Data‐Driven Discovery of Soil Moisture Flow Governing Equation: A Sparse Regression Framework

Abstract

AbstractConventionally, soil moisture dynamics are mathematically modeled by the Richardson‐Richards equation, whose derivation is based on the conservation of mass and the Buckingham‐Darcy law. However, it is complicated and even impossible to finish such rigorous derivations based on physical principles due to the complexity and uncertainties in the vadose zone. In this work, we propose a data‐driven sparse regression framework. For the first time, we discover the time‐dependent nonlinear soil moisture flow equation from only volumetric water content observations. The framework leverages linear approximations and group sparsity techniques. Except for a few assumptions, it requires no prior information, including a specific constitutive relationship model, boundary conditions, and initial conditions. Several numerical experiments are tested to demonstrate that the framework successfully discovers the underlying soil moisture flow equation from data and tends to discover the parsimonious equation governed by dominant physical processes. Besides, the identified nonlinear coefficients, which represent soil hydraulic properties, fit well with the actual coefficients, although they deviate slightly at near‐saturated ends. The results demonstrate the satisfactory performance of the proposed framework under various scenarios. Despite being based on a homogeneous soil assumption, this study provides a new perspective for deriving soil moisture flow governing equations.