|
Article information
2020 , Volume 25, ¹ 2, p.92-102
Chetyrbotskiy V.A., Chetyrbotskiy A.N.
Parametric identification of the dynamics model in the system fertilizer-soil-plant
Modern mathematical models for the simulation of dynamics in the “fertilizer-soil-plant” system, the components of which are agricultural plants, soil microorganisms and elements of their mineral nutrition, are considered. Based on the analysis of the adopted provisions, a model that takes into account the relationships and the specific nature of the joint changes in its components has been developed. The mathematical formalization of the model equations is carried out, for the construction of which the concept of the "resource-consumer"system was used. In this case, the consumer is the biomass of plants, and the content of the main elements of its mineral nutrition distributed in the narrow basal zone of plants is a resource. The dynamic equations of the model follow the basic principle of chemical kinetics, according to which the result of the interaction between dynamic variables in the systems of the profile in question is determined by their product. The equations also contain the self-limitation factor, which sets the growth rate of the curve for the logistic equation and the specific rate of the model variables saturation effect. Thus, the specific rate of change in biomass is determined by its natural growth rate, the weighted sum of the nutrient contents in plants, and intraspecific competition. The rate of change in the content of these elements per unit of biomass is proportional to their current content in the rhizosphere and to the factor of the mutual influence of the elements on each other. The parameters are estimated and the adequacy of the model to sample distributions is established. An array of experimental data on the growth of spring wheat (Krasnoufimskaya-100) on peat lowland soil, the preliminary soil treatment of which was carried out using nitrogen, phosphorus, and potassium fertilizers, is used as sample distributions. The coefficients obtained as a result of parameter estimation and the calculated distributions of model dynamic variables with a sufficiently high degree of adequacy correspond to their experimental distributions and reflect the real situation of the system evolution.
[full text]
Keywords: rhizosphere, elements of plant mineral nutrition, logistic equation, search for extremum of a functional
doi: 10.25743/ICT.2020.25.2.008
Author(s):
Chetyrbotskiy Valentin Alexandrovich
Position: manager
Office: Joint Stock Company Apatit
Address: 119333, Russia, Apatity
E-mail: Vel4232@gmail.com
Chetyrbotskiy Alexandr Naumovich
Dr.
Position: Leading research officer
Office: Russian Academy of Sciences - Far Eastern Branch - Far East Geological Institute
Address: 690022, Russia, Vladivostok
E-mail: Chetyrbotsky@yandex.ru
References:
[1]. Kaurichev I.S., Panov N.V., Rozov N.N. Pochvovedenie [Soil Science]. Moscow: Agropromizdat; 1989: 719. (In Russ.)
[2]. Thornley J.H.M. Mathematical models in plant physiology: A qauantitative approach to problems in plant and crop physiology. N.Y.: Academic Press; 1976: 318.
[3]. Riznichenko G.Yu., Rubin A.B. Mathematical models of biological production processes. Moscow: MGU; 1983: 302. (In Russ.)
[4]. Thornley J.H.M., France J. Mathematical models in agriculture: Quantitative methods for the plant, animal and ecological sciences. 2nd edition. Wallingford, UK: CABI; 2007: 906.
[5]. Margalef R. Perspectives in ecological theory. Chicago: University of Chicago Press; 1986: 112.
[6]. Roose T., Keyes S.D., Daly K.R., Carminati A., Otten W., Vetterlein D., Peth S. Challenges inimaging and predictive modeling of rhizosphere processes. Plant Soil. 2016; 407(1-2):9–38.
[7]. Svirezhev Yu.M., Logofet D.O. Sustainability of biological communities. Moscow: Nauka; 1978: 352. (In Russ.)
[8]. Darrah P.R., Jones D.L., Kirk G.J.D., Roose T. Modeling the rhizosphere: a review of methods for “upscaling” to the whole plant scale. European Journal of Soil Science. 2006; (57): 13–25.
[9]. Mineev V.G. Agrochemistry. Moscow: MGU; 2006: 714. (In Russ.)
[10]. Bard Y. Nonlinear parameter estimation. New York; London: Academic Press; 1974: 341.
[11]. Efremova, M.A., Drichko, V.F. Effect of potassium on the physicochemical properties of lowland peat soil. Agrokhimiya. 2010; (4):3–10. (In Russ.)
[12]. Sladkova N.A. Raspredelenie tsinka i kadmiya v sisteme torfyanaya pochva—rastenie pod vliyaniem fosfornykh i kaliynykh udobreniy [Distribution of zinc and cadmium in peat soil-plant system under the influence of phosphorus and potassium fertilizers]: Dis. ... kand. biol. nauk. SPb.; Pushkin: SPbGAU; 2016: 187. (In Russ.)
[13]. Chetyrbotsky, V.A. A mathematical model of the phosphorus distribution in the rhizosphere. Proc. of the Intern. Scienc. Conf. Students, Graduate and Young Scientists. “Lomonosov-2019”. Moscow: MGU; 2019:212–214. (In Russ.)
[14]. Samarsky, A.A., Mikhailov, A.P. Mathematical modelling: Ideas. Methods. Examples. Moscow: Fizmatlit; 2001: 320. (In Russ.)
[15]. Sobol I.M., Statnikov R.B. The choice of optimal parameters in problems with multiple criteria. Moscow: Nauka; 1981: 110. (In Russ.)
[16]. Bolch B.W., Huang C.J. Multivariate statistical methods for business and economics. 1 Edition. N.Y.: Prentice-Hall; 1974: 329.
[17]. Dyachenko A.N., Shagalov V.V. Khimicheskaya kinetika geterogennykh protsessov. Uchebnoe ðosobie [Chemical kinetics of heterogeneous processes: study guide]. Tomsk: Izd-vo TPU; 2014: 102. (In Russ.)
Bibliography link:
Chetyrbotskiy V.A., Chetyrbotskiy A.N. Parametric identification of the dynamics model in the system fertilizer-soil-plant // Computational technologies. 2020. V. 25. ¹ 2. P. 92-102
|
