Semi-analytical methods for simulating the groundwater-surface water interface

Groundwater-surface water interaction is a key component of the hydrologic cycle. This interaction plays a key role in many environmental issues such as the impacts of land use and climate change on water availability and water quality. Modeling of local and regional groundwater-surface water interactions improves understanding of these environmental issues and assists in addressing them. Because of the physical and mathematical complexities of this interaction, numerical approaches are generally used to model water exchange between subsurface and surface domains. The efficiency, accuracy, and stability of mesh-based numerical models, however, depend upon the resolution of the underlying grid or mesh. \nGrid-free analytical methods can provide fast, accurate, continuous and differentiable solutions to groundwater-surface water interaction problems. These solutions exactly satisfy mass balance in the entire internal domain and may improve our understanding of groundwater-surface water interaction principles. However, to model this interaction, analytical approaches typically required simplifying, sometimes unrealistic, assumptions. They are typically used to implement linearized mathematical models in homogenous confined or semi-confined aquifers with geometrically regular domains. \nBy benefiting from the strengths of both analytical and numerical approaches, grid-free semi-analytical methods may be able to address more challenging groundwater problems which have been out of reach of traditional analytical approaches, and/or are poorly simulated using mesh-based numerical methods. Here, novel 2-D and 3-D semi-analytical solutions for the simulation of mathematically and physically complex groundwater-surface water interaction problems are developed, assessed and applied. Those models are based upon the series solution method and analytic element method (AEM) and are intended to address groundwater-surface water interactions induced by pumping wells and/or the presence of surface water bodies in naturally complex stratified unconfined aquifers. Semi-analytical solutions are obtained using the least squares method, which is used to determine the unknown coefficients in the series expansion and the unknown strengths of analytic elements. The series and AEM solutions automatically satisfy the groundwater governing equation. Hence, the resulting solutions are exact over the entire domain except along boundaries and layer interfaces where boundary and continuity conditions are met with high precision. A robust iterative algorithm is used to implement a free boundary condition along the phreatic surface with a priori unknown location. \nThis thesis addresses three general problem types never addressed within a semi-analytic framework. First, a steady-state free boundary semi-analytical series solutions model is developed to simulate 2-D saturated-unsaturated flow in geometrically complex stratified unconfined aquifers. The saturated-unsaturated flow is controlled by water exchange along the land surface (e.g., evapotranspiration and infiltration) and the presence of surface water bodies. The water table and capillary fringe are allowed to intersect stratigraphic interfaces. The capillary fringe zone, unsaturated zone, groundwater zone and their interactions are incorporated with a high degree of accuracy. This model is used to assess the influences of important factors on unsaturated flow behavior and the water table elevation. Second, a 3-D free boundary semi-analytical series solution model is developed to simulate groundwater-surface water interaction controlled by infiltration, seepage faces and surface water bodies along the land surface. This model can simulate the water exchange between groundwater and surface water in geometrically complex stratified phreatic (unconfined) aquifers. The a priori unknown phreatic surface will be obtained iteratively while the locations of seepage faces don’t have to be known a priori (i.e., this is a constrained free boundary problem). This accurate grid-free multi-layer model is here used to investigate the impact of the sediment layer geometry and properties on lake-aquifer interaction. Using this method, the efficiency of widely-used Dupuit-Forchheimer approximation used in regional groundwater-surface water interaction models is also assessed. Lastly, this 3-D groundwater-surface water interaction model is augmented with AEM solutions to simulate horizontal pumping wells (radial collector well) for assessing surface water impacted by pumping and determining the source of extracted well water. The resulting model will be used to assess controlling parameters on the design of a radial collector well in a river bank filtration system. This 3-D Series-AEM model, in addition, mitigates the limitations of AEM in modeling of general 3-D groundwater-surface water interaction problems.

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