Concepts and dimensionality in modeling unsaturated water flow and solute transport

Many environmental studies require accurate simulation of waterand solute fluxes in the unsaturated zone. This paper evaluatesone- and multi-dimensional approaches for soil water flow as wellas different spreading mechanisms to model solute behavior atdifferent scales. For quantification of soil water fluxes,Richards equation has become the standard. Although currentnumerical codes show perfect water balances, the calculated soilwater fluxes in case of head boundary conditions may dependlargely on the method used for spatial averaging of the hydraulicconductivity. Atmospheric boundary conditions, especially in thecase of phreatic groundwater levels fluctuating above and below asoil surface, require sophisticated solutions to ensureconvergence. Concepts for flow in soils with macropores andunstable wetting fronts are still in development. One-dimensionalflow models are formulated to work with lumped parameters inorder to account for the soil heterogeneity and preferentialflow. They can be used at temporal and spatial scales that are ofinterest to water managers and policymakers. Multi-dimensionalflow models are hampered by data and computation requirements.Their main strength is detailed analysis of typicalmulti-dimensional flow problems, including soil heterogeneity andpreferential flow. Three physically based solute-transportconcepts have been proposed to describe solute spreading duringunsaturated flow: The stochastic-convective model (SCM), theconvection-dispersion equation (CDE), and the fractionaladvection-dispersion equation (FADE). A less physical concept isthe continuous-time random-walk process (CTRW). Of these, the SCMand the CDE are well established, and their strengths andweaknesses are identified. The FADE and the CTRW are more recent,and only a tentative strength weakness opportunity threat (SWOT)analysis can be presented at this time. We discuss the effect ofthe number of dimensions in a numerical model and the spacingbetween model nodes on solute spreading and the values of thesolute-spreading parameters. In order to meet the increasingcomplexity of environmental problems, two approaches of modelcombination are used: Model integration and model coupling. Amain drawback of model integration is the complexity of theresulting code. Model coupling requires a systematic physicaldomain and model communication analysis. The setup andmaintenance of a hydrologic framework for model coupling requiressubstantial resources, but on the other hand, contributions canbe made by many research groups.