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Library of Congress Cataloging-in-Publication Data
Forest growth and yield modeling / Aaron R. Weiskittel... [et al.].
p. cm.
Includes index.
ISBN 978-0-470-66500-8 (hardback)
1. Trees–Growth–Computer simulation. 2. Forest productivity–Computer simulation.
3. Trees–Growth–Mathematical models. 4. Forest productivity–Mathematical models. I. Weiskittel, Aaron R.
SD396.F66 2011
634′.0441–dc23
2011014943
A catalogue record for this book is available from the British Library.
This book is published in the following electronic format: ePDF 9781119998525; Wiley Online Library 9781119998518; ePub 9781119971504; Mobi 9781119971511
Preface
In 1994, Jerome Vanclay published a comprehensive and definitive text on forest growth and yield modeling. Since then, significant changes in data availability, computing power, and statistical techniques have largely changed the state of forest growth and yield modeling in a rather short time period. This new book attempts to build on the successful approach of the 1994 book and provide a broad perspective on all aspects of forest growth and yield modeling.
Most foresters, students, and even researchers treat forest growth and yield models as incomprehensible and outdated black boxes that are frustrating to use and with predictions that can be inaccurate. Yet, growth and yield predictions are still central to answering a variety of practical and research questions on a daily basis, often with little appreciation of how the models actually operate, their key assumptions, and the difficulty of the task at hand. As with the previous edition, this book attempts to make growth models more accessible to a wider audience by exploring their individual components, discussing aspects of their construction, and, most importantly, describing their limitations. Specific attention is given to individual tree growth models because they are the tool most commonly used for practical decisions. For each type of growth model, several example growth models from different regions of the world are described in detail so that the differences between modeling approaches are better illustrated and the black-box nature of specific models is lessened.
The text is intended for practitioners, researchers, and students alike. Given their relative lack of coverage in other books, two detailed chapters on measuring site productivity and competition are given, which could be used in several undergraduate and graduate-level university courses. There are also individual chapters that describe whole-stand/size-class, individual tree, process-based, and hybrid models. The key growth model components discussed in detail are increment equations, static equations, mortality, and regeneration/recruitment. Other chapters include combining models of different resolutions, modeling silvicultural treatments, and potential future directions. Finally, chapters on model evaluation, model development, and model use are given to guide future efforts. The extensive bibliography should serve as a useful guide for specific references on more advanced topics.
A team of authors with a diverse background and expertise was assembled to provide a comprehensive and international perspective. The book's original author, Dr. Jerome Vanclay, provided expertise on all aspects of growth models, particularly models developed in the southern hemisphere and for tropical forests. Dr. John Kershaw, a co-author on Wiley's fourth edition of the Forest Mensuration book, brought a perspective on growth and yield models used in North America, particularly Canada. Dr. David Hann has an extensive career working on forest growth and yield models and is the developer of the ORGANON growth model, which is widely used in the US Pacific Northwest. Finally, Dr. Aaron Weiskittel has spent time working with process and hybrid models and is currently developing an individual tree growth model for the northeastern North America.
Acknowledgements
The authors acknowledge the help of many friends and colleagues during the preparation of this book. Drs. Peter Marshall (University of British Columbia), David Marshall (Weyerhaeuser Company), and Quang Cao (Louisiana State University) provided useful feedback on the content and organization of the text. Greg Johnson (Weyerhaeuser Company), Jim Goudie (Canadian Forest Service), Dr. Robert Monserud (retired, US Forest Service), Dr. Rongxia Li (University of Maine), University of Washington Stand Management Cooperative (SMC), US Forest Service, and New Brunswick Department of Natural Resources provided data useful in the construction of several figures.
Dr. Phil Radtke (Virginia Polytechnic Institute and State University), Dr. Peter Gould (US Forest Service), Dr. Laura Leites (Pennsylvania State University), Dr. Jeff Gove (US Forest Service), Dr. Martin Ritchie (US Forest Service), Dr. Jeremy Wilson (University of Maine), Dr. Thomas Ledermann (Austria Federal Forest Office), Dr. Laura Kenefic (US Forest Service), Dr. Duncan Wilson (Oklahoma State University), Matthew Russell (University of Maine), Joshua Sjostrom (University of Maine), Elijah Shank (University of Maine), and Elizabeth McGarrigle (University of New Brunswick) reviewed several chapters. Special thanks to Drs. Robert Curtis (US Forest Service), Oscar García (University of Northern British Columbia), and Dave Hyink (retired, Weyerhaeuser Company) for extensive reviews of the book. Special thanks are due Clare Lendrem for an outstanding job as copy-editor.
