Modeling the Forest Stand Growth Dynamics Based on the Thermodynamic Approach
DOI:
https://doi.org/10.37482/0536-1036-2022-3-213-225Keywords:
forest ecosystem, thermodynamics of nonequilibrium processes, forest stand growth dynamics modeling, yield tables, ecological and physiological modelAbstract
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.
Downloads
References
Александров Г.А., Голицын Г.С. Критерий подобия для роста лесных насаждений // Докл. АН. 2012. Т. 446, № 1. С. 110–113. Alexandrov G.A., Golitsyn G.S. A Similarity Criterion for the Forest Stand Growth. Doklady Akademii nauk = Doklady Biological Sciences, 2012, vol. 446, no. 1, pp. 110–113. (In Russ.). https://doi.org/10.1134/S0012496612050018
Волькенштейн М.В. Биофизика. М.: Наука, 1988. 592 с. Volkenstein M.V. Biophysics. Moscow, Nauka Publ., 1988. 592 p. (In Russ.).
Зотин А.И. Термодинамический подход к проблемам развития, роста и старения. М.: Наука, 1974. 184 с. Zotin A.I. Thermodynamic Approach to the Problems of Development, Growth and Aging. Moscow, Nauka Publ., 1974. 184 p. (In Russ.).
Карев Г.П. Системное моделирование лесных сообществ // Сиб. экол. журн. 2001. № 4. С. 518–528. Karev G.P. System Modeling of Forest Communities. Sibirskij ecologiccheskij zhurnal = Siberian Journal of Ecology, 2001, no. 4, pp. 518–528. (In Russ.).
Корзухин М.Д. Построение кривых хода роста древостоев на основе обобщенной модели Берталанфи по данным государственного лесного реестра // Лесоведение. 2019. № 2. С. 105–114. Korzukhin M.D. Generalized von Bertalanffy’s Model Applied to Yield Curve Calculation Based on the State Forest Inventory Data. Lesovedenie = Russian Journal of Forest Science, 2019, no. 2, pp. 105–114. (In Russ.). https://doi.org/10.1134/S0024114819020049
Корзухин М.Д., Семевский Ф.Н. Синэкология леса. СП б.: Гидрометеоиздат, 1992. 192 с. Korzukhin M.D., Semevskiy F.N. Synecology of Forest. Saint Petersburg, Gidrometeoizdat Publ., 1992. 192 p. (In Russ.).
Лисицын В.И. Эколого-физиологическая модель динамики роста однопородного древостоя // Актуальные направления научных исследований XXI века: теория и практика. 2017. Т. 5, № 1(27). С. 213–215. Lisicin V.I. An Ecological and Physiological Model of the Dynamics of Growth of One-Species Tree Stands. Aktual’nye napravlenia naucnyh issledovanij xxi veka: teoria I praktika = Current Directions of Scientific Research of the XXI Century: Theory and Practice, 2017, vol. 5, no. 1(27), pp. 213–215. (In Russ.).
Лисицын В.И., Мусиевский А.Л., Сериков М.Т. Математическое моделирование и оптимизация роста смешанных насаждений // Математическое моделирование, компьютерная оптимизация технологий, параметров оборудования и систем управления лесного комплекса. Воронеж: ВГЛТА , 1997. С. 139–143. Lisitsyn V.I., Musiyevskiy A.L., Serikov M.T. Mathematical Modeling and Optimization of Growth of Mixed Plantations. Mathematical Modelling, Computer Optimization of Technologies, Equipment Parameters and Control Systems of the Forest Sector. Voronezh, VGLTA Publ., 1997, pp. 139–143. (In Russ.).
