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Simulation of Ground-Water Discharge to Biscayne Bay

Cross-Sectional Ground-Water Flow Models

Two cross-sectional models were developed at the local scale to simulate the discharge of ground water to Biscayne Bay. These models were developed in conjunction with the regional-scale model to achieve two objectives. First, the cross-sectional models were used to help facilitate development of the regional-scale model. The cross-sectional models simulate flow in only two dimensions, and therefore, run relatively fast compared to the three-dimensional, regional-scale model. For this reason, the cross-sectional models are better suited for calibrating certain aquifer parameters and performing a comprehensive sensitivity analysis. The second objective for developing the cross-sectional models was to simulate the ground-water discharge patterns in detail with a fine level of spatial resolution. Because of limitations in computer processing, a regional-scale model cannot efficiently simulate local-scale ground-water discharge patterns in detail.

The two cross-sectional models were constructed along ground-water flow lines toward Biscayne Bay. The northern model simulates ground-water flow in the Coconut Grove area. The central model simulates flow for the Cutler Ridge area near the Deering Estate. A cross-sectional model was not designed for the Mowry Canal transect because the transect does not follow a ground-water flow line. The cross-sectional models were designed to simulate average ground-water flow conditions from March 1998 to February 1999. This period of time was selected because it corresponds with the period when field data were collected for this study. The hydrogeologic stresses included in the model are lateral flows from inland, net recharge, and ground-water discharge to Biscayne Bay.

Model Design

A common method for orienting two-dimensional, cross-sectional models is to align the horizontal axis with a linear or curving ground-water flow line. This method relies on the definition of a flow line, which does not allow ground water to flow across the line. Ground-water flow, therefore, can be simulated in two dimensions, one along the flow line and the other in the vertical direction. This is the general approach used for the Coconut Grove and Deering Estate cross-sectional models. For both areas, a ground-water flow line was drawn through the monitoring wells using the 1993 water-table maps (figure 4 and figure 5) and contours of the water table from a preliminary simulation of the regional-scale model. The inland extent for each model (fig. 16) is located west of the saltwater tongue and near a monitoring well or surface-water feature. The models extend offshore, past locations where measured ground-water salinities in monitoring wells were equal to the salinity of seawater. Based on field data and preliminary results from the regional-scale model, the general orientation and extent of the cross-sectional models seem reasonable for simulating local-scale ground-water discharge to Biscayne Bay.

Figure 16. Location of the two-dimensional, cross-sectional models for (A) Coconut Grove (B) and Deering Estate. [click on images above for larger versions]

One major difference between the two models is the simulated horizontal distance. From the coast, the Coconut Grove model extends 5,900 m inland, whereas the Deering Estate model extends 1,550 m inland. This is because the saltwater tongue is much farther inland near Coconut Grove than at the Deering Estate transect. The total lengths of the flow line simulated by the Coconut Grove and Deering Estate models are 8,000 and 2,165 m, respectively. The vertical distances used for the two models are relatively similar, with the difference explained by the spatial variability in the base of the Biscayne aquifer. The base of the Coconut Grove model is 40 m below sea level, and the base of the Deering model is 33 m below sea level.

For each model, a finite-difference grid was developed to adequately discretize the model domain. One of the objectives for grid development was to sufficiently discretize the model domain while minimizing the total number of model cells. For Coconut Grove, this results in a regularly spaced grid with 40 cells in the horizontal direction and 20 cells in the vertical direction. Each rectangular cell in the Coconut Grove model is 200 m horizontal by 2 m vertical. For the Deering Estate model, an irregularly spaced grid was constructed with 149 cells in the horizontal direction and 33 cells in the vertical direction. For most of the model domain, the cells are 10 m horizontal by 1 m vertical. Near the western boundary, however, the horizontal lengths of the model cells increase to a maximum length of 100 m to allow for finer resolution at the coast while maintaining the same total number of cells. Finer horizontal and vertical resolution was used for the Deering Estate model because more ground-water wells were available for calibration than for the Coconut Grove model.

The boundary conditions used for the Coconut Grove model (fig. 17A) generally are the same as those used for the Deering Estate model (fig. 17B). Recharge is applied to the inland portion of the upper boundary in both models. Biscayne Bay is represented by a horizontal constant freshwater head boundary with a constant salt concentration equivalent to that of seawater, 35 kg/m³ (kilograms per cubic meter). By specifying a constant freshwater head boundary in layer 1, the elevation for the bottom of Biscayne Bay corresponds to the center elevation of layer 1; thus, the simulated bay bottom is flat with an elevation of -1.0 m for Coconut Grove and -0.5 m for Deering Estate. The eastern vertical boundary also is represented by a constant freshwater head boundary with a constant salt concentration of 35 kg/m³. The constant freshwater head values, which increase with depth, were calculated using equation 8. The lower boundary of each model (a no-flow boundary) represents the base of the Biscayne aquifer. For the western boundary, a constant freshwater flux is evenly apportioned to each of the model cells. This freshwater flux represents the general flow of ground water toward the coast.