Finally, thanks to the encouragement, patience, and understanding of friends and family.
Chapter 1
Introduction
All models are an abstraction of reality that attempt to conceptualize key relationships of a system. Models can be both quantitative and conceptual in nature, but all models are integrators of multiple fields of knowledge. Consequently, models generally have several important and varied uses. Forest growth and yield models are no different. Foresters often have a general sense of a stand's developmental trajectory and what can be done to alter it. However, it generally takes years of experience to achieve this level of expertise and, even then, quantifying the predictions can be difficult. Forest growth models attempt to bridge this gap by providing model users the ability to predict the future condition of the forest. Ultimately, growth models are the quantitative generalizations on the knowledge of forest stand development and their response to silvicultural treatments.
Forest growth and yield models have a long, and rapidly expanding, history of development (, ). Their development and use has particularly increased in the last two decades, due in part to the greater availability of personal computers to perform both data analysis and complex simulations (). This has resulted in a wide array of modeling approaches, each with their own advantages and disadvantages. In particular, models differ in the type of data used and the method of construction. This book attempts to provide an overview of the primary concepts involved in forest modeling, the various techniques used to represent the determinants of growth, and the techniques needed to both develop and use a growth model properly.
Although the concepts of forest growth and yield have long been a part of forestry, they have been defined and named in various ways, particularly in the US (Bruce, 1981). In this book, increment is defined as the difference between tree or stand dimensions from one time period to the next, while growth is the final dimension from one time period to the next. In other words, increment is determined by either solving a growth equation or by observing growth at two points of time (Bruce, 1981).
This book is focused on models that predict the development of a single forest stand (). Although a distinction between empirical and mechanistic models is often made (e.g. Taylor et al., 2009), this is not a useful metric of differentiation, as all models are on a spectrum of empiricism. Instead, this book groups forest stand development models into four broad categories: (1) statistical models; (2) process; (3) hybrid; and (4) gap (; ).
Categories of quantitative single stand forest development models and their definition, use, advantages, and disadvantages.
Statistical models rely on the collection and analysis of data that will characterize the targeted population in a manner that allows statistical variability to be estimated for parameters. The primary intent of statistical models is for prediction of forest stand development and yield over time. Process models represent key physiological processes (e.g. light interception, photosynthesis), often for understanding and exploring system behavior, which are then combined to characterize both tree and stand development. Hybrid models merge features of statistical and process models and are used both for understanding and for prediction. Gap models are designed to explore long-term ecological processes, generally for understanding interactions that control forest species succession. Models that integrate the development of multiple forest stands, such as landscape models, exist (e.g. Mladenoff, 2004), but will not be covered in this book.
Within any given model category, models differ in their resolution (both spatial and temporally), spatial dependence, and degree of determinism. Spatial resolution refers to the basic unit for predictions, with the simplest being a whole-stand approach (Chapter 4), and the individual-tree approach is the most detailed (Chapter 5). A size-class model is a compromise between the whole-stand and individual-tree approaches (Chapter 4). Some process models even have a spatial resolution of an individual leaf within a tree crown. In addition, a significant amount of effort has been made in combining predictions from models with different spatial resolutions (Chapter 10).
Temporal resolution is the basic time step for model predictions. Several process models have daily or even hourly time steps, while statistical models generally have 1- to 10-year temporal resolutions. Models also vary in their use of spatial information. Distance-dependent or spatially explicit models require spatial location information; often individual-tree x–y coordinates are needed. Distance-independent or spatially implicit models do not require this information.
Finally, models differ in their use of deterministic approaches, which means that a particular function will always return the same output return value for any given set of input values. In contrast, stochastic approaches incorporate some purely random element and will give different return values in successive runs with any given set of input values. Stochasticity can be an important element of forest modeling, as some relevant factors like natural disturbances that ultimately govern the growth and yield of a particular stand can be random or unpredictable. However, a model with too many stochastic elements can make interpretation a challenge.
Stochasticity is one approach for addressing the variability that is inherent in all aspects of modeling. Even models in fundamental sciences like physics and chemistry have purely random elements. However, biological systems are even more variable and models need to recognize the important sources. Therefore, the models examined in this book have a framework that is based upon our current biological knowledge and are parameterized with the knowledge that the parameters are uncertain.
