Models for tree taper form: the gompertz and vasicek diffusion processes framework

Abstract

In this work, we employ stochastic differential equations (SDEs) to model tree stemtaper. SDE stem taper models have some theoretical advantages over the commonly employedregression-based stem taper modeling techniques, as SDE models have both simple analytic formsand a high level of accuracy. We perform fixed- and mixed-effect parameters estimation for the stemtaper models by developing an approximated maximum likelihood procedure and using a data set oflongitudinal measurements from 319 mountain pine trees. The symmetric Vasicek- and asymmetricGompertz-type diffusion processes used adequately describe stem taper evolution. The proposedSDE stem taper models are compared to four regression stem taper equations and four volumeequations. Overall, the best goodness-of-fit statistics are produced by the mixed-effect parametersSDEs stem taper models. All results are obtained in the Maple computer algebra system.