Sampling Techniques for Forest Inventories [ Active ]

Preface

Inventories are the bases for forest management planning, with the goal being the optimal utilization of resources under given constraints. To accomplish this, managers must collect, summarize, and interpret information . that is perform statistical work. The development and improvement of forest management practices, which began toward the end of the Middle Ages, have strongly depended on the parallel evolution of inventory techniques and statistical methodology, in particular sampling schemes. Without these, current forest inventories would be impossible to conduct.

Over the last 80 years, the number of techniques, the demand for more and better information, and finally the mere complexity of their incumbent investigations seem to have grown exponentially. Furthermore, the increased importance of related problems in landscape research and ecology (keywords e.g. biomass, carbon sequestration, and bio-diversity) as well as their interactions with the sociological and economic environment have required specialized procedures for data collection and statistical inference. However, their accompanying economic constraints have necessitated cost-efficient approaches in performing all of these tasks.

The objective of this textbook is to provide graduate students and professionals with the up-to-date statistical concepts and tools needed to conduct a modern forest inventory. This exposition is as general and concise as possible. Emphasis has been placed deliberately on the mathematical-statistical features of forest sampling to assess classical dendrometrical quantities. It is assumed that the reader has a sufficient understanding of elementary probability theory, statistics, and linear algebra. More precisely, one must be able to calculate unconditional and conditional probabilities and understand the concepts of random variables, distributions, expectations, variances (including their conditional versions as derived and summarized in Appendix B), central limit theorem and confidence intervals, as well as utilize the least-squares estimation technique in linear models (using matrix notation). The standard notation of naive set theory (e.g. AB, A¿B, A\B, A ¼ B, A ½ B, x ¸ A, A x, x /¸ A) is presented throughout. Likewise, the reader will ideally have some prior knowledge of the general economic-political background of forest inventories and aspects of mensuration (e.g. the handling of instruments), plus skills in remote sensing and geographical information systems (GIS). MSc and PhD students in Forestry, and particularly in Forest Management, will almost surely have had introductory courses in all of these topics. This book will also be useful to experienced forest biometricians who wish to become rapidly acquainted with a modern approach to sampling theory for inventories, as well as some recent developments not yet available in book form.

The fundamental concepts and techniques, as used primarily in sociological and economics studies, are presented in chapter 2 and can be summarized as design-based survey sampling and inference for finite populations (of e.g. geographical areas, enterprises, households, farms, employees or students), usually so large that a full survey (census) is neither feasible nor even meaningful. Inclusion probabilities and the Horvitz-Thompson estimator form the cornerstone of this chapter and are also essential to a forest inventory. More advanced topics are addressed in chapter 3. Excellent classical works at the intermediate mathematical level include those by Cochran (1977) and S¨arndal et al. (2003), and in French by Gourieroux (1981) and Till´e (2001). Likewise, Cassel et al. (1977), Chaudhuri and Stenger (1992), Chaudhuri and Vos (1988), and Till´e (2006) describe more complicated mathematical and statistical themes.

Key references (in English) for sampling theory in forest inventories are from de Vries (1986) and Schreuder et al. (1993). Those compiled by Kangas and Maltamo (Eds, 2006) and K¨ohl et al. (2006), the latter containing an extensive bibliography, give broad and up-to-date introductions to this subject, but without proofs of the exhibited statistical techniques. Johnson (2000) provides an elementary and encyclopedic (900 pp!) review of standard procedures, while the writing of Gregoire and Valentine (2007) is an excellent introduction to modern concepts in sampling strategies with interesting chapters on some specific problems. Pard´e and Bouchon (1988) and Rondeux (1993), both writing in French, as well as Z¨ohrer (1980), in German, present basic overviews with emphases on practical work. Unfortunately, none of these authors, except Gregoire and Valentine (2007) in some instances, utilize the so-called infinite population or Monte Carlo approach that is much better suited to forest inventories and, in many ways easier to understand. Therefore, this formalism for inventories, within a design-based framework, is developed here in chapter 4 (foundations and one-phase sampling schemes) and in chapter 5 (two-phase sampling schemes). It rests upon the concept of local density, which is essentially an adaptation of the Horvitz-Thompson estimator. These two chapters give a full treatment of one-phase and two-phase sampling schemes at the point (plot) level, under both simple random sampling and cluster random sampling, with either one-stage or two-stage selection procedures at the tree level. These techniques usually suffice for most routine inventories or serve as building blocks for more complex ones. The treatment of cluster-sampling differs markedly from the classical setup, being simpler and easier from both a theoretical and a practical point of view. Simulations performed on a small real forest with full census illustrate the techniques discussed in chapters 4 and 5. Those results are then displayed and critiqued in

Appendix A. More advanced topics, such as model-dependent inference and its interplay with model-assisted techniques (g-weights), as well as small area estimations and analytical studies, are dealt with in chapter 6. Geo-statistics and the associated Kriging procedures are presented in chapter 7. Using a case study, chapter 8 describes various estimation procedures. Chapter 9 tackles the difficult problem of optimal design for forest inventories from a modern point of view relying on the concept of anticipated variance. The resulting optimal schemes are illustrated in chapter 10 with data from the Swiss National Forest Inventory. Chapter 11 outlines the essential facts pertaining to the estimation of growth and change. Finally, chapter 12 provides a short introduction to transect-sampling based on the stereological approach. A small number of exercises are also proposed in selected chapters.

It is worth mentioning that the formalism developed in chapters 4, 5 and 6 can be used to estimate the integral of a function over a spatial domain – a key problem in such fields as soil physics, mining or petrology. This is a simpler alternative to the geostatistical techniques developed in chapter 7, which are usually more efficient, particularly for local estimations.

This book is based partly on the writings of C.E. S¨arndal, as adapted to the context of a forest inventory. In addition, references are made to research, both recent and older, by outstanding forest inventorists, including B. Mat´ern and T.G. Gregoire, as well as to the author's own work and lectures at ETH Zurich. Whenever feasible, proofs are given, in contrast to most books on the subject. These occasionally rely on heuristic arguments to minimize the amount of mathematics to a reasonable level of sophistication and spacing. It cannot be overemphasized that readers should not only have a good command of definitions and concepts but also have at least a sufficient understanding of the proofs for the main results.

The scope of this book is restricted when compared to the seemingly unlimited field of applications for sampling techniques within environmental and sociological-economic realms. Nevertheless, the average reader will need time and endurance to master all of the topics covered. Many sections are therefore intended for either further reading or specific applications on an as-needed basis, or they will facilitate one's access to more specialized references. Readers who desire to familiarize themselves quickly with the key aspects of a forest inventory can in a first perusal focus their attention on the following topics: chapters 1, 2 (sections 2.1 to 2.6), 4 and 5, plus a brief glance at the case study in chapter 8. This should suffice for tackling standard estimation problems (without the planning aspects). Courageous readers who persevere through this entire tome should be able to consult all of the current literature on forest sampling (and partly on general survey sampling) and, why not, eventually contribute their own solutions to existing and oncoming challenges?