also considered as alternative bases for ground-level classification, including: total volume per ha, merchantable volume per ha, each of basal area and stems per ha separately, Lorey’s height (i.e., mean height weighted by basal area), and quadratic mean diameter (i.e., diameter equivalent for the mean basal area per tree). The study area was located in Alberta, Canada, within structurally complex, mixedspecies stands. In conducting this evaluation, the leading questions I asked were: 1. How correlated are LiDAR and ground-level data? 2. Are there distinct differences in distributions of LiDAR data with respect to stand structure classes as defined in Chapter 2? 3.  If new systems of classification are developed using LiDAR data alone, how well do these LiDAR classes relate to distributions of both stems and basal area per ha by DBH for determining ground-level stand structure class similarities and differences? How does this compare with the use of distributions of other ground variables, such as volume with respect to DBH or alternatively height?  4. If new systems of classification are developed following the methods in Chapter 2 based on ground measured distributions, how well do these ground classes relate to similarities and differences in distributions of LiDAR data?  70  5. How does the number of stand structure classes affect classification results (re: questions 3 and 4)? The first question was used to explore whether relationships obtained for other study areas would be similar for this area with structurally complex stands and to initially indicate whether using LiDAR data for diagnosing differences in stand structure might be promising. The second question further explores whether a relationship might exist between LiDAR and predetermined ground-measured stand structure classes. The third and fourth questions address whether LiDAR data could be used to represent ground stand structure where ground data are not available (Question 3), and, then whether LiDAR data can be used to predict ground stand structure classes where sufficient ground data are available to establish a relationship (Question 4). Finally, since the number of stand structure classes might impact the effectiveness of LiDAR data, the number of classes was varied and the results compared (Question 5).  4.2 4.2.1  Materials and Methods Study Area Description  The study area was located in the southwest of Alberta, Canada near Cochrane within the Spray Lake Sawmills Forest Management Agreement (FMA) area, and near the eastern boundary of Banff National Park. The study area covered 32,013 ha of land, of which 26,444 ha are forested. Two parcels of land are represented: the north side of the Bow and the Ghost Rivers (51o18’34’’ N, 115o00’53’’ W) encompassing 18,615 ha in gross area and south of Highway 1 (51o02’49’’ N, 114o52’53’’ W) in an area known as Kananaskis Country encompassing 13,398 ha. These areas were selected because they represented a cross section of forest types covering the range of forest conditions found in the FMA as a whole. The study area extends from 1300 m to 2000 m in elevation, and is divided into Lower Foothills (237 ha, 0 to 30% slopes dominated by closed mixedwood forest and shrub vegetation), Upper Foothills (2423 ha, 16 to 45% slopes dominated by closed conifer forest), Montane (27,605 ha, 0 to 15% slopes dominated by closed mixed forest and grassland) and SubAlpine (1,748 ha, 16 to 100% slopes dominated by open and closed conifer forest) Natural Sub-Regions (Natural Regions Committee 2006). These forested areas are predominantly 71  comprised of the following tree species: lodgepole pine (Pinus contorta var. latifolia Dougl. ex. Loud., Pl), white spruce (Picea glauca (Moench) Voss, Sw), Englemann spruce (Picea englemannii Parry ex Engelm., Se), black spruce (Picea mariana (Mill.) B.S.P., Sb), balsam fir (Abies balsamea (L.) Mill., Fb), subalpine fir (Abies lasiocarpa (Hook.) Nutt., Fa), interior Douglas-fir (Pseudotsuga menziesii var. glauca (Beissn) Franco, Fd), aspen (Populus tremuloides Michx., Aw) and balsam poplar (Populus balsamifera L., Pb). These species often grow as mixed-species stands, resulting in both vertical and horizontal complexity.  4.2.2 4.2.2.1  Data Ground Data  In 2008, ground plots were established and used to estimate a number of forest attributes using LiDAR data (Aasland et al. 2009) following the methods developed by Næsset (2004). Prior to ground sampling, maps of the Alberta Vegetation Inventory (AVI) forest cover polygons (Resource Information Management Branch 2005) were obtained. These maps were based on manual interpretations of 1989 and 1990 aerial photographs, followed by updates for natural disturbances and forest management activities, up until 2007. Updates were primarily related to logging, road construction, and silviculture. A 3 km x 3 km systematic grid of potential sample points, with four plots on each side, was randomly located. Using the AVI forest cover polygon information, individual plots within the 16-plot square grid were discarded if they were located in polygons that: i) were not forested; ii) had stand heights less than 7 m; or iii) had crown closure losses of more than 75% due to recent human or natural disturbances. Also using the AVI polygons, four strata were defined as eligible for sampling: open pine (predominantly Pl) stands with up to 50% crown closure; closed pine stands with more than 50% crown closure; stands with a spruce (Sw, Se, and Sb) and/or fir (Fa, Fb, and Fd) overstory, with or without a broadleaf (Aw and Pb) understory; and stands with a broadleaf or low density spruce or fir overstory, with predominantly broadleaf species in the understory. Plots not in eligible types (e.g., black spruce bog) were excluded. Finally, any plot that was partly disturbed based on 2001 aerial photographs was removed. The list of remaining plots in each stratum was then ordered based on the criteria of obtaining a spatial distribution of plots with a target of approximately 50 plots per stratum.  72  In the field, each plot centre was located using a Trimble GEO-XH GPS unit calibrated and differentially corrected to Cansel Survey’s permanent base station located in Calgary, Alberta (approximately 60 km from the study area). Where plot centres were under a canopy of trees, the GPS unit was moved to an opening and the distance and bearing to the plot centre using a compass and a measuring tape were recorded. Any plot with an estimated error in spatial location of more than 1 m was discarded from this study. Also, once plots were located in the field, the plot was again assessed and discarded if it had evidence of disturbance or it did not fall in one of the four eligible strata defined prior to sampling. Any discarded plot was replaced by the next plot in the list for that stratum. As a result, plots were spatially distributed and the target of approximately 50 plots per stratum was obtained. At each plot centre, three concentric plots were established. First, a circular plot of radius 10 m (314 m2 area) was established and all live trees with DBH ≥ 6 cm were tallied by 2 cm DBH class and species (main plot). This plot was used to obtain plot-level statistics. At the same plot centre, a variable radius (height sample tree) plot (i.e., prism plot) was established with a target of 7 to 13 trees in the plot, and all live trees were measured for height (0.5 m precision) using a Vertex IV and Transponder T3 ultrasound hypsometer (Haglöf Sweden AB, 2007) and for DBH (1 mm precision) using a diameter tape. Trees with damaged tops were either excluded, or, in cases where damage was minimal, the height to damage was measured and an estimate was made of the expected height without damage. These data were used to provide locally-estimated heights from DBHs on the main plot. Finally, a 5.64 m radius (site index) plot (i.e., 0.01 ha) was established and the top height tree (i.e., largest by DBH) of the one or two dominant species were measured for height, DBH, and the breast height age (i.e., number of rings at 1.3 m above ground). These measures were used to determine site index (not used in this study).  4.2.2.2  LiDAR Data  The LiDAR data were collected by Airborne Imaging in Calgary, Alberta, Canada under contract to Alberta Sustainable Resource Development (Alberta Sustainable Resource Development 2008). The LiDAR data were collected using an Optech 3100 system at a flying speed of 1600 knots, a scan angle of 50 degrees, a side overlap of 50%, and a point 73  spacing of 0.75 m. Data in the northern portion of the study area were collected on September 13, 2005 at an average above ground flying height of 1300 m and a scan frequency of 29 Hz. In the southern portion, data were collected between June 29 and July 4, 2006 at an average above ground flying height of 1200 m and a scan frequency of 30 Hz. The horizontal datum and vertical datum were NAD83 CSRS and CGVD28, respectively. The Geoid model applied to the study area was HT2.0. All data were located in UTM Zone 11. The realized maximum scan angle was 16 degrees from nadir and the average LiDAR pulse return density was 0.7 per m2.  4.2.3 4.2.3.1  Data Compilation Ground Data  At each sample point, measured heights on the variable radius plots were compared to heights estimated from DBH using models developed for Alberta species (Huang and Titus 1992; Huang 1994). For trees with damage, the field-estimated heights were considered measured heights. A measured-to-estimated height ratio was then calculated for each species in the plot by summing the measured heights and dividing by sum of the estimated heights for the same trees using the models. In cases where a species occurred in the main plot, but was not represented in the height sample, an average measured-to-estimated height ratio was obtained using all of the height sample trees in the variable radius plot regardless of species. Then, using the 10 m radius circular plot at the same point, the following calculations were performed: 1. All trees in each DBH class (all classes are 2 cm in width) were assigned the midpoint of the DBH class (i.e., trees in the class 6 cm ≤ DBH < 8 cm were assigned a DBH of 7 cm); 2. The height was estimated using the appropriate species height model and the assigned DBH; and 3. The height estimate was modified using the average measured-to-estimated height ratio resulting in localized height estimates. As a result, all trees tallied in the 10 m radius plots had DBH and height. Tree basal area (m2) was calculated for each tree. Gross total volume (i.e.., volume from ground to tree tip, 74  hereafter termed just “gross volume”, m3) was estimated for each tree by: i) inputting the DBH and height into species-specific, variable-exponent taper models for the Montane region (Huang 1994; Alberta Natural Region 9) to obtain estimated radii from ground to tip; and ii) numerically integrating area using the estimated radii over the tree stem to obtain volume. Similarly, merchantable volume (m3) was estimated for each tree from a 0.30 m height above ground to a 15 cm top diameter inside bark; trees with DBH < 15 cm were given a merchantable volume of 0. Per tree values for each 10 m radius plot were then summarized to obtain the following ground-plot variables (hereafter just termed “ground variables”): i) gross volume per ha (VG, m3 ha-1); ii) merchantable volume per ha (VM, m3 ha-1); iii) basal area per ha (G, m2 ha-1); iv) quadratic mean DBH (DG, cm, mean diameter weighted by basal area); v) Lorey’s height (H, m, mean height weighted by basal area per ha); and vi) stems per ha (N, stems ha-1). Tree-level values were also used to calculate the reverse cumulative distributions of Nx and Gx by 2 cm increments of DBH (i.e., the plot stems and basal area per ha for all trees greater than or equal to a given diameter threshold, x, where the threshold is set equal to the minimum DBH assigned to each 2 cm width DBH class) following the procedures developed in Chapter 2. Similarly, reverse cumulative distributions for Nx and Gx were calculated by height increments of 1 m, and for VGx, and Hx, each with respect to DBH and then height, as additional measures of stand structure. To classify the ground plots using the distributions of Nx and Gx by DBH as proposed in Chapter 2, the reverse cumulative distributions of Gx and Nx were standardized across plots. For Nx, the steps were: 1. Ground plots were organized from smallest to largest stems per ha, and a rank from 1 (minimum stems per ha) to n plots (maximum stems per ha) was assigned; 2. This rank was then expressed as a proportion by dividing the rank from 1 to n by n resulting in a plot rank from 0 to 1; 3. The relative reverse cumulative distribution of N was calculated by dividing by the stems per ha for the plot; and 4. The relative reverse cumulative distributions of N were multiplied by the plot rank to obtain a standardized reverse cumulative distribution (RNx).  75  The plots were similarly ranked by basal are per ha to obtain RGx. As well as standardizing the reverse cumulative distributions across plots, these rank transformations provided equal weights to stems and basal area per ha and to small versus large trees since stems per ha tends to be larger for smaller trees and basal area per ha tends to be larger for larger trees. The maximum DBH and height for the study sample tree measurement data were 69 cm and 31.2 m, respectively. The maximum DBH class was 57 cm. Using RNx and RGx, plots were classified into one of the 17 previously defined stand structure classes in Chapter 2 using the stand structure compiler written in Python 2.6 and a minimum DBH of 6 cm. In the algorithm, the minimum Euclidean distance between plot RNx and RGx and the class centroid of RNx and RGx for the original 17 classes were used to assign each plot to a stand structure class. Mean plot-level statistics (mean, maximum, minimum, standard deviation) were then used to represent each of the ground variables (i.e. VG6, VM6, etc., where the subscript “6” indicates the lower bound DBH in cm for inclusion in the plot) by stand structure class in combination with leading species. A leading species was determined for each plot according to the maximum percent of basal area in either deciduous (Aw, Pb), pine (Pl), or spruce (Sw, Sb). The ground-based classification was also obtained using RNx and RGx and the stand structure classification algorithm (in this case using a fuzzy c-means algorithm and Euclidean distances based on Bezdek (1981)) for 5, 10, and 15 classes. This process was also repeated using VGx. These calculations were needed to address Questions 3, 4 and 5.  4.2.3.2  LiDAR Data  A DEM representing the ground profile was created from the LiDAR data by Blom Geomatics using TerraScan, version 8 (Soininen 2005). The LiDAR data were spatially registered to each ground plot. For each extracted point-cloud distribution, the LiDARderived variables (hereafter termed “LiDAR variables”) obtained were: (i) reverse cumulative distribution of the proportion of total ground and above ground first returns by 1 m height increments  2 m (PFx), where the distributions indicate proportions of returns at a maximum for x= 2 m and decline to 0 as the height of first returns increases up to a 76  maximum; (ii) reverse cumulative distributions of proportions of last returns by 1 m height increments  2 metres (PLx); iii) areas under the discrete distribution of the proportions of ground plus above ground of total first returns ≥ 2 m in height, in 1 m increments, summed to produce reverse cumulative distributions (AFx); and iv) areas under the discrete distribution of the proportions of total last returns ≥ 2 m, summed to produce reverse cumulative distributions (ALX). The maximum heights of first and last returns for the study data were 28 m and 27 m respectively.  4.2.4 4.2.4.1  Statistical Analyses Correlations Between LiDAR and Ground Variables  Simple (Pearson’s) correlations and bivariate scatterplots were obtained to indicate the strength of relationships between ground (VG6, G6, H6, N6, DG6, RN6 and RG6) and LiDAR (PF2, PL2, AF2, and AL2) variables to address the first question. Then, as an indication of multivariate correlation between each of the same ground variables excluding RN2 and RG2, and all of the LiDAR variables, log10-log10 linear models were fitted using ordinary least squares, backwards stepwise regression with a significance level of 0.05 for inclusion of variables. The distributions of residual errors were visually assessed for normality and equal variances. Strong relationships were taken as evidence that distributions of first and/or last returns would be good indicators of distributions of ground stand structure. Finally, the log10-log10 relationships were used to estimate the mean values in the original units for each ground variable using combinations of LiDAR variables. After converting the predicted log10 values back to original units, a correction factor (CF) was applied as follows (Sprugel 1983): CF = exp ((2.303*SEE2)/2) where SEE is the standard error of estimate associated with the log10 regression equation. The constant, 2.303, converts the log10 estimate of SEE to a natural logarithm. The mean difference in the predicted minus actual values (i.e., bias) was also calculated for each variable along with the root mean squared error (RMSE) associated with the predicted value. 77  4.2.4.2  Variation of LiDAR Variables by Stand Structure Class  The variability of the LiDAR variables by the 17-class system of stand structure classification presented in Chapter 2 determined using stems and basal area per ha distributions was examined and used to address Question 2. Box plots of PF2, PL2, AF2 and AL2 by stand structure class were obtained. Larger differences in distributions of LiDAR variables among stand structure classes indicate a stronger potential for using LiDAR data as a means of differentiated ground stand structure classes.  4.2.4.3  Stand Structure Classes Using Cluster Analysis of LiDAR Data  To address Question 3, cumulative distributions of the variables PFx, PLx, AFx and ALx by x=1 m in height starting at x= 2 m were clustered using a fuzzy c-means cluster algorithm and Euclidean distances (Bezdek 1981) developed in Python 2.6. All combinations of one to four variable sets were explored in terms of developing 5, 10, and 15 classes. To assess whether these LiDAR classes represented ground-measured stand structure, the mean ground variables (VG6, G6, N6, H6, RN6, and RG6) were computed for each LiDAR class. Bonferroni tests derived from the Šidák (1967) inequality (Ludbrook 1998) were used to test for significant differences in the mean values amongst multiple pairs of classes for each of the ground variables using an overall significance level of 0.05. Re-substitution statistics were also obtained by: i) calculating the mean cumulative distributions of VGx, Gx, Nx, and Hx ground variables by LiDAR class (i.e., ground-variable centroids); ii) calculating the Euclidean distance between a plot and the LiDAR groundvariable centroids; iii) assigning the plot to the LiDAR class based on the minimum Euclidean distance; iv) comparing the chosen LiDAR class to that originally assigned to the plot; and v) summarizing these results as a re-substitution error rate. This process was also implemented using both of the RGx and RNx distributions in combination in a manner analogous with that used to develop and apply the original classification developed in Chapter 2. The means and re-substitution error were repeated for each of the three LiDAR classifications (i.e., 5, 10, and 15 classes). A low re-substitution error rate would indicate that LiDAR classes represent stand structure differences. 