Forest growth models have several components. At minimum, forest stand development models must represent growth (Chapter 6) and mortality (Chapter 8). Models must also have components that relate the traditional tree measurements of diameter and height to other attributes like total volume or biomass with the use of static equations (Chapter 7). Comprehensive growth models include components to predict regeneration and ingrowth (Chapter 9) and representation of silvicultural treatments (Chapter 11). In addition, understanding the key biological determinants of growth and yield, namely competition (Chapter 2) and site potential productivity (Chapter 3), is important.
1.1 Model development and validation
As with most fields, forest modeling is both an art and a science. Ideally, the development of any model involves a comprehensive understanding of the system and an approach for detecting the crucial relationships. This often means that modelers must be multidisciplinary. In addition, model development is often an iterative and collaborative effort between modelers, fundamental scientists, and model users. The process of modeling is an assessment of current understanding of forests, information needed for management, and crucial knowledge gaps.
Consequently, research questions can often be generated by assessment of model strengths and weaknesses. This also illustrates an important modeling distinction, namely the use of models for prediction versus understanding, which will be further discussed below. Although there are important general modeling philosophies like Occam's principle of parsimony, which suggests that models should be as simple as possible, but as complex as necessary (Kimmins et al., 2008), achieving this is often easier said than done.
Regardless of modeling approach, empirical data of one type or another will be required for either model construction (Chapter 14) or model evaluation (Chapter 15). Data can often vary greatly in its quality and overall usefulness for modeling. Among others, data quality is influenced by how well the data represents the population of interest, the variables collected, and the degree of measurement error, which is often an overlooked yet important determinant of predictability (e.g. Hasenauer and Monserud, 1997). The statistical tools used to construct models are continually changing and evolving. Chapter 14 provides a brief overview of the key statistical techniques in order to give a better context to statistical forest growth and yield models.
To be useful for a given purpose, a model must be representative of reality to some degree. Consequently, a variety of methods have been used to verify model predictions (Chapter 15). This has ranged from simple statistical tests to complex stochastic simulations. Each has their own merits, but, in general, models must be verified using multiple approaches to ensure full reliability. If model predictions are found to be inadequate, a larger question quickly becomes how to fix or re-calibrate the model. This can often be a complicated undertaking, but emerging approaches may simplify the process.
1.2 Important uses
Models are tools designed to be used in a variety of ways (Chapter 16). The key uses of any well-developed model are prediction and education in its broadest sense (). In forestry, some key prediction roles of growth models are (1) update forest inventories; (2) assess alternative forest silvicultural systems; (3) determine the influence of disturbance agents like insects or disease; (4) estimate sustainable yield of forest products; and (5) generalize regional trends. Growth and yield information is required to make all major forest management decisions. Some of the basic decisions that require accurate growth and yield information include: (1) even-aged stand-level decisions; (2) uneven-aged stand-level decisions; (3) forest- or ownership-level decisions; and (4) regional and national decisions. The type of information needed from a forest growth and yield model to make these different decisions depends on the spatial and temporal level at which information is needed ().
Uses of growth and yield models to aid in key forest management decisions.
Even-aged stand-level |
Planting density; thinning strategy; fertilization strategy; species or species mix; rotation length |
Hann and Brodie (1980) |
Uneven-aged stand-level |
Sustainable diameter distribution; cutting cycle length; species mix; fertilization strategy; conversion strategy |
Hann and Bare (1979) |
Forest or ownership level |
Schedule of stand treatments; allowable harvest; wildlife habitat; aesthetics |
Bettinger et al. (2009) |
Regional or national level |
Carbon sequestration potential; allowable harvest; wildlife habitat |
Bettinger et al. (2005) |
For example, a silviculturist would primarily use a growth and yield model to project the development of the stand under alternative treatment strategies such thinning or fertilization regimes. A forest planner would likely use a growth and yield model to stratify individual stands in a forest into homogeneous units, project the development of each stratum, and use a harvest scheduler to determine the optimal silvicultural system and allowable harvest. A policy-maker would generally use a growth and yield model to depict regional or national trends like carbon sequestration potential or sustainable harvest levels to set effective policies. In fact, growth models were used in the United States, by the Chicago Climate Exchange and the California Climate Action Registry, to set standards for carbon credit trading and greenhouse gas registries at regional and national scales.
Additional uses of models are the visualization of management alternatives and the assessment of forest stand dynamics on wildlife habitat and streamside conditions for fish habitat. Consequently, the implications of basing decisions on a growth and yield model at any level are often quite significant, which both model developers and users need to be aware of.
