Mathematical model of water vapor sorption by soils with a linear source-drainage

Abstract

The generalization of the mathematical model of water vapor sorption by soils of an agricultural landscape in the case of a non-stationary linear source- drainage present in the soil system is considered. The problem of studying the dynamics of the sorption process, the volumetric soil moisture of an agricultural landscape, is formalized by a problem with an initial condition for the inhomogeneous Riccati equation with a linear right-hand side, the integration of which is not a trivial task. In contrast to the classical model of M. Griesemer for the sorption of water vapor by soils and the sorption model with a stationary source previously considered by the authors, the introduction of a non-stationary source- drainage function into the model significantly complicated the task of integrating the model equation and studying the sorption model, required the use of methods from the analytical theory of differential equations, but increased the diversity of flow regimes of the modeled process and expanded the possibilities for controlling this process. Using methods of the analytical theory of differential equations, a solution to a model problem was found, with the help of which an assessment was made of the dynamics of the main indicator of the sorption process – the volumetric soil moisture. As a result of the mathematical analysis of the dynamics of the sorption process, it was established that the entire variety of theoretically possible flow regimes of the simulated sorption process is formed depending on the values of two main adjustable parameters of the model - the coefficient of the ratio of the constant initial humidity to the constant equilibrium humidity and the angular coefficient of the linear source-drainage function. By varying these parameters, it becomes possible to control the process being studied: to simulate the sorption process under conditions of intensive soil moisture, under conditions of critical soil drying, under steady-state conditions, etc. The research results can be applied to further studies of moisture dynamics in the profile of texture-differentiated reclaimed soils.