78  Cohen’s (1960) coefficient of agreement, KHAT, was used to evaluate each contingency table (initial versus estimated class assignments) in terms of the level of correspondence between the LiDAR versus ground classes. This statistic is used to assess the level of correspondence between two classifiers after accounting for the probability of occurrence by random chance. A KHAT value of 1 indicates perfect correspondence with no random chance, and a value of 0 indicates that the level of correspondence could have been purely by random chance. The best classification involving some combination of initial LiDAR variables to construct the classification, consisting of either 5, 10 or 15 classes, and reconstituted in terms of the one of the ground-based variable distributions with respect to height or diameter was identified as that having a maximum KHAT value. Where more than one system of classification (i.e., where there were alternative numbers of LiDAR variables used to derive a classification) was identified as having the same KHAT value, the set with the fewest number of LiDAR variable distributions was identified as being the best. This system was then used as a benchmark representing the best LiDAR system of classification in terms of its ability to be reconstituted using ground variables. This benchmark could then be compared with the best reconstituted result using the preferred ground variable combination of RNx and RGx, for 5, 10 or 15 classes as identified by the maximum KHAT value.  4.2.4.4  Predicting Ground Stand Structure Classes Using LiDAR Variables  To address Question 4, first ground-based classifications were developed for 5, 10 and 15 classes using cumulative distributions for VGx, and also for RNx and RGx combined. Out of these, the variable VGx was most related to LiDAR variable distributions based on the results of analysis relating to Question 3 Then, each of the two ground-based classifications was predicted using mean distributions for all combinations of one to four LiDAR distribution variables (i.e., PFx, PLx, AFx and/or ALx). The best combination of number of classes (i.e., 5, 10, or 15) and LiDAR distribution variables (i.e., one to four variables) was selected for each of the ground-based classifications according to the maximum KHAT value. Where more than one system of classification was identified as having the same KHAT value (i.e., where there were alternative numbers of LiDAR variables used to replicate a ground classification), 79  the set with the fewest number of LiDAR variable distributions was identified as being the best. This process was used to determine the number of classes, based on best relationships with LiDAR variables, for each ground-based classification variable set. Based on these preliminary analyses, multivariate discriminant analysis (MDA, Systat Software Inc. 2004; Dillon and Goldstein 1984) was used to predict ground-based stand structure (Y-variable) from LiDAR variables (X-variables). The number of ground-based stand structure classes was based on the best relationships between VGx and LiDAR variables, as well as between RNx and RGx combined and LiDAR variables. A subset of the LiDAR variables (PFx, PLx, AFx and ALx), was used as the X-variables, based on simple correlations between the ground reverse cumulative distributions by DBH (i.e., RGx, RNx , where x = 6, 8, 10,…) versus the LiDAR reverse cumulative distributions by height (i.e., PFx, PLx, AFx and ALx, where x = 2, 3, …). In particular, five LiDAR heights with highest correlations with ground variables over the range of DBHs were selected. MDA was conducted using backwards stepwise elimination with a significance level of 0.15 to allow more variables to be retained than a significance level of 0.05.  4.2.4.5  Influence of Different Numbers of Classes on Classification Success Rate  Since the choice of 5, 10, 15 or 17 structure classes can be viewed as arbitrary, the influence of numbers of classes was examined by calculating changes in KHAT with respect to an increasing number of classes between 2 and 15 in steps of 1 (Question 5) using the fuzzy cmeans algorithm developed in Python 2.6. Two ground-first classifications (VGx alone, and RNx and RGx combined) were represented, along with two LiDAR-first based classifications (AFx alone and in combination with ALx). KHAT values were determined by way of resubstitution using selected LiDAR and ground variables respectively and graphically displayed.  80  4.3 4.3.1  Results Ground Data  Of the 189 ground plots included in the study, 51%, 27%, and 22% were in the pine (P), spruce/fir (S), and deciduous (D) species groups, respectively (Table 4.1). Generally, tree heights in the deciduous group were shorter than in other groups. Pine plots had a wide range of density (N), whereas the spruce/fir plots had a higher range of basal area (G). In the original 17 stand structure classes presented in Chapter 2, classes 1 to 11 generally represent less complex single-layered stands, with trees concentrated in a relatively narrow range of DBHs. Increases in the class number in these classes generally represents increasing basal area and volume per ha. Stand structure classes 13 to 17 represent multilayered or complex stand conditions, with the trees distributed across a wide range of DBHs. Stand structure class 12 represented stands of intermediate complexity. When applied to this forest area, only 14 of the original 17 classes were found (Table 4.2). Although distributions of stems and basal area per ha by DBH class were used to develop the stand structure classes, the classes showed high between class variability and low within class variability, especially for G, VG and VM (Figure 4.1). Stand structure classes 3, 5 and 6 were predominantly pine plots, with mean basal areas per ha of 15, 31 and 21 m2 ha-1, mean stems per ha of 640, 1319 and 1197 stems ha-1, and mean merchantable volumes of 82, 138 and 234 m3 ha-1, respectively (Figure 4.1). Stand structure class 11 most commonly occurred in spruce/fir plots. Stand structure classes 2, 4, 9, and 11 were each represented by fewer than five plots.  4.3.2  Correlations Between LiDAR and Ground Variables  The ground variables ranked from highest to lowest correlations with LiDAR variables were (Table 4.3): VG6 (0.83, AF2), VM6 (0.82, AF2), G6 (0.80, AF2), RG6 (0.79, AF2), H6 (0.72, AL2), RN6 (0.57, PF2), N6 (0.51, PF2), DG6 (0.41, AL2). The LiDAR variables similarly ranked are as follows: AF2 (0.83, VG6), AL2 (0.81, VM6), PF2 (0.75, G6) and PL2 (0.61, both VG6 and VM6). Based on these simple correlations, it is evident that these four LiDAR variables were strongly correlated with ground volume and basal area. Further, stronger correlations were obtained for area under the distributions, particularly AF2 than for proportions. 81  Table 4.1. Summary statistics for pine (P), spruce/fir (S), and deciduous (D) species groups, where: H6 is Lorey’s mean tree height (m) for all stems  6 cm dbh; N6 is the stems ha-1; G6 is basal area (m2 ha-1); DG6 is quadratic mean diameter (cm); VG is total volume (m3 ha-1); and VM is merchantable volume (m3 ha-1). (n=189 ground plots).  Variable* Statistic H6 mean maximum minimum standard deviation  D 12.9 (n=41 plots) 19.9 6.3 2.9  P 15.7 (n=97 plots) 23.6 8.1 3.4  S 16.4 (n=51 plots) 22.4 7.3 4.0  ALL 15.3 (n=189 plots) 23.6 6.3 3.7  N6  1147  1184  974  1119  maximum 2451 minimum 127 standard deviation 578.8  5220 32 774.5  2801 64 570.6  5220 32 687.2  G6  mean maximum minimum standard deviation  25.0 47.1 3.7 11.7  31.5 59.1 4.0 12.4  30.1 70.5 5.7 16.2  29.7 70.5 3.7 13.5  DG6  mean maximum minimum standard deviation  17.1 25.0 9.8 4.0  20.1 49.0 11.2 5.6  20.8 33.8 10.8 5.2  19.7 49.0 9.8 5.3  VG6  mean maximum minimum standard deviation  155 351 17 87  257 580 20 122  255 695 31 162  234 695 17 134  VM6  mean maximum minimum standard deviation  106 304 1 73  192 499 9 107  191 559 13 133  173 559 1 114  mean  82  Table 4.2. Numbers of plots by stand structure class (SSCLASS) for pine (P), spruce/fir (S), deciduous (D) and all species combined.  SSCLASS  D  P  S ALL  1  7  4  7  18  2  3  1  4  3  6 17  7  30  4  1  5  6 21  4  31  6  7 22  8  37  7  4  1  2  5  9  8  4  1  5  9  8  3  11  10  2  1  3  11  1  2  3 23  12  4  8 11  13  1  1  3  5  14  2  3  3  8  41 97 51  189  ALL  83  6000  80 70  5000  60  G (m2/ha)  N (trees/ha)  4000 3000 2000  50 40 30 20  1000 0  10 0  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  Stand StructureClass  Stand Structure Class 50  30  40  H (m)  DG (cm)  20  30 20  10  10 0  0  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  700  700  600  600  500  500  500  400 300 200 100 0  VM (m3/ha)  600  VM (m3/ha)  VG (m3/ha)  700  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  Stand StructureClass  Stand StructureClass  400 300  400 300 200  200  100  100 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  0  0  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  StructureClass 0 1 2 3 4 5 6 7 8 9 10 11 12 13Stand 14 15 StandStructureClass  StandStructureClass  Figure 4.1. Box plots for stems per ha (N), basal area per ha (G), Lorey’s mean tree height (H), quadratic mean diameter (DG), and gross (VG) and merchantable (VM) volume per ha by stand structure class (n=189 plots). (Central line = median; upper and lower ends of the box = approximate 75 th and 25th percentiles, respectively; “whiskers” indicate approximate 95 th and 5th percentiles, respectively; asterisks indicate extreme values). (n=189 ground plots) 84  Table 4.3. Pearson correlations (r) between ground variables, including the ranked transformed basal area (RG6) and stems (RN6) per ha above 6 cm DBH (see Table 1 for a description of remaining variables) versus LiDAR variables: percent of total first (PF2) and last (PL2) returns  2 m, and area under the distribution for first (AF2) and last (AL2) returns 2 m.  Ground Variables  LiDAR variables*  N6  G6  H6  DG6  VG6  VM6  RG6  RN6  PF2  0.51  0.75  0.36  0.02  0.65  0.58  0.73  0.57  PL2  0.08  0.56  0.55  0.32  0.61  0.61  0.53  0.17  AF2  0.28  0.80  0.67  0.28  0.83  0.82  0.79  0.34  AL2  0.08  0.69  0.72  0.41  0.78  0.81  0.66  0.16  *Correlations  0.8 are underlined. High to moderately high adjusted R2 values were obtained for the log10-log10 regression models for VM6, VG6, and G6 and H6 (Table 4.4). The LiDAR variables, AL2, PF2, and PL2, were most dominant with respect to estimating ground-level variables, while AF2 was not significant in all but one case. The logarithmic transformed PF2 and AF2 were perfectly correlated (r = 1) since areas were calculated by integrating proportions. The inclusion of both would result in an inability to fit the regression model. The logarithmic transformed PL2 and AL2 were less correlated (r = 0.67). Mean biases were low for most of the variables, the exception being DG6 with a mean difference in predicted versus actual value of -4.8 cm. This is relative to a predicted mean value of 19.4 cm. The coefficient of variation was lowest for H6 (13.6%), followed by G6 (26.8), VG6 (30.2), VM6 (33.6), N6 (52.6), and DG6 (78.8).  85  Table 4.4. Log-log models for ground variables predicted from LiDAR variables (ns= not significant at α=0.05), and associated sample based summary statistics. (See Tables 4.1 and 4.3 for descriptions of the ground plot and LiDAR variables respectively. n=189 ground plots).  Ground Variables LiDAR variables  N6  G6  H6  DG6  VM6  VG6  Constant  0.535  0.422  1.904  2.124  2.809  2.028  PF2  1.384  0.764  -0.142  -0.323  ns  0.588  PL2  ns  -0.456  -0.528  -0.326  -1.433  -0.937  AF2  ns  ns  ns  ns  0.297  ns  AL2  -0.205  0.611  0.644  0.485  1.887  1.221  189  189  189  189  189  189  2  3  3  3  3  3  MSE  0.063  0.019  0.005  0.008  0.037  0.023  SEE  0.251  0.138  0.067  0.087  0.193  0.151  F  59.46  168.63  121.7  42.77  236.86  241.61  Prob>F  0.000  0.000  0.000  0.000  0.000  0.000  Radj2  0.383  0.728  0.658  0.400  0.790  0.797  1052.6  29.1  15.2  19.4  173.9  228.7  Bias  -66.7  -0.6  -0.1  -4.8  -0.7  -0.9  RMSE  553.7  7.8  2.1  15.3  58.4  69.1  CV(%)  52.6  26.8  13.6  78.8  33.6  30.2  NOBS DF  Meanp  * DF= model degrees of freedom; log10 units: MSE= mean squared error; SEE= standard error of estimate; F=F statistic with associated probability of a greater F value (Prob>F); Radj2=adjusted R-squared; Original units: Meanp = predicted mean for all plots in original units, and associated Bias, Root Mean Squared Error (RMSE) and Coefficient of Variation (CV).  86  4.3.3  Variation in LiDAR Variables by Stand Structure Class  The LiDAR variable AF2 showed high variability between, and low variability within, the 14 remaining stand structure classes (Figure 4.2). Since this variable is strongly related to VG6 (Tables 4.3 and 4.4), this result is consistent with the between and within class variations shown for VG6 (Figure 4.1). Similarly, boxplots of AL2 and to a lesser extent PL2 by stand structure class appear to follow trends associated with VM6 (Figure 4.1). In contrast, PF2 increased starting in stand structure class 1 and reached a maximum proportion of total returns in class 8, followed by a small decrease down to 11, followed by a larger decrease to 13 and an increase in 14. This trend reflects canopy closure differences (data not shown). Since classes 7, 8, 9, 10, and 11 had relatively high basal areas per ha (Figure 4.1), PF2 was consistently greater than 70%. Overall, the LiDAR variables seem to reflect differences in ground-measured structural characteristics used for the stand structure classification.  4.3.4  Stand Structure Classes Using Clustering of LiDAR Data  As noted in the methods, the LiDAR data were clustered into 5, 10 and 15 classes according to different scenarios including different combinations of 1 to 4 reverse cumulative distributions in PFx, PLx, AFx, and ALx at x = 1 m in height. Each classification was then reconstituted using each of the following ground distribution variables in turn (i.e., VGx, Gx, Nx, and Hx) as well as RNx and RGx combined. The best structural classification produced a KHAT value of 0.536 with 5 LiDAR-based classes (Table 4.5). The LiDAR classification was based on the reverse cumulative distributions of AFx and ALx. The ground based approximation was based on the reverse cumulative distributions of VGx with respect to DBH. Approximately 64 % of the plots were assigned to the same class based on the ground reconstituted system of LiDAR classification.  87  100  60  90 50  80  40  PLPL 2 (%)  PFPF 2 (%)  70 60 50 40  30 20  30 10  20 10  0  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  StandStructureClass  Stand StructureClass  15  9  9  8 7  7  10  6  5  AL2 (m) (m) HL 2 HL  6  HL  AF22(m) (m) HF HF  8  5 4  2  2  1  1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  0 0 1 Stand StructureClass  4 3  3  0  5  0  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  2 3 4 5 6 7 8 9 10 11 12 13 14 15 Structure Class Stand  StandStructure Class  Figure 4.2. Box plots for percents of first (PF2) and last (PL2) returns above 2 m in height and areas under first (AF2) and last returns (AL2) above 2 m in height by ground-stand structure class.  88  Table 4.5. A ground plot approximation of a LiDAR-based system of stand structure classification. The LiDAR classifications were based on the reverse cumulative distributions of AFx and ALx at 1 metre height intervals below 28 m and down to a minimum of 2 m. The ground-based approximation was based on the reverse cumulative distributions of gross volume per ha (VGx, top) and relative basal area and numbers of stems per ha (RGx, RNx combined, bottom) with respect to DBH at 2 cm intervals, starting at 56 cm diameter class down to a minimum of 6 cm.  Ground Analogue-VGx LiDAR  1  1  13  2  2  3  4  1  5 ALL % Correct KHAT 4  2  30  18  72.2  0.630  32  93.8  0.736  3  1  2 23 19 12  57  40.4  0.203  4  1  7  7 26  41  63.4  0.372  5  3  7  3 28  41  68.3  0.453  18 39 38 50 44  189  63.5  0.536  ALL  Ground Analogue – RGx, RNx 1  1  18  77.8  0.645  32  87.5  0.642  57  33.3  0.112  2  41  31.7  0.111  4 17  41  41.5  0.220  26 45 42 39 37  189  48.1  0.346  14  2  4  28  3  2  4  1 13 12 13  5  9  ALL  3  4 19 17 15 11  Using the LiDAR data to reconstitute the ground-based systems of classification, five different classifications produced a KHAT statistic greater than or equal to 0.5. All of them had five classes. The first and third ranked systems of ground-based classification were based on cumulative distributions of VGx with respect to DBH. The second ranked system utilized the distribution of Gx with respect to height and the fourth and fifth ranked system utilized VGx with respect to height. The five LiDAR-based classes derived using AFx and ALx were contrasted using Bonferroni pairwise comparisons of group mean values for N6, G6, H6, DG6, VG6 and VM6, using a p < 89  0.05 as a threshold for indicating significant differences (Table 4.6, Figure 4.3). Differences amongst every pair of classes were significant for G6, H6, VG6 and VM6. Class 2 was the lowest in density (N6) with an average of 693 stems per ha and was significantly different from 3, 4 and 5, but not significantly different from Class 1 that was the second lowest in density with 994 stems per ha. With respect to quadratic mean diameter (DG6), Class 1 had the largest value (31.3 cm) and was significantly different from the remaining classes. Class 2 with the lowest quadratic mean diameter (16.7 cm) was significantly different from Class 5 that had the second highest value (26.0 cm). Finally, differences in the same five classes according to LiDAR statistics were also summarized as a cross validation of the LiDAR classifications. Significant differences were found amongst all pairs of classes with respect to AF2 and AL2. This was as expected since the cumulative distributions associated with these variables were used as the bases for developing the system of classification in the first place. With respect to PF2, Class 1 was found to be significantly different from Classes 2, 3 and 4. Classes 1 and 5 were undifferentiated (p=1). Classes 3 and 4 were undifferentiated with respect to PL2 (p= 0.297), but otherwise means and standard errors associated with the remaining classes were significantly different.  