Water Resources Research

Implications of anthropogenic river stage fluctuations on mass transport in a valley fill aquifer

Authors


Abstract

[1] In humid regions a strong coupling between surface water features and groundwater systems may exist. In these environments the exchange of water and solute depends primarily on the hydraulic gradient between the reservoirs. We hypothesize that daily changes in river stage associated with anthropogenic water releases (such as those from a hydroelectric dam) cause anomalous mixing in the near-stream environment by creating large hydraulic head gradients between the stream and adjacent aquifer. We present field observations of hydraulic gradient reversals in a shallow aquifer. Important physical processes observed in the field are explicitly reproduced in a physically based two-dimensional numerical model of groundwater flow coupled to a simplistic surface water boundary condition. Mass transport simulations of a conservative solute introduced into the surface water are performed and examined relative to a stream condition without stage fluctuations. Simulations of 20 d for both fluctuating river stage and fixed high river stage show that more mass is introduced into the aquifer from the stream in the oscillating case even though the net water flux is zero. Enhanced transport by mechanical dispersion leads to mass being driven away from the hydraulic zone of influence of the river. The modification of local hydraulic gradients is likely to be important for understanding dissolved mass transport in near-stream aquifer environments and can influence exchange zone processes under conditions of high-frequency stream stage changes.

1. Introduction

[2] Time-dependent variations in surface water stage in both fresh and salt water environments are acknowledged to strongly influence local groundwater flow [Cooper, 1959]. Variations in surface water stage can arise from many natural and anthropogenic sources including: precipitation and flood events, tidal oscillation, wave induced displacement, dam releases, and associated reservoir drawdown. These stream stage fluctuations are known to influence hydraulic gradients in the region surrounding the stream. In fact, time varying surface water stage is frequently used to estimate aquifer hydraulic diffusivity [Ferris, 1952; Rowe, 1960; Pinder et al., 1969; Reynolds, 1987; Swamee and Singh, 2003].

[3] More specifically, shallow groundwater and surface water in humid glaciated regions are often strongly linked because of the relative position of the water table to the land surface [Winter et al., 1998]. In these settings, changes in groundwater head or surface water head are transmitted to the adjacent reservoir. For example, river stage increases during spring runoff events have been observed to cause a corresponding increase in groundwater elevations and frequently results in reversal of the stream from gaining to losing conditions [Squillace, 1996]. This process, resulting in shallow localized water flow into the stream banks, is often termed “bank storage” [Todd, 1955] and has been acknowledged to play a role in reducing flood peaks in addition to serving as a storage reservoir for contaminants. The maximum distance that bank storage water migrates is a function of river bed and river bank hydraulic conductivity as well as the hydraulic gradient between the surface water body and aquifer.

[4] Short-term fluctuations of surface water bodies are an important control on groundwater flow in coastal environments [Glover, 1959; Reilly and Goodman, 1985] and possibly in riverine environments too. Tidal fluctuations of ocean and estuarine waters have been observed to modify coastal discharge of groundwater, especially in environments where the aquifer material is thin compared to the magnitude of tidal fluctuation [Ataie-Ashtianti et al., 1999]. Short-term fluctuations such as wave-induced displacement, hyporheic flux, and tidal oscillation have been observed to induce nutrient release from sediment pore fluids during low-flow summer conditions in estuarine environments [Linderfelt and Turner, 2001]. In a study investigating the interaction between shallow groundwater, saline surface water, and contaminant discharge at an estuarine boundary, Westbrook et al. [2005] studied the influence of tidal oscillation on mixing at the interface. They observed groundwater flow reversals induced by a tidally influenced river which led to groundwater seepage into river sediments and freshening of interface water on outgoing tidal cycles. Yim and Mohsen [1992] developed a 1-D numerical model to simulate mass transport from a contaminant plume to a tidal estuary. They compare models with and without tidal fluctuation and find that although concentrations near the interface are less in the simulation with tidal fluctuations, the velocity gradients are much greater, and allow more mass exchange from the aquifer to the estuary.

[5] In managed surface water settings (e.g., dammed rivers typical of the Northeast US) frequent fluctuations of surface water bodies have been observed to modify adjacent aquifer hydraulic heads on a timescale proportional to the fluctuations in head of the surface water body. The periodicity of the head fluctuations in managed surface water bodies is dependent on water use, but is of a much shorter timescale (and often more regular) than natural fluctuations in stream stage. In some cases, reversals of a stream from gaining to losing have been observed on a daily basis [Friesz, 1996] because of regular releases of water from upstream reservoirs. It is unknown what effects these reversals have on important groundwater surface water processes, such as mixing in the hyporheic zone [Ryan et al., 2004; Arntzen et al., 2006] and nutrient cycling [Kim et al., 1992].

[6] Similarly, changes to the geochemistry of either reservoir can also be transmitted across the boundary at rates proportional to the water flux. In a detailed study of bank storage in Iowa, Squillace [1996] investigated the geochemical response of bank storage water to a spring-melt runoff event. Gradient reversals between the Cedar River and the adjacent alluvial aquifer were observed, creating losing river conditions. After the flood subsided, gaining river conditions returned. A modeling study showed a factor of 5 increase of groundwater flux to the river during the first three weeks after the runoff event. Elevated levels of a groundwater contaminant, atrazine, were observed in the bank storage water.

