Until the advent of numerical modeling in the 1960s, much of the literature on the interaction of surface water with groundwater in alluvial aquifers was concerned with analytical solutions to 1-dimensional flow of groundwater to fully penetrating streams [ Rorabaugh, 1964; Glover, 1964; Hall, 1968]. This approach is still being used today to estimate groundwater recharge from streamflow hydrographs [ Bevans, 1986], and automated computer-based techniques for using these analytical methods were recently developed [ Rutledge, 1992]. Determination of groundwater baseflow from recession analysis of streamflow hydrographs, commonly referred to as hydrograph separation, also has a long history [ Hall, 1968], but continues to receive considerable attention. For example, methods for determining the baseflow component of streamflow graphically have recently been developed by the Institute of Hydrology (United Kingdom) [1980], by Wahl and Wahl [1988], and by Rutledge [1992]. Mathematical digital filtering has also been used recently to determine the baseflow component of streamflow [ Nathon and McMahon, 1990; Chapman, 1991]. Although hydrograph analysis continues to be used, most recent studies have used other analytical techniques and numerical modeling.
Heij [1989] used analytical methods to determine travel times of water seeping from surface water into contiguous aquifers in The Netherlands. He found a linear relation between the surface-water level and the infiltration rate and an inverse relation between the surface-water level and the average time it takes water particles to flow into the streambank. Bank storage, the movement of surface water into groundwater at times of high river stage, was the focus of a study by Hunt [1990] who developed an approximate flood-routing solution for coupled groundwater and open-channel flow equations. Neglecting seepage initially, solution of a linearized kinematic wave equation was used to obtain a solution for the groundwater movement. This in turn was used to obtain a second-order solution for the flood routing. An example of using this approach indicated that changes created in the downstream hydrograph by bank storage could be as large as changes created by retaining all terms in the open-channel flow equations and routing the flood down the channel with no bank storage.
Zhang [1992] developed solutions for transient flow in an aquifer-aquitard system that considers storativity in a confined layer in response to abrupt changes in water level, uniform changes in water level, and steady rates of seepage from a river. From these equations, he determined groundwater levels for both the aquifer and the aquitard, as well as rates and total volume of seepage from the river. Transient conditions were also of interest to Rastogi [1991], who determined seasonal groundwater flow to a river reach bounded by two reservoirs, where the water-table aquifer was underlain by an impermeable bed. The objective was to determine the amount of groundwater that could be developed from this aquifer system that was receiving seepage from the upstream reservoir, losing seepage to the downstream reservoir, and receiving seepage from the river.
The depletion of streamflow by pumping groundwater from the contiguous alluvial aquifer has been a major impetus to studies of the interaction of groundwater and surface water. A recent paper on this problem [ Wallace et al., 1990] was concerned with comparing a dimensionless volume of stream depletion over a pumping cycle with maximum rate of stream depletion at a practical state of dynamic equilibrium. Dimensionless plots of equations developed by applying superposition principles to analytical solutions for steady continuous pumping were used in the study. Although the plots provided a way to quickly determine the time at which a practical state of dynamic equilibrium is reached, the study also indicated that under some conditions approximating cyclic pumping using steady continuous pumping at the equivalent cycle-average rate is inadequate. In another study involving the effects of pumping groundwater on streamflow, Spalding and Khaleel [1991] compared the results of several analytical solutions to a two-dimensional groundwater flow model. They found that simplifying assumptions needed for use of the analytical methods resulted in differences in streamflow depletion from the numerical model that ranged from 20 percent, due to neglect of partial penetration, to 45 percent, due to neglect of clogging layer resistance, after 58 days of pumping.
Use of the analytic element method [ Strack, 1989] has recently been expanded for modeling the interaction of groundwater and surface water. Mitchell-Bruker [1993] used this method to investigate the hydrologic effects of changing recharge and boundary conditions on groundwater flow in the Pere Marquette River Basin, Michigan. She found that, especially on the local scale, as recharge varies areally, the contributing area to a surface-water body changes. The boundaries of regional groundwater systems are more stable because the local variations tend to be averaged.
Statistical methods have also been used recently to study problems related to the interaction of groundwater and surface water. For example, Adamowski and Feluch [1991] proposed a new nonparametric regression model to investigate the relation between fluctuations in groundwater levels and time series of streamflow. They determined that the nonparametric method resulted in more accurate predictions than those obtained from parametric regression. In another study involving time-series analysis, Niestle and Reusing [1990] compared Autoregressive Moving Average and Fractional Gaussian Noise models to assess their reliability for the analysis of drought risk of the Nile River at Aswan, Egypt. River discharges were converted to water levels, which were then used as input to a simulation model of the interaction of the Nile River with groundwater. Although statistics on low streamflow have been used for many years in studies of the interaction of groundwater and surface water, Vogel and Kroll [1992] found that in western Massachusetts baseflow recession constants could be used as a surrogate for basin hydraulic conductivity and drainable soil porosity.