4.3.5  Predicting Stand Structure Classes Using Ground Calibrated LiDAR Variables  Question 4 focused the investigation on using LiDAR data as a means of predicting ground based classes. There were two ground classifications, one based on VGx alone and the other based on RNx and RGx. There were also two levels of LiDAR information deployed in this process. The first represented a minimum of information and relied on developing mean LiDAR return profile statistics for each of the ground classes. The second involved an increase in information through the use of MDA to maximize the correlation between LiDAR return profile statistics and ground classifications.  90  Table 4.6. Means and standard errors for ground plot and LiDAR statistics for 5 LiDAR classes defined by cumulative distributions of AFx and ALx. (See Tables 4.1 and 4.3 for descriptions of the ground plot and LiDAR variables)  Mean LiDAR  Nobs  N6  G6  H6  DG6  VG6  VM6  AF2  AL2  PF2  PL2  1  18  994  46.4  20.5  25.2  450.6  376.2  12.9  6.3  82.0  41.6  2  32  693  11.0  10.9  17.3  59.0  33.3  2.3  0.9  37.7  13.5  3  57  1299  32.0  15.8  19.3  244.4  172.9  8.0  3.1  73.5  28.4  4  41  1150  25.1  13.6  18.3  170.2  115.5  5.4  2.1  64.7  24.1  5  41  1227  38.3  17.5  20.9  325.2  251.6  10.7  4.5  81.6  34.7  ALL  189  1119  29.7  15.3  19.7  234.1  173.3  7.5  3.1  68.1  27.6  Standard Error 1  18  78  2.6  0.4  1.1  26.7  22.3  0.3  0.3  1.7  2.1  2  32  98  0.9  0.6  1.4  5.4  4.3  0.2  0.1  3.2  1.4  3  57  96  1.3  0.3  0.6  10.0  7.5  0.1  0.1  1.4  1.3  4  41  131  1.4  0.4  0.7  10.5  8.5  0.2  0.1  1.9  1.8  5  41  83  1.3  0.3  0.6  13.4  11.1  0.2  0.2  1.4  1.3  ALL  189  50  1.0  0.3  0.4  9.7  8.3  0.2  0.1  1.4  0.9  * Nobs is the number of ground plots.  91  80  6000  70  5000  60 50  G  N  4000 3000  40 30  2000  20 1000 0 0  10 1  2  3 LC  4  5  0 0  6  1  2  3 LC  4  5  6  1  2  3 LC  4  5  6  50  30  40  20  H  DG  30 20  10 10  1  2  3 LC  4  5  0 0  6  700  700  600  600  500  500  400  400  VM  VG  0 0  300  300  200  200  100  100  0 0  1  2  3 LC  4  5  6  0 0  1  2  3 LC  4  5  6  LiDAR Structure Class Figure 4.3. Box plots of N, G, H and VG with respect to LiDAR classes derived from the log-transform variable set. (See Fig. 4.1 for description of box plots.)  92  Starting with the first level of information, ground-based classes were produced using cumulative distributions of VGx with respect to DBH. The LiDAR distributions of PFx and PLx were then used to reconstitute these classes. The maximum KHAT value was 0.489 (Table 4.7). This maximum value was associated with five ground classes. This represented a slight decline over the previous LiDAR classification with five classes based on AFx and ALx, where the ground based analogue classification produced a KHAT of 0.536. A ground-based system of classification was also produced using cumulative distributions of RNx and RGx combined. The maximum KHAT value was 0.410 based on the five-class ground-based system reconstituted once again using the LiDAR distributions PFx and PLx (Table 4.8). This represented a slight improvement over the previous LiDAR classification with five classes based on AFx and ALx, where the ground-based analogue classification produced a KHAT of 0.346. As expected, the differentiation of resultant classes generally improved with regards to increased differences in mean ground variable values and/or decreased standard errors when compared with the LiDAR classes (Table 4.9 versus Table 4.6). The change was particularly notable when describing differences amongst the classes in terms of N6. However, the differences between the classes diminished for the LiDAR analogue class statistics, AFx and PFx. For ALx and PLx, there was no large loss in differences between the groups. This is consistent with what was found based on the LiDAR variables used to reconstitute the best classifications involving either VGx or the combination of RNx and RGx.  93  Table 4.7. Contingency tables for the LiDAR Analogue and MDA classifications versus the 5-class ground based system of classification using the cumulative distributions of VG x with respect to diameter class.  LiDAR Analogue Ground  1  1  4  2  2  2  4  5  5 ALL  4  5  ALL  % Correct  KHAT  5  80.0  0.746  6  48  85.4  0.567  1 41  3  3 1 19  12  11  44  43.2  0.242  1  4  7  1  18  38.9  0.280  1  13  12  1  47  74  63.5  0.293  12  55  36  21  65  189  62.4  0.489  5  80.0  0.764  6  48  85.4  0.572  LiDAR MDA 1 2  41  3  2  4  2  5 ALL  1  4  8  1 27  5  10  44  61.4  0.393  1  4  10  1  18  55.6  0.468  12  10  1  51  74  68.9  0.331  54  42  17  68  189  70.4  0.591  94  Table 4.8. Contingency tables for the LiDAR Analogue and MDA classifications versus the 5-class ground based system of classification using the cumulative distributions of RG x and RNx with respect to diameter class.  LiDAR Analogue Ground  1  2  1  20  1  2  3  4  35  1  5  5  ALL  % Correct  KHAT  6  27  74.1  0.554  41  85.4  0.598  3  1  2  17  9  9  38  44.7  0.285  4  2  11  4  18  9  44  40.9  0.204  5  13  9  7  10  39  25.6  0.077  ALL  36  31  39  34  189  52.9  0.410  49  LiDAR MDA 1  16  1  1  9  27  59.3  0.452  2  28  2  10  1  41  68.3  0.489  3  1  24  8  5  38  63.2  0.417  8  6  18  7  44  40.9  0.167  8  9  16  39  41.0  0.210  41  46  38  189  54.0  0.421  4  5  5  6  ALL  27  37  95  Table 4.9. Means and standard errors for ground plot and LiDAR statistics for 5 ground based classes defined by cumulative distributions of RGx and RNx. (See Tables 4.1 and 4.3 for descriptions of the ground plot and LiDAR variables)  Mean Ground  Nobs  N6  G6  H6  DG6  VG6  VM6  AF2  AL2  PF2  PL2  1  27  967  45.6  19.5  25.3  421.5  350.1  11.7  5.3  80.8  37.4  2  41  588  11.2  12.5  19.1  68.6  44.5  3.3  1.2  42.4  16.0  3  38  1869  34.2  13.7  15.7  237.6  146.0  8.1  2.8  78.4  26.2  4  44  786  23.6  15.6  20.3  182.1  138.6  6.9  3.0  66.8  28.5  5  39  1429  40.5  16.6  19.4  333.4  251.8  9.4  4.0  77.8  33.2  ALL  189  1119  29.7  15.3  19.7  234.1  173.3  7.5  3.1  68.1  27.6  Standard Error Ground 1  27  65  1.7  0.4  0.7  20.0  16.6  0.4  0.3  1.7  1.8  2  41  79  0.7  0.7  1.3  5.7  5.3  0.3  0.2  2.9  1.8  3  38  127  1.0  0.3  0.3  8.7  6.8  0.3  0.2  1.7  1.7  4  44  39  0.6  0.5  0.6  8.8  8.3  0.3  0.2  1.6  1.5  5  39  71  1.0  0.4  0.3  12.1  9.9  0.3  0.2  1.8  1.6  ALL  189  50  1.0  0.3  0.4  9.7  8.3  0.2  0.1  1.4  0.9  * Nobs is the number of ground plots. The two five-class systems of ground classification, VGx, and RNx combined with RGx, were each used separately to formulate the Y-variables in an MDA. The LiDAR variables used to represent the X-variables were reduced to a smaller subset based on the correlations of PFx, PLx, AFx and ALx versus RGx and RNx with respect to an increase in DBH (Table 4.10). For the minimum DBH threshold of 6 cm, the correlations for all LiDAR variables reached a maximum at a height greater than or equal to 3 m. As DBH thresholds increased, the height of maximum correlations for all of the LiDAR variables increased up to a height of 19 m. This height was consistently associated with a DBH threshold of 32 cm. Beyond this DBH threshold, the LiDAR height of maximum correlation declined. Therefore, height thresholds 96  of 3 and 19 m, and intermediary height thresholds of 7, 11, and 15 m were selected as the five X-variables for each of PFx, PLx, AFx and ALx in the MDA. Table 4.10. Maximum correlation coefficients for selected height of LiDAR return variables and corresponding DBH thresholds associated with RGx or RNx. (See Tables 4.1 and 4.3 for descriptions of the ground plot and LiDAR variables.)  RGx HT  PFx  PLx  RNx AFx  ALx  PFx  PLx  AFx  ALx  Correlation Coefficient 3  0.75  0.64  0.82  0.76  0.66  0.58  0.70  0.68  7  0.80  0.74  0.81  0.78  0.69  0.66  0.70  0.69  11  0.77  0.77  0.78  0.78  0.68  0.69  0.69  0.68  15  0.77  0.76  0.77  0.75  0.70  0.68  0.70  0.67  19  0.73  0.72  0.73  0.72  0.69  0.66  0.69  0.66  DBH Threshold (cm) 3  6  16  12  18  14  20  20  20  7  10  16  14  18  14  20  20  20  11  14  16  16  18  20  20  20  20  15  22  20  22  22  24  24  24  24  19  32  32  32  32  32  32  32  32  Using backwards stepwise MDA and the VGx five-class system, the final X-variable set included PFx at 7, 15 and 19 m in height and PLx variables at the same heights. A decision was made to remove AF19 that was also part of the backwards stepwise solution. This was achieved with no loss in the overall classification success rate of 70.4% (Table 4.7). The rationale was that the best LiDAR-reconstituted ground classification did not include AFx, but did include distributions related to the remaining variables, PFx and PLx. An overall KHAT of 0.592 was obtained, relative to the value of 0.489 obtained for the LiDAR reconstituted classification using PFx and PLx. The individual class success rates for MDA ranged from 56% to 85%. 97  For the RNx and RGx combined five-class system, the final X-variables were PFx at 3, 7, and 15 m and PLx variables at 7 and 19 m. The best LiDAR-reconstituted classification was also realized using PFx and PLx. A success rate of 54% and a KHAT value of 0.421 were obtained (Table 4.8). This can be compared with a success rate of 52.9% and a KHAT of 0.410 in the LiDAR-reconstituted classification prior to the use of MDA. Additionally, the MDA class-specific success rate ranged from 41% to 68%, indicating a more even distribution of errors amongst all of the classes when using MDA compared with 25% to 85% when using the simple LiDAR analogue-based system of classification. The groundbased classification had a greater success rate at the extremes with respect to all of the ground variables except numbers of stems per ha, as exhibited by the higher classification success rates for Classes 1 and 2 (Table 4.9). Class 5 had the lowest classification success rate both before and after MDA. In terms of mean basal area and volume, Class 5 is most closely related to Class 1 (i.e., Classes 1 and 5 are more similar to each other than either of them are to the remaining classes). As a result, the increase in the number of correct classifications for Class 5 appears to come at the cost of an increase in misclassification of Class 1. MDA redistributed the error more evenly amongst classes, but only very slight gains were obtained in the overall classification success rate. 4.3.6  Influence of Different Numbers of Classes  With regards to Question 5, the KHAT value generally declined with an increasing number of classes, but this was not a smooth decline (Figure 4.4). In particular, the VGx groundbased classification and LiDAR-based analogue using PFx and PLx (VG-PF, PL in Figure 4.4) had a KHAT value of 0.614 with two classes, dropped to 0.454 with three classes, increased to 0.611 with four classes, and then followed a more steady decline with an increasing number of classes. The AFx LiDAR classification reconstituted using the ground variables RGx and RNx (labeled as AF-RG, RN) declined somewhat steadily down to a KHAT equal to 0.292 at eight classes, increased to 0.402 (close to the value observed with four classes of 0.404) before starting a somewhat steady decline down to 0.289 with 15 classes.  98  0.7 0.6  KHAT  0.5 0.4 0.3 0.2 0.1 0 2  3  4  5  6  7  8  9  10  11  12  13  14  15  Number of Classes AF,AL - VG  AF - RG,RN  VG - PF,PL  RN,RG - PF,PL  Figure 4.4. The change in KHAT with an increasing number classes. LiDAR classes were derived using AFx and ALx combined and AFx alone and were reconstituted using VGx, and RGx and RNx combined. Ground classes were derived using VGx, and RNx and RGx combined, and both of these classifications were reconstituted using LiDAR distributions PF x and PLx.  4.4  Discussion  The main issue addressed in this chapter was whether LiDAR data could be used effectively to represent stand structure defined by ground variables, particularly as it relates to distributions of stems and basal area per ha by DBH. These ground-based distributions provide inputs into individual tree models to forecast future plot or stand and forest conditions (Pretzsch et al. 2006). These distributions are also important for many kinds of forest and stand management evaluations and decisions, including identification of suitable habitats for different kinds of bird species (e.g., Hansen et al. 1995; Millington et al. 2011), determining preferred crown fire-hazard reduction strategies (Fiedler and Keegan 2003), and minimizing timber versus environmental value tradeoffs through time while deploying 99  alternative uneven-aged stand management techniques (Buongiorno et al. 1994). The study area for this chapter was located in structurally complex, mixed-species stands of Alberta, Canada; however, similar kinds of stand structure measures have been useful for describing other stand types and stand dynamics (e.g., Chapters 2 and 3; Kohyama 1993; Yue et al. 2008). The use of reverse cumulative distributions for stand structure avoids the problem of restricting measures of similarities and differences in stand structure to some arbitrary definition of diameter classes as noted in Chapter 2. For example, if similarities and differences in stand structure were based on two diameter classes (e.g., above and below 15 cm DBH), this would give an inordinate amount of weight to the determination of how many trees fall above or below this value. As a result, differences between two plots may appear to be relatively large using this definition when DBH values in both are close to the 15 cm DBH cutoff. Further, small changes in the DBH value used would result in large changes in the perceived similarity or difference. At the other extreme, if DBH class widths are relatively small, one DBH class may contains trees while an adjacent one may not; this kind of condition may not be a good indicator of significant differences in stand structure (Yue et al. 2008). The cumulative distributions approach avoids this problem by representing DBH distributions along a continuum. The use of cumulative distributions is in contrast with the research of Maltamo et al. (2004) and Packalén and Maltamo (2008) who used discrete DBH classes and Most Similar Neighbour (Moeur and Stage 1995) methods to relate LiDAR return distributions to ground characteristics. However, there are some similarities in the approach used by Maltamo et al. (2006) with that used in this dissertation. They ranked trees in each plot from smallest to largest by height and then recorded the DBH at each 10-percentile of basal area, starting at the top of the canopy and moving towards the bottom (pers. com., Packalén 2011). Also, Gobakken and Næsset (2005) placed emphasis on estimating basal area and associated diameters at given density percentiles using seemingly unrelated regression where stems per ha were ranked from smallest to largest by DBH. In the method introduced in Chapter 2, as  100  well as using cumulative distributions, both stems and basal area per ha were used as combined variables. This is unlike these other studies. As noted in Chapter 2, the rationale for including cumulative distributions for both stems and basal area per ha was that this gives equal weight to small and large trees. The reverse cumulative distributions of stems per ha tend to follow an approximate negative exponential pattern given an increase in diameter, where differences are most apparent in the smaller diameters. In contrast, basal area reverse cumulative distributions decline linearly (complex or two layered stands) or follow a strong reverse sigmoid pattern (single layered stands), with differences more evident in the middle to upper diameters. Further, non-parametric (empirical) distributions were used to represent stand structure, whereas other studies used parametric distributions. For example, Thomas et al. (2008) used a finite mixture model of Weibull (1951) probability density functions to reflect bimodal or trimodal stand structure conditions and then used LiDAR metrics to predict parameters of the finite mixture model. The parametric approach is constrained by the need to define the specific density distribution. However, it is difficult to find one density distribution that represents the wide range of stand conditions (e.g., Podlaski and Zasada 2008; Nagel et al. 2007). Other authors used non-parametric distributions, as in this study, for distributions of volume, basal area or stems per ha by diameter (e.g., Maltamo et al. 2006). Also the work of Frazer (2007) and the use of L-moments introduced by Hosking (1990) are of interest. Lmoments (i.e., mean, variance, skewness and kurtosis) can be calculated from empirical distributions and as a result can be used to represent a wide variety of parametric distributions. Five questions were posed to address whether LiDAR data might be useful in measuring ground-measured stand structure. The first question posed was: How well do LiDARderived variables correlate to ground-measured stand structure variables? The results indicated that total and merchantable volume, basal area and relative basal area above 6 cm DBH (i.e., VG6, VM6, G6 and RG6) were strongly correlated with the area under the proportions of first returns for heights above 2 m (i.e., AF2). This LiDAR-derived variable 101  accounts for both stocking and the distribution of trees with respect to height. Therefore, AF2 was related to volume and basal area per ha since these ground measures give greater weight to taller, larger diameter trees and are strongly affected by the proportion of area stocked by trees. Hollaus et al. (2009) used a similar approach to obtain a LiDAR-derived variable to estimate volume per ha in a 128 km2 alpine area in Austria. In contrast, the proportion of first returns above 2 m, PF2, clearly relates to effects of stocking, but provides little or no information on the distribution of returns with respect to height. The LiDARderived variable AL2 was also strongly correlated with VM6 and to a lesser extent VG6, but only moderately correlated with G6. Lorey’s mean tree height, H6, did not exhibit strong correlations with the LiDAR-derived variables (highest correlation of 0.72 with AL2). Since stocking has no bearing on the determination of Lorey’s mean tree height, this is perhaps not surprising. The fitted log-log models between ground measured and LiDAR-derived variables further indicated that LiDAR variables are useful structural indicators. Similar results were found by Næsset (2007) and Säynäjoki et al. (2008). To address the second question, which was whether differences would be found in LiDARderived variables within the structure classes, ground and LiDAR summary statistics were examined across the 17-class system of classification developed in Chapter 2. The differences in ground statistics by stand structure class were similar to those found for the very different stands in the Williams Lake, BC study area used in Chapter 2, supporting the stand structure classification system. However, only 14 of the 17 classes were represented in the Alberta study area of this chapter. In terms of LiDAR-derived variables, PF2 seemed to correspond with estimates of crown closure and canopy height by stand structure class; the remaining variables showed a closer correspondence to basal area and volume with each class. This is consistent with the interpretation of PF2 as an indicator of stocking. However, there was considerable overlap in LiDAR-derived variables between the stand structure classes, indicating that these LiDAR-derived variables may not distinguish stand structure classes with high accuracy. Since only 14 classes were represented in the Alberta study area, this indicated that the number of classes and associated numbers of plots per class may have an important bearing on the results of stand structure classification using LiDAR-derived variables. 