[7] In this paper, we focus on small-amplitude daily oscillation of stream stage through explicit numerical modeling of field conditions. Chemical flux into and out of the groundwater system is assumed to be a function of the magnitude of stream stage fluctuation and may actually be magnified because of dispersive-driven transport processes. A large body of literature exists concerning the impacts of enhanced dispersive mixing in transient flow fields [Goode and Konikow, 1990; Bellin et al., 1996; Dagan et al., 1996; Naff, 1998; Cirpka and Attinger, 2003; Dentz and Carrera, 2003, 2005]. Transient flow fields are acknowledged to locally increase dispersive transport by creating velocity variations that drive dispersion. Kim et al. [2000] studied an oxygen isotope plume in an aquifer, where significant fluctuations in the velocity field are caused by temporal changes in recharge rate and lake levels. In this system, heterogeneity, fluctuations in recharge rate, and distance from the transient boundary stresses had a significant influence on the vertical transverse dispersion of the plume, while dispersion caused by fluctuations in lake levels alone were found to have a relatively small effect on enhanced transport.

[8] We begin with reviewing the impact of daily (i.e., short-term) stream stage fluctuations on groundwater flow patterns and investigate the magnitude of short-term fluctuations on mass transport in a hypothetical contaminated surface water to clean groundwater scenario. We find that under conditions of oscillating river stage, significant mass may be introduced to the aquifer by dispersive processes, even though no net water flux to the aquifer occurs over time.

2. Groundwater Response to Daily Stream Stage Fluctuations in Charlemont, Massachusetts

[9] Friesz [1996] reported on the hydrology of stratified drift and streamflow in the Deerfield River Basin of Western Massachusetts, and made measurements of groundwater head during ∼0.5 m fluctuations in river stage resulting from water releases from an upstream dam. Aquifer materials in this region consisted of medium-grained sands to boulders in the alluvium and fine silt to medium sand of glacial origin in the deeper, partially confined portion of the aquifer. The Deerfield River here is approximately 40 m wide. On the north side, normal to the river there are two terraces, the lower one being the floodplain which is 1 m above the riverbed, and the second 50 m to the northeast, which is 5 m above the first terrace. Continuing on the same perpendicular transect toward the northeast, the unconsolidated sediments extend another 500 m to the surrounding bedrock hills. The wells from the Friesz [1996] report are located on the lower terrace. The aquifer is geometrically constrained by the surrounding bedrock valley. The depth to bedrock at the study site is 33 m, determined by seismic refraction surveys conducted by the authors in 2006. Piezometers were installed in two clusters on a site adjacent to the Deerfield River 5.5 km downstream from the Fife Brook hydroelectric dam. Piezometers in each cluster consisted of 5 cm diameter PVC casing with a 1.5 m screened interval at the sampling depth (midpoint of screen). The ‘riverbank’ cluster was located 3 m from the bank, with 3 piezometers 2.4, 8.5 and 17.1 m deep. The ‘far’ well cluster was located 38.4 m from the Riverbank cluster (41.4 m from the river bank), with 3 wells 3.4, 10.3, and 22.3 m deep. Water levels were recorded in the piezometers every 5 min for a 72 h period during which the released flow from Fife Brook Dam fluctuated between 3.5 m3 d−1 and 27.5 m3 d−1. Large releases from the dam lasted 10 and 12 h while smaller releases lasted 15 and 13.5 h. The river stage fluctuated a maximum of 0.45 m during the larger of the releases. Unfortunately, the river stage at the location of the piezometers was not measured, but discharge was recorded at USGS gauging station 01168500 located 4.6 km downstream in Charlemont, Massachusetts.

[10] The response of the aquifer system to stream stage fluctuations measured in three riverbank piezometers is presented in Figure 1. Also presented on Figure 1 is the discharge in the stream as measured at the gauging station downstream from the piezometers. The time series depicted begins with a recession in streamflow and then an increase at 186.5 Julian d. Since the stream gauge is located 4.6 km downstream, approximately a 1 h lag exists between the response of the aquifer hydraulic head relative to the downstream measured streamflow. The heads in the riverbank cluster piezometers all rise in response to an increase in stream discharge (stage). The head in the shallow piezometer increases gradually while heads in the medium and deep piezometers respond by first rising sharply then dropping and then rising gradually again. The initial response of the medium and deep piezometers is interpreted to record poroelastic loading of the aquifer by an increase in stress on the aquifer (because of the mass of increased streamflow). The deep piezometers follow a similar pattern as the shallow piezometer by rising until about 186.9 Julian d when a recession in streamflow occurs. The change in hydraulic head is much slower during recession of streamflow, a characteristic previously shown to be indicative of bank storage. The cycle of hydraulic head rise and fall in relation to streamflow repeats itself again showing a similar behavior.

Figure 1.

Measured response of aquifer system to fluctuations in stream stage. Data from piezometers are relative to mean above sea level and recorded at 5 min intervals. Symbols are used to distinguish between different piezometers and streamflow data. The timing of stage changes and stream discharge data lag each other because the gauge is 4 km downstream from piezometers. Data presented by Friesz [1996].

[11] Hydraulic heads in the far cluster (not shown) have similar trends compared with the riverbank cluster, but importantly they do not indicate gradient reversals as in the riverbank suggesting a fairly narrow zone of hydraulic influence of the river. The change in head level corresponding with the river stage attenuates with depth for both the riverbank cluster and the far cluster. The pulse dissipates horizontally where changes in head (amplitude attenuation) in the far cluster wells are less than in the riverbank piezometers. Additionally, the shape of the water table wells response is quite different from that in the deeper wells because the water table responds to a free surface (atmospheric pressure) and the deeper wells are interpreted to be weakly confined to confined.

