Системный подход к модели роста деревьев в лесу на основе уравнения Берталанффи

Abstract

A universal, systematic approach has led to the identification of such indicators as the speed of the process of death and the development of forests. These forest indicators naturally depend on the type of trees in the forest, their state of health, as well as the degree of environmental impact. In forestry, there is a single generalized model of the growth and death of trees in the form of a growth model. The development model proposed by Von Bertalanffy is also known in relation to any growth indicator, mainly the diameter of the tree. The article is devoted to the issues of a systematic approach to the process of tree growth using the Bertalanffy growth model. The aim of the study was to find a relationship between the diameter and height of trees at which the target functional, compiled on the basis of the Bertalanffy model, reaches a maximum with some improvement. The improvement of the model is carried out as follows: a generalized indicator P, defined as the product of the diameter and height of the tree, is introduced for consideration. In general, this indicator determines the longitudinal section of trees and may be useful in forestry. On the other hand, a similar indicator, the product of D2 · H, is widely used in calculating biomass in trees, which indicates that the introduced indicator is sufficiently informative. Some restrictive conditions are assumed for the desired function of the relationship between the diameter and height of trees. To find the optimal ratio between these two indicators, a target function containing the desired function is formed on the basis of the Bertalanffy model. The problem of unconditional variational optimization is formulated and solved, as a result of which the optimal type of the desired function is calculated at which the target functional reaches a maximum.