Modeling of Root Water Uptake Dynamics and Solute Movement in Agricultural Fields Using Crank–Nicolson Finite Difference Method

Abstract

ABSTRACT Understanding root water uptake (RWU) and solute transport dynamics is critical for sustainable agriculture and groundwater protection. While existing models often rely on proprietary software, this study develops a novel, open‐source numerical framework using Python programming to simulate coupled water flow (Richards' equation) and solute transport (advection‐dispersion equation) in variably saturated soils. The model's key innovation lies in its modular integration of a crop‐specific, exponentially‐declining RWU function for Jowar, Green Gram, and Safflower within a Crank–Nicolson finite difference scheme, validated against analytical benchmarks. Results show that RWU is concentrated in the upper 30 cm of soil, decreasing exponentially with depth and time, creating localized hotspots that intensify advective solute transport. Hydraulic conductivity and pore water velocity were identified as primary enhancers of solute mobility, while retardation factors and specific water capacity mitigated solute migration. This computationally efficient framework provides a transparent and adaptable tool for optimizing irrigation and fertilizer management, highlighting the necessity of integrating soil heterogeneity and dynamic root growth in future model developments.