A framework for quantitative analysis of surface water‐groundwater interaction: Flow geometry in a vertical section

Abstract

A numerical model is used to examine groundwater flow in vertical section near surface water bodies, such as lakes, wetlands, ponds, rivers, canals, and drainage and irrigation channels. Solutions are generated partly by superposition to achieve computational efficiency. A large number of flow regimes are identified, with their characteristics controlled by regional water table gradients, recharge to the aquifer, water body length, aquifer anisotropy, and the hydraulic resistance of the bottom sediments. Different flow regimes are distinguished by the presence and nature of groundwater mounds or depressions near the edges of a surface water body and by corresponding stagnation points. Ranges of values for dimensionless flow parameters over which particular regimes occur are determined for six representative geometries and presented in the form of transition diagrams. Increasing anisotropy or sediment resistance and decreasing the length of a water body relative to aquifer thickness are shown to have similar effects on flow geometry, the main effect being an increasing tendency for stagnation points to form in the interior of the aquifer. Flow-through behavior becomes more prevalent with decreasing anisotropy and sediment resistance and increasing water body length. land surface also plays a role, as does negative recharge, i.e., net evapotranspirative discharge from the land surface.This paper provides a general framework for surface 1Now at Nield Consulting, Nedlands, Western Australia.Paper number 94WR00796. 0043-1397/94/94 WR-00796505.00 water-groundwater interaction, but is sti!l limited by a number of simplifying assumptions. In particular, we assume steady saturated groundwater flow, a shallow water body (relative to aquifer thickness), a long water body (such that a two-dimensional approach in vertical section is valid), and homogeneity in hydraulic conductivity. These simplification• reduce the number of site-specific components of our model, allowing some general features of surface watergroundwater interaction to emerge. Since a primary objective of this paper is to provide guidance for preliminary assessment of water bodies which have not been extensively monitored, the simplifying assumptions are probably justified. Application of the paper to a wide variety of real-word settings is facilitated by describing the geometry, aquifer properties, and flow conditions in terms of a small number of nondimensional parameters. Previous WorkOver the past two decades, increasing recognition of the need to address problems affecting lakes has led to numerous field and numerical investigations of lake-aquifer systems. Born et al. [1979] compiled hydrogeological data for numerous lakes in NorthAmerica and identified three broad classes of groundwater flow patterns near lakes: recharge (if the lake recharges the aquifer over the entire lake bed), discharge (if the aquifer discharges water to the lake over the entire lake bed), and flow-through (if water in different areas of the lake bed moves through the lake bed in...

Surface water‐groundwater interaction near shallow circular lakes: Flow geometry in three dimensions

“…Equation (4) is the three-dimensional equivalent of the water balance expression for vertical section models [Nield et al, 1994, equation (11) …”

“…The domain is assumed to extend a distance L upgradient and downgradient of the lake, and the width of the domain is chosen to be 2W. Nield et al [1994] chose L = 2B for modeling flow in a vertical section. In three dimensions the distance L could reasonably be defined relative to either B or 2a.…”

“…Focusing on scales of lake size and aquifer depth, it is natural to adopt different definitions depending on the ratio of the diameter of the lake to the thickness of the aquifer, 2a/B. For a small flow-through lake, with 2a/B << 1, a boundary at a distance of L = 2B seems far away [Nield et al, 1994]. A large flowthrough lake, however, with 2a/B >> 1, has a capture zone extending to the bottom of the aquifer, and a boundary at L = 2B is fairly close.…”

Using reactive solutes to constrain groundwater flow models at a site in northern Wisconsin

“…Stream/groundwater interactions have been studied in great detail in recent years, both from a physical flow perspective [Nield et al, 1994;Squillace, 1996] and from a water chemistry perspective [e.g., Harvey and Bencala, 1993]. Many studies have relied on qualitative estimates of shallow groundwater flow patterns [Hill, 1990a, b;Squillace, 1996].…”

“…Many studies have relied on qualitative estimates of shallow groundwater flow patterns [Hill, 1990a, b;Squillace, 1996]. More recently, groundwater flow modeling has been explicitly incorporated into stream/groundwater studies [Nield et al, 1994; Meigs and Bahr, •995; Squillace, •996; Harvey and Bencala, 1993]. The advantage of numerical flow modeling is that the conceptual model of flow is formalized such that it can be quantitatively compared to field observations and be either refuted or supported.…”