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Modeling the Forest Stand Growth Dynamics Based on the Thermodynamic Approach. P. 213–225

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Viktor I. Lisitsyn, Michael V. Drapalyuk, Nikolai N. Matveev

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The forest ecosystem is a common example of the functioning of open thermodynamic systems. The work analyzes the change in the entropy of an open thermodynamic system where the following processes can be realized: absorption of short-wave solar radiation – differentiation process; total biomass growth process associated with the consumption of resources for respiration and competition. As a result of these processes, the negative entropy flow enters the system, and the positive entropy is produced in the system. As the stand grows, its biomass reaches a maximum, which corresponds to the steady state in the ecosystem. It is shown that, in accordance with the Prigogine’s theorem, the specific entropy production in an open system takes on a minimum positive value. With a further increase in the age of the stand, the steady state of the open thermodynamic system evolves to an equilibrium state, at which a decrease in the plant biomass is observed, and the entropy tends to a maximum value in accordance with the 2nd law of thermodynamics (ecosystem decay). The analysis of the behavior of an open thermodynamic system forms the basis of a new ecological and physiological model of the stand growth dynamics. The model proposed uses the following parameters: the biomass of an individual tree and the number of trees per hectare. In order to model the biomass growth dynamics of an individual tree, the von Bertalanffy equation is used. It contains a dynamic equation describing growth of an individual due to resource uptake and limitation of growth due to resource consumption. The equation that characterizes the dynamics of stand size derives from the condition of reaching the maximum biomass of the stand during the stand’s growth. In general, the stand’s dynamics model has only three independent parameters. They are the onset time of the steady state, the resource consumption rate and the factor linking the area and biomass of the organism. The model verification is presented by calculating the biomass dynamics for full (normal) pine plantations of the first five quality classes (Ib, Ia, I, II, III). The model’s quality is assessed by the dimensionless Nash-Sutcliffe model efficiency coefficient, the value of which is usually greater than 0.95. This corresponds to a description of the data that is close to ideal.


Viktor I. Lisitsyn, Candidate of Physics and Mathematics, Assoc. Prof.; ResearcherID:AAL-8681-2021, ORCID:
Michael V. Drapalyuk, Doctor of Engineering, Prof.; ResearcherID: AAP-5563-2020, ORCID:
Nikolai N. Matveev, Doctor of Physics and Mathematics, Prof.;
ResearcherID: AAP-4873-2020, ORCID:


Voronezh State University of Forestry and Technologies named after G.F. Morozov, ul. Timiryazeva, 8, Voronezh, 394087, Russian Federation;,


forest ecosystem, thermodynamics of nonequilibrium processes, forest stand growth dynamics modeling, yield tables, ecological and physiological model

For citation

Lisitsyn V.I., Drapalyuk M.V., Matveev N.N. Modeling the Forest Stand Growth Dynamics Based on the Thermodynamic Approach. Lesnoy Zhurnal = Russian Forestry Journal, 2022, no. 3, pp. 213–225. (In Russ.).


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