Evaluating the use of canal seepage and solute concentration observations for aquifer parameter estimation
Introduction
Within the last decade, the use of automated inverse techniques to estimate parameters that govern groundwater flow and transport have become more common. Further analysis of the resulting parameter set that provides the best fit between observed and simulated values often leads to the conclusion that the problem is ‘ill-posed’. The non-uniqueness and instability of the solution generally influence the ill-posedness (Yeh, 1986, Carrera and Neuman, 1986a, Sun, 1994, McLaughlin and Townley, 1996). In an unstable solution small measurement errors translate into large fluctuations of parameter values during the calibration process and end in unrealistic final estimates. A non-unique solution is caused by the fact that different combinations of parameter values lead to similar simulation results of, e.g. hydraulic head. It is accepted that ill-posedness can be overcome. One approach suggested to improve the physical plausibility of an ill-posed model is to adapt model parameterization. This includes (1) the selection of an appropriate number of parameters to avoid overparameterization (Sun et al., 1995), (2) the evaluation of different parameterization schemes, e.g. zonation versus interpolation (Keidser and Rosbjerg, 1991), and (3) the incorporation of regulating prior statistics typically based on field measurements (Carrera and Neuman, 1986b). A second promising way to better constrain the model is to include other field observations, in addition to hydraulic head in the calibration process. Results of published studies suggest that information on fluxes at aquifer boundaries (Poeter and Hill, 1997, Hill et al., 1998, D'Agnese et al., 1999, Beckers and Frind, 2001), and pore water solute concentration (Strecker and Chu, 1986, Wagner and Gorelick, 1987, Sun and Yeh, 1990a, Sun and Yeh, 1990b, Keidser and Rosbjerg, 1991, Medina and Carrera, 1996, Anderman and Hill, 1999) are useful in reducing parameter correlation in order to identify model parameters. Anderman et al. (1996) combined several measurements of hydraulic head, one calculated lake seepage value, and two mean advective travel-time observations of a sewage-discharge plume at Otis Air Force Base, Cape Cod, for the estimation of five parameters. They found the travel-time observations to improve the model calibration. Keating and Bahr (1998) added concentrations of natural non-conservative solutes such as calcium to constrain a groundwater flow model. Although their resulting models were not unique, they found the simulated concentrations to reproduce the observations qualitatively well. Inverse techniques that simultaneously take advantage of water fluxes and natural solute concentration have not been applied extensively to field systems. This could be due to a lack of combined measurements on water exchange between groundwater and surface water and information on the spatial and temporal variability in pore water solute concentrations. Furthermore, the use of concentration data to simultaneously estimate parameters of flow and transport can lead to significant computational efforts and model convergence is typically slow.
Previous models for our study area in Southeast Florida were typically calibrated solely on available data of hydraulic head (Merrit, 1995). In the present study, seepage at canal/aquifer boundaries (q) and groundwater chloride (c) concentration observations were used along with the hydraulic head data (h) to estimate parameter values for a 3D groundwater model of an area along the eastern boundary of Everglades National Park (ENP). We estimated a maximum of six parameters in our inverse simulations. Our main focus was on quantifying the benefit of observation types in addition to head (i.e. q and c data) in estimating the model parameters. Because the true parameter values are unknown in a natural aquifer, we evaluated the different parameter sets obtained from the various calibrations by comparison of predicted and observed h, q, and/or c values during two periods not used in calibration (a 10-day canal drawdown test in 1996 and a 4-month time period in 1997). The present work is, to our knowledge, the first large-scale field study incorporating a large number of transient observations of hydraulic head, boundary fluxes, and pore water tracer concentration in a fully coupled 3D groundwater flow and advective–dispersive solute transport inversion.
Section snippets
Modeling approach
A conceptual hydrogeologic model was developed based on existing knowledge of the geologic, hydrologic, and hydraulic site conditions. An initial set of hydrogeologic parameter values was used for the numerical model. The model was constrained by measured and interpolated boundary conditions (Fig. 1). Next, simulated and measured values of h, and/or q, and c were compared for a 6-month period of 1998 and, depending on the fit, updated parameter estimates were calculated automatically using
Hydrogeological setting
The study site is located about 50 km southwest of Miami, Florida, along the eastern boundary of ENP (Fig. 2). The climate is subtropical, with a hot, humid wet season (May through October) and a mild dry season (November through April). Average annual precipitation at nearby Homestead Station was 158 cm from 1940 to 1992 with 75–80% of the rainfall occurring during the wet season (Merrit, 1995).
The field site was chosen due to its major local and environmental interest. The ‘Frog Pond’, which
Data collection
Daily hydraulic head measurements from a total of 27 wells were used in different combinations for model calibration and prediction (Fig. 3). Observations of four groundwater wells and six canal stage sites were added to set up the model boundary conditions. Fluxes between a defined canal reach and the aquifer were calculated from the difference of daily measured flows at upstream and downstream structures, or at nearby flow-calibrated, acoustic velocity meters. Water flux between canal and
Model calibration
Groundwater flow and coupled chloride transport was simulated with a 3D, two-layer finite-difference model covering a rectangular area of more than 100 km2 (Fig. 2, Fig. 3). The two layers represented the Miami Limestone and Fort Thompson Formation. The model was divided in 103 columns and 106 rows, equaling a total of 21836, 100 m by 100 m, cells. This discretization ensures accurate reproduction of canal dimensions and minimizes the effects of numerical dispersion in the solute transport
Calibration results
We tested model uniqueness and stability by using the calculated diagnostic statistics of the models, and by variation of initial parameters by one magnitude. The initial and final parameter values for each calibrated model were evaluated for their parameter sensitivity and correlation. The composite scaled parameter sensitivities (see Section 2), which depend on each parameter value and the number of observations used, were normalized by the sum for all the parameters for each model in order
Model evaluation
Each of the seven models were evaluated by comparing predicted (i.e. simulated) values of head and seepage flux to those measured during a canal drawdown test on L-31W, and by comparing predicted values of head, seepage flux and chloride concentration to those measured during a 4-month time period in 1997. Prediction is defined by a MODFLOW and coupled MT3D simulation, where the results of heads, seepage fluxes, and concentrations are compared to corresponding field measurements of another time
Conclusions
We compared seven groundwater models calibrated on different measurement types of hydraulic head, canal seepage fluxes and pore water chloride concentration. Automated inverse techniques were used for the groundwater flow and coupled solute transport model calibration. Methods to calculate diagnostic statistics of the seven models were applied to the initial and final estimated parameter values in order to distinguish non-unique models. We found that:
- 1.
While the initial parameter sensitivities do
Acknowledgements
The presented work has been supported by the US Army Research Office (DAAH04-96-1-0046), and a jointly sponsored fellowship from the Swiss National Science Foundation and the ‘Ciba-Geigy Jubiläumsstiftung’. We greatly appreciate the help from the South Florida Water Management District (Angela Chong) and the ENP Service, which provided most of the hydrologic data. Comments of Karin Bernet, David Genereux, Jim Saiers, William Yeh and one anonymous reviewer have been very useful in improving the
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