Shooting the Numerical Solution of Moisture Flow Equation with Root Water Uptake Models: A Python Tool

Modeling the water uptake by plant roots is a key issue in studying soil processes, which are governed by water dynamics: a comprehensive understanding and forecast of such dynamics is a relevant issue in managing water resources. Typically, movement of water in soils and uptake by roots are described by the Richards' equation with a sink term, and numerical treatment of this problem is still a challenge, together with its practical implementations in user-friendly softwares. In order to tackle this problem, in the present paper we propose a simple and computationally fast algorithm developed as a Python code, implementing a numerical approach based on the shooting method, a classical tool for handling boundary value problems (BVPs) arising here from a discretization recently introduced for Richards' equation: such a method is applied to the linearized Richards' equation with Gardner's hydraulic functions. This method is implemented also in MATLAB, in order to accomplish comparisons with built-in MATLAB solver for parabolic partial differential equations. The Python code is made available to readers, and is intended to be an easy tool for handling this problem in the framework of Gardner's constitutive relations, filling the gap of other commercial codes, which do not provide choice of Gardner functions. Many numerical simulations are performed: the results are promising, since the proposed method behaves efficiently and in some cases it is able to converge even when the MATLAB solver fails; mass balance properties and order of accuracy issues are also investigated.