A numerical model for transient-hysteretic flow and solute transport in unsaturated porous media

A two-dimensional flow and transport model was developed for simulating transient water flow and nonreactive solute transport in heterogeneous, unsaturated porous media containing air and water. The model is composed of a unique combination of robust and accurate numerical algorithms for solving the Richards', Darcy flux, and advection-dispersion equations. The mixed form of Richards' equation is solved using a finite-element formulation and a modified Picard iteration scheme. Mass lumping is employed to improve solution convergence and stability behavior. The flow algorithm accounts for hysteresis in the pressure head-water content relationship. Darcy fluxes are approximated with a Galerkin and Petrov-Galerkin finite-element method developed for random heterogeneous porous media. The transport equation is solved using an Eulerian-Lagrangian method. A multi-step, fourth-order Runge-Kutta, reverse particle tracking technique and a quadratic-linear interpolation scheme are shown to be superior for determining the advective concentration. A Galerkin finite-element method is used for approximating the dispersive flux. The unsaturated flow and transport model was applied to a variety of rigorous problems and was found to produce accurate, mass-conserving solutions when compared to analytical solutions and published numerical results.     

Time aggregation of nitrogen leaching in relation to critical threshold values

Leaching of nitrate contributes to the deterioration of groundwater and can consequently have a negative influence on the quality of our drinking water. Critical threshold values for nitrogen leaching are established to preserve groundwater quality. A critical threshold value for nitrate leaching of 50 mg 1⁻¹ (11.3 mg N 1⁻¹), similar to the drinking water standard, serves as a threshold value for European countries. However, the temporal aggregation scale on which this threshold value should be considered is unknown. A well tested simulation model was used to evaluate the exceedance of the threshold value at different time aggregation levels, ranging from one day till 30 yr. For three different soil structure types within one soil type and a selected fertilisation regime, the aggregated nitrogen leaching over 30 yr was 11.4, 19.2 and 10.6 mg 1⁻¹. Considering an aggregation level of one day, the critical threshold value of 11.3 mg N 1⁻¹ was exceeded 2973, 5801 and 2556 times, respectively, for the three structure types during 30 yr. By considering other time aggregation levels, a clear relation resulted between time aggregation level and the number of time elements during which the critical level was exceeded. Results strongly indicate that a critical threshold value for leaching should include an associated time-aggregation level.