Author(s)

D. Crevoisier

Abstract

This paper presents an analytical or semi analytical method capable of predicting water bidirectional transfers in a soil under different irrigation systems, and specifically for micro and furrow irrigation systems. The method developed in this article uses the Green’s function to solve Richards’ equation. Some assumptions are made that allow the equation to be linearized and thus solved. The Green’s function is a well-known method used to solve the partial differential equation (PDE) with constant coefficients in simple geometries and general boundary conditions. The singularity of the method lies in its approach to Richards’ equation in real irrigation contexts as it superposes simple solutions which can be treated by Green’s function method. This work has two main aims: to propose analytical and explicit forms of water content in the soil, and to treat irrigation scenarios (unspecified furrow shapes in the case of furrow irrigation, heterogeneous initial conditions, which take into account precipitation events and plant uptakes, etc.) in a simple and operational manner. It also allows the evaluation of the coefficients of the solute transfers equation which depend on soil water content. This equation can then be solved with the same approach developed for water transfers. We present here the main principles of the model, the first results and improvements that could be made in the future. Keywords: furrow irrigation, analytical method, Green’s function, water and solute transfers, bidirectional. 1 Introduction Inadequate irrigation and fertilization practices can have important environmental impacts: waste of water, nitrate pollution. Furrow irrigation is one

Keywords

furrow irrigation, analytical method, Green’s function, water and solute transfers, bidirectional.