[12] The data presented in Figure 1 demonstrate three important aspects controlling processes in the aquifer-river system as a result of changes in stream stage: (1) a strong connection between the river and shallow flow system in the aquifer exists; (2) vertical gradients in the river bank piezometer change direction from upward at low river stage to downward at higher river stage, switching from a gaining stream to a losing stream as the water is released from the dam; and (3) these processes are repeated on short-term (daily) basis. These three components of the system are explicitly represented in a physically based numerical model of groundwater flow to delineate the impacts of stream stage changes on mass transport processes in a shallow aquifer.

3. Modeling Approach

[13] A hydraulic model is built to simulate the oscillatory nature of hydraulic head in an aquifer caused by daily river stage fluctuation. The diurnal stage changes caused by upstream dam releases raise the stage of the stream by 0.5 m. Groundwater flow models are developed to simulate hydraulic head, while reproducing the observed vertical gradient reversals (Figure 1). Using the modeled transient hydraulic head distribution and corresponding velocity field, conservative advective-dispersive transport simulations are performed using MT3D/MS [Zheng and Wang, 1998]. A comparison of modeled fixed high stage and oscillating stages is performed and analyzed to investigate the role of time-dependent river stage changes on dilution/concentration of solutes in near-stream environments of an aquifer as characterized by mass exchange between the two reservoirs.

3.1. Hydraulic Modeling of Stream Stage Fluctuations

3.1.1. Base Model Geometry and Properties

[14] A transient, two-dimensional groundwater flow model is built using the finite difference code U.S. Geological Survey Modular three-dimensional finite-difference groundwater flow model (MODFLOW) [McDonald and Harbaugh, 1988]. The model domain, 500 m wide, 33 m deep consists of 9 layers, representing glacial and alluvial deposits in a symmetric bedrock river valley. The bottom and right side of the model are no flow boundaries, the left side, a symmetry boundary, is also a no flow boundary, while the top is modeled as a free (water table) surface. Columns are spaced 1 m apart on the left side of the model and coarsen to 50 m on the right. Grid spacing is refined near the river at the top left corner of the model (Figure 2). A river boundary condition is modeled using the MODFLOW river package (RIV5) and is assigned to the 20 cells adjacent to the symmetry boundary in layer 1, for a total width of 20 m. The river bottom elevation is fixed at 30 m with a 0.2 m thick river bed. There are no other hydraulic sources or sinks present in the base model.

Figure 2.

Grid geometry and hydrostratigraphic units for hydraulic flow model of stream stage reversals. Location of river boundary cells is indicated with crosshatched lines. Hydraulic head observation points are marked with solid black dots. Layer shading (from white to dark gray) indicates specific hydrostratigraphic units. See text and Table 1 for more details on hydraulic properties.

[15] Three hydrostratigraphic units are present in this model. These units explicitly reproduce observed hydrostratigraphy at the Charlemont field site. Unit 1, consist of layers 1–5 and are designated as unconfined units. The unconfined unit represents the upper 5 m (each layer is 1 m thick) of stratigraphy at the Charlemont site. Unit 2 corresponds to layers 6 and 8, and unit 3 consist of layers 7 and 9. Both Units 2 and 3 are modeled in MODFLOW as confined units and represent the lower 28 m of stratigraphy. The physical and hydraulic properties of these layers are listed in Table 1. These values represent model calibration for the two large stage releases presented in Figure 1 and are referred to as our base case models. Hydraulic observation points (Figure 1) are positioned at elevations of 31 m, 26 m, and 12 m above the model datum. These observation points are located 3 m from the edge of the river and are chosen to match the positions of the screened intervals in the field data discussed previously. A value of 31.25 m is used for the initial hydraulic heads for the transient model. In the base modeling case, river stages are varied instantaneously at 0.5 d increments from 31.5 to 31.0 m with 0.5 d stress periods divided into 10 time steps of 1.2 h each repeated for a 20 d period. All of the oscillating simulations begin with a high head (i.e., 31.5 m).

Table 1. Properties of Hydrostratigraphic Units in the Base Hydraulic Modela
UnitLayer (Thick) (m)K (m s−1)Ss (m−1)D (m2 s−1)Layer Anisotropy (−)MODFLOW Layer Type (−)
  • a

    Value reported for unconfined aquifer is specific yield and has unitless dimensions.

11–5 (5)1.4 × 10−32.1 × 10−10.221Unconfined
26 (3), 8 (13)8.8 × 10−56.0 × 10−51.51/10Confined
37 (2), 9 (10)3.5 × 10−46.0 × 10−55.81/10Confined

3.1.2. Base Model Results

[16] Model results of hydraulic head at 3 observation locations for the simulation parameters discussed above are presented in Figure 3a. As in the field data (Figure 3b) the low hydraulic head in the shallow observation location corresponds to low stream stages and high hydraulic head corresponds to high stream stages. The shallow aquifer heads fluctuate above and below the medium and deep observation locations heads, inducing the stream to switch from a gaining stream at low stage to a losing stream at high stage on a daily basis. As anticipated, the hydraulic head fluctuations in the model mirror that of the stream stage with an amplitude reduction being a strong function of distance from the stream. The head amplitude (difference between high and low head during a stream stage reversal) in the deep well is the smallest of the three observation points because of its relative distance (depth) from the fluctuating stream. Theory predicts that a phase shift should also be apparent, but for the properties of the aquifer being simulated here and the time step chosen a shift is not observed. Simulations with refined time steps (10 min) showed small phase shifts (∼20 min) between the shallow and deep piezometers with the amplitude difference between the two simulations negligible.

Figure 3.

(a) Simulated and (b) observed head response to stage fluctuations in shallow, medium, and deep observation wells. Important hydraulic phenomena captured in the simulations are the reversals in the vertical gradients of hydraulic heads. In Figure 3a we indicate times where contours of hydraulic head in Figure 4 are plotted.

