A difference equation approach to developing tree profile equations

Abstract

A second-order constant-coefficient nonhomogeneous difference equation is presented as a template for deriving a model form to predict above breast height tree stem profiles. Comparative analysis of the precision and bias of the model with several commonly used polynomial models on a white oak ( Quercus alba L.) tree profile data set indicates that the difference approach produces profile equations equivalent in precision and bias to the traditional methods for constructing profile equations. Because the fitted equations can be forced easily through two upper stem diameters, the model has the distinct advantage over other modeling methods by allowing the model to be adjustable for differing form classes and points. Also, because the solution of the difference equation is always path invariant, no matter which stem profile diameters the equation is forced through, the same tree profile is generated. As the method does not require a total height, it is adaptable to situations where profile measurements are only taken to an indefinite merchantable height.