Figure 17. Boundary conditions and finite-difference grid for the (A) Coconut Grove and (B) Deering Estate models. [click on images above for larger versions]

For both models, a stage value of 0.22 m was used to calculate the value for freshwater head assigned to each cell of the bay boundary. A stage value of 0.22 m represents an average value for sea level from 1989 to 1998 and was calculated from the downstream station at structure S-123. A net recharge value of 38 cm/yr (centimeters per year), which includes evapotranspiration, was assigned to the overlying recharge boundaries in both models. While this value is a rough estimate, the sensitivity analysis (presented later in this section) suggests that the model is not very sensitive to recharge. The hydraulic gradient was used to estimate the constant flux assigned to the western boundary. Based on the 1993 water-table maps (figure 4 and figure 5) and the results of the regional-scale simulation, the approximate hydraulic gradient for the Coconut Grove area is 4 x 10^-5 m/m (meters per meter). The hydraulic gradient for the Deering Estate area cannot be estimated from the water-table maps (figure 4 and figure 5) because there are not enough contours, but results from a preliminary simulation of the regional-scale model suggested that 5 x 10^-5 (meter of head per meter of lateral distance) may be reasonable. Attempts were made to maintain these hydraulic gradients at the western boundaries during the calibration of horizontal hydraulic conductivity. The actual flux value, therefore, is a result of calibration.

Model Calibration and Simulation Results

The Coconut Grove and Deering Estate cross-sectional models were calibrated by adjusting the boundary stresses and aquifer parameters, within a range of reasonable values, until simulated conditions generally matched the conditions observed in the field. In both models aquifer parameters are represented by a homogenous distribution rather than a more complex heterogeneous distribution. Results obtained from this simplistic method for calibrating the cross-sectional models are thought to be useful for calibrating the regional-scale model.

The two models were calibrated to data collected from monitoring wells located on or near the model transects. The data values used in the calibration are presented in table 2. For monitoring wells that are not located directly on a model transect, the horizontal distance was specified as the approximate distance of the monitoring well from the coastline. This method for projecting the monitoring wells onto a model axis assumes that contours of head and salinity are parallel to the coastline and perpendicular to the model cross section. This assumption may limit confidence in the calibration if actual contours of salinity and head are not parallel to the coast. The elevation of the screen center was used to locate the measurements of head and salinity within the vertical section of the model. Most of the well screens are 1.52 m in length, which means that the heads and salinity values measured at the wells were vertically averaged over this distance. Although the screen length is longer than the cell height for the Deering Estate model, the vertically averaged head and salinity values should not cause significant errors in the model calibration.

The aquifer parameters and boundary stresses used in the final versions of the calibrated models for Coconut Grove and Deering Estate are presented in table 4. The parameters and stresses used in the Coconut Grove model are comparable to within one order of magnitude to the parameters and stresses used in the Deering Estate model. Results from the calibrated models generally match with field data (fig. 18). The simulated transition zone appears to be of reasonable width, the toe is simulated near the position observed in the field, and the simulated water table is similar in elevation to measured ground-water levels. It is clear, however, that the models do not accurately simulate ground-water salinities directly beneath Biscayne Bay near the shoreline; in both models, simulated values of ground-water salinity are too high. A combination of aquifer parameters that would reproduce these low salinity values could not be found with a spatially homogeneous distribution. This suggests that the low salinities beneath the bay may be affected by a complex distribution of hydraulic conductivity. For example, a highly transmissive aquifer layer that is bounded on the top and bottom by lower permeability units could possibly transmit lower salinity ground water offshore beneath the bay. The constant-concentration boundary condition used for Biscayne Bay also may be causing increased salinities beneath the bay. Recent research has shown that specifying the concentration for inflow from a constant-head boundary may be more appropriate than a constant-concentration boundary for certain applications. Future simulations may also benefit from better estimates of salinity for Biscayne Bay; for the cross-sectional models, the salinity value used to represent the bay (35 kg/m³) is probably too high.