[17] The general trends in the observed data (Figure 3b) are captured in the modeled heads, namely the head gradient reversals. The field data show more complex temporal patterns, such as poroelastic loading of the aquifer, that are not captured with this first-order model of hydraulic head fluctuations. Poroelastic loading effects are observed only in deeper parts of aquifer (the semiconfined units) as the fluid is compressed by the increase in total stress on the aquifer skeleton. In general the head change induced by loading is on the order of 10s of centimeters and lasts for a short time before being masked by the diffusive pressure wave associated with the stream stage change. The fact that this transient is short and that it is swamped by the diffusive wave leads us to believe that its effect on the overall hydraulics of the system is negligible for the problem explored in this paper.

[18] The response of porous media to modifications in hydraulic boundary conditions is known to cause modifications in fluid pressure that can persist for long spatial and temporal scales [Neuzil, 2003]. During fluctuations in stream stage the response of the aquifer is observed to lag behind the changing stream stage conditions (Figure 4). In the base case model, contours of hydraulic head indicate that the hydraulic head field is vertically and horizontally heterogeneous, with zones of localized hydraulic head anomalies. These anomalies buffer the stream-aquifer interface and represent the outer reaches of the aquifer affected by the stream stage head. It is assumed that these zones will grow in size and duration proportional to change in stream stage head and aquifer and streambed parameters.

Figure 4.

Contours of hydraulic head during (a) a high stage (31.5 m) and (b, c) at two times (see Figure 3 for exact times) following a switch to a low (31.0 m) stream stage. Time lag in fluid flow creates vertically (Figure 4b) and horizontally (Figure 4c) distinct zones of hydraulic head adjacent to the stream. Theses zones border the stream and represent transient features associated with stream stage reversals. Contour line intervals are 0.01 m. White lines differentiate stratigraphy of the site.

3.1.3. Hydraulic Model Sensitivity Analysis

[19] The efficiency with which stream stage changes influence hydraulic gradients (and hence groundwater velocity distribution) in an aquifer depends on (1) degree of connection of the stream to the aquifer, (2) magnitude and frequency of the stream stage fluctuation, and (3) hydraulic properties of the aquifer itself [Hsieh et al., 1987; Wang and Davis, 1996]. We now examine the sensitivity of modeled heads to items (1) and (3) by varying stream bed conductance and aquifer diffusivity, respectively.

[20] Stream bed conductance is a lumped model parameter in the MODFLOW river package that induces head loss between the stream and the aquifer proportional to stream bed width and bed thickness and controls the degree of connection of stream to aquifer. The river bed conductances are modified by 5 orders of magnitude and the measured hydraulic response of the aquifer system (diurnal head amplitudes) is plotted against river bed conductance for the shallow and deep observation points (Figure 5a). Diurnal head amplitude refers to the difference between maximum and minimum head values for each screened interval within the observation well in 1 d. Larger magnitudes of river bed conductance increase the diurnal head amplitude for both observation points. The shallow aquifer head amplitudes are more responsive than deep head amplitudes, and with increased river bed conductance the difference between shallow and deep amplitudes increases. The base model cases are the middle set of points in Figure 5a. At low values of conductance, the aquifer is essentially disconnected to the stream (i.e., no aquifer response). As the river bed conductance approaches large magnitudes, a change in river stage is transferred almost instantaneously to the aquifer (mimicking a constant head boundary). At these large values, the response of the aquifer is solely controlled by aquifer diffusivity.

Figure 5.

Model-produced sensitivities of head fluctuations in shallow (triangles) and deep (squares) observation locations to (a) changes in river bed conductance and (b) changes in unit 1 diffusivity. Base case simulations are the middle data points in Figures 5a and 5b.

[21] Aquifer diffusivity, the ratio of saturated hydraulic conductivity to the specific storage (or specific yield for unconfined aquifers), controls the transient hydraulic response of the aquifer. Knowledge of aquifer diffusivity and the length scale over which hydraulic head changes allows for the calculation of the time it takes for a head change at an observation point. Hydraulic diffusivity for hydrostratigraphic unit 1 is varied by five orders of magnitude to investigate model sensitivity to this parameter. Diurnal head amplitudes for shallow and deep observation points are plotted as a function of unit 1 diffusivity. Increases in diffusivity correspond to bounded increases in diurnal head amplitude in both shallow and deep observation points. The rate of increase in the shallow observation point is greater than that of the deep observation points. As unit 1 diffusivity is increased the head amplitude reaches a maximum, which is controlled by the base case river bed conductance parameter. Like river bed conductance, low aquifer diffusivities will hydraulically disconnect the aquifer from the stream thus reducing the influence of these high-frequency stream stage changes on hydraulic head. We now investigate the influence of stream stage fluctuations on mass transport mechanisms in the above-described aquifer.

3.2. Mass Transport Modeling of Stream Stage Fluctuations

[22] Using the mass transport code MT3D-MS and TVD (total variation diminishing) solver coupled with MODFLOW, a conservative solute is introduced to the aquifer from the stream using a point source and it's fate is explored. The TVD solver is a higher-order Eulerian numerical technique that is known to reduce the effects of numerical dispersion compared to other solvers. The point source is assigned to the river cells to simulate effects of surface water contamination on the underlying groundwater system. The point source is not a boundary condition in the formal sense and uses the stream-aquifer flux term, qs (m d−1), to calculate the mass flux entering or leaving the system, equation imageCs, where n (−) is the aquifer porosity and Cs is a fixed concentration of the solute in the stream. This is different than a specified head/specified concentration (SHSC) boundary condition which is discussed later in the paper. The fixed solute concentration (Cs) in the stream is set to 100 mg/L. The initial concentration in the aquifer is 0 mg/L and all boundaries in the model are assigned to have no mass flux. In each set of transport simulations, we combine the transport model with either the oscillating stage models (discussed above) or a hydraulic model with a fixed high stage to test mass transport behavior under different stream management conditions. No molecular diffusion is simulated in any of these models because of the short timescale of the simulations and presence of high groundwater velocities (and hence high mechanical dispersion) near the stream. Preliminary simulations with nonzero molecular diffusion coefficients showed no significant difference in simulations. Thus, the two modeled mass transport mechanisms are advection and mechanical dispersion.

