Conceptual and Mathematical Statement of the Process of Heavy Metals Migration in the System «Soil – Agricultural Plant»

Abstract

The mathematical modeling was used to describe the functioning and organization of natural ecosystems as well as various approaches to the classification of environmental models to describe both the individual processes and their interactions on the base of the real system patterns. Using the system analysis, the components of the system «soil-agricultural plant» are identified and analyzed separately interconnected by bilateral cause-effect relationships. It was shown that the origin of the studied system is artificial, while specific of the components is material. By the nature of interaction with the environment it is an open system, the sequence of events in which is not deterministic and is probabilistic. In developing the conceptual model of heavy metal migration in the system «soil-agricultural plant», a number of assumptions were made: the main mechanism of heavy metals input into crops is the root one; the process of chemical element transfer between the components of the system can occur in forward and reverse directions; in the processes of migration between the components of ecosystems, the transit of heavy metals can take place; the foliar flow of heavy metals is taken into account, mediated, in the transfer constants from the soil to the above-ground phytomass of crops; it is assumed that the investigated chemical element is isolated from the parts of plants into the soil. The accepted limitation in the development of the conceptual model of the TM migration process in the system «soil-agricultural plant» is the formalization of the initial information to quantifiable indicators. Based on the results of the system analysis, adopted approaches and assumptions, a conceptual model of TM migration in the system of «soil-agricultural plants» is developed, with the allocation of the main blocks (compartment): arable soil layer (0-30 cm), aerial phytomass of plants, the root system of plants (root and tuber fields), the subsurface layer of the soil. Mathematical description of the dynamics of migration of chemical elements between the individual components of the studied system «soil-agricultural plant» is presented by a system of linear differential equations of 1 st order. The process of migration between the compartments are determined by the constants of transfer of a chemical elements, based on literature data and average values of coefficients of accumulation of Zn, cu, Pb, Cd in the most common crops.