Temperature and water content estimation in soils of the semi-arid region of Brazil using finite difference and CFD

Determining the temperature and water content of soil, at a given instant or along time, is fundamental to understand several soil-related phenomena and processes. Evaporation, aeration, chemical-reaction rates and types, biological processes such as germination and growth of seeds, root development, nutrient and water uptake by roots, and decomposition of organic matter by microbes, are all strongly influenced by soil temperature. On the other hand, infiltration of water through the soil surface allows soil to temporarily store water, making it available for uptake by plants and organisms living in soil. Furthermore, soil water content is closely related to physical and chemical properties of soil, such as oxygen content and demand, which impacts root breathing, microbial activity and soil chemical balance. The accurate evaluation of these two parameters and their interconnection is even relevant in semi-arid regions, where climate conditions are particularly difficult, such as the north-eastern zone of Brazil. Thus, the use of computational models and coupled approaches are imperative for rigorous descriptions. This work presents a contribution to estimate soil temperature and water content, by solving the heat transfer equation and the Richards equation, respectively, through finite differences. As input, the model uses the experimental material composition of the soil, the time-dependent temperature profile at the surface and information about the regional rain regime. Three different numerical approaches were implemented: explicit, simple implicit and the Crank–Nicolson method. The calculations for temperature and water content of the soil obtained with these computational models were compared with the results from Computational Fluid Dynamics (CFD). The relative differences between the numerical methods were less than 0.006% by solving the heat transfer equation and less than 2.75% using the Richards equation. The maximum relative differences within the model, including both a constant and a variable water-content profile, were 3.28%. The results from the computational model using the CFX tool have maximum relative differences of 0.6%, which contributes to verifying the accuracy of the implemented methods.