[23] Simulations of mass transport from stream to aquifer are performed at longitudinal dispersivity values ranging from 0 m (advection only) to 10 m and run for a period of 20 d. Dispersivity, a term whose magnitude controls the degree of hydrodynamic dilution as a fluid flows through a porous media, is well known to be a strong function of spatial scale [Zheng and Bennett, 1995] and these values bound the range likely to be representative of most field conditions. A plot of the mass introduced into the aquifer as a function of time for different values of dispersivity and stage conditions is presented in Figure 6. Results from only one simulation of fixed high stage conditions is presented as the total mass introduced into the aquifer under fixed stage conditions is not sensitive to changes in dispersivity. Despite this, the solute distribution within the aquifer is sensitive to dispersivity even though the total mass input into the system is identical. This phenomena is further observed by comparing the mass introduced into the aquifer during the first 0.5 d of simulation time (when both conditions have a fixed stage) for oscillating and high stage cases (Figure 6a). All lines are coincident until the first stage change (at 0.5 d) when oscillating and high stage simulations diverge from one another. Under this condition, flux into the aquifer through the point source is only dependent on qs and thus dispersive flux is zero. As the simulations progress further in time (Figure 6b) the discrepancy between the mass introduced into the aquifer becomes greater. The 10 m dispersivity oscillating case introduces the most mass into the aquifer after 20 d or 20 stream stage oscillation events. The oscillating stage condition at 1 m and 10 m dispersivity actually introduce more mass into the aquifer than fixed high stage case. This is nonintuitive as the 20 d total water flux into the aquifer from oscillating cases is zero while fixed high stage simulations introduce significant (nonzero) water to the aquifer.

Figure 6.

Mass introduced into the aquifer through a fixed high stream stage (solid line) and oscillating stream stage (various dashed lines) as a function of aquifer dispersivity (value indicated in parentheses). Data is plotted versus (a, b) time and (c) the sum of the flow in stream per unit length of stream. All cases depict a rapid increase in mass transfer and a gradual reduction as concentration gradients become smaller. When plotted against the volume of water in the stream (Figure 6c), 1 and 10 m dispersivity oscillating simulations show more mass input into aquifer during the 20 d simulation period. High stream stage simulations are not sensitive to changes in aquifer dispersivity.

[24] The fixed high stage case has a high head for 20 d of simulation time and oscillating cases have a high stage only half of the time (10 d). Instead of plotting mass introduced into the aquifer as function of time we plot the mass versus cumulative amount of water moving through the stream during the 20 d simulation period by calculating the volume (per unit length of stream) of water in the stream for both the oscillating and high fixed stage. This indicates (Figure 6c) that for an equivalent amount of water in the stream, the oscillating case at 10 m dispersivity introduces almost twice the amount of mass in the aquifer than the fixed high stage case. Additionally, the 1 m dispersivity case introduces more mass into aquifer than a high fixed stage.

3.2.1. Solute Plume Distributions

[25] The distribution of solute mass within the aquifer at 20 d expressed as concentration for the 10 m dispersivity oscillating and fixed high stage case are presented in Figure 7. Both simulations show an extended plume that has moved approximately 50 m away from stream boundary with concentrations greatest closer to the stream. As shown above, the solute mass input into the aquifer for the oscillating case is much greater than the fixed high stage case and concentrations differ markedly near and under the stream. Concentrations are more evenly distributed beneath the stream under oscillating conditions most likely because of the frequent groundwater velocity reversals in this region. The vertical extent of the plume in the oscillating case is also greater than the fixed high stage case, an observation not easy to make using a one-dimensional model. Investigations of simulations with homogeneous stratigraphy (compared to the layered model here) show even a larger discrepancy between the vertical plume geometries. The stratigraphy at this site is clearly causing a preferential horizontal plume geometry. In the oscillating simulations 75% of the mass is in the unconfined portion of the aquifer system with 25% in the semiconfined portions of the aquifer. During early simulation time, 10 d or less, most of the mass is in the unconfined portion of the model. More mass will be transported into the deeper confined portion of the model with longer simulation times. The oscillating simulations appear to drive mass into the confined part of the model quicker and more efficiently then the fixed high stage simulations. Please refer to auxiliary material for time series plots of solute concentration maps and solute distributions for models with homogeneous properties. We now examine the mechanisms driving excess mass transport in the oscillating cases.

Figure 7.

Filled contour plots of concentration of solute in the aquifer after 20 d of simulation time for the 10 m dispersivity oscillating and fixed high stage case. (top) The distribution of mass is mixed extensively under the stream (located from 0–15 m) compared to that of (bottom) fixed high stage case. The mass input into the aquifer causes higher concentrations throughout the aquifer for the oscillating case compared to the fixed high stage. The plumes have similar longitudinal dimensions away from the stream but differ markedly in the near-stream region.

