Modelling of soil moisture change during the operation of the “Frigate” sprinkler

Abstract

The irrigation process is one of the most important elements of technologies for growing crops on irrigated soils. The tasks of ensuring optimal soil water regime, eliminating gravita-tional water losses outside the zone of active moisture exchange and promoting the fullest use of plants of bioclimatic potential of the region require modeling of soil moisture dynamics in the process of wetting, as well as structures and technologies related to irrigation facilities. Soil moistening in the south of Ukraine is carried out mainly by sprinkling with the use of a Frigate sprinkler, which is largely close to the natural processes of moisture in soil structures, especially with the use of the latest Xi-Wob sprinklers, which provide uniform irrigation and uniform droplet size. The aim of the article is to develop a model of soil moisture change, which will determine the moisture content in both the root and near-surface layers of the soil and prognoses the movement parameters of the "Frigate" sprinkler elements. The designs of sprinklers currently available allow to provide uniform intensity of spraying of drops on all working area of "Frigate" sprinkler, therefore it is possible to choose a separate point for modeling. The data obtained for one point can be extended to the entire work area. The Darcy equation is used to mathematically describe the movement of water in the soil. The finite difference method was used to solve the Darcy equation based on the initial and boundary conditions. Assuming that within each soil element the humidity changes linearly, and replacing the partial derivatives of moisture in depth and time with the analogues, the discretized model of soil moisture dynamics in the final differences was obtained, which allows you to predict moisture at any time due to hydro-soil characteristics in previous time and boundary conditions. Discretization of the Darcy equation made it possible to obtain a model of the dynamics of the humidity of the root layer in the space of states. It turned out to be nonlinear due to the hydrophysical characteristics of the soil and was linearized by transformation into the Taylor series. The developed mathematical model of soil moisture change in the space of states allows to determine the moisture content in both the root and near-surface soil layer depending on its hydrological characteristics, type of cultivated plants, volume of water entering the fields from irrigation systems or in the form of random precipitation used to predict the movement parameters of the "Frigate" sprinkler elements.