Abstract
In this work, we employ stochastic differential equations (SDEs) to model tree stem taper. SDE stem taper models have some theoretical advantages over the commonly employed regression-based stem taper modeling techniques, as SDE models have both simple analytic forms and a high level of accuracy. We perform fixed- and mixed-effect parameters estimation for the stem taper models by developing an approximated maximum likelihood procedure and using a data set of longitudinal measurements from 319 mountain pine trees. The symmetric Vasicek- and asymmetric Gompertz-type diffusion processes used adequately describe stem taper evolution. The proposed SDE stem taper models are compared to four regression stem taper equations and four volume equations. Overall, the best goodness-of-fit statistics are produced by the mixed-effect parameters SDEs stem taper models. All results are obtained in the Maple computer algebra system.
Highlights
Stem taper modeling is an attractive way to estimate tree size variables, both in forestry research and practice, due to its analytical flexibility
The most difficult challenge of stem taper modeling is in modeling tree species with stems that differ from an idealized shape
This paper focuses on two stem taper modeling frameworks, which can be classified into stochastic differential equations and regression models
Summary
Stem taper modeling is an attractive way to estimate tree size variables, both in forestry research and practice, due to its analytical flexibility. These types of models have been increasingly used for forest inventory and growth forecasting tools. The most difficult challenge of stem taper modeling is in modeling tree species with stems that differ from an idealized shape. This situation often leads to isolation of many tree species from stem taper modeling process. Many types of taper modeling techniques have been proposed and applied over the years. The most traditionally used stem taper parametric equations are regression models, which are classified into segmented polynomial [1], variable exponent [2], mechanistic [3], and stochastic differential equation [4,5] methods
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