3.2.2. Analysis of Mass Transport Modeling Results

[26] When the stream stage in the oscillating case is lowered, water in the near-stream environment begins to flow back into the stream, carrying with it a portion of the mass introduced during the previous high stage. Not all mass introduced during the high stage (which is identical for all three dispersivity cases) flows back into the stream during the low stage because of dispersive transport. Over the time period of simulations presented here the advective case (0 m dispersivity) is most efficient in removing the previously introduced solute mass (Figure 8). Simulations with increasingly larger dispersivities (1 m and 10 m) have more mass retained in the aquifer system. As the number of oscillations of the stream stage increase the simulations show more total mass stored in the aquifer as the storage effects are additive. The largest discrepancy between mass input into the aquifer and mass removed is at early times when (1) the hydraulic gradients and (2) the concentration gradients between the stream and aquifer are largest. The difference in mass-in versus mass-out decreases over time and results in late time flattening of the curves in presented Figure 6b. During the transition from high stage to low stage, mass transported into the aquifer is driven back into the stream at a rate proportional to the water flux. During early times, all oscillating simulations input more mass than is removed. This is due to the hydraulic head gradients reaching equilibrium with the oscillating stream stage condition. The late time flattening of the curve in Figure 6b of the advection-only case is due to the reduced hydraulic head gradients in the hydraulic zone of influence. As time progresses the advection-only case (as evidenced by the steep positive slope at early time in Figure 8) becomes more efficient in removing mass until it approaches a steady condition where mass introduced during a high stage is removed during a low stage. The 1 and 10 m dispersivity simulations show the same overall trend but their trajectories are quite different, and thus, the time it takes for these simulations to reach a steady state is longer for higher dispersivity. This difference is attributable to mechanical dispersion within the aquifer itself.

Figure 8.

The amount of mass removed during stage reversals as a function of dispersivity values (indicated in parentheses). In early times, mass removal is low during the 0.5 d low stages but quickly increases as hydraulic gradients stabilize within the aquifer. The advection-only case (0 m dispersivity) is the most efficient at removing mass from the aquifer.

4. Discussion of Mass Transport Results

[27] Our favored mass retention mechanism involves dissolved mass being transported both vertically and horizontally into the aquifer away from the river boundary, thereby reducing the available mass adjacent to the river to be removed from the system (Figures 9a and 9b). Simulations with high dispersivity values display concentration profiles in Unit 1 that show the longest transport distances after one stage reversal (Figure 10a) and 10 stage reversals (Figure 10b). Simulations with no dispersive transport mechanisms (dispersivity of 0 m) show the most compact and localized concentration profiles and therefore have more mass located near the river boundary. However, over time this mass is transported further from the river boundary and is essentially disconnected from the short-term influence of the river (Figures 9a and 9b). The end result is that more mass is input to the aquifer as a function of transport parameters, namely dispersion, and diffusion (although not explicitly simulated here). In oscillating cases, (Figures 9a and 9b) the river imparts a zone of influence in the aquifer, whose size is dependent on the head gradient and the aquifer diffusivity. When mass is introduced into the river, it is transported by advection into this zone, as the stage drops back down, mass is transported back into the river from the aquifer, however some mass remains. This is due to the velocity gradients causing mass to be driven outside the two-dimensional rivers zone of influence. As dispersion is decreased, the oscillating heads are more efficient in removing mass from the aquifer, which means less mass leaves the zone of influence and therefore less total mass is introduced into the aquifer. Dispersion is a factor in transport in the oscillating case because flow velocities remain high compared to a fixed high stage (Figure 9c), where solute transported by dispersion is controlled by the decreasing head gradients.

Figure 9.

Schematic showing solute front at (a) high and (b) low stage of oscillating case and (c) constant high stage of fixed stage case. In Figure 9a, river stage is high, and the two dashed curves represent the contributions of advection (hydraulic zone of influence) and the combined effects of advection and dispersion on solute transport into the aquifer. Figure 9b shows a low stage where groundwater flow directions are reversed. Inside the hydraulic zone of influence, solute is transported back to the stream because of advection, but beyond the zone of influence, velocity gradients force solutes deeper into the aquifer. Figure 9c shows fixed high stage with the plume of solute transport as a function of time represented by dashed lines. Notice lines get closer together as time increases.

Figure 10.

Horizontal concentration profiles in unconfined portion of aquifer (unit 1) for first high and low stages (first reversal) and concentrations after 10 reversals. Dispersivity values are indicated in legend. During the first stage reversal, hydraulic and concentration gradients are high and cause significant amount of mass to enter the aquifer. Simulations with high dispersivity values are efficient in transporting this mass beyond the hydraulic influence of the stream. At later times, solute mass that has moved beyond the hydraulic influence of the stream is not influenced by the stream stage.

[28] While the above mechanisms explain the dependence of mass input into the aquifer on dispersivity, it does not specifically address the differences in oscillation versus fixed stage river conditions. As shown in Figure 4, gradients in hydraulic head during stream stage changes in the region surrounding the stream are dynamic and therefore must influence mass transport processes during these events. High stage oscillation events deliver a relatively constant amount of mass over time (for the simulation parameters in this study ∼0.7 kg). Compared to the fixed high stage that inputs a maximum of ∼0.4 kg and decreases following an exponential trend to ∼0.05 kg over 20 d (Figure 11). We attribute these differences to temporal evolution of hydraulic head gradients in the oscillating versus fixed stage cases. Figure 12 illustrates the nature of horizontal hydraulic head gradients between the stream and aquifer for both an oscillating and fixed stage conditions. The local hydraulic gradients near the stream are enhanced following a stream stage reversal resulting in a large mass flux term (qsCs) and the addition of more mass to the aquifer. During the first 0.5 d of simulation time both cases have the same hydraulic head and the gradients are identical. As the stage reverses the horizontal gradients oscillate with the changing stage and the fixed high stage raises the overall water table, reducing hydraulic gradients in the near-stream environment. No net change in water table position is observed for oscillating cases, consistent with the fact that no net water flux enters the aquifer under the oscillating case compared to significant water flux in the fixed cases. This mechanism of hydraulic gradient modification and the influence of transport properties (dispersion) on mass retention in the aquifer, explains the pumping mechanism responsible for enhanced transport. This brings us to the nonintuitive conclusion that more net mass is input into the aquifer under a condition of zero net water flux compared to conditions of significant water flux in the fixed high stage case. We now briefly examine the dependence of mass input to aquifer on aquifer porosity and to the magnitude of stream stage oscillation.

