The Further Development of Stem Taper and Volume Models Defined by Stochastic Differential Equations

Abstract

AbstractStem taper process measured repeatedly among a series of individual trees is standardly analyzed by fixed and mixed regression models. This stem taper process can be adequately modeled by parametric stochastic differential equations (SDEs). We focus on the segmented stem taper model defined by the Gompertz, geometric Brownian motion and Ornstein-Uhlenbeck stochastic processes. This class of models enables the representation of randomness in the taper dynamics. The parameter estimators are evaluated by maximum likelihood procedure. The SDEs stem taper models were fitted to a data set of Scots pine trees collected across the entire Lithuanian territory. Comparison of the predicted stem taper and stem volume with those obtained using regression based models showed a predictive power to the SDEs models.KeywordsDiameterGeometric Brownian motionGompertz processOrnstein-Uhlenbeck processTaperTransition probability densityStochastic differential equationVolume