Numerical simulation of irrigation scheduling using fractional Richards equation

Abstract

A method of soil moisture content prediction is presented using fractional differential generalization of one-dimensional Richards equation for the purposes of decision support in irrigation. We propose to use water head dynamics data gathered in the beginning of growth season to perform a calibration of the model by the meta-heuristic particle swarm algorithm. Van Genuchten model is used to describe water retention curve. The cases of the known values of its coefficients along with their identification from water head dynamics data are considered. The paper presents the results of model verification for both classical Richards equation and its fractional differential generalization. For the conditions of sprinkling irrigation in the south of Ukraine, we estimate the accuracy of modelling the water head dynamics measured by the Watermark sensors and the accuracy of seasonal irrigation rate assessment. The obtained results show that the use of water transport model that take soil fractality into consideration has no effect on assessing seasonal irrigation rate but gives up to 7% increase in accuracy while predicting the time and rate of next irrigation application.