102  An alternative to using LiDAR-derived variables that estimate ground stand structure classes is to derive stand structure classes using LiDAR data directly. The third question asked how well stand structure might be described using LiDAR instead of ground data. To answer this question, LiDAR data representing all combinations of cumulative distributions in AFx, ALx, PFx and PLx with respect to height were used to produce 5, 10 and 15 LiDAR classes. Average ground-based distributions in RNx and RGx with respect to DBH were then used to represent centroids for each of the LiDAR classes. For a given number of classes and a given combination of LiDAR variable cumulative distributions, all of the ground plots were then reclassified based on the nearest neighbour distance to ground-variables centroid. This indicated the degree of consistency between LiDAR and ground classification perspectives. The results were disappointing, with the correct class being identified only 48.1 % of the time, along with a KHAT value of 0.346 with a five-class system of classification. A maximum KHAT value of 0.381 was obtained using a 10-class system of classification with a corresponding success rate of 45%. Since the ground centroids included stems per ha by DBH, as used in the ground stand structure classification system, the success rates were low. LiDAR-derived variables were strongly correlated to basal area and to volume, but were only weakly correlated to stems per ha. At least part of the reason for low correlation with stems per ha is that LiDAR returns tend to increase and then diminish with an increase in depth through the canopy. The numbers of returns are higher in the upper canopy, whereas often there are many stems in the lower canopy. Greater weight would need to be placed on LiDAR returns lower in the canopy to better estimate stems per ha, particularly to include stems in the understory (Korpela et al. 2011). This is of particular concern as the density of dominant trees increase, causing canopy height distributions based on LiDAR to be increasingly unimodal even where the stand structure would indicate a multimodal distribution pattern (Maltamo et al. 2005). My results indicated that LiDAR data do not represent stand structure based on ground distributions of stems and basal are per ha well. However, the LiDAR stand structure classifications did relate well to volume as a stand structure measure.  103  MDA was used to evaluate the fourth question of how well the ground-measured stand structure classes can be predicted using LiDAR data to do the classification. The success rate reached a maximum of 54% when trying to assign stand structure classes derived from ground measured stems and basal area per ha distributions (i.e., RGx and RNx). When ground stand structure was defined by volume per ha distributions (VGx), the results improved, with success rates from 62% to 70%. As noted with regards to using the LiDARbased stand structure classes, the LiDAR variables do not relate well to stems per ha, and therefore do not represent the stems per ha distribution either when classes are derived using LiDAR data or when LiDAR data are used to present stand structure classes derived using ground measured stems per ha. Based on these results, it may be tempting to simply ignore the understory component that often contributes higher numbers of stems per ha since stand structure classification based on LiDAR-derived variables could be used. However, there are many applications of stand structure where the understory component is important. For example, when fire suppression has been practiced for an extensive period of time, ingress of smaller trees has lead to increased fire severity (Bekker and Taylor 2010), particularly in forests characterized by low severity fire regimes (Noss et al. 2006). Locating and thinning some of the small stems can help to restore landscapes to conditions that are less fire prone. Catastrophic outbreaks of mountain pine beetle in western Canada and the United States have resulted in an intense interest in understory seedling and sapling characteristics as a potential source of increased resilience (e.g., Diskin et al. 2011; Dhar and Hawkins 2011). Also, the ability to reasonably forecast future forest and stand conditions and their impacts on resource values and ecosystem services, particularly over intermediate to longer term time horizons, depends on information concerning the abundance of small trees (Buongiorno et al. 1994; Dhar and Hawkins, 2011; Millington et al. 2011). Given that LiDAR is useful on a relatively small spatial scale (e.g., 18 m by 18 m grid cell), particularly with respect to larger trees in the overstory, further research is needed to find systematic and broadly applicable approaches for using LiDAR data to characterize understory.  104  The last question posed in this chapter concerned the impact of the number of classes on stand structure classes based on LiDAR-derived variables and based on ground variables. The general trend was that classification successes using either system decreased with increasing numbers of classes. However, there were distinct thresholds when moderate to large improvements in classification success occurred. The exact reason for this is not obvious. One possible reason may be that there are asymmetries in the LiDAR versus ground based data that are essentially the main source of classification error when it comes to evaluating the success of analogue systems of classification. However, this needs to be further investigated.  4.5  Conclusions  The primary focus of this chapter was whether LiDAR data could be used for stand structure classification, either to predict previously developed ground stand structure classes, or to develop useful LiDAR-based stand structure classes. Generally, the LiDAR data did not relate well to ground stand structure classes based on stems and basal area per ha by DBH. Likely, this is due to difficulties in estimating stems per ha using LiDAR data, particularly, stems per ha in the understory layers. Since understory layers are important for a wide variety of forest management objectives, procedures that more reliably estimate the stems per ha distributions by DBH using LiDAR data are needed. For example, new LiDAR-based indices may be better related to certain ground plot characteristics, particularly understory characteristics, and especially when overstory leaf area density increases (Maltamo et al. 2005). Although the LiDAR data did not relate well to stand structure based on stems and basal area per ha by DBH class, these data did relate well to volume per ha by DBH. Based on this investigation, ground data are critical as a source of information for stand structure elements. However, LiDAR data may be coupled with ground data and other data, including digital photography, and an inventory system developed to meet needs of forest managers. Further investigation of LiDAR coupled with these other data sources is needed.  105  Chapter 5: Conclusions 5.1  Contributions to Knowledge  5.1.1  Summary  The primary contributions of this dissertation are: 1. The introduction of a new measure of stand structure, based on non-parametric, reverse cumulative distributions of stems and basal area per ha with increasing DBH; 2. The derivation of a meaningful system of stand structure classification without any a priori decision as to what the classes should mean or how they should be interpreted; 3. A demonstration of how this kind of classification can be used as a tool for describing and diagnosing different succession pathways based on certain assumptions involving the forecasting of future stand development patterns using an individual tree growth model; and 4. An evaluation of how this kind of measure and approach to classification might be extended for the purpose characterizing high resolution forest inventories using discrete return airborne laser scanning (i.e., LiDAR).  5.1.2  Chapter 2 Synopsis: Research Conclusions and Implications  The research presented in Chapter 2 was aimed at maximally differentiating stands by stand structure using differences in distributions of stems and basal area per ha by DBH. The main objective was to provide easier identification of stand structure classes in the field, as well as to provide a stand structure classification system that is precise, consistent, and reliable, thereby facilitating communications amongst a wide variety of practitioners. This stand structure classification approach was designed to avoid problems that result from: using size-density relationships (e.g., Reynolds and Ford 2005); fitting plot and stand conditions into already defined structural stages and patterns of succession (e.g., Franklin et al. 2002) or into prescriptive classes (e.g., silviculture systems; Smith et al. 1997); reducing a wide variety of observed DBH distributions to a single functional form based with the aid of a few parameters (Nagel et al. 2007); and applying the notions of layers (see Latham et al. 1998), cohorts, and indices (McElhinny et al. 2005). DBH was the key structural variable because it can be easily measured (the exceptions being trees with multiple stems or pronounced buttresses), it is well-correlated with height, and it is a key variable for forecasting future 106  stand development patterns using individual tree growth and mortality models. Further, DBHs are related to recruitment and decay of coarse wood debris, which is important for assessing forest fire risk and to deriving habitat ratings for small mammals. In this stand structure classification system, a new measure of stand structure similarity was introduced. This measure involved the construction of non-parametric (i.e., empirical) cumulative distributions of stems and basal area per ha greater than a given DBH threshold, resulting in two reverse cumulative distributions. These distributions were rank-adjusted by stems and basal area per ha for the plot. The similarity in stand structure between two plots or stands was then determined as the sum of the absolute differences for these two ranked reverse cumulative distributions. The rationale for selecting this distance metric was: 1. the metric can be easily generated from plot data that are commonly measured with a relatively high level of precision, and relatively easily collected in forest surveys; 2. cumulative distributions avoided the problem of arbitrarily defining DBH class limits; 3. non-parametric distributions were chosen since there is no parametric distribution that can be used to represent the entire range of tree diameter distributions amongst a wide variety of forest types (Nagel et al. 2007); 4. both stems and basal area per ha were used as the foundation for this measure since stems per ha gives greater weight to smaller trees, whereas basal area per ha gives greater weight to larger trees; 5. the ranking procedure was used to give equal weight to both reverse cumulative distributions, and ranking also contributed to a more balanced distribution of plots amongst stand structure classes; and 6. a single distance measure was created by summing absolute differences in the two distributions. This distance metric is based on cumulative distributions, an approach used in other research as referred to in previous chapters (e.g. Kohyama 1989; Binkely et al. 2006; Maltamo et al. 2006).  107  Species were not used in developing stand structure classification in this dissertation. Further, spatial proximity among stems was not included. For some applications, there may be a need to include species and/or spatial proximity. The goal was to develop a system of classification that was simple in concept, with the potential to be applied to a wide variety of conditions, rather than being constrained by species compositions. Also, spatial proximity (i.e., stem mapping) is not commonly available. A final decision was the desired number of classes. The “Goldilocks Principle” was applied wherein the number of classes was not too many, such that they could not be retained in the memory of an individual forestry professional, and not too few to be of any practical use, rather, “just right”. Following extensive investigations using the study data in Chapter 2, an appropriate number of classes was chosen as 17. In developing this classification system, it was further envisioned that users would be apply the stand structure classes in the field with a high degree of success without having to establish plots following training and experience. Field testing has been used to evaluate this system and it showed promise; however, reporting on this component is outside the scope of this dissertation. A cluster algorithm was developed using the distance metric described previously with the specific goals of: 1. avoiding path dependencies in the process of deriving a system of classification based on a fixed number of classes, particularly as this problem relates to bottom up (agglomerative) or top down (divisive) classification processes; and 2. producing reasonably well-balanced numbers of observations per class. These concerns were partly highlighted by the understanding that variation in DBH distributions occurs along a continuum and that any grouping is in some way arbitrary or subjective in nature. In essence, the variation in stand structure may not manifest “natural” clusters, especially in complex and highly diverse stands.  108  The cluster algorithm started with a random assignment of observations to each class according to a uniform distribution. It progressed by moving each observation in turn from one class to each of the others, determining the minimum ratio of the change in within-tobetween distances, and recording the associated class to which the observation might be newly assigned. The lowest minimum ratio amongst all of the observations was then used to determine the observation to be moved and the new class to be assigned. With each iteration, the minimum ratio associated with each move increased steadily, albeit with minor fluctuations, until it reached a value of 1, when the algorithm was terminated. The resulting classes were evaluated on the basis of differences in: the cumulative distributions in stems and basal are per ha; whole stand or plot statistics; the Gini coefficient (Lexerød and Eid 2006); and the stand structure variance index (STVI; Staudhammer and LeMay 2001). This new stand structure classification approach was also compared with a more standard approach involving the use k-means clustering and whole stand statistics. Finally, the system of classification was validated using a process of re-substitution. The new distance metric and algorithm in combination produced a meaningful system of classification according to differences in whole stand statistics (basal area and stems per ha), cumulative distributions in stems per ha and basal area per ha, and STVI. The classes were less well differentiated according to the Gini coefficient. This was explained by the fact that this coefficient was scaled relative to the mean diameter for each plot, in contrast to STVI where the index was scaled relative to the maximum tree diameter (140 cm) across the entire dataset. The re-substitution validation process revealed that only one of the 421 plots was misclassified, thereby meeting the overall goals of producing a system of classification capable of being applied in a consistent, reliable and verifiable manner, using easily measured attributes. Further, the algorithm successfully produced a reasonably balanced distribution of observations amongst the classes. This was attributed to two properties of the process. First, the cumulative distributions for each of stems and basal area per ha were rescaled according to their rank in terms of total numbers of stems and basal area. The effect of this procedure 109  was to cause any outliers in the sample space to be drawn more toward the middle and to cause areas that were better represented in the sample space to be proportionately more distanced, with the overall result that the distances between neighbours were more precise within a given sample space. Also, the distances used to derive the ratio for (re)allocating plots to classes were based on total rather than mean distances from all of the observations in a given class. As a result, whenever an observation was added to a given class, that class became less attractive in terms of its potential to accept another observation. This is in contrast to the approach used in k-means clustering and is analogous to using total sum of squares instead of mean sum of squares as the basis for determining distances of a given observation from a given group. However, the algorithm was not completely successful in removing path dependencies. This appears to be a common problem associated with this kind of algorithm (Duda et al. 2001). As a result, the algorithm was run several times and the best solution was identified as that with the minimum ratio of total within to between class differences. This research demonstrated that it is possible to produce a system of stand structure classification that exhibits meaningful differences across a wide range of forest conditions. This was achieved without any a priori decision as to what the classes should mean.  5.1.3  Chapter 3 Synopsis: Research Conclusions and Implications  The purpose of Chapter 3 was to investigate the feasibility of adopting and adapting the system of stand structure classification, presented in Chapter 2, for the purpose of diagnosing different stand or ecological succession pathways. The main question addressed was whether it was possible to determine a succession pathway relative to a known starting point as defined by site (in the IDFdk3/01 site series for the example used), stand structure class, along with other attributes such as species composition, basal area, and stems per ha. The research was carried out by inputting plot data into an individual tree model (PrognosisBC; BC Ministry of Forests 2008) and projecting the plots forward for 155 years at 5-year intervals. It was assumed that there would be no exogenous disturbances and no new  110  regeneration or ingress into these plots, thereby representing an ideal or benchmark set of projections against which other realities might intervene. All of the outputs at each 5-year interval were classified into 1 of the 17 stand structure classes. A chart of potential succession pathways was derived by looking at all pairs of “From-To” stand structure class combinations. This revealed a global pattern of succession summarizing the results of all the simulations in three dimensions: (1) sequence in time along the vertical axis, (2) stand density roughly represented on the horizontal axis, and (3) complexity roughly represented within this two dimensional space by the structure class (Figure 3.1). This provided an alternative starting point when compared with stand density management diagrams (Drew and Flewelling 1979) for example, or with the various kinds of related indices referred to in Section 1.3. Further, the approach I used provided a more direct, quantifiable description of potential patterns of change in diameter distributions with time than heuristic approaches. The next part of the analysis involved determining whether knowledge of stand structure class was useful in reducing the potential range of possible succession patterns, and where different pathways emanated from a single class, whether or not there were additional structural details within a stand structure class that could be used to explain the differences. To gain insight into these questions, the individual tree model projections were summarized according to the amount of time spent in each stand structure class, and plots were assigned to a class, or succession pathway (SP) using hierarchical clustering. Detailed investigations into the SP’s emanating from stand structure classes 3 and 4 led to the following conclusions: 1. there were meaningful differences in the succession pathways emanating from stand structure classes 3 and 4, but there was also some overlap insofar as a plot could start in either one of these structures but follow similar pathways beyond these starting positions; and 2. differences in SP’s from a single stand structure class can be explained based on species composition in the overstory and understory (these being related to distributions with respect to diameter) as well as corresponding densities. 