Evaluation of nonlinear equations for predicting diameter from tree height

With the emergence and advancement of airborne laser scanning technology over the past decade, individual tree height can be easily measured over a large area of forests with a comparable degree of accuracy to conventional ground-based methods. In laser scanning based large-scale forest inventories, the need to predict diameter from remotely sensed tree height calls for a systematic evaluation of equation forms as the first step towards a well-developed approach to developing diameter–height equations. This study evaluated more than 30 height–diameter equations in the forest biometrics literature to select candidates for deriving equation forms for diameter–height equations. The evaluation was based on four criteria: (i) the height–diameter function is inversable; (ii) the inverse function is continuous and monotonically increasing over a specified working range of total tree height; (iii) diameter at breast height is equal to zero when tree height equals breast height in the inverse function; and prefera...

[1]  Vicente S. Monleon,et al.  Challenges to Estimating Tree Height via LiDAR in Closed-Canopy Forests: A Parable from Western Oregon , 2010, Forest Science.

[2]  J. H. Smith,et al.  The potential of Weibull-type functions as flexible growth curves , 1978 .

[3]  N. Draper,et al.  Applied Regression Analysis. , 1967 .

[4]  Y. Lei,et al.  Features and Partial Derivatives of Bertalanffy-Richards Growth Model in Forestry , 2004 .

[5]  Paula Soares,et al.  A critical look at procedures for validating growth and yield models. , 2003 .

[6]  Boris Zeide,et al.  Analysis of Growth Equations , 1993 .

[7]  Robert A. Monserud,et al.  An evaluation of diagnostic tests and their roles in validating forest biometric models , 2004 .

[8]  L. Pienaar,et al.  The Chapman-Richards Generalization of Von Bertalanffy's Growth Model for Basal Area Growth and Yield in Even - Aged Stands , 1973 .

[9]  James R Murphy,et al.  Nonlinear Regression Modelling , 1985 .

[10]  M. Heurich.  Automatic recognition and measurement of single trees based on data from airborne laser scanning over the richly structured natural forests of the Bavarian Forest National Park , 2008 .

[11]  David A. Ratkowsky,et al.  Handbook of nonlinear regression models , 1990 .

[12]  S. Reutebuch,et al.  A rigorous assessment of tree height measurements obtained using airborne lidar and conventional field methods , 2006 .

[13]  UNIFYING SIGMOID UNIVARIATE GROWTH EQUATIONS , 2005 .

[14]  K. Ramachandran,et al.  Mathematical Statistics with Applications. , 1992 .

[15]  L. Zhang.  Cross-validation of Non-linear Growth Functions for Modelling Tree Height–Diameter Relationships , 1997 .

[16]  J. MacKinnon,et al.  Estimation and inference in econometrics , 1994 .

[17]  D. Gujarati,et al.  Essentials of Econometrics , 1992 .

[18]  Raymond J. Carroll,et al.  Measurement error in nonlinear models: a modern perspective , 2006 .

[19]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[20]  Robert L. Bailey,et al.  Modeling and Prediction of Forest Growth Variables Based on Multilevel Nonlinear Mixed Models , 2001 .

[21]  N. Draper,et al.  Applied Regression Analysis: Draper/Applied Regression Analysis , 1998 .

[22]  Eben N. Broadbent,et al.  Spatial partitioning of biomass and diversity in a lowland Bolivian forest: Linking field and remote sensing measurements , 2008 .

[23]  Daniel Wallach,et al.  Mean squared error of prediction as a criterion for evaluating and comparing system models , 1989 .

[24]  Huiquan Bi,et al.  Flexible taper equation for site-specific management of Pinus radiata in New South Wales, Australia , 2001 .

[25]  D. Fekedulegn,et al.  Parameter Estimation of Nonlinear Models in Forestry. , 1999 .

[26]  A. Kozak,et al.  Does cross validation provide additional information in the evaluation of regression models , 2003 .

[27]  J. Vauhkonen,et al.  Combining tree height samples produced by airborne laser scanning and stand management records to estimate plot volume in Eucalyptus plantations , 2011 .

[28]  Douglas P. Wiens,et al.  Comparison of nonlinear height–diameter functions for major Alberta tree species , 1992 .

[29]  D. Fekedulegn,et al.  Parameter estimation of nonlinear growth models in forestry , 1999 .

[30]  Kuldeep Kumar,et al.  A comparative study for the estimation of parameters in nonlinear models , 1996 .

[31]  Margarida Tomé,et al.  A generalized nonlinear mixed-effects height-diameter model for Eucalyptus globulus L. in northwestern Spain. , 2010 .

[32]  C. Peng,et al.  Developing and Validating Nonlinear Height-Diameter Models for Major Tree Species of Ontario's Boreal Forests , 2001 .

[33]  YangYuqing,et al.  Comparison of different methods for fitting nonlinear mixed forest models and for making predictions , 2011 .

[34]  S. Huang,et al.  Development of ecoregion-based height–diameter models for white spruce in boreal forests , 2000 .

[35]  B. Zeide,et al.  Selection of site trees: the combined method and its application , 1993 .

[36]  Harold E. Burkhart,et al.  An Evaluation of Sampling Methods and Model Forms for Estimating Height-Diameter Relationships in Loblolly Pine Plantations , 1992, Forest Science.

[37]  D. Hall.  Measurement Error in Nonlinear Models: A Modern Perspective , 2008 .

[38]  D. Donald,et al.  Management of Radiata Pine , 1993 .

[39]  John R. Moore,et al.  Allometric equations to predict the total above-ground biomass of radiata pine trees , 2010, Annals of Forest Science.

[40]  S. Shapiro,et al.  An Analysis of Variance Test for Normality (Complete Samples) , 1965 .

[41]  Lindi J. Quackenbush,et al.  Using error-in-variable regression to predict tree diameter and crown width from remotely sensed imagery. , 2010 .

[42]  Ian Ferguson,et al.  Campaign and site effects in LiDAR prediction models for site-quality assessment of radiata pine plantations in South Australia , 2010 .

[43]  H. A. Meyer.  A mathematical expression for height curves. , 1940 .

[44]  S. Popescu.  Estimating biomass of individual pine trees using airborne lidar , 2007 .

[45]  G. Meek.  Mathematical statistics with applications , 1973 .

[46]  G. L. Martin,et al.  Comparison of constant and variable allometric ratios for estimating Populus tremuloides biomass , 1987 .

[47]  R. L. Bailey,et al.  Height-diameter models for tropical forests on Hainan Island in southern China , 1998 .

[48]  Ewa M. Bielihska,et al.  COMPARISON OF DIFFERENT METHODS , 1994 .

[49]  N. Draper,et al.  Applied Regression Analysis , 1966 .

[50]  C. Raymond.  Influence of prior land use on wood quality of Pinus radiata in New South Wales, Australia , 2008 .