Methods for Quantitatively Describing Tree Crown Profiles of Loblolly pine (Pinus taeda L.)

Physiological process models, productivity studies, andwildlife abundance studies all require accuraterepresentations of tree crowns. In the past, geometricshapes or flexible mathematical equations approximatinggeometric shapes were used to represent crown profiles.Crown profile of loblolly pine (Pinus taeda L.) wasdescribed using single-regressor, nonparametric regressionanalysis in an effort to improve crown representations.The resulting profiles were compared to more traditionalrepresentations. Nonparametric regression may be applicablewhen an underlying parametric model cannot be identified.The modeler does not specify a functional form. Rather, adata-driven technique is used to determine the shape acurve. The modeler determines the amount of local curvatureto be depicted in the curve. A class of local-polynomialestimators which contains the popular kernel estimator as aspecial case was investigated. Kernel regression appearsto fit closely to the interior data points but oftenpossesses bias problems at the boundaries of the data, afeature less exhibited by local linear or local quadraticregression. When using nonparametric regression, decisionsmust be made regarding polynomial order and bandwidth.Such decisions depend on the presence of local curvature,desired degree of smoothing, and, for bandwidth inparticular, the minimization of some global error criterion.In the present study, a penalized PRESS criterion (PRESS*)was selected as the global error criterion. When individual-tree, crown profile data are available, the technique ofnonparametric regression appears capable of capturing moreof the tree to tree variation in crown shape than multiplelinear regression and other published functional forms.Thus, modelers should consider the use of nonparametricregression when describing crown profiles as well as in anyregression situation where traditional techniques performunsatisfactorily or fail.