Simulation of Ground-Water Discharge to Biscayne Bay

Model Limitations

Numerical models of ground-water flow are limited in their representation of the physical system because they contain simplifications and assumptions that may or may not be valid. Results from ground-water flow models have a degree of uncertainty primarily because detailed three-dimensional distributions of aquifer parameters are rarely, if ever, available. Results from solute-transport models have more uncertainty because they depend on ground-water velocities calculated from flow models and other uncertain parameters specific to solute transport. Variable-density, ground-water models have even more uncertainty and error associated with them because ground-water velocities are affected by solute concentrations. Results from variable-density models must be evaluated with caution because of uncertainties and potential errors inherent in these types of models. The cross-sectional and regional-scale models developed for this study clearly have uncertainty and error. Limitations in the numerical models that may cause errors in the results can be divided into two categories: (1) invalid assumptions or approach implemented by the numerical simulation code, and (2) inaccurate conceptual model, aquifer parameters, boundary conditions, or initial conditions.

SEAWAT is a relatively new code that has not been widely used by ground-water modelers. However, the code has been verified with a number of benchmark problems, and the results compare well with results from other codes and analytical solutions. Inherent in the SEAWAT code are a number of assumptions that may limit the reliability of the numerical models developed for this study. The most limiting assumption is that of an equivalent porous medium. Numerous investigators have documented the presence of preferential pathways in the Biscayne aquifer. These pathways may provide the mechanisms for transporting fresh ground water to offshore springs in Biscayne Bay. The SEAWAT code and finite-difference codes in general are not designed to simulate conduit flow. Instead, the effects of conduits are indirectly incorporated into the model by increasing the bulk hydraulic conductivity. At large scales, this approach is probably valid for simulating flow volumes, but may not accurately represent the transport processes. For these reasons, results from the cross-sectional models are limited if conduits affect ground-water flow at the Coconut Grove and Deering Estate transects. Results from the regional-scale model may be limited as well. The accurate simulation of flow volumes in variable-density, ground-water systems depends on the accurate simulation of the transport processes. Although the regional-scale model seems to reasonably represent the flow and transport processes, there is a level of inherent error in the model that cannot be quantified without a more thorough study of conduit flow in the Biscayne aquifer.

Inaccuracies in the model simulations are probably the result of inaccurate conceptual models or errors in aquifer parameters, boundary conditions, and/or initial conditions. Based on the complex nature of variable-density ground-water systems, the cross-sectional models were calibrated with an assumption of steady state. Kohout and Klein (1967) report that the transition zone can respond to recharge events. However, chloride concentrations measured at the Coconut Grove, Deering Estate, and Mowry Canal transects, however, did not show substantial fluctuations, which may suggest that an assumption of steady state may be valid at least for the short duration when chlorides were monitored. A more significant problem with the cross-sectional models is that simulated concentrations beneath Biscayne Bay are too high. Results from recent simulations suggest that this problem could be resolved by using the specified concentration for inflow as the solute-transport boundary type for Biscayne Bay. Inaccurate aquifer parameters in the model could also result in simulated concentrations that are too high beneath the bay. Kwiatkowski (1987) used a heterogeneous distribution of hydraulic conductivity in his variable-density, cross-sectional model of Deering Estate to better match the distribution of observed heads. Observed heads suggest that there may be a vertical section of higher hydraulic conductivity between two vertical sections of lower hydraulic conductivity (Kwiatkowski, 1987). This distribution for hydraulic conductivity was tested in the present study; although it was possible to better simulate the observed heads, the simulated concentrations of salinity did not match observed concentrations. It is likely that a heterogeneous distribution of aquifer parameters is controlling ground-water flow patterns at Deering Estate, making it difficult to calibrate with the available data. The results from the Deering Estate model, therefore, contain some error, but as a general representation of coastal ground-water flow, the model results probably are reasonable.

In the development of a ground-water model for southern Miami-Dade County, Merritt (1996a) calibrated aquifer parameters and boundary conditions by matching observed fluctuations in head and canal flow. Based on Merritt's (1996a) accurate simulation of head fluctuations and canal flow, the calibrated aquifer parameters and boundary conditions seem to be reasonable approximations of the physical system, although they probably contain some level of error. The distribution of hydraulic conductivity and the storage value derived by Merritt (1996a) were used in the regional-scale model for the area south of the Tamiami Canal (Merritt's model domain) and the area north of the Tamiami Canal (outside of Merritt's model domain). The aquifer parameters used in the regional-scale model, therefore, probably contain some error. However, based on the capability of the regional-scale model to simulate fluctuations in head, canal baseflow, and the general position of the saltwater interface, the model seems to be a reasonable representation of the physical system.

The processes of rainfall, runoff, recharge, and evapotranspiration were difficult to represent in the regional-scale model because of their complex interrelations. Simplifications were used to represent these processes in the model, adding uncertainty to the reliability of model results. For example, the model does not simulate evapotranspiration from the unsaturated zone, which may be an important process along the Atlantic Coastal Ridge (fig. 2) where the unsaturated zone is relatively thick. The quantity of unsaturated zone evapotranspiration probably is indirectly included in one of the other model processes, such as runoff, baseflow to canals, or evapotranspiration from the water table.

Horizontal and vertical discretization in the regional-scale model also introduces error in model results. Because the model cells are 1,000 by 1,000 by 5 m, the effects of canals and well fields are averaged over large volumes. This averaging will cause results from the regional-scale model to be imprecise at smaller scales. Additionally, the large model cells probably cause a certain level of numerical dispersion, which may limit the capability of the model to accurately simulate the position and characteristics of the freshwater-saltwater transition zone. Numerical dispersion in the model, therefore, could affect the simulated ground-water discharge values to Biscayne Bay.

Results from the regional-scale model suggest that fresh ground-water discharge to Biscayne Bay is a small component of the total freshwater discharge to the bay. Although this conclusion is important, it indicates that there is a large degree of uncertainty in the simulated discharge values. Small errors in the other water-budget components can substantially affect the simulated ground-water discharge rates. It appears that simulated values of fresh ground-water discharge are within the error tolerance of the model. However, the spatial trends, which show most of the fresh ground-water discharge to tidal canals and the northern half of Biscayne Bay, probably are reasonable.

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