Modeling Dynamics of Structural Components of Forest Stands Based on Trivariate Stochastic Differential Equation

Abstract

Research Highlights: Today’s approaches to modeling of forest stands are in most cases based on that the regression models and they are constructed as static sub-models describing individual stands variables. The disadvantages of this method; it is laborious because too many different equations need to be assessed and empirical choices of candidate equations make the results subjective; it does not relate to the stand variables dynamics against the age dimension (time); and does not consider the underlying covariance structure driving changes in the stand variables. In this study, the dynamical model defined by a fixed-and mixed effect parameters trivariate stochastic differential equation (SDE) is introduced and described how such a model can be used to model quadratic mean diameter, mean height, number of trees per hectare, self-thinning line, stand basal area, stand volume per hectare and much more. Background and Objectives: New developed marginal and conditional trivariate probability density functions, combining information generated from an age-dependent variance-covariance matrix of quadratic mean diameter, mean height and number of trees per hectare, improve stand growth prediction, and forecast (in forecast the future is completely unavailable and must only be estimated from historical patterns) accuracies. Materials and Methods: Fixed-and mixed effect parameters SDE models were harmonized to predict and forecast the dynamics of quadratic mean diameter, mean height, number of trees per hectare, basal area, stand volume per hectare, and their current and mean increments. The results and experience from applying the SDE concepts and techniques in an extensive whole stand growth and yield analysis are described using a Scots pine (Pinus sylvestris L.) experimental dataset in Lithuania. Results: The mixed effects scenario SDE model showed high accuracy, the percentage root mean square error values for quadratic mean diameter, mean height, number of trees per hectare, stand basal area and stand volume per hectare predictions (forecasts) were 3.37% (10.44%), 1.82% (2.07%), 1.76% (2.93%), 6.65% (10.41%) and 6.50% (8.93%), respectively. In the same way, the quadratic mean diameter, mean height, number of trees per hectare, stand basal area and stand volume per hectare prediction (forecast) relationships had high values of the coefficient of determination, R2, 0.998 (0.987), 0.997 (0.992), 0.997 (0.988), 0.968 (0.984) and 0.966 (0.980), respectively. Conclusions: The approach presented in this paper can be used for developing a new generation stand growth and yield models.