FOREST MENSURATION Managing Forest Ecosystems Volume 13 Series Editors: Klaus von Gadow Georg-August-University, Göttingen, Germany Timo Pukkala University of Joensuu, Joensuu, Finland and Margarida Tomé Instituto Superior de Agronomía, Lisbon, Portugal Aims & Scope: Well-managed forests and woodlands are a renewable resource, producing essential raw material with minimum waste and energy use. Rich in habitat and species diversity, forests may contribute to increased ecosystem stability. They can absorb the effects of unwanted deposition and other disturbances and protect neighbouring ecosystems by maintaining stable nutrient and energy cycles and by preventing soil degradation and erosion. They provide much-needed recreation and their continued existence contributes to stabilizing rural communities. Forests are managed for timber production and species, habitat and process conservation. Asubtle shift from multiple-use managementtoecosystems managementis being observed and the new ecological perspective of multi-functional forest managementis based on the principles of ecosystem diversity, stability and elasticity, and the dynamic equilibrium of primary and secondary production. Making full use of new technology is one of the challenges facing forest management today. Resource information must be obtained with a limited budget. This requires better timing of resource assessment activities and improved use of multiple data sources. Sound ecosystems management, like any other management activity, relies on effective forecasting and operational control. The aim of the book series Managing Forest Ecosystemsis to present state-of-the-art research results relating to the practice of forest management. Contributions are solicited from prominent authors. Each reference book, monograph or proceedings volume will be focused to deal with a specific context. Typical issues of the series are: resource assessment techniques, evaluating sustainability for even-aged and uneven-aged forests, multi-objective management, predicting forest development, optimizing forest management, biodiversity management and monitoring, risk assessment and economic analysis. The titles published in this series are listed at the end of this volume. Forest Mensuration By Anthonie van Laar Somerset West, South Africa and Alparslan Akça Universität Göttingen, Germany AC.I.P. Catalogue record for this book is available from the Library of Congress. ISBN-13 978-1-4020-5990-2 (HB) ISBN-13 978-1-4020-5991-9 (e-book) Published by Springer, P.O. Box 17, 3300 AADordrecht, The Netherlands. www.springer.com Printed on acid-free paper All Rights Reserved © 2007 Springer No part of this work may be reproduced, stored in a retrieval system, or transmittedin any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without writte n permission from the Publisher, with the exception of any material supplied specifically for the purpose of being enteredand executed on a computer system, for exclusive use by the purchaser of the work. Anthonie van Laar was born in the Netherlands in 1923. He studied forest scienceattheUniversityandResearchCentreWageningenbetween1941and 1949. In 1958 he emigrated to South Africa and obtained his D.Sc. degree in Forest Science at the University of Stellenbosch (1961), thereafter Dr.oec.pub (1973), and Dr.hab. (1979) at the University of Mu¨nich. His theses dealt with forest biometry and growth modeling. Since his retirement in 1988, van Laar continuedhisinvolvementinthesesubjects,moreparticularlyingrowthmodels forEucalyptusgrandis. Alparslan Akc¸a (born 1936) studied forestry at the University of Istanbul, Turkey and at the University of Freiburg, Germany. He received his doctorate in forestry at the University of Freiburg on identification of land use classes and forest types by means of microdensitometer and discriminant analyses in 1970, for his habilitations in photogrammetry and geodesy at the University of Istanbul in 1976, and in forest inventory and forest management at the University of Go¨ttingen in 1981. He was Professor for Forest Management, ForestInventory,andRemoteSensingattheUniversityofGo¨ttingen.Heretired in 2001. His main research interest is in forest mensuration, forest inventory, andremotesensinginforestry. PREFACE Forest mensuration is one of the most fundamental disciplines within forest and related sciences. It deals with the measurement of trees and stands and the analysis of the resultant information. During the early days of sustained forest management simple measurement and estimation methods and with the analysisofinventoryandresearchdatawereavailable.Themiddleoflastcen- tury, however, witnessed a worldwide increase in the need for more quanti- tative information about trees and stands. This generated the need for more sophisticatedmethodstoobtainandanalyzeforestdata.Thisdevelopmentwas followedbyaphenomenalexplosionofinformation. During the past decades there has been fruitful cooperation between the Institute of Forest Inventory and Forest Growth, formerly “Institute of Forest Management and Forest Yield Sciences” of the University of Go¨ttingen, Germany and the Faculty of Forestry of the University of Stellenbosch, South Africa.Thisbookisoneoftheresultsofthisfruitfulcooperationbetweenthese institutions. The first edition of this book was published in 1997 by Cuvilliers in Go¨ttingen. It was completely revised and supplemented with a presentation and review of recently developed tools and methods to measure and analyze forestry-relateddata.Thepurposeofthisbookistoprovideinformationabout the subject for those readers who are involved in this category of quantitative methods.Sincethemiddleoflastcenturytheincreasedavailabilityofpersonal computers, and software and the consensus that statistical methods are indis- pensable for estimating tree and stand parameters