Physically based mathematical models in soil science: History, current state, problems, and outlook (Analytical Review)

Abstract

The formation, development, and some problems of the current physically based models of water and solute transfer are considered in this review. These models appeared about a half century ago. They were based on the basic laws of soil physics and other branches of soil science (laws of balance, transfer, diffusion, hydrodynamic dispersion, etc.) described by the corresponding equations and programs and supported by the experimental data in the form of physically based parameters. At present, one of the main problems in the development, adaptation, and application of these models is that the current and future mathematical models should rest upon the experimental support with a clear physical basis characterizing the nature of the phe nomenon described. This experimental support enables creating research models, drawing conceptual con clusions, and, hence, understanding, analyzing, and managing soil processes. This is apparently possible only if the set of methods for the experimental support of models is substantiated, preferably in direct physical experiments and under field conditions close to the future model prognoses.

Diagnosis of human-induced degradation of soils of the Azov-Cuban lowland

“…The specific surface area of the solid phase was determined using the standard method, a new method was the use of evacuation, which accelerated the saturation process [16].…”

Carbonate Calcium Equilibrium in Soil Solution as a Driver of Heavy Metals Mobility

“…Аz y (22) where the coefficient A depends on temperature; at 25 o C, A = 0.5085; z is the charge of the particle (ion or associate); μ* is the effective ionic strength of the solution.…”

“…Maximum permissible concentrations are: for drinking water the Cd (MPC) is 0.001 mg l -1 (8), Pb in soil 32 mg kg -1 soil dry weight (DW) [9]; Sr in water 7 mg l -1 [10]. Of great Importance is aspect of drivers of HMs and another chemicals water transfer in soil, vadose zone, aquifers, landscape, catchment basin [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], even selective chemical extraction of HMs from soil [30]. The contents of total and water-soluble HMs forms in the original soil are linked to its geographical location, ionic composition of soil solution, genesis.…”

Mathematical Methods and Computer Modeling to Predict the Formation of the Fill Grounds

“…Currently, any justification of projects and calculations for projects in urban infrastructure is impossible without the use of computers and computer programs [9]. At the same time, it should be remembered that it is necessary to take into account all factors of a preliminary study of territories in mathematical modeling [5].…”