111  Stand structure classes 3 and 4 were selected for comparison, in part because they represented stand structures that occurred early on the progression and were more or less at the same level in the progression. As a result, the wide variety of observed SP’s were presumed to have passed through one of these two classes at some point in time, even though many of the plots represented starting stand conditions beyond these structural stages of development. In this way, if different patterns of progression could be readily explained with reference to these two classes, then it seemed reasonable to assume that this would also be the case starting in any one of the other classes. A more complete investigation would be required to follow up on this point. Four broad patterns of succession were also observed in the process of analyzing these data as follows (Figure 3.1): 1. a high density, single layered stand structure class progression typified as 248, where the progression proceeds at a relatively slow rate; 2. a moderate density, single layered stand structure progression typified as 135 and/or 69 and/or 10; 3. a moderate density complex pathway, dominated by large tree growth and associated with species that can reach a large size typified by 3 and/or 5141516; and 4.  a moderate density mixed complex-single layered pathway, where the progression is at first dominated by large tree growth until such time as a moderate to dense understory becomes large enough to alter the pathway toward a more single layered kind of stand structure pathway, typified by the progression 3141210.  These patterns revealed just how complex the concept of stand structure can be. When progressions from one class to the next are summarized as a linear process without explicit joins and intersections, a lot of important detail is missed. A detailed, quantitative understanding of this process provides a foundation for determining appropriate management interventions that alter the pathway and rates of progression to produce desired future forest conditions. The classification itself provides the opportunity to describe the initial conditions and alterations in simple terms that can provide a common basis of understanding. 112  While it was possible to illustrate stand structure progressions in a two-dimensional space using the structure classification, in reality the space is complex (i.e., multidimensional). The concept of complexity can be stated more clearly using the stand density management diagram (Drew and Flewelling 1979) as the basis for discussion. This two-dimensional diagram of average volume per tree versus stand density can be expanded to a third axis to represent variation in stand structure or distributions of trees with respect to size. However, since diameter distributions are often skewed and/or multimodal, a fourth axis would be needed to represent these characteristics. For example, the Gini coefficient or STVI used to assess the stand structure classes (see also Knox and Peet 1989) might represent this complexity. However, further dimensions might be needed to reflect stand structure. Overall, a combination of both classification (reflecting different stand structures in discrete terms) and indices (proxies for differences in distributions across a continuum) might be most effective for the purpose of identifying and communicating patterns of succession.  5.1.4  Chapter 4 Synopsis: Research Conclusions and Implications  The primary focus of this research was on stand structure classification using LiDAR without ground plot calibration data, versus LiDAR with ground plot calibration. This included: 1. development of a system of classification using LIDAR metrics derived from cumulative distributions in the numbers of first and last returns above 2 m was used to indicate the feasibility of using LiDAR data for stand structure without the use of a priori ground classes; 2. an emphasis on estimating stand structure as represented by distributions in the stems and basal area per ha from ground measures, but with consideration of other variables; and 3. consideration of a number of LiDAR cumulative first and last returns distributions metrics to predict the ground-based stand structure classes. The stand structure classification procedures developed and described in Chapter 2 were used. Additionally, a fuzzy c-means cluster algorithm developed by Bezdek (1981) was used  113  and the number of stand structure classes was allowed to vary from the 17 presented in Chapter 2. The results confirmed what many other investigators have found: LiDAR is an effective tool for estimating volume and basal area per ha, both in total and with respect to reverse cumulative distributions by DBH. This was attributed to the fact that volume and basal area give more weight to larger DBHs and that LiDAR returns tend to better represent the top of the canopy layer which is dominated by larger DBH trees. However, even when only five classes were used, using LiDAR variables assign plots to classes resulted in only a 48.1 % success rate in predicting the ground stand structure class based on stems and basal area distributions by DBH. When the basis for the ground stand structure classes was changed to distributions of volume per ha by DBH, the classification rate increased to 63.5%. Reversing this process by using stand structure classes based on LiDAR returns and then representing these LiDAR classes by ground measured stems and basal area per ha centroids, a success rate of 52.9% was obtained. When volume distributions were used as centroids of LiDAR classes, the success rate was 62.4% . Finally, using multiple discriminant analysis (MDA) where ground-based stand structure class was predicted from LiDAR metrics, the success rate was 54% using five ground classes based on stems and basal area per ha and 70.4% based on the cumulative distribution of volume. Given that LiDAR returns tend to be increasingly skewed toward the top of the canopy as canopy density increases, there is a corresponding trend toward understory conditions becoming increasingly obscured. As a result, the LiDAR data were not effective for classifying stand structures where the classification includes stems per ha distributions. In essence, it is difficult to distinguish a dense overstory condition with a dense understory versus one with little or no understory. Two potential solutions to this problem are: (1) developing other LiDAR metrics that might better reflect understory stems per ha (for example, differences in first and last return distributions); and (2) adding other variables that might be available, such as species composition and site and disturbance variables. Since  114  stems per ha is important to forest management for a number of objectives, these potential improvements should be investigated.  5.2 5.2.1  Project Strengths and Limitations Primary Strengths of Project  As noted in Section 5.1.1, the main contribution of this dissertation was the introduction of non-parametric reverse cumulative distributions in two dimensions (stems and basal area per ha by DBH) to indicate similarities in stand structure. For a given level of site occupancy or stocking, there is a range in distributions of trees by DBH (see Zeide 2005). As a result, stand structure is uniquely defined in terms of both cumulative distributions. Further, since cumulative distributions were used, there was no need to define DBH class limits and the use of empirical distributions avoided the need for defining theoretical distributions. The stand structure classification system developed in Chapter 2 could be used to illustrate patterns of succession and to provide a basis for further explanation as to why these patterns occurred as shown in Chapter 3. The classification can be linked directly to growth model outputs without any a priori definitions as to what the stages of progression should be. The result was that the classification provided a more objective means for investigating potential patterns of succession and for evaluating explanations regarding the preconditions necessary for their emergence. From one point of view, Chapter 3 did little more than explain what was already contained within an individual tree model. While this may be true, the stand structure classification was useful for explaining the growth trajectories in terms that a practitioner could use in undertaking stand management assessments without necessarily having to resort to establishing plots and using the model to explore every single case. The stand structure classification thus provides a comprehensive basis for comparing different scenarios and outcomes in terms of what can happen and why. This can help practitioners visualize and communicate the outcomes as a basis for making different kinds of treatment recommendations under particular circumstances.  115  The main contribution in Chapter 4 was a further illustration of the challenge of using LiDAR data for assessing stand structure, when stand structure is related to stems per ha by DBH. Better results were obtained when stand structure was defined by volume or basal area per ha. However, stems per ha, particularly for trees in the lower canopy, is needed for a number of forest management purposes including habitat assessment, regeneration success, and fuel loading for fire risk. In this respect, the results were as expected. However, improvements are possible and Chapter 4 was useful for establishing a baseline for comparison. Given the level of interest in utilizing LiDAR for forest inventory, and given the wide variety of locations, techniques and data collection standards, such benchmarks would be useful as a basis for synthesis of results from studies involving a variety of circumstances and investigators. The strength of this work has also been demonstrated in terms of its potential for application in resolving forest management issues (Appendix A). These include assessment of impacts of mountain pine beetles on timber supply, evaluation of silviculture treatment options, and evaluation of wildlife species habitat supplies, on tree, stand and landscape scales. There is considerable potential to use the type of stand structure classification developed in this dissertation to better link strategic plans with tactical plans. In particular, guidelines and prescriptions derived from strategic level planning can be formulated using the stand structure classification system to help guide application of planned activities in a reliable and verifiable way. In the process, a stand structure classification system can help to overcome deficiencies associated with forest inventories that are often reasonably accurate at the landscape (i.e., large) scale, but are frequently considerably imprecise on the scale of individual polygons (e.g. Thompson et al. 2007; McDermid et al. 2009).  5.2.2  Project Scope and Limitations  The project scope and limitations are briefly summarized here since this topic also sets the stage for discussion of future research directions. The cumulative distribution approach as formulated herein did not account for species differences. For some applications, representing stand structure by DBH alone may not be sufficient. For example, results in Chapter 3 suggested that it was important to know whether the overstory consisted 116  predominantly of Douglas-fir or lodgepole pine, since the latter species could not reach the large DBH sizes needed to meet the criteria for eligibility certain kinds of stand structure classes. Differences in spatial distribution were also not included in the development of the stand structure classification. Further, the use of heights as well as DBH might result in useful stand structure classes for some purposes. Some research on all three aspects (species, spatial distributions, and use of height and DBH) was performed, but results were preliminary and not reported in this dissertation. Chapter 3 demonstrated the feasibility of using the system of classification for mapping potential and realized patterns of succession. Four broad patterns of succession were identified. One of the problems encountered was that strong signals emerged only when there was a high degree of overlap in terms of both the number and types of classes in the sequence, as well as in duration of time spent in each class. This means that two plots starting at widely separated points in the potential sequence of classes should perhaps be joined to expose the full time range of a sequence. Although the potential for use of stand structure for succession pathways was demonstrated, further testing in different forest ecosystems is warranted. As noted previously, a different approach to evaluating LiDAR as a tool for classification purposes was used in Chapter 4. Although challenges in using LiDAR for stand structure based on stems per ha by DBH are clear in these results, further research into LiDAR data for stand structure is needed. In Chapters 2 and 3, 17 stand structure classes were used. Chapter 4 introduced the topic of how many stand structure classes should be used and what measures might be employed to indicate the appropriate number of classes to use.  5.3 5.3.1  Future Research and Development Development of Classification Support Tools  One of the initial goals following development of the classification presented in Chapter 2 was to provide classification support tools and training for practitioners. The objective was 117  to facilitate the reliable use of the classification without the need to establish plots, except where boundary conditions or a considerable degree of uncertainty were encountered and where the cost associated with incorrect classification was high. It was envisioned that the installment of a stand structure compiler on a handheld device would facilitate this learning process. Users could train themselves to identify stand structures, to begin with by establishing plots and inputting the plots into the compiler. With time they could begin to declare the stand structure class and test themselves against the compiler to improve their skills. Eventually they would build up their knowledge of the classification to a level that they could apply it more intuitively with an acceptable level of success, say greater than 80% of the time. In addition, an initial or prototype field guide was produced, including ground level photographs, 70 mm stereo photograph pairs, written descriptions, and a key to support identification and differentiation of classes (Farnden et al. 2003). While the stand structure compiler was useful, field staff also asked for support information in two other kinds of formats: 1. a tabular format illustrating the similarities and differences between the stand structure classes at selected diameter threshold reference points; and 2. a stand structure key. The classification can also be challenging to apply for the purpose of representing areas larger than 5 ha, particularly where there is considerable within-stand variation. One possibility is that various polygons delineated on aerial photographs might be sampled reasonably intensively, classified using the stand structure compiler, labeled, and put into a photo library.  5.3.2  Incorporating Tree Species into the System of Classification  Another topic of concern is how to go about incorporating the joint distributions of tree species by diameter into the system of stand structure classification. One attempt was made to do this using an enhanced version of the algorithm referred to in Chapter 2 in combination with 1799 delineated polygons, consisting of a total of 25,462 timber cruising plots in the dataset (ForesTree Dynamics Ltd. 2005). The dataset represented five common tree species. 118  Modifications included development of cumulative distributions for each type in the number of stems and basal area per ha by tree species and diameter, and then using the algorithm to develop a system of classification. Other modifications were also made. As before, the algorithm worked reasonably well. However, the final product could be improved due to: 1. the increased complexity in the distributions of trees with respect to both species and diameter required an increased number of classes to obtain a reasonable level of precision; 2. addition of the tree species dimension reduced the efficiency with which similarities and differences in the diameter distributions across all species were classified within a given class, even when there were up to 250 classes included in the classification; and 3. explicit inclusion of tree species caused the system of classification to be limited to the range of data for which it was calibrated since new species could not be added. Alternative approaches for integrating species into a system of classification need to be explored.  