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

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 support the analytical findings of the paper.

Numerical Identification of Boundary Conditions for Richards’ Equation

“…We set hydraulic parameters for clay loam texture [23,25] K s = 0.5458 cm/h, θ s = 0.4686, θ r = 0.1060, n = 1.3954, α = β = 0.0104 cm −1 .…”

“…Richards' equation indirectly connects even to honeybee populations through its impact on plant growth (as soybean, rapeseed, sunflower) and the availability of nectarproducing flowers. Proper irrigation and soil moisture management play a role in ensuring a suitable environment for both plants and honeybees [25,26]. The paper [6] studies model verification both for classical and fractional Richardsons' equations using measurements data for soybean sprinkling irrigation.…”

“…In an irrigation setting, an optimal control approach was implemented in [25] for Richards' equation, focusing on the reduction of water consumption and the enhancement of root water absorption.…”