Assessment of Finite Difference Models for Water Content Determination in Soils of the Semi-Arid Region of Brazil

The water content in soil and its variation with depth are critical for numerous processes, significantly influencing plant growth, soil mechanics, and physical and chemical properties. In the semi-arid region of northeastern Brazil, where the Caatinga biome is located, accurate estimation of soil water content is crucial due to severe water scarcity and highly variable precipitation patterns. This study aimed to evaluate the sensitivity and accuracy of a computational model for predicting soil matric potential and water content. The model solves the Richards’ equation using three finite difference methods: explicit, implicit, and Crank-Nicolson. The methods were applied to three soil textures (sandy loam, silt, and clay), and a preliminary analysis was performed to identify the optimal time (dt) and spatial (dz) steps for achieving relative differences below 1%. The model predicted acceptable behavior for soil matric potential and water content, particularly for sandy loam, which required finer steps (1 second, 1 cm) compared to silt and clay (10 seconds, 5 cm). Two test cases from the literature were used for further validation. Finally, the model was applied to soil textures typical of northeastern Brazil, confirming its ability to capture the dynamics of soil water content in this region. The results highlight the applicability of this computational approach to semi-arid soils, contributing to improved water management and crop production strategies.