A preliminary model for optimal control of moisture content in unsaturated soils

TL;DR

This paper introduces an optimal control model for irrigation that minimizes water use and maximizes plant water uptake in unsaturated soils, supported by numerical simulations demonstrating its potential effectiveness.

Contribution

It develops the first-order optimality conditions for controlling moisture in soils via Richards' equation within an irrigation context, providing a new framework for efficient water management.

Findings

Model supports optimized irrigation strategies

Numerical simulations validate the analytical approach

Framework addresses water scarcity in agriculture

Abstract

In this paper we introduce an optimal control approach to Richards' equation in an irrigation framework, aimed at minimizing water consumption while maximizing root water uptake. We first describe the physics of the nonlinear model under consideration, and then develop the first-order necessary optimality conditions of the associated boundary control problem. We show that our model provides a promising framework to support optimized irrigation strategies, thus facing water scarcity in irrigation. The characterization of the optimal control in terms of a suitable relation with the adjoint state of the optimality conditions is then used to develop numerical simulations on different hydrological settings, that supports the analytical findings of the paper.