and for testing statistical hypotheses,hadaconsiderableimpactontheprogressofforestmensurationas aresearchandmanagementtool. vii viii Preface Ithasbeenwrittenforforestrystudentsandforpracticalforesters,anddoes not presuppose a more than elementary knowledge of mathematics and statis- tics. However, because of the notable influence of statistics on forest mensu- ration methods and techniques, and the crucial role of sampling techniques, it reviews and evaluates elementary statistical concepts. At the same time it was thought to be imperative to discuss spatial structure and diversity and to addachapteronconventionalanddigitalremotesensing.Numerouspractical examples have been included in this edition. They are thought to be particul- arly useful for university and college students. Additional information about specific topics has been added for the benefit of the advanced reader and was writteninitalics. ForestmensurationasascientifictooloriginatedinEuropeandhasalways played an important role in the practice of forest management. In addition to conventional terrestrial methods, quantitative remote-sensing techniques form an integral part of the forest mensuration curriculum at the University of Go¨ttingen. Countries in the southern hemisphere can derive considerable benefits from this longtime experience. Conversely, short-rotation plantation forestryinthesouthernhemisphereandmoreparticularlyinSouthAfricaacted asastimulusfortheapplicationofstatisticsandotherquantitativemethodsas adecision-makingtool. The Authors are greatly indebted to Mrs. J. Wirkner for proofreading the Englishtextofthefirstedition,Mrs.S.Ru¨digerforthetechnicaldrawingsand graphs,andMr.W.Tambourforhisillustrations.Wewouldfurthermoreliketo sincerelythankMr.Th.BeischandMr.H.Heydeckefortheirconstantsupport in electronic data-processing matters, as well as Mrs. F.J.A. Allwright, who assistedwiththecorrespondenceandEDPinStellenbosch. The authors gratefully acknowledge the inclusion of research data from various sources, more particularly from the Faculties of Forestry at the Universities of Go¨ttingen and Stellenbosch respectively and those obtained fromProfessorProdaninFreiburgandDr.ForrestinAustraliacouldbeincor- porated into the current edition. They gratefully acknowledge permission from Professor Dr. H.C.H. Kramer and Professor Dr. A. Akca, the authors of “Waldmesskunde,” to include numerous drawings from this book. And finally oursincerethanksareduetoSpringerandEditorsofthebookserieswhomade thepublicationofthiseditionpossible. AnthonievanLaar Stellenbosch,SouthAfrica AlparslanAkc¸a Go¨ttingen,Germany May2007 SUMMARY The management of forests and tree plantations requires a quantitative esti- mateofthecurrentandfuturevolumeandbiomassoftimberandby-products, at national, regional, and local levels. Such information is also needed for forest-policy decisions. Forest and forestry research requires a great deal of additional information, for example about the density of forests and stands, diversity, spatial distribution of trees within stands, the size and size distribu- tion of trees within stands, and the expected growth of trees and stands. For- est mensuration is the discipline which deals with these topics. During recent years,considerableprogresshasbeenmadetodevelopmethodsformeasuring tree and stand characteristics, but also in instrumentation and in the statistical analysis of forest mensurational information. Sampling, based on inferential statistics,playsadominantroleinforestmensurationandforestinventory,pri- marily because of the high cost of collecting and processing field data. Mod- ern sampling methods make it possible to find an optimum sampling strategy whichproducessufficientlyaccurateestimatesatthelowestcost.Quantitative information is primarily obtained by ground surveys, aerial photographs, and satelliteimageryareincreasinglyappliedtoobtainbasicinformationaboutthe spatial distribution of forests, possibly also to classify these forests according tospecifiedcategoriesandtosupplementgroundsurveys. Inthisbooktheauthors,whoareemeritusprofessorsattheUniversitiesof StellenboschandGo¨ttingeninSouthAfricaandGermanyrespectively,summa- rizeandreviewcurrentlyusedforestmensurationandforestinventorymethods. Alargenumberofworkedexampleshavebeenadded,primarilyforthebenefit ofundergraduateandpostgraduatestudents. ix CONTENTS PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Chapter1: INTRODUCTION . . . . . . . . . . . . . . . . . . . . 1 Chapter2: STATISTICALPREREQUISITES . . . . . . . . . . . 5 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . 5 2 SCALESANDUNITSOFMEASUREMENT . . . . . . . . 6 2.1 Scalesofmeasurement . . . . . . . . . . . . . . . . . 6 2.2 Unitsofmeasurement . . . . . . . . . . . . . . . . . 7 3 GRAPHICALPRESENTATIONOFDATA . . . . . . . . . . 7 4 DESCRIPTIVESTATISTICS . . . . . . . . . . . . . . . . . 9 5 PROBABILITYDISTRIBUTIONS . . . . . . . . . . . . . . 13 5.1 Normaldistribution . . . . . . . . . . . . . . . . . . . 13 5.2 Binomialdistribution . . . . . . . . . . . . . . . . . . 15 5.3 Poissondistribution . . . . . . . . . . . . . . . . . . . 16 5.4 Distributionofχ2 . . . . . . . . . . . . . . . . . . . 17 5.5 Distributionofstudent’st . . . . . . . . . . . . . . . 18 6 ESTIMATION . . . . . . . . . . . . . . . . . . . . . . . . . 20 6.1 Bias,precisionandaccuracy . . . . . . . . . . . . . . 20 6.2 Estimators . . . . . . . . . . . . . . . . . . . . . . . 22 6.3 Estimatingaccuracy . . . . . . . . . . . . . . . . . . 23 7 REGRESSIONANDCORRELATIONANALYSIS . . . . . . 25 7.1 Simplelinearregression . . . . . . . . . . . . . . . . 25 7.2 Correlationanalysis . . . . . . . . . . . . . . . . . . 26 7.3 Multipleregressionanalysis . . . . . . . . . . . . . . 26 7.4 Nonlinearregression . . . . . . . . . . . . . . . . . . 27 8 MOVINGAVERAGE . . . . . . . . . . . . . . . . . . . . . 27 xi