Figure 11.

A comparison of the mass input into the aquifer for a high fixed stage and oscillating stage. Mass introduced into the aquifer during high stages (for all time) of the oscillating case is relatively constant, whereas the mass input over time for a fixed high stage decreases significantly. This decrease is directly related to the fact that net water flux is directed into the aquifer.

Figure 12.

Horizontal head profiles for the (a) first high/low (first reversal) and fixed stage and (b) stage reversal/fixed stage at 9.5 and 10 d. During the first stage reversal (Figure 12a), hydraulic gradients in the high fixed and oscillating stage simulations are similar. At later times (Figure 12b), hydraulic head profiles in the oscillating case are similar to early time, whereas the fixed high stage are less steep, broader, and explain the differing mass flux into the aquifer presented in Figure 11.

4.1. Influence of Magnitude of Stream Stage Oscillation on Mass Flux

[29] To evaluate the influence of large stream stage oscillations on mass flux into the aquifer we performed a number of simulations holding longitudinal dispersion constant and increasing river stage levels (Figure 13). In all simulations, mass flux increases into the aquifer with increased stage heads. As discussed above, total mass flux for fixed stage simulations are not sensitive to changes in dispersivity, therefore, fixed stage results are plotted against the oscillating stage results for 10, 1, and 0 m longitudinal dispersion (Figure 13). The oscillating case delivers more mass into the aquifer than the fixed case at lower stage amplitudes for all values of dispersion. However, with increasing stage heads the fixed case will eventually transport more mass into the aquifer than the oscillating case. This is because the water table in the aquifer takes longer to equilibrate to the high stage, allowing hydraulic gradients to stay large over a greater period of time and inducing more mass flux. The difference between the maximum head and initial head (termed here max initial head) where this occurs is controlled by the dispersivity of the oscillating stage cases (Figure 13).

Figure 13.

Mass introduced into aquifer from stream as a function of magnitude of high stage and magnitude of oscillation from initial head values (maximum stage height, initial aquifer head). Simulations with highest dispersivity values introduce most mass into aquifer until hydraulic gradients become large enough such that fixed high stage introduces more mass. This transition is a function of aquifer dispersivity.

4.2. Sensitivity of Model Results to Numerical Boundary Conditions

[30] To evaluate the influence of different numerical representations of the surface water/groundwater interface on mass transport, we created parallel models. One model uses the river package and point source (RPPS) and the other uses specified head and specified concentration boundaries (SHSC). The boundary values of both models were the same, heads of 31.5 m, and specified concentrations of 100 mg/L for the high stage comparisons. These cases represent two end members; one with zero dispersive flux into the aquifer from the surface water (RPPS) and a case with maximum dispersive flux (SHSC).

[31] During high stage base RPPS simulations, the amount of mass transmitted into the aquifer after 20 d is unchanged for dispersion values of 10 m, 1 m, and with dispersion off (0 m). However, with SHSC, the amount of mass in the aquifer after 20 d increases with greater dispersion values. The total mass into the aquifer after 20 d for zero dispersion is identical for both boundary conditions, indicating that dispersive flux from stream to aquifer is significant for the SHSC case. The reason for a difference between these two simulations is the specified concentration boundary condition. The RPPS river bed conductance term regulates how much water will pass from the river into the aquifer; acting as a water flux control. With RPPS, solute flux from the river to aquifer is solely water flux-dependent whereas, the SHSC is dependent on both the hydraulic gradient and concentration gradient. Therefore, with greater dispersion, the spatial distribution of solute plume is larger because of the specified boundary concentration of 100 mg/L and the initial condition of 0 mg/L creating larger concentration gradients and allowing more mass to enter the aquifer. Oscillating simulations (results not shown) with the SHSC show similar trends to those presented with RPPS but the SHSC simulations all show higher mass input into the aquifer, because of the larger dispersive flux from surface water feature to aquifer. To this end, a case with zero dispersive flux into the aquifer from the surface water (RPPS) and a case with maximum of dispersive flux (SHSC) both show the overall trends of more net mass input into the aquifer despite having significantly less net water flux for simulations lasting 20 stream stage cycles.

4.3. Sensitivity of Results to Aquifer Porosity

[32] Aquifer porosity is an additional transport parameter that can influence the movement and concentrations of solute. The discussion of porosity sensitivity in this section is limited to its transport effects and not on hydraulic effects (i.e., specific yield). Porosity influences the amount of solute mass stored in a porous media at a given concentration. Porosity has the separate influence (in the formulation presented here) of modifying the average linear velocity used in transport simulations. All of the simulations presented up until this point maintain a fixed porosity in the unconfined layers of 28%. Reducing the transport porosity in the presented models would have the effect of increasing the average linear velocity (and thus advective transport) and reducing the volume of available storage space for solute which could potentially influence concentration gradients.

