Two-dimensional mathematical modeling of water regime of soil at drip irrigation

Abstract

Goal. The objective of the study is to develop a method for predicting the dynamics of soil moisture under drip irrigation based on mathematical modeling by the two-dimensional Richards equation stated in terms of pressure. Methods. The results of the study were obtained by the method of mathematical modeling and verified experimentally. To discretize the Richards equation, a locally one-dimensional finite-difference scheme was used. Systems of linear algebraic equations obtained after the discretization were solved by the Thomas algorithm. To determine the hydrophysical functions of the soil and its constants, a complex of laboratory studies was used. Measurement of suction pressure in the soil was carried out using Watermark sensors. Results. Two empirical coefficients, as well as the parameter of the partitioning of evapotranspiration into the evaporation and transpiration components, are proposed to be added to the mathematical model. Their selection minimizes the impact of evapotranspiration assessment errors and the errors of the determination and modeling of water supply on the overall accuracy of the forecast. The selection of these coefficients is proposed to be carried out by a metaheuristic particle swarm optimization algorithm on the base of measurements within one irrigation cycle. The results of the verification of the proposed methodology on the data obtained growing corn in the production conditions under drip irrigation in the South of Ukraine are presented. In Analyzing the data of mathematical modeling, the average accuracy of modeling volumetric moisture content equal to ~1% was obtained and theoretical expectations regarding the process of transpiration and evaporation from the near-surface soil layers were confirmed. Conclusions. The presented results allow with a controlled discretion to predict the state of soil moisture, in particular, moistened zones, along with its availability to plants, and can be used during the design of drip irrigation systems increasing their efficiency.