1. Abstract

In the work reported here, we develop a two-dimensional diffusion model for surface-water movement, and we test this model against hydrologic data collected from the Shark River Slough of the Florida Everglades. The equations that govern the model are derived under the assumptions that surface-water flow is laminar and that a power-law relationship quantifies the dependence of flow velocity on water depth. We simplify the model formulation by assuming uniform rates of evapotranspiration, a constant ground-surface slope, and spatially homogeneous vegetative cover. In both inverse and predictive simulations, model calculations closely match surface-water stages measured over a 27-km transect within the slough.

2. Objectives

• Construct a two-dimensional model for the transient flow of water over vegetated surfaces.
• Test the model in both inverse and predictive modes against data on hydraulic head collected from the central portion of Shark River Slough.
• Define the level of model complexity required to accurately simulate surface-water movement over large scales within natural wetland systems.

3. Site Description The Shark River Slough serves as the primary means of delivery of freshwater from Water Conservation Areas 3A and 3B to the Florida Bay and the Gulf of Mexico (see site map). Sawgrass and spikerush, interspersed with dry tree islands, represent the dominant vegetation types within the slough. The central part of the slough is underlain with organic muck, which, in turn, is underlain by limestone. Depth of water in the slough is on the order of a meter or less. Water quality measurements made at site S1 for a one-year period beginning in October 1997 reveal that surface-water concentrations of total dissolved solids range from 60 mg/L to 350 mg/L.

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4. Model Development

The model is based on the nonlinear diffusion equation, which is derived by combining the appropriate forms of the continuity and the momentum equations. In two-dimensional form, the nonlinear diffusion equation can be expressed as

(1)

where h is hydraulic head, S_y is specific yield, K_f is the surface-water conductivity coefficient, d is water depth, is an exponential constant, E is the evapotranspiration rate, and P is precipitation rate. Equation (1) is derived by assuming that the inertial and acceleration terms of the momentum equations are negligible and by assuming that overland flow velocity can be expressed as a power function of water depth. We solved the diffusion equation using a finite-difference method with a predictor-corrector time-stepping scheme.

5. Model Domain

• We simulated surface-water flow dynamics within a region of Shark River Slough measuring 27 km in length and 10 km in width (see site map).
• We assumed no-flow conditions across the southeastern boundary (SEB) and across the segment of the northwest boundary (NWB) located downgradient of the NP203 site.
• We assigned specified-head conditions along the remaining boundary segments of the model domain on the basis of stage measurements at sites NE5, NP202, NP203, and P35.
• We assumed uniform evapotranspiration rates and accounted for the spatial distribution in rainfall with a three-zone discretization using rainfall data collected at sites P33, P35, and P36.

6. Sequence of Simulations

• We report the results of two simulations: one calibration simulation, designed to estimate uniform values of K_f and , and one forward simulation, designed to assess the predictive capability of the calibrated model.
• The 243-day calibration period began 18 June 1996 and ended 15 February 1997
• The 194-day prediction period began 17 January 1998 and ended 29 July 1998.

7. Model Calibration

Model-calculated hydraulic heads (solid lines) closely reproduce measured heads (symbols) for the calibration period. Best-fit values of K_f and are 6.18 x 10⁶ m^0.6 d^-1 and 0.439, respectively. The dashed lines represent rainfall rates, as measured at P33, P35, and P36, and the heavy line near the bottom of each plot represents evapotranspiration rates, measured at P33.

8. Model Prediction

Using the best-fit values of K_f and determined from from calibration, the model predicts both the spatial and temporal variations in head along the 27-km long transect with good success.

9. Conclusions

Our model is based on several simplifying assumptions, which are necessary given the lack of data on the spatial distribution in wetland properties and vertical fluxes of water. The key assumptions of the model are that (1) evapotranspiration rates are uniform throughout the domain, (2) variability in rainfall rates can be described with a three-zone discretization, (3) exchanges of water between the surface and subsurface are negligible, (4) the ground-surface slope is uniform, and (5) the frictional resistance parameters (i.e., K_f and ) are constant in time and space. When taken in context to these assumptions, our results suggest that accurate predictions of surface-water flow for extended times and over long distances can be accomplished without extensive characterization of the the spatial variability in the source-sink terms and by treating the physical properties of the wetland as homogeneous.

10. Acknowledgments

This research was supported in significant part by DOI's Critical Ecosystem Studies Initiative, a special funding initiative for Everglades restoration administered by the National Park Service; and in part by USGS's Florida Caribbean Science Center. We thank Gordon Anderson, Ed German, and Kevin Kotun for providing us with access to data on rainfall, evapotranspiration, and surface-water levels.

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