[33] We performed a sensitivity analysis by varying the porosity for the unconfined aquifer to values of 0.28, 0.21, 0.10, and 0.05 and run fixed stage and oscillating stage transport simulations at a dispersivity of 10 m. For fixed stage the total mass input into the aquifer is not sensitive to changes in total porosity (with values of 2.7 kg for all simulations) but the mass distribution within the aquifer is sensitive to porosity. This sensitivity mimics that for the dispersivity discussed above. For an oscillating case, as with the dispersivity, the mass input into the aquifer is sensitive to porosity. The most mass is input into the aquifer at the highest porosity values with values of 4.4, 3.8, 2.9, and 2.4 Kg for porosities of 0.28, 0.21, 0.10, and 0.05 respectively. The solute distribution within the models is sensitive porosity (as with the fixed stage) most notably as the seepage velocity is increased. As porosity is decreased, advective solute transport is enhanced relative to dispersive transport and leads to smaller amounts of mass under the oscillatory stage condition. At the lowest values of porosity less mass is introduced into the aquifer compared to a fixed stage, although this is under the condition of an unconfined aquifer porosity that is less than the specific yield, which is unrealistic. For realistic values of porosity for the aquifer in consideration (those values greater that 0.21) more mass is input into the aquifer under oscillatory conditions compared to fixed conditions. For detailed plots of porosity sensitivity, please see the available auxiliary material.

[34] Additional factors, such as recharge, evapotranspiration, and regional groundwater gradients control the spatial extent of velocity reversal zones and magnitude of groundwater velocities in the vicinity of the stream-aquifer interface. As water table gradients are increased toward the surface water body (strongly gaining stream), the efficiency of this “pumping” mechanism is likely to be decreased. In the reverse case (a losing stream), this mechanism is likely to be more efficient. The controlling factors for simple mass transport in hydrodynamic stream water/groundwater settings are oscillating stage frequency, the magnitude of the stream stage change, and the shallow subsurface material properties and stratigraphy. These should be the primary parameters to define when investigating solute movement through groundwater and surface water interfaces in relatively short temporal and spatial scales. Stream width, although not explicitly considered, is another parameter that merits additional consideration in this process. This pumping mechanism is likely to be important to consider when investigating exchange zone processes under conditions of transient stream stage changes.

[35] These two-dimensional simulations also provide insight into the impacts of aquifer stratigraphy on transport and interactions between surface and groundwater. Simulations assuming a homogeneous model domain show significantly different solute distributions and mass input rates that would presumably be obscured in an equivalent one-dimensional model. Thus, the effect of stratigraphy and the fact that under oscillating flow conditions, more mass is introduced into the lower-permeability aquifer units (weakly confined units) suggests that two- (and also three-) dimensional flow have important and critical bearings on how mass is introduced to and internally distributed in this aquifer system.

5. Conclusion

[36] Mass transport from a surface water body to groundwater under conditions of fluctuating river stage shows enhanced mixing and significant mass transport under conditions of zero net water flux. The mass flux into the aquifer increases for two values of aquifer dispersivity (1 and 10 m) as well as surface water model representations. In this work we present field data documenting anthropogenic impacts of surface water fluctuations on groundwater heads that lead to significant velocity variations within the subsurface aquifer materials. Modeled impacts of these surface water–induced velocity variations significantly impact the subsurface transport of dissolved mass compared to control simulations. Modeling results suggesting a pumping mechanism inducing net mass flux of solute under conditions of zero net water flux that suggest an important role of aquifer dispersive transport in driving mass into and out of surface water body. This study is the first to document potential enhanced transport mechanisms as applied to high-frequency surface water fluctuations caused by anthropogenic water releases.

[37] Groundwater velocities in the near-stream environment appear to be the most important factor controlling mass flux. Dispersive properties and concentration gradients of the aquifer act to transport this mass away from the stream. Groundwater velocities increase with higher head in the river in both the oscillating and fixed cases. Results demonstrated here are consistent with the enhanced transport conditions observed in transient flow fields [Dentz and Carrera, 2005; Cirpka and Attinger, 2003; Dentz and Carrera, 2003; Naff, 1998; Bellin et al., 1996; Dagan et al., 1996; Goode and Konikow, 1990]. Although the work by Kim et al. [2000] showed in a lake-aquifer system that mixing of conservative tracer was influenced more by recharge transients compared to surface water fluctuations, in a river dominated setting we show that stage fluctuations can be quite significant. This is especially enhanced when the source of the contaminant is located in the fluctuating surface water body. We show here that strongly connected surface and groundwater systems can induce significant hydraulic transients that influence mass transport through enhanced dispersion. These anthropogenic high-frequency stage changes have the potential for disrupting nutrient and geochemical processes in the near-stream environment.

[38] In humid regions, where the water table is near the ground surface, surface waters and groundwaters often interact with each other. There is a range of conditions and environments (coastal, estuarine, and riverine) where oscillating stream stage changes can create a potential for enhanced transport when compared to steady stream stages of the same magnitude. Using groundwater flow and mass transport modeling techniques, the dominating parameter for mass transport in this setting is groundwater velocity (qs), which remains relatively high (near the stream) under oscillating conditions compared to fixed high stage conditions. The larger velocities in oscillating stream stage models allow for greater hydrodynamic dispersion compared to a high stage model creating excess mixing and hence more transport even under conditions of zero net flux of water (i.e., no long-term storage of water) into the aquifer.

Acknowledgments

[39] We would like to thank Paul Friesz for his graciousness in sharing his field data at the Charlemont study site. Additionally, we would like to thank Steve Mabee and David Ahfeld for helpful comments on an earlier version of this paper. The helpful comments of three anonymous reviewers greatly improved the paper. We thank Brian Berkowitz for his editorial role. Partial support for this study was funded by the University of Massachusetts-Amherst faculty research grant (FRG) program.

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