Because the models did not accurately represent the relatively low salinities beneath Biscayne Bay, the simulated ground-water discharge patterns may be inaccurate. Despite this probable error, a plot of simulated discharge relative to distance from shore for the Deering Estate model is shown in figure 19. Simulated values of ground-water discharge were calculated by tabulating the flow from the active model domain into the constant-head cells that represent Biscayne Bay. Model results suggest that most of the ground-water discharge to Biscayne Bay is very near the coast. The field data suggest, however, that ground-water discharge to Biscayne Bay may occur as far offshore as 500 m (fig. 10). The negative ground-water discharge values indicate that seawater is being circulated back into the aquifer. A similar plot of discharge for the Coconut Grove model is not included because all ground-water discharge is to the first constant-head cell representing Biscayne Bay.

Figure 19. Simulated ground-water discharge to Biscayne Bay for the Deering Estate model. Discharge includes freshwater and brackish-water components. [larger image]

Water budgets were prepared from the results of the Coconut Grove and Deering Estate models to provide general insight into the coastal ground-water flow systems. As expected, simulated water budgets indicate that volumetric inflows are roughly equivalent to outflows (fig. 20). Differences between volumetric inflows and outflows are explained by the 2.5 percent density difference between freshwater and seawater. For both models, recirculated seawater (inflow from eastern constant-head boundaries) comprises a large percentage of the simulated ground-water discharge to Biscayne Bay. This supports the notion by Kohout (1960a) that only a fraction of the total ground-water discharge to Biscayne Bay is fresh ground water from farther inland. Based on the water budgets, the models suggest that about 35 to 60 percent of the submarine discharge is recirculated seawater, but these estimates may be affected by the model's inability to simulate concentrations beneath the bay.

Sensitivity Analysis

A sensitivity analysis was performed to evaluate the effects of the different aquifer parameters and boundary conditions on the simulated ground-water heads and salinities. For each sensitivity run, only the examined parameter or boundary condition is adjusted from the value used in the calibrated model, referred to as the base case. For each model, parameters were qualitatively assigned either a small, moderate, or large effect based on the simulated salinities and heads.

The value for horizontal hydraulic conductivity, K_h, has a moderate effect on the simulated heads and salinities. When the value for K_h decreases, simulated heads increase and the salinity contours move seaward (pls. 1 and 2). The opposite occurs when K_h increases. Interestingly, the effects of K_h are most pronounced with the 0.05 and 0.5 relative salinity contours. K_h does not significantly affect the 0.95 contours, which tend to be "locked" at the coast. Thus, for the same set of aquifer parameters and boundary conditions, simulations with lower values of K_h will result in a narrower transition zone relative to simulations with larger values for K_h. This observation, which applies to both the Coconut Grove and Deering Estate models, is probably due to higher dispersion for simulations with high values of K_h.

Figure 20. Simulated water budget for the (A) Coconut Grove and (B) Deering Estate models. [larger image]

The effect of vertical hydraulic conductivity, K_v, ranges from small to large depending on the model and whether the value is increased or decreased. It is evident from plates 1 and 2 that K_v affects the simulated distribution of salinity. Decreases in K_v cause the 0.95 salinity contours to move seaward and extend beneath Biscayne Bay. By using K_v values that are lower than the ones used in the two base case models, simulated values of ground-water salinity could decrease beneath the bay. While this would improve the model results beneath the bay, a decrease in K_v would worsen the match between observed and simulated salinities at the base of the aquifer. This further supports the notion that the distribution for hydraulic conductivity is not homogeneous. Increases in K_v do not significantly affect salinity contours. There seems to be a threshold beyond which increases in K_v no longer affect model results.

Surprisingly, longitudinal dispersivity, _L , does not significantly affect simulated salinities and heads; however, transverse dispersivity, _T , does significantly affect the model results. Although _L does not seem to affect model results, _L values in the calibrated models were held 10 times larger than _T , a ratio commonly reported in the literature. When low _T values are used, salinity contours become elongated and extend farther inland. High _T values tend to produce salinity contours that are more vertical. Combining lower _T and K_v values may be one way to better match the available field data. Such a simulation might produce higher salinities at the base of the aquifer and lower salinities beneath the bay.

Changing the flux at the western boundary, Q/m, has a moderate effect on model results. The effect is nearly opposite to changing K_h. When Q/m is decreased, salinity contours move inland and heads decrease. When Q/m is increased, salinity contours move seaward and heads increase. The fact that Q/m has the opposite effect of K_h means that many different combinations of K_h and Q/m could produce the same head and salinity distribution, but discharge patterns may be different.

The cross-sectional models are not very sensitive to changes in recharge. When recharge rates are increased, salinity contours move slightly seaward and the heads slightly increase. When recharge rates are decreased, salinity contours move slightly landward and the heads decrease.