5.3.3  Spatial Considerations  Another opportunity for expansion of the classification system relates to knowledge about differences in the spatial distributions of trees. This concept is more directly related to the notion of horizontal rather than vertical structure. The research described in Chapter 2 was preceded by an effort to explicitly include spatial distributions of trees assessed at various scales (J.S. Thrower & Associates Ltd. 2001; ForesTree Dynamics Ltd. and J.S. Thrower & Associates Ltd. 2002). The basic concept was as follows. One-tenth ha square permanent sample plots were divided into quadrants. The cumulative proportions of quadrants occupied by trees were recorded with respect to increasing tree diameter. All of the quadrants were further subdivided into another set of quadrants and the cumulative distributions were recalculated with reference to the proportions of total resultant grid cells occupied with respect to increasing diameter. The process was continued down to a very small grid size. Differences in the distributions with respect to increasing diameter and decreasing cell size were used to develop a system of classification. While this process worked, the main limitations were the need for stem mapped plots and a concern for how similarities and 119  differences in spatial distributions could be communicated for purposes of practical application. Spatial distributions of trees are of interest (Gadow and Hui 1999; Pretzsch 2009). It would be worthwhile to investigate similarities and differences in these distributions with respect to the classification system developed in Chapter 2. Using a distance dependent individual tree model, the influence of different spatial arrangements on patterns of succession could also be further investigated.  5.3.4  Rescaling Classification Variables  One of the issues in stand structure classification is the scales of the variables used in the classification. For example, cumulative distributions of stems and basal area per ha are affected by the ranges of these variables as well as the range of DBH. In this dissertation, ranks were used to standardize variable scales. However, other methods could be used. For example, the proportions of stems and basal area per ha associated with each plot or stand observation could provide a scale-invariant approach. In such an approach, each of the cumulative distributions would vary between 0 above the maximum tree diameter to 1 below the minimum diameter for a given plot or stand observation. Differences in total stems and basal area per ha would no longer be included as part the classification. What would remain is the relative distribution of stems and basal area per ha across a range of diameters. As a result, the total stems per ha representing a given observation could then be multiplied by the proportional representation of the distribution of trees with respect to diameter to recover the cumulative distributions in stems per ha. The same recovery procedure could also be applied using total basal area per ha. In this way the effects of scale relating to differences in total stems or basal area per ha are separated from knowledge of differences in their distributions with respect to diameter. It is not known how this would affect the ease of use of the classification system in the field. However, there may be benefits in terms of a more accurate classification representing similarities and differences in distributions with respect to diameter without additional, confounding effects of scale. This may also provide an opportunity to reduce the number of classes.  120  It is also possible to remove the effects of scale associated with the range of diameter. There are a number of possibilities, including, for example, always setting the maximum tree diameter associated with a given plot to 1. The main concern with this idea is that it places too much emphasis on a single observation. Another suggestion is to divide all of the individual tree diameters by mean tree diameter or quadratic mean tree diameter. This would ensure that that all of the distributions had a common reference point that matches with that of Reineke’s (1933) Stand Density Index or Curtis et al.’s (1981) Relative Density respectively. Such a connection may be useful.  5.3.5  Additional Research Topics  There are other topics regarding stand structure classification that require further investigation, including: 1. extending the application of these techniques to other regions and forest types; 2. testing the system of classification for underwriting forest fire risk, assessing wildlife habitats, and assessing forest; and 3. further research into LiDAR metrics for estimating small and large tree diameter distributions, along with utilization of other sources of data.  5.4  Concluding Remarks  Knowledge can be gained by clarifying the language around what kinds of objects we are referring to or what kinds of processes affect how such objects interact. Stands of trees are more than the mere sums of their parts; they have structure in the same way that a heap of disassembled motorcycle parts is not the same as a running machine delivered from the factory (Koslicki 2008). The challenge is that stands of trees have a rich variety of structures and structural components, particularly when the concept of a stand is extended in the form of a forest ecosystem. The basic premise of this dissertation is that the most common structural features associated with the wide variety of stands of trees and with their associated forested ecosystems are based on or directly related to distributions in basal area and stems per ha with respect to size, particularly diameter at breast height. Therefore, it was proposed that 121  these attributes be the starting point for the development of a high-level system of stand structure classification. Such a system could be modified for various kinds of specific applications. The next step was to specify criteria for identifying preferred systems of classification, and to find or develop a set of methods that would fulfill those criteria. This was the topic of Chapter 2. Most of the criteria were fulfilled, but not all. The classification derived in Chapter 2 was evaluated in Chapter 3 to determine whether it provided a solid foundation for mapping and determining different patterns of succession. The system of classification produced a framework for revealing different patterns. Stand attributes were found for explaining why a particular observation would follow one path and not the others even when starting from a single stand structure class. The system of classification provided a solid foundation for mapping and determining different patterns of succession. Classifications of the kind derived in Chapter 2 were evaluated in Chapter 4 to determine whether they provided a solid foundation for mapping the spatial distribution of stand structure classes at a high resolution using LiDAR. A moderate level of success was obtained; the primary limitation was the ability to use this remote sensing tool to account for the numbers of understory trees, particularly under conditions of dense overstory. In this case the reliable application of the system of classification is limited by the medium available for interpretation and by the techniques used for interpretation; this could potentially be overcome with more research. Overall, the approach to stand structure classification developed in this dissertation has potential for broad application across a wide variety of forest types. The approach is more objective and can be more easily reproduced when compared with heuristic methods for developing systems of classification. It provides a tool that is complimentary to the use of stand density and stem size distribution indices, and could be modified to incorporate other attributes such as species composition. This system can provide for more reliable, verifiable and consistent communications amongst forest management specialists and stakeholders about the existence of different kinds of stand structures and how they may change with time. 122  References Aasland, T. 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Environ. 87:171-182.  143  Appendices Appendix A A Graphical Summary of 17 Stand Structure Classes A.1  Overview  Stand structure classes are summarized herein with reference to the simulated dataset produced in Chapter 3 using 140 cases as input into the individual tree growth model, PrognosisBC (v 3.01.001; BC Ministry of Forests 2008; Figures A.1, A.2, and A.3). On the left hand side of each figure is a selected profile view of a particular plot representing each stand structure class produced using the Stand Visualization System (v 3.36; McGaughey 2002). Each picture is labeled with the associated succession pathway in terms of the stand structure class progression (normal text) and the number of simulated years spent in each class (subscripts). In the middle of the figure is a graph illustrating the average distributions in the basal area per hectare (blue bars) and number of stems per hectare (red bars) for each stand structure class, expressed in terms of percent by 5 cm DBH class. On the right hand side is a table providing means, standard deviations (SD) and coefficients of variation for each of the following whole stand statistics: quadratic mean diameter (DG); stems per hectare (SPH); basal area per hectare (G); gross stem volume per hectare (VG); merchantable stem volume per hectare for all trees over 12.5 cm dbh , to a 10 cm diameter top (inside bark), and a 30 cm tall stump; Lorey’s mean tree height (HL); live crown (LC) percent; and Crown Competition Factor (CCF; Krajicek et al. 1961).  144  1  SP: 110 35 515 75 615 1220 920 1045 1120  Stand Structure Class 1 Statistics  100 90 80 70 60 50 40 30 20 10 0 0  10  20  30  40  Percent of Basal Area  2  SP: 210 420 865 955 105  10  20  30  40  10  20  30  40  10  20  30  40  80  90 100  N=8 Units MEAN cm 6 ha 10042 m2/ha 24 m3/ha 61 m3/ha 12 m 7 % 61 % 92  SD 1 4247 4 15 9 1 7 17  CV 19 42 18 24 79 12 11 18  50  60  70  80  90 100  Percent Stems Per Hectare  Variable DG SPH G VG VM HL LC CCF  N=123 Units MEAN cm 17 ha 1448 m2/ha 17 m3/ha 109 m3/ha 86 m 17 % 58 % 62  SD 6 2429 4 29 30 4 13 18  CV 34 168 26 27 34 25 23 28  50  60  70  80  90 100  Percent Stems Per Hectare  Variable DG SPH G VG VM HL LC CCF  N=42 Units MEAN cm 7 ha 9540 m2/ha 38 m3/ha 146 m3/ha 50 m 10 % 47 % 134  SD 1 3506 6 37 18 1 11 31  CV 18 37 16 25 37 15 23 23  Stand Structure Class 5 Statistics  0  SP: 640 1285 1130  70  100 90 80 70 60 50 40 30 20 10 0 10  20  30  40  Percent of Basal Area  6  60  Variable DG SPH G VG VM HL LC CCF  Stand Structure Class 4 Statistics  0  SP: 515 620 1250 1015 1155  50  Percent Stems Per Hectare  100 90 80 70 60 50 40 30 20 10 0 Percent of Basal Area  5  90 100  SD CV 4 28 999 119 2 25 11 27 13 45 4 26 5 6 10 22  Stand Structure Class 3 Statistics  0  SP: 435 8120  80  100 90 80 70 60 50 40 30 20 10 0 Percent of Basal Area  4  70  N=15 Units MEAN cm 15 ha 841 m2/ha 8 m3/ha 42 m3/ha 28 m 14 % 76 % 45  Stand Structure Class 2 Statistics  0  SP: 310 515 620 1255 1135 1620  60  100 90 80 70 60 50 40 30 20 10 0 Percent of Basal Area  3  50  Percent Stems Per Hectare  Variable DG SPH G VG VM HL LC CCF  50  60  70  80  90 100  Percent Stems Per Hectare  Variable DG SPH G VG VM HL LC CCF  N=161 Units MEAN cm 15 ha 1707 m2/ha 26 m3/ha 196 m3/ha 149 m 18 % 38 % 71  SD 3 1296 3 41 41 3 15 32  CV 20 76 11 21 27 14 41 45  Stand Structure Class 6 Statistics  100 90 80 70 60 50 40 30 20 10 0 0  10  20  30  40  Percent of Basal Area  50  60  70  80  90 100  Percent Stems Per Hectare  Variable DG SPH G VG VM HL LC CCF  N=278 Units MEAN cm 20 ha 1190 m2/ha 32 m3/ha 304 m3/ha 264 m 23 % 33 % 72  SD 3 643 5 67 67 3 12 35  CV 17 54 17 22 25 13 37 49  Figure A.1. Selected pictures of stand structures in classes 1 to 6, including succession pathways (SP); associated stand structure class average distributions (middle graph) in percent of basal area per hectare (blue bars) and stems per hectare (red bars) by 5 cm DBH classes; and stand structure class statistics (right tables, mean, standard deviation and percent coefficient of variation) derived from individual tree growth model (PrognosisBC) simulated dataset described in Chapter 3. 145  7  SP: 725 860 970  Stand Structure Class 7 Statistics  100 90 80 70 60 50 40 30 20 10 0 0  10  20  30  40  Percent of Basal Area  8  SP: 845 9105 105  10  20  30  40  10  20  30  40  10  20  30  40  70  80  90 100  Variable DG SPH G VG VM HL LC CCF  N=327 Units MEAN cm 13 ha 4080 m2/ha 48 m3/ha 357 m3/ha 223 m 19 % 34 % 161  SD 2 1563 4 73 70 3 9 35  CV 16 38 8 20 31 17 28 22  50  60  70  80  90 100  Percent Stems Per Hectare  Variable DG SPH G VG VM HL LC CCF  N=335 Units MEAN cm 18 ha 2050 m2/ha 50 m3/ha 496 m3/ha 396 m 27 % 31 % 142  SD 2 522 3 65 60 3 9 27  CV 11 25 6 13 15 11 29 19  50  60  70  80  90 100  Percent Stems Per Hectare  Variable DG SPH G VG VM HL LC CCF  N=126 Units MEAN cm 24 ha 1098 m2/ha 49 m3/ha 529 m3/ha 477 m 30 % 36 % 128  SD 2 257 3 56 44 2 11 27  CV 10 23 6 11 9 8 30 21  Stand Structure Class 11 Statistics  0  SP: 1210 995 1050  60  100 90 80 70 60 50 40 30 20 10 0 10  20  30  40  Percent of Basal Area  12  CV 21 50 14 16 23 15 19 23  Stand Structure Class 10 Statistics  0  11155  50  Percent Stems Per Hectare  100 90 80 70 60 50 40 30 20 10 0 Percent of Basal Area  11 SP:  90 100  SD 3 1925 5 37 34 2 8 28  Stand Structure Class 9 Statistics  0  SP: 1075 1180  80  100 90 80 70 60 50 40 30 20 10 0 Percent of Basal Area  10  70  N=82 Units MEAN cm 12 ha 3872 m2/ha 37 m3/ha 234 m3/ha 152 m 16 % 42 % 123  Stand Structure Class 8 Statistics  0  SP: 915 10105 1135  60  100 90 80 70 60 50 40 30 20 10 0 Percent of Basal Area  9  50  Percent Stems Per Hectare  Variable DG SPH G VG VM HL LC CCF  50  60  70  80  90 100  Percent Stems Per Hectare  Variable DG SPH G VG VM HL LC CCF  N=215 Units MEAN cm 32 ha 609 m2/ha 46 m3/ha 547 m3/ha 516 m 34 % 34 % 92  SD 4 178 5 56 53 3 11 23  CV 12 29 10 10 10 8 33 25  Stand Structure Class 12 Statistics  100 90 80 70 60 50 40 30 20 10 0 0  10  20  30  40  Percent of Basal Area  50  60  70  80  90 100  Percent Stems Per Hectare  Variable DG SPH G VG VM HL LC CCF  N=541 Units MEAN cm 23 ha 1100 m2/ha 40 m3/ha 415 m3/ha 370 m 28 % 36 % 99  SD 5 538 4 67 70 3 8 27  CV 20 49 10 16 19 13 21 28  Figure A.2. Selected pictures of stand structures in classes 7 to 12, including succession pathways (SP); associated stand structure class average distributions (middle graph) in percent of basal area per hectare (blue bars) and stems per hectare (red bars) by 5 cm DBH classes; and stand structure class statistics (right tables: mean, standard deviations and percent coefficient of variation) derived from individual tree growth model (PrognosisBC) simulated dataset described in Chapter 3. 146  13  SP: 1310 1430 1520 1295  Stand Structure Class 13 Statistics  100 90 80 70 60 50 40 30 20 10 0 0  10  20  30  40  Percent of Basal Area  14  SP: 1430 835 1210 970 1010  10  20  30  40  10  20  30  40  CV 41 112 30 27 21 21 17 16  60  70  80  90 100  Variable DG SPH G VG VM HL LC CCF  N=127 Units MEAN cm 25 ha 1003 m2/ha 25 m3/ha 214 m3/ha 194 m 25 % 60 % 77  SD 8 1291 4 38 41 5 8 14  CV 33 129 18 18 21 20 13 18  50  60  70  80  90 100  Percent Stems Per Hectare  Variable DG SPH G VG VM HL LC CCF  N=125 Units MEAN cm 31 ha 789 m2/ha 31 m3/ha 318 m3/ha 291 m 30 % 57 % 81  SD 10 938 5 46 55 6 8 18  CV 33 119 15 14 19 21 13 22  Stand Structure Class 16 Statistics  0  1745 16110  50  Percent Stems Per Hectare  100 90 80 70 60 50 40 30 20 10 0 10  20  30  40  Percent of Basal Area  17 SP:  90 100  SD 8 1777 6 39 25 4 11 10  Stand Structure Class 15 Statistics  0  SP: 16155  80  100 90 80 70 60 50 40 30 20 10 0 Percent of Basal Area  16  70  N=19 Units MEAN cm 20 ha 1590 m2/ha 21 m3/ha 145 m3/ha 119 m 20 % 63 % 67  Stand Structure Class 14 Statistics  0  SP: 1520 125 16130  60  100 90 80 70 60 50 40 30 20 10 0 Percent of Basal Area  15  50  Percent Stems Per Hectare  Variable DG SPH G VG VM HL LC CCF  50  60  70  80  90 100  Percent Stems Per Hectare  Variable DG SPH G VG VM HL LC CCF  N=278 Units MEAN cm 37 ha 617 m2/ha 39 m3/ha 456 m3/ha 427 m 35 % 53 % 82  SD 12 633 6 64 62 5 11 17  CV 32 103 17 14 14 15 21 21  Stand Structure Class 17 Statistics  100 90 80 70 60 50 40 30 20 10 0 0  10  20  30  40  Percent of Basal Area  50  60  70  80  90 100  Percent Stems Per Hectare  Variable DG SPH G VG VM HL LC CCF  N=119 Units MEAN cm 49 ha 422 m2/ha 40 m3/ha 511 m3/ha 492 m 39 % 57 % 76  SD 11 808 6 77 79 6 13 18  CV 23 191 15 15 16 15 23 24  Figure A.3. Selected pictures of stand structures in classes 13 to 17, including succession pathways (SP); associated stand structure class average distributions (middle graph) in percent of basal area per hectare (blue bars) and stems per hectare (red bars) by 5 cm DBH classes; and stand structure class statistics (right tables, mean, standard deviation and percent coefficient of variation) derived from individual tree growth model (PrognosisBC) simulated dataset described in Chapter 3.  147  A.2  Stand Summary  The results from Chapter 3 can be compared with those of Chapter 2 (Figure A.4 versus Figure 2.2). In particular it can be observed that the maximum number of stems per hectare declines more sharply with an increase in stand structure class in the simulated stands versus the natural stands in Chapter 2. This difference is most likely caused by: a) the small tree mortality equation, and/or the assumption that there is no small tree recruitment, particularly in the more complex stands as large tree mortality proceeds. The result is that quadratic mean diameters are larger in the simulated stands (DG in Figure A.4; QMD in Figure 2.2) when compared with the actually observed stands. Finally, it is also noted that the stand volumes tend to be slightly larger than those found in the natural stands; this may be due to differences in the methods used to compute the merchantable volumes. However, it can also be observed that the basal areas associated with stand structure class 4 for example, are much larger in the simulated stands, and the numbers of stems per hectare tends to exceed those in the natural stands. Once again this may be related to the mortality functions and/or issues relating to stocking. Additional statistics were produced by using PrognosisBC (v 3.01.001; BC Ministry of Forests 2008; Figure A.4) to underwrite further comparisons amongst the stand structure classes produced in Chapter 2.  