Two-dimensional model for water, heat, and solute transport in furrow-irrigated soil .1. Theory
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Because of salinity, many areas with irrigated farmland have suffered from reduced food and fiber production, especially where irrigation water or soil contains large amounts of soluble salts. In those areas, ridge-furrow tillage is a common practice and furrow irrigation is a popular irrigation method. Effects of water content, temperature, and solute concentration on transport phenomena in soil are hard to predict without complex models. The geometry of a ridge-furrow surface contributes to complexities in heat and vapor transport, and hence, in the distribution of water, temperature, and salt in soil. To improve understanding of water, heat, and solute transport in furrow-irrigated and salt-affected soil, we developed a two-dimensional mechanistic model using the Galerkin finite element method (FEM). The model was designed to consider interactive effects of water content, temperature, and solute concentration on water, heat, and solute transport. To simulate field conditions, an energy balance equation was applied to the ridge-furrow surface to provide boundary conditions for water and heat transport. To utilize a single FEM solver, equations governing transport of water, heat, and salt in soil were generalized as a diffusive-convective type equation. Numerical schemes for the model were tested by comparing simulated results with analytical or semianalytical solutions. Good agreements between FEM and analytically calculated soil water content, temperature, and solute concentration were obtained.