Саушкин В.В., Матвеев Н.Н., Постников В.В., Камалова Н.С., Лисицын В.И., Евсикова Н.Ю., Жужукин К.В., Нгуен Хоай Тхыонг. Исследование влияния импульсного магнитного поля и адсорбированной воды на свойства древесины методом инфракрасной спектроскопии // Лесотехн. журн. 2018. Т. 8, № 2(30). С. 222–232. Saushkin V.V., Matveev N.N., Postnikov V.V., Kamalova N.S., Lisitsyn V.I., Evsikova N.Yu., Zhuzhukin K.V., Nguen H.T. Investigation of the Influence of Pulse Magnetic Field and Adsorbed Water on the Properties of Wood by the Method of Infrared Spectroscopy. Lesotekhnicheskiy zhurnal = Forestry Engineering Journal, 2018, vol. 8, no. 2(30), pp. 222–232. (In Russ.). https://doi.org/10.12737/article_5b24061b468a19.01199073
Швиденко А.З., Щепащенко Д.Г., Нильсон С., Булуй Ю.И. Таблицы и модели хода роста и продуктивности насаждений основных лесообразующих пород Северной Евразии: (нормативно-справочные материалы). Изд. 2-е. М.: Рослесхоз, Междунар. ин-т приклад. систем. анализа, 2008. 886 с. Shvidenko A.Z., Shchepashchenko D.G., Nil’son S., Buluy Yu.I. Tables and Models of Yield and Biological Productivity of the Main Forest-Forming Species Stands of Northern Eurasia: (Regulatory and Reference Materials). Moscow, Rosleskhoz Publ., 2008. 886 p. (In Russ.).
Alexandrov G.A., Golitsyn G.S. Biological Age from the Viewpoint of Thermodynamic Theory of Ecological Systems. Ecological Modelling, 2015, vol. 313, pp. 103–108. https://doi.org/10.1016/j.ecolmodel.2015.06.022
Jorgensen S.E., Svirezhev Y.V. Towards a Thermodynamic Theory for Ecological Systems. Oxford, Elsevier, 2004. 366 p.
Landsberg J. Modelling Forest Ecosystems: State of the Art, Challenges, and Future Directions. Canadian Journal of Forest Research, 2003, vol. 33, no. 3, pp. 387–395. https://doi.org/10.1139/x02-129
Larocque G.R. Forest Models. Encyclopedia of Ecology. Ed. by S.E. Jørgensen, B.D. Fath. Amsterdam, Elsevier, 2008, pp. 1663–1673.
Nash J.E., Sutcliffe J.V. River Flow Forecasting through Conceptual Models Part I – a Discussion of Principles. Journal of Hydrology, 1970, vol. 10, iss. 3, pp. 282–290. https:// doi.org/10.1016/0022-1694(70)90255-6
Ogawa K. Mathematical Consideration of the Age-Related Decline in Leaf Biomass in Forest Stands under the Self-Thinning Law. Ecological Modelling, 2018, vol. 372, pp. 64–69. https://doi.org/10.1016/j.ecolmodel.2018.01.015
Prigogine I. Etude thermodynamique des phénomènes irréversibles. Thesis. Liège, Desoer, 1947. 143 p. (In Fr.).
Robinson A.P., Ek A.R. The Consequences of Hierarchy for Modeling in Forest Ecosystems. Canadian Journal of Forest Research, 2000, vol. 30, no. 10, pp. 1837–1846. https://doi.org/10.1139/x00-117
Von Bertalanffy L. Biophysik des Fließgleichgewichts. Wiesbaden, Springer, 1953. 56 p. (In Ger.). https://doi.org/10.1007/978-3-663-20198-4
Zhang X., Cao Q.V., Wang H., Duan A., Zhang J. Projecting Stand Survival and Basal Area Based on a Self-Thinning Model for Chinese Fir Plantations. Forest Science, 2020, vol. 66, iss. 3, pp. 361–370. https://doi.org/10.1093/forsci/fxz086
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 В.И. Лисицын, М.В. Драпалюк, Н.Н. Матвеев (Автор)
This work is licensed under a Creative Commons Attribution 4.0 International License.