There is a strong correlation (0.886) between Lorey’s mean  tree height (HL) and the quadratic mean tree diameter (DG; Figure A.4). The mean live crown percent (LC%) was calculated by weighting each tree by the basal area represented in each plot. LC% tends to be lowest in stand structure classes 5, 6, 8, 9, 10, 11 and 12. Stand structure classes 4, 7, 8, 9 and 10 tend to manifest the highest crown completion factors (CCF). As a result classes 8, 9 and 10 appear to be classes associated with the highest levels of competition and the least vigorous trees in terms of the potential for response from release. These same classes are associated with highest levels of basal area.  148  60  20000  50 40  SPH (/ha) SPH  2 GG(m ha-1) (m2/ha)  15000  30 20  10000  5000 10 0  0  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  Stand Structure Class  700  60  600  50  500  VM (m3 ha-1)  70  VM (m3/ha)  DG (cm)  Stand Structure Class  40 30  400 300  20  200  10  100  0  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  Stand Structure Class  0  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  Stand Structure Class  Figure A.4. Box plots representing whole stand statistics by stand structure class for the simulated dataset produced using an individual tree model in Chapter 3: basal area per hectare (G), number of stems per hectare (SPH), quadratic mean diameter (DG), and merchantable volume per hectare (VG). (Box plots: Central line is the median, the top of the box is the 75 percentile, the base of the box is the 25% percentile, whiskers indicate 95% and 5% percentiles, and asterisks and circles indicate outliers.)  149  50  700 600  40 -1  VG (m ha ) VG (m3/ha)  30  400  3  HL (m)  500  20  300 200  10 100 0  0  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  Stand Structure Class  Stand Structure Class 90  300  80 70 200 CCF (%)  LC (%)  60 50 40  100  30 20 10 0  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  0  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  Stand Structure Class  Stand Structure Class  Figure A.5. Box plots representing whole statistics by stand structure class for the simulated dataset produced using an individual tree model in Chapter 3: Lorey’s mean tree height (HL), gross stem volume (VG), live crown percent (LC), and Crown Competition Factor (CCF). (Box plots: Central line is the median, the top of the box is the 75 percentile, the base of the box is the 25% percentile, whiskers indicate 95% and 5% percentiles, and asterisks and circles indicate outliers.)  150  The relative distributions of interior Douglas-fir ((Pseudotsuga menziesii var. glauca (Beissn.) Franco) and lodgepole pine (Pinus contorta var. latifolia (Engelm.) Critchfield) can be compared in terms of their distributions with respect to average tree size (HL, DG) within a plot by stand structure class (Figure A.6). In stand structure classes 10, 11, 13, 14, 15 and 16 Douglas-fir exhibits a much larger tree size than lodgepole pine and the relative occurrence of larger tree sizes is an important variable in determining the appropriate stand structure class (Figures A.1, A.2 and A.3). This is evidence of the importance of species  HL (m)  50  50  40  40  30  30  40  20  30  10  20  0  DG (cm)  50  HL (m)  differences in determining potential pathways for succession.  20 10  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  Douglas-f ir Lodgepole Pine  Douglas-f ir 0 Lodgepole Pine  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  Stand Structure Class  Stand Structure Class  10 0  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  Douglas-f ir Lodgepole Pine  Stand Structure Class Figure A.6. Box plots representing Lorey’s mean tree height (HL; left) and quadratic mean tree  diameter (DG; right) distribution of Douglas-fir (red) and lodgepole pine (blue) by stand structure class for the simulated dataset produced using an individual tree model in Chapter 3. (Box plots: Central line is the median, the top of the box is the 75 percentile, the base of the box is the 25% percentile, whiskers indicate 95% and 5% percentiles, and asterisks and circles indicate outliers.)  151  References BC Ministry of Forests. 2008. PrognosisBC home page. Available from http://www.for.gov.bc.ca/hre/gymodels/progbc/index.htm [accessed Jan. 17 2012]. Krajicek, J.E., Brinkman, K.A., and Gingrich, S.F. 1961. Crown competition – a measure of density. Forest Sci. 7:35-42. Cited in Davis, L.S. and Johnson, K.N. 1996. Forest management. Third edition. McGraw-Hill Book Company, New York, NY, US.  McGaughey, R.J. Stand Visulaization System. Version 3.30. Pacific Northwest Research Station, US Forest Service, USDA, Portland, OR, US. Pp. 141. http://forsys.cfr.washington.edu/winsvs/manual.pdf [accessed Mar. 22 2012]  152  Appendix B Applications of Stand Structure Classification in Forest Resources Management B.1  Introduction  The stand structure classification (Chapter 2), successional pathways (Chapter 3), and stand structure via remote sensing data (Chapter 4) can be applied in a broad range of inventory, forest management and forest estate planning activities.  As evidence of this, I present three  cases where these methods were applied to illustrate the usefulness in this chapter. The objectives of this appendix were: 1. To illustrate how stand structure classification can be used to improve forest management; and 2. To discuss the importance of stand structure classification for these and other applications. The overall hypothesis was that stand structure classification is critical to forest management, and that the system based on cumulative stems and basal area by DBH provides the basis for this stand structure information. In the first case study, stand structure classification (Chapter 2) was used to improve forestlevel forecasts of the natural disturbances, particularly, epidemic insect attack. In the second case, stand structure classification (Chapter 2) and successional pathways (Chapter 3) were used to provide information that could be used to improve prescriptions for stand management. In the third case study stand and stock tables were used in combination with an individual tree model to forecast wildlife habitat supplies for 14 species in a large landscape area in British Columbia. B.2  Forest-level forecasts of impacts of Mountain Pine Beetle on economic access to  timber. The epidemic attack by Mountain Pine Beetles (MPB; Dendroctinus pondersosae Hopkins) has impacted more than 17.5 million ha of forest land in BC as of 2010 (BC Ministry of Forests, Lands and Natural Resource Operations 2011). To ameliorate the impacts of MPB 153  attack on timber supply in a large forested area of over 2 million ha in the Williams Lake and 100 Mile House Timber Supply Areas (TSA) under license to Lignum Limited, forest estate modeling was used to develop harvest scheduling priorities2. To improve forest estate planning, particularly harvest scheduling during and following beetle attacks, stand structure was added to each forested polygon in the forest inventory for the study area described in Chapter 2.  Forest inventory data included attributes for each  forested polygon, particularly, species composition, stand height class, age class, crown closure and site index class. Other model-derived variables were also available for each inventory polygon, including estimated volume per ha. Imputation involved log-odds modeling was used to impute stand structure classification for each forest polygon using a reference database of the ground plots (see Chapter 2 for the description of ground plots) geospatially linked to forest cover polygons.  The forest polygon attributes coupled with the  actual (ground plots in the polygon) or imputed (no ground plots in the polygon) stand structure class were then used to impute stand and stock tables (i.e. volume and stems per ha by DBH class) for each forest polygon. For the forecast of the forest land, the area was separated into five subareas, and the observed (beetle attack has occurred) or expected (beetle attack has not yet occurred) dates of beetle attack were added to each area. The expected rate of spread was specified using the proportions of area attacked or estimated to be attacked by MPB in each year. These data were provided by Shawn Meisner, RPF (Riverside Forest Products Ltd., Williams Lake, BC; pers. comm. 2006), who is a harvest planning forester with experience directing forest operations in the study area. Simulation of MPB attack within each area then proceeded by: 1.  Randomly selecting a stand for initial beetle attack starting within each landscape unit, starting in the initial year of attack identified for that unit.  2  Project funded by the Innovative Forest Management Agreement between Lignum Ltd and the Province of  British Columbia. 154  2. The attack then proceeded from three to five years within the stand using the imputed or actual stand table. Trees within the stand were attacked, using a random selection of lodgepole pine (Pinus contorta var. latifolia (Engelm.) Critchfield) trees above 8 cm DBH with a bias toward selecting larger diameter trees in preference to smaller ones. 3. Additional stands were randomly selected for attack in the same year to meet the proportion of attack in the year. 4. The process was repeated for each year in a 20-year forecast period. Influences of growth and mortality due to causes other than MPB were not considered in this process. 5. During the forecast period, stands were scheduled for harvest under different forest harvest scenarios (not described here). Further, a breakdown of trees into log sizes (based on inside bark top diameters) and grades was included with each plot or stand a stock table. An expected rate of decline in log grade and volume recovery for lodgepole pine trees was then incorporated into the projections starting from the date of initial, simulated attack of each individual tree by MPB,. A transition probabilities matrix for log grades starting from the death date was developed to implement this process based on professional opinion and experience with grade decline in MPB-impacted stands. As a result, harvest attributes included the information needed for value assessment: numbers of logs by species, DBH class and grade, and numbers of dead lodgepole pine by DBH class and grade which declined with time since attack. Using these data, the revenue for each stand was estimated based on knowledge of local log prices for different sizes and grades (pers. comm. Shawn Meisner 2006). The estimated revenue was coupled with estimated harvest costs using a set of appraisal equations (BC Ministry of Forests 2002) to produce the estimated net revenue for each stand over time. This forecast model could then be used to simulate a variety of scenarios, and assess the outcomes in terms of possible revenue. Questions that could be addressed concerning the preferred harvest schedule in response to the MPB epidemic include: Is it better to pursue high value, and green stands of timber in advance of the attack, or to salvage timber as soon 155  as possible after it has been attacked in an effort to retain economically accessible timber over a long period of time? Does the answer vary depending on the percentage of pine in each stand? Does the answer vary by stand structure class and associated differences in their estimated aerial distributions between one operating area and the next? What impact could partial cutting have on the outcome? How might the presence of understory trees change the preferred prescription? The stand structure classification facilitated this process via the imputation of stand and stock tables for each stand. This was particularly important given the vast size of the forest area of more than two million ha. While the forest inventory attributes may not be sufficient to address these questions directly, the attributes coupled with stand structure classes may still be sufficiently detailed to estimate stand and stock tables needed for value assessments. As noted in Chapter 4, new advances in forest inventory data including LiDAR data should further advance the accuracy of within stand information needed to assess value. B.3  Developing intensive silviculture treatment option plans  British Columbia distinguishes between two types of silviculture, “basic” and “intensive “. The former is defined as follows (BC Ministry of Forests 2008): “Harvesting methods and silviculture operations including seed collecting, site preparation, artificial and natural regeneration, brushing, spacing and stand tending, and other operations that are for the purpose of establishing a free-growing crop of trees of a commercially viable species and are required in a regulation or silviculture prescription.” “Intensive silviculture” refers to practices that are not required to meet “free growing” criteria established under legislation. Since intensive silviculture often involves an increased investment into stand management, improved knowledge over which stands may respond by increasing growth and value is essential to cost-effective management. Knowledge of the likely succession of stands over time can result in improved silviculture treatments including intensive silviculture. 156  In this application, the stand successional pathways described in Chapter 3 were used to help inform silviculture prescriptions for complex stands of the Interior Douglas-Fir (IDF) biogeoclimatic ecosystem classification zone (Steen and Coupe 1997) near Williams Lake, BC. The process to apply the stand structure success pathways is illustrated in Figure B.1. As described in Chapter 3, ground plots were established and measured, then forecasted using a single-tree growth model, the stand was then classed into a stand structure class, and successional pathways were identified (Steps 1 to 4).  Then, for application, forest  practitioners were trained to identify stand structures and patterns of succession in the field (Step 5). A field guide was developed for this purpose (Moss 2009). Further, photographs were also used in defining stand structure class and succession pathway (Step 6), by creating a set of representative photographs for each stand structure class. To facilitate this, one or more plots of the forest inventory were identified in each stand type (Step 7), based on species composition, stand structure class and succession pathway, site description, as well as other variables such as basal area per ha and silviculture prescription type. As noted in Figure 5.1, the feedback loop “F1” allows for cases where a stand condition does not match well with a known case in the inventory and therefore has no adequate sample plot representation. In that case, additional ground plots would be needed. The silviculture prescription can then be made each stand type (Step 8), and the response can be estimated using existing growth and yield models (Step 9). The forest area can then be forecasted in time (Steps 10a and 10b), leading to a management plan (Step 11). The “F2” feedback loop (Steps 8 to 10) involves evaluation of silviculture treatment responses at the stand and forest level forecasts, allowing for other stand management alternatives that might be explored.  157  START  1. Establish Plots In Target Area Representative of a Wide Range of Site & Stand Conditions  2. Forecast Changes In Tree & Stand Conditions using Individual Tree Growth Model  4. Identify Common Succession Patterns  3. Classify Changes Using Stand Structure Classification  F1  6. Photo Interpretation Inventory  5. Train Practitioners To Identify Stand Structures and Succession Pathways In The Field  11. Develop Forest Management Plan  10 b. Forest Estate Analysis  Species Composition Stand Structure Class Succession Pathways Site Series / Site Index  10a. Evaluate Forest & Stand Level Social, Economic & Environmental Costs and Benefits  7. Match Computer Forecasts With Inventory Label  F2 8. Develop Silviculture Prescriptions  9. Forecast Treatment Responses  Figure B.1. A diagram illustrating the complete process for developing a forest management plan in complex Interior Douglas-fir / lodgepole pine forest types. Lines marked with a bold F lines indicate feedback loops where either additional plots must be established to represent new stand types and succession patterns, or where further investigations are required to develop appropriate silviculture and harvesting prescriptions (from DWB Consulting Services Ltd. et al. 2010).  158  The results from this analysis can then be summarized in the form of prescription guidelines associated with different types of stand structure that can be used to guide implementation of the strategic plan. Figure B.2 provides an example for: Forest landscape unit (Albion Forest); Inventory stratum (AU 5); estimated total area, and area eligible for treatment (1122 ha); and reference to plot used for GY (M500) simulations, and associated stand number (STANDID 419). In this illustration, untreated, treated and three harvest-removals were simulated. The figure shows: 1. Succession pattern 1310 1430 1520 1295, where the first number indicates the current stand structure class and the subscript indicates the expected number of years to remain in that class before migrating to the next class; 2. Site type IDFdk3/01, which is IDF zone, dry cool type 3, site series 01; 3. Species composition FD100, where FD is a tree species, Douglas-fir, and the subscript represents the percentage of the type represented by that species; 4. Site and stand related attributes including: age, dominant species (DSP), dominant tree height (DHT), Lorey’s mean tree height (LHT), site index (SI; base age 50 years at breast height), crown closure percent (CC), quadratic mean diameter (QMD), live crown ratio (CR), stems per ha (SPH), basal area per ha (BPH), and merchantable volume (MVOL). 5. Economic indicators associated with implementing treatment guidelines, Internal Rate of Return (IRR) and Net Present Value (NPV) at a chosen discount rate of 2%; 6. Silviculture prescription, including description of current diameter distributions along with the target removals and retentions, and the next target harvest date following treatment; 7. A written description of the stand type; 8. A picture or profile diagram of the stand type; and 9. A graph of the expected or desired harvest schedule, volume removed, and treatment response relative to the untreated stand condition. This guideline may also be supported by a map indicating where different stand conditions are located within a given landscape, including species composition, expected patterns of succession, and recommended prescriptions (Figure B.3). 