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Developing a Computational Technique for Modeling Flow and Transport in a Density-Dependent Coastal Wetland/Aquifer System

By Eric Swain, Christian Langevin, and Melinda Wolfert

U.S. Geological Survey Center for Water and Restoration Studies, Miami, FL., USA

FTLOADDS flowchart
Figure 1. FTLOADDS flowchart. [larger image]
The USGS Center for Water and Restorations Studies has continued its numerical modeling in the coastal regions of the southern Everglades. A combined model referred to as Flow and Transport in a Linked Overland-Aquifer Density Dependent System (FTLOADDS) is the latest step in an ongoing effort to develop and refine the numerical representation of flow and transport in this area. FTLOADDS is a numerical framework that includes and coordinates execution of the SWIFT2D hydrodynamic surface-water model and the SEAWAT ground-water model. The SWIFT2D and SEAWAT models are designed to account for salinity transport in each regime, surface-water and ground-water flow, and the associated affects of density variations on flow. The FTLOADDS coupling passes the necessary information between the two models. This involves passing aquifer heads and ground-water salinity from SEAWAT to SWIFT2D and computed leakage volumes and salt fluxes from SWIFT2D to SEAWAT.

The original modeling application is referred to as the Southern Inland and Coastal Systems (SICS) model. As part of this application, the SWIFT2D model was used to represent the surface-water regime and modified to account for the effects of rainfall, evapotranspiration, and other factors. Model setup utilized numerous field studies to define the input parameters for frictional resistance, evapotranspiration, land elevation, and flow calibration. Approximate ground-water boundaries were defined, but a more accurate scheme was needed. Previous coupled models represent the water-level/flow relation in both the surface-water and ground-water regimes to various degrees of complexity. However, to represent the hydrologic conditions in a coastal area, such as the northeastern shoreline of Florida Bay, salinity transport must be considered, because the induced density variations affect ground-water flow, surface-water flow, and the leakage rate between the two regimes. Consequently, transport must also be represented in these flow computations. The ideal candidate for simulating the ground-water regime is the SEAWAT model, which links the well-known MODFLOW three-dimensional ground-water flow model with the MT3DMS transport code. The FTLOADDS coupling allows SWIFT2D and SEAWAT to retain as much of their original form as possible, because only relevant information is exchanged.

A primary requirement of any simulation is to conserve mass. In FTLOADDS, the amount of water and salt passed from one model must equal the amount received by the other, and be computed by the most valid technique known. To conserve mass between the models, their timesteps must be reconciled. Given the hydrodynamic nature of the surface-water computation, the surface-water timesteps are almost always much shorter than the ground-water timesteps. As in other models, the most logical place for the computation of leakage is in the shorter timestep surface-water model, SWIFT2D. A subroutine was created for SWIFT2D that computes a leakage volume for each timestep based on ground-water and surface-water head using the equation:

Qleak = Cleak Acell (Hgw - Heq + Drho),

where

Qleak = leakage flow (L3/T),

Cleak = leakage coefficient (1/T),

Acell = surface area of model cell (L2),

Hgw = freshwater equivalent aquifer head (L),

Hsw = freshwater equivalent surface-water head (L),

Drho = (Zcell - Zelev) (rhoave - rhof) / rhof,

Zcell = elevation of center of aquifer cell (L),

Zelev = land elevation (L),

rhoave = average density of ground water and surface water (M/L3), and

rhof = density of fresh water (M/L3).

Within this equation, effects of density variation on head gradient are accounted for in the subroutine when calculating leakage. The leakage flow is multiplied by the timestep length to obtain a leakage volume, which is added or subtracted from the surface-water cell. The leakage volumes for each surface-water timestep are summed, and sent back to the ground-water model to be added or subtracted from the corresponding aquifer cell.

The net salt flux between surface water and ground water must also be taken into account. When the leakage volume is computed for a surface-water timestep, salt flux is computed based on flow direction. If the flow is upward from ground to surface water, the salt mass flux is calculated by multiplying leakage volume and ground-water salinity. The calculated salt mass is added to the surface-water salt mass in the SWIFT2D transport subroutine. If flow is downward from surface to ground water, the salt mass flux is calculated as the product of leakage volume and surface-water salinity. The total salt mass flux is summed for the surface-water timesteps and divided by the total leakage volume. This gives an equivalent salinity concentration for the total leakage over the ground-water timestep. Whichever direction the leakage is moving, the computed equivalent salinity is used in SEAWAT as the concentration of the water added or removed from the aquifer as leakage. This concentration only reflects the proper salt mass exchanged; If there are multiple reversals in leakage direction during the surface-water timesteps, and the salinity of the ground water and surface water are very different, the equivalent concentration can be very large. If the direction of the net leakage water volume is opposite than the direction of net salt flux, the equivalent concentration computed can be negative.

The flowchart of FTLOADDS is shown in figure 1. For each ground-water timestep, SWIFT2D is called first, using the final ground-water head from the previous timestep to compute leakage. Computed leakage and salinity is passed to SEAWAT for the ground-water timestep. A comparison of measured salinity values at McCormick Creek, a coastal creek in the SICS study area, with values computed in SWIFT2D alone (no ground water), and in FTLOADDS (with ground water) is shown in figure 2. The coupling to the SEAWAT model within FTLOADDS has resulted in a marked improvement in the ability to represent salinity.

The FTLOADDS coupled SWIFT2D/SEAWAT model has greatly improved the ability to model coastal wetland scenarios for restoration science. Using this continuously improving tool, water resource managers will be able to answer the critical restoration questions for the Everglades and Florida Bay.

graph comparing measured salinity values at McCormick Creek, with values computed in SWIFT2D alone (no ground water), and in FTLOADDS (with ground water), from July 1996 through November 1999
Figure 2. Salinity at McCormick Creek. [larger image]

Contact: Eric Swain, U.S. Geological Survey, 9100 NW 36th St. Ste. 107, Miami Fl, 33178, Phone: 305-717-5825, Fax: 305-717-5801, edswain@usgs.gov


(This abstract was taken from the Greater Everglades Ecosystem Restoration (GEER) Open File Report 03-54)

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