Real-Time Trajectory Modelling of the Mean Tree Volume in a Forest Stand Through a Nonsymmetric Diffusion Process Analogy

This study focuses on the diffusion processes to predict the mean tree volume in a forest stand, considering the variability and uncertainty associated with regional, operational, and environmental factors. The distribution and spatial arrangement of trees within a given forest area, as well as dynamic fluctuations and complex uncertainties, are all represented by the nonsymmetric stochastic differential equations of the Gompertz-type. This study proposes a trivariate system of mixed-effect parameters, Gompertz-type Stochastic Differential Equations (SDEs) that quantify the dynamics of the trivariate distribution of tree size components (diameter, potentially occupied area, and height) against age in a stand. The newly developed model has demonstrated that it is possible to accurately predict, track, and explain the dynamics of mean tree volume yield and growth in a forest stand as trees grow over time. Theoretical findings are demonstrated using observed data from Lithuania's permanent experimental plots that are mixed-species and uneven-aged. The model is implemented using the Maple symbolic algebra system.