159  Albion Forest Prescription Guideline AU 5. Stand Summary  Total Area: 1122 Ha. Estimated Treatment Area: 1122 Ha  STANDID 419 - CYCLE 0 - M500 – MOFR GTG 189: 13 10 ( 14 30 15 20 12 95 ) IDFdk3/01 Age (y)  DSP  125  FD  DHT (m) 16.4  LHT (m) 15.1  Species Composition: FD100 SI (m)  CC (%)  QMD (cm)  CR (%)  SPH (# ha -1)  BPH (m2 ha -1)  MVOL (m 3 ha -1 )  11.4  40  8.5  60  3707  21.0  80.3  Stand Level Analysis IRR 1.2% NPV (@2%)-173 $ha- 1  SilviculturePrescription: OverstoryThinning & Juvenile Spacing; Harvest in 2050 DBH Class 0-2.5 2.5-7.5 7.5-12.5 12.5-17.5 17.5-27.5 27.5-52.5 >52.5 Total  Target BDq Curve BA Density (SPH) (m2/ha) 260 186 0.4 133 1.0 95 1.7 116 4.5 98 10.8 887  18.4  Existing stand Treatment Removal Post Treatment Density BA Volume Density BA Volume Density BA Volume (SPH) (m2/ha) (m3/ha) (SPH) (m2/ha) (m3/ha) (SPH) (m2/ha) (m3/ha) 1332 0.5 1332 0.5 1665 1.7 1387 1.2 278 0.5 420 3.0 420 3.0 150 2.7 150 2.7 70 2.5 8.6 70 2.5 8.6 60 7.8 46.1 28 4.7 27.9 32 3.1 18.2 2.7 16.1 10 10 2.7 16.1 21.0 70.8 3707 2757 9.2 44.0 950 11.8 26.9  This unit represents moderately overstocked stands with a moderate basal area of larger stems and a small component of veterans. The basal area structure has a large deficit of mid -size stems and many of the larger stems are of poor quality and vigour This analysis unit is typical of the residual structure left by selective harvesting.  Treated Stand Succession Pattern: 1320 1425 155  Harvest Schedule 600 500 400 300  .  200 100 M erachantable Volu me (m 3/ha)  0 0  2  4  6 8 10 12 14 16 18 20 22 24 26 28 30 Cycle Number (5 y intervals)  UNTREATED  TREATED  H1  H2  H3  Figure B.2. An illustration of prescription guideline developed for the purpose of meeting strategic level outcomes. 160  Albion Village  Albion Forest  Figure B.3. A map of analysis units and associated inventory attributes that are consistent with the growth curves assigned to each unit, including: species composition, initial stand structure class with the time spent in each class noted as a subscript, and the untreated stand succession pattern indicated in parenthesis. The prescriptions are as follows: spacing (S), overstory removal (OR), selection harvesting (HS; applied to “multi-layered or complex stands”), partial harvesting (HP; applied to stands that were not analyzed in detail) and rehabilitation (R; applied to stands that are believed to be stagnant and have a light overstory, i.e. stand structure class 13).  161  For this application, again, stand structure classes, particularly succession pathways, were critical to providing the information to inform forest management. B.4  Forecasting wildlife species habitat supplies  McCann et al. (2011) undertook a wildlife habitat suitability and supply assessment for 14 species in the Quesnel TSA in the central interior of British Columbia, as follows (Notes on habitat preferences or requirements are from McCann et al. 2011 and Fenger et al. 2006 unless otherwise noted. The notes focus on stand structure characteristics important for estimating species’ habitat supplies. Other factors were also considered by McCann et al. (2011) in modeling supply, including for example, levels of disturbance due to harvesting or recreation activities, and potential for predation.): Primary cavity nesters 1. Three toed woodpecker (Picoides dorsalis; sensitive to harvesting.) 2. Black-backed woodpecker (Picoides arcticus; forages almost exclusively on old ,burned or diseased trees in mature and older stands of lodgepole pine or mixed conifers dominated by lodgepole pine.) 3. Northern flicker (Colaptes auratus; this species is responsible for most cavities and is considered a keystone species. It usually excavates its nest cavities in dead tops of live trees or in snags or stumps – it requires weakened sapwood and extensive heart-wood decay.) Secondary cavity nester 4. Barrows goldeneye (Bucephala islandica; Nest trees may be hardwoods or conifers that are almost always dead and must be large.) Open nesters 5. Great blue heron (Ardea Herodias; a blue listed species. This species builds large, shallow stick nests in the largest of trees – mainly at heights of 20 to 70 m. The nests are generally located within 3 km of lakes or wetlands.) 6.  Rusty blackbird (Euphagus carolinus; associated with black spruce bogs and dead trees in standing water.)  7. Northern goshawk (Accipiter gentilis; it is recommended that no harvesting, salvage logging or construction of roads occur within a 12 ha area surrounding 162  a nest. However, the thinning of some small trees to provide access to prey and promote canopy growth is recommended in old growth with > 60 percent crown closure and trees > 60 cm DBH, while at the same maintaining some below-canopy hiding cover.) Ungulates 8. Moose (Alces alces; this species requires 20 to 30% of their winter range to provide snow interception cover, particularly where snow depths can exceed 90 cm. This kind of cover requires canopy closure of 40 to 65% and generally stands over 60 years of age (Wall et al. 2011.) 9. Mule deer (Odocoileus hemionus; This species is at its northern limit in the Quesnel TSA, and is dependent on low elevation stands of Douglas fir for snow interception, as well as foliage and arboreal lichens as source of food (Waterhouse et al. 1993). Low volume partial cutting (typically 20% volume removal) using small group selection openings up to 10 m in diameter is recommended for accommodation of timber extraction and maintenance of Mule deer winter ranges (Armleder et al. 1986)). 10. Mountain caribou (Rangifer tarandus caribou; this species is particularly dependent on arboreal lichens (Alectoria sarmentosa and Bryoria spp.) for winter forage (Mountain Caribou Technical Advisory Committee 2002). Undisturbed old growth forests provides optimal caribou habitat.) 11. Mountain goat (Oreamnos americanus; this species is sensitive to disturbance from industrial activity particularly around mineral licks, trails and natal areas (Hengeveld et al. 2004) 12. Grizzly bear (Ursus arctos; this species is not heavily dependent on stand structure features, except under some conditions for security, day bedding (heat relief, rain interception, or warmth) and some types of forage (salmon in streams, ants in logs, ungulates; Gyug et al. n.d.).) Small furbearers 13. American marten (Martes Americana; maternity dens are located in largediameter snags, hollow logs, slash piles or underground burrows. Nonmaternity dens are often beneath large stumps or root masses of large trees. 163  Mature forest > 25 ha is needed to provide sufficient forest interior habitat. It is recommended that abundant coarse woody debris be retained (> 20 cm DBH). Multi-storey canopies with 30 to 70 percent crown closure and low to moderate understory shrub densities encourage prey populations for the marten.) 14. Wolverine (Gulu gulu; this species is not dependent on stand structure features. Both males and females are positively associated with subalpineavalanche habitats in summer and winter, and negatively associated with helicopter skiing, backcountry skiing and recent logging (Krebs et al. 2007). These vertebrate species were selected: (1) for the purpose of representing a broad cross section of habitat requirements for sensitive and indicator species in the TSA, and (2) as identified as focal species (Lambeck 1997) in higher level plans (BC Ministry of Natural Resource Operations 2007) and strategic planning activities (Type 3 Silviculture Strategy; Buell et al. 2006). The Quesnel forest inventory dataset was reduced from over 500 thousand polygons to 16733 based on similarities in Biogeoclimatic variant, leading and secondary species and associated species percentages by volume, stand height, crown closure and site index. Stand and stock table attributes were imputed to each of the units in the Quesnel TSA (Moss, I. 2009b). Each of the resultant stand and stock tables was then input into PrognosisBC (v. 4.0; BC Ministry of Forests 2009) and forecast to a starting date of 2008, and then at 5-year intervals beyond that date for a period of 150 years. Additional mortality was then assigned to the projected tables to account for historical and expected future MPB impacts starting in 1999 and ending in 2024. Information on stand structure and coarse woody debris (CWD) was derived from the PrognosisBC output and used to complete habitat suitability and supply assessments for each of the species referred to above. B.5  Importance of stand structure classes to forest management  The three examples illustrate that stand structure classification (Chapter 2), associated succession pathways (Chapter 3), and related live and dead tree data have application in 164  inventory, forest management, and forest estate planning activities. As well as being relevant examples, they are characteristic of common activities. The first example showed how stand structure classes can be used to provide within stand details that are essential for valuing timber. Although the application was for natural disturbances, this could also be applied for a range of natural and human disturbances. As noted by many (e.g. Bardon n.d., Stier 2003), timber value depends on species, size and log grades primarily, and these are derived from within stand information that can be obtained via stand structure classes (Moss et al. 2005). If stand structure classes were commonly added to forest inventory attributes, these data could routinely be obtained and used in forest estate planning activities. This would then provide a more realistic simulation environment for exploring reasonably stable tree and stand development patterns and their interactions with natural and human induced disturbances operating at multiple scales (Papaik et al. 2010). In the second example, stand structure classification is used along with stand succession to propose silvicultural treatments, and then to forecast outcomes of these treatments at the landscape level.  Again, within stand information is critical to selecting silvicultural  treatments. Often, simple treatments are simulated due to inventory data constraints, or links between more complex treatments and associated growth response are bridged using a few basic assumptions. In many kinds of forest estate modeling in British Columbia for example, “natural stands” are typically assigned a yield curve representing merchantable volume versus stand age. Following clear cutting, all of the volume is removed and the stand may then be assigned to a new “managed stand” yield curve perhaps based on planting trees of certain species, at certain densities. If instead the “natural stands” are partially cut, say by removing 30% of the volume, then it is often assumed that the stand will return to a point along the same curve where the volume is equal to the total volume before harvest minus 30%. Assumptions of this kind ignore subtleties relating to knowledge of diameter distributions and associated prescriptions that are specifically targeted toward removing only selected portions of that distribution, perhaps also targeted toward certain species, and subsequent treatment responses in terms of projected ingress, growth and mortality. With the 165  addition of within stand information provided via stand structure classes, more realistic silvicultural treatments could be simulated, when coupled with individual tree growth models (Teuffel et al. 2006). The alternative of obtaining within stand measures (i.e., plots) on each polygon is not cost-feasible. Further, the results from growth and yield and forest estate modeling can be utilized in developing prescription guidelines, and these guidelines may be applied operationally with a view toward ensuring that the treatments are in assigned to appropriate site and stand conditions. In the third example, wildlife biologist, Robert McCann (pers. comm. 2011) regarded the stand structure and deadwood data as being “invaluable from a habitat modeling perspective”. This was the first time in this part of British Columbia that he and his associates were able to incorporate information on the density of stems by size class and tree species or broad tree species groups. In addition, McCann noted the potential for using the CWD recruitment data to estimate: locomotion costs to animals travelling through MPB stands, foraging by bears, and cover for rodents, etc. He also noted from a broad perspective, that the stand and stock table representations and associated individual tree growth model projections provided a better representation of future landscape patterns when compared with standard practices and provided new insights into habitat supply. These examples illustrate how the kinds of information related to stand structure classification can be broadly applied, not only where forest estate planning drives timber availability, but where land planning drives management of conservation areas for biodiversity and wildlife habitat suitability and supply assessment.  166  References Armleder, H.M., Dawson, R.J., and Thompson, R.N. 1986. Handbook for timber and mule deer management coordination on winter ranges in the Cariboo Forest Region. Land Management Handbook Number 13. Ministry of Forests, Victoria, BC, CA.  Bardon, R.E. n.d. Timber sales. A planning guide for landowners. North Carolina Cooperative Extension Service, North Carolina State University, Raleigh, NC, US. http://www.ces.ncsu.edu/forestry/pdf/ag/ag640.pdf [accessed Jan. 18 2012].  BC Ministry of Forests. 2002. Interior Appraisal Manual. Revenue Branch, BC Ministry of Forests, Victoria, BC, CA.  BC Ministry of Forests 2008. Glossary of Forestry Terms in British Columbia. BC Ministry of Forests, Victoria, BC, CA. http://www.for.gov.bc.ca/hfd/library/documents/glossary/Glossary.pdf [accessed Jan 18 2011].  BC Ministry of Forests. 2009. PrognosisBC home page. Available from http://www.for.gov.bc.ca/hre/gymodels/progbc/index.htm [accessed Jan. 18 2012]. BC Ministry of Forests, Lands and Natural Resource Operations. 2011. Facts about B.C.’s Mountain Pine Beetle. BC Ministry of Forests, Lands and Natural Resource Operations, Victoria, BC, CA. 2 pp. http://www.for.gov.bc.ca/hfp/mountain_pine_beetle/Updated-Beetle-Facts_Apr2011.pdf [accessed Jan, 18 2012].  BC Ministry of Natural Resource Operations. 2007. Quesnel sustainable resource management plan (SRMP). BC Ministry of Natural Resource Operations, Williams Lake, BC, CA. http://ilmbwww.gov.bc.ca/slrp/srmp/north/quesnel/index.html [accessed Jan. 18 2012].  Buell, M., Sutherland, G., and Williams, D. 2006. Quesnel TSA silviculture strategy (Type 2) and habitat analysis (Type 3). Cortex Consulting Inc., Victoria, BC, CA. http://www.for.gov.bc.ca/ftp/hfp/external/!publish/fft_standards_on_cms_web/SilvicultureStrateg yDocuments/Quesnel_TSA_26/QuesnelTSAType2and3AnalysisReport.pdf [accessed Jan. 18 2012]. 167  DWB Consulting Services Ltd., Tesera Systems Inc., and B.A. Blackwell Forestry Consultants. 2010. Development of an incremental silviculture investment plan for the Tolko IFPA area. Unpublished report. Tolko Industries Ltd., Cariboo Woodlands Division, Williams Lake, BC, CA.  Fenger, M., Manning, T., Cooper, J., Guy, S. and Bradford, P. 2006. Wildlife & trees in British Columbia. Lone Pine Publishing, Edmonton, AB, CA.  Gyug, L., Hamilton, T. and Austin, M. n.d. Grizzly bear. http://www.env.gov.bc.ca/wld/frpa/iwms/documents/Mammals/m_grizzlybear.pdf [accessed Jan. 18 2012].  Hengeveld, P.E., Wood, M.D., Ellis, R., McNay, R.S., and Lennox, R. 2004. Mountain goat habitat supply modeling in the Mackenzie Timber Supply Area, North-Central British Columbia. PEFWCP report No. 290. Peace/Williston Fish and Wildlife Compensation Program, Prince George, BC, CA. http://www.bchydro.com/pwcp/pdfs/reports/pwfwcp_report_no_290.pdf [accessed Jan 18 2012].  Krebs, J., Lofroth, E.C., Parfitt, I. 2007. Multiscale habitat use by wolverines in British Columbia, Canada. J. Wildlife Habitat Manage. 71(7): 2180-2192.  Lambeck, R.J. Focal species: A multi-species umbrella for nature conservation. Conserv.Biol.11(4):849-856.  McCann, R., McNay, R.S., Brumovsky, V. Moss, I., Fenger, M., Voller, J., Sulyma, R., and Snively, M. 2011. Multi-species habitat supply in the Quesnel Timber Supply Area, British Columbia. Wildlife Infometrics Inc. Report No. 372a. Wildlife Infometrics Inc., Mackenzie, BC, CA. http://www.for.gov.bc.ca/hfd/library/FIA/2011/LBIP_8162001a.pdf [accessed Jan 18 2012].  Moss, I., Capling, S., Meisner, S., and Conly, D. 2005. Timber value: reconciling sawmill and timberland managers’ perspectives. Unpublished report. ForesTree Dynamics Ltd., Victoria, BC, CA.  168  Moss, I. 2009. Stand structure classification: The cumulative distribution approach. A pictorial guide to 17 stand structure classes and 40 growth type groups in the IDFdk3/01 site series in south central British Columbia. Unpublished Report. Tesera Systems Inc., Victoria, BC, CA.  Moss I. 2009b. An approach to classifying inventorying polygon stand structure characteristics. In: Extending forest inventory and monitoring over space and time. Proceedings of IUFRO Division 4, May 19-22, Quebec City, QC, CA. http://blue.for.msu.edu/meeting/proceed.php [accessed Jan 18 2012]. Mountain Caribou Technical Advisory Committee. 2002. A strategy for the recovery of Mountain Caribou in British Columbia. Version 1.0. Ministry of Water, Land and Air Protection, Victoria, BC.  Papaik, M.J., Fall, A., Sturtevant, B., Kneeshaw, D., Messier, C., Fortin, M.J., and Simon, N. Forest processes from stands to landscapes: exploring model forecast uncertainties using cross-scale model comparison. Can J. Forest Res. 40:2345-2359.  Steen, O.A. and Coupe, R.A. 1997. A field guide to forest site identification for the Cariboo Forest Region. B.C. Min. Forests, Victoria, B.C. Land Management Handbook No. 39. BC Ministry of Forests, Victoria, BC, CA. http://www.for.gov.bc.ca/hfd/pubs/Docs/Lmh/Lmh39.htm [accessed Jan. 18 2012].  Stier, J.C. 2003. What is my timber worth? And why? Forestry Facts 97:1-4. University of Wisconsin Extension. Department of Ecology and Management, School of Natural Resources, University of Wisconsin, Madison, WI, US. http://forestandwildlifeecology.wisc.edu/extension/Publications/97.PDF [accessed Jan. 18 2012].  Teuffel, K.V., Hein, S. Kotar, M., Preuhsler, E.P., Puumanalainen, J., and Weinfurter, P. End user needs and requirements. In Hasenauer, H. (ed.) Sustainable forest management growth models for Europe. Springer, Berlin, DE. Pp. 19-38. Wall, W.B., Blisle, M., and Luke, L.A. 2011. British Columbia’s interior: Moose habitat decision aid. BC J. Ecos. Manag. 11(3):45-49. http://jem.forrex.org/index.php/jem/article/viewFile/46/39 [accessed Jan. 18 2012].  169  Waterhouse, M.J., Armleder, H.M. and Dawson, R.J. 1994. Winter food habits of Mule Deer in the central interior of British Columbia. Research Note 113. Research Branch, Ministry of Forests, Victoria, BC, CA. http://www.for.gov.bc.ca/hfd/pubs/Docs/Mr/Rn/Rn113.pdf [accessed Jan. 18 2012].  170  

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