There are several complex issues facing the practice of forestry today, like assessing the effects of climate change, forest carbon neutrality, and long-term sustainability. Answering these open questions with empirical data is often difficult, requires long-term investment, or is impossible. Consequently, growth and yield models are widely used by scientists as research tools to test hypotheses and understand system behavior. For example, the ORGANON growth and yield model (Hann, 2011) has been widely used by scientists to answer several research questions on a broad array of topics ranging from forest management, planning, and economics, to conservation issues ().
Examples of the applied uses of the ORGANON growth and yield model.
Forest management |
Maguire et al. (1991) |
Examine the influence of alternative management on wood quality |
Welty et al. (2002) |
Assess strategies for managing riparian zones |
Wilson and Oliver (2000) |
Strategies for density management to ensure stability |
Sessions et al. (2004) |
Manage the consequences of wildfire |
Forest planning |
Johnson et al. (2007a) |
Develop large-scale, long-term plans for usage of forested landscapes |
Sessions et al. (2000) |
Develop mature forest habitat |
Shillinger et al. (2003) |
Predict future timber supply |
Johnson et al. (2007b) |
Large-scale assessment of socioeconomic effects on forest structure and timber production |
Economics |
Birch and Johnson (1992) |
Determine the economic impact of green tree retention |
Fight et al. (1993) |
Conduct a financial analysis of pruning alternatives |
Busby et al. (2007) |
Evaluate the opportunity cost of forest certification |
Latta and Montgomery (2004) |
Create cost-effective older stand structures |
Wildlife |
Hayes et al. (1997) |
Evaluate response of wildlife to thinning |
Calkin et al. (2002) |
Managing for wildlife biodiversity |
Lichtenstein and Montgomery (2003) |
Assessing influence of timber management on wildlife biodiversity |
Andrews et al. (2005) |
Strategies for creating northern spotted owl nesting sites |
Nalle et al. (2004) |
Strategies for joint management of timber and wildlife |
Models are good research tools as they allow the construction of what-if scenarios and experimentation with different parameter settings. In addition, the development and construction of any growth model often leads to new and interesting research questions. This is because model development largely requires making and testing key assumptions, assessing patterns, and providing full disclosure, which are all basic tenets of the scientific method. In other words, developing a model requires the processes or system being modeled to be conceptualized and understood.
Forest growth and yield models are useful tools for education, a role that ORGANON has often played (Marshall et al., 1997). This is because models require hands-on interaction, synthesis of multiple concepts, and critical thinking skills to assess the appropriateness of output. In addition, combining model prediction with visualization tools (Chapter 16) allows visual demonstration of key concepts like stand structure and stratification, which can be difficult to achieve with just words or in the field.
1.3 Overview of the book
Forest growth modeling is an evolving and comprehensive field that can be difficult to describe fully. Previous books on forest growth modeling have either become outdated (e.g. Vanclay, 1994), focused primarily on one geographic region (e.g. Hasenauer, 2006), or are specific to a particular modeling approach (e.g. Landsberg and Sands, 2011). This book attempts to provide a comprehensive overview of forest models from multiple perspectives in order to be useful to model developers, scientists, students, and model users alike.
The book is divided into 17 individual chapters that give an overview of the key concepts determining growth and yield (Chapters 2, 3), the different types of modeling approaches (Chapters 4, 5, 12, 13), and the various dimensions of developing, validating, and using a growth model (Chapter 14, 15, 16). Example models are described in detail for each modeling approach to illustrate key differences and provide information on some of the more widely used models ().
Model name, type, resolution, distance dependence, stochasticity, region, primary species, and reference for example models considered in the text.
In particular, the components of statistical, distance-independent, individual-tree models are discussed in detail (Chapters 6, 7). Attention is given to this type of modeling approach because it has been widely adopted and extensively used for operational management planning. For example, statistical, distance-independent, individual-tree models are currently available and used throughout the United States (Crookston and Dixon, 2005), western Canada (e.g. Temesgen and LeMay, 1999), central Canada (e.g. Bokalo et al., in review), eastern Canada (e.g. Woods and Penner, 2007), central Europe (e.g. Monserud et al., 1997), and northern Europe (e.g. Hynynen et al., 2002). The approach has been preferred because it can be used in a wide range of stand structures, particularly in uneven-aged (Peng, 2000) and mixed species stands (Porté and Bartelink, 2002). Throughout the book, specific attention is given to the ORGANON growth and yield model of the United States Pacific Northwest (Hann, 2011), as it has a long history of continuous development, is applicable to a large number of conifer and hardwood species in a wide array of stand conditions, and has been rigorously tested.
It is our hope that the book can help promote a more comprehensive understanding of forest models, and guide future modeling efforts.