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Modeling decadal timescale interactions between surface water and ground water in the central Everglades, Florida, USA
Tritium measurements from 25 wells at seven sites in WCA-2A are shown plotted as a function of depth in the aquifer in Fig. 5A. The data were temporally averaged because no clear temporal trends existed for samples collected over the 4-year sampling period. Based on the results of the sensitivity analysis, and on the examination of residence times of surface-water and ground-water flowing horizontally in WCA-2A relative to the half-life of tritium, horizontal transport of tritium both in surface water and ground water were expected to have minimal effects on vertical distribution of tritium in the aquifer. Therefore, tritium data from different locations in the wetland were combined by averaging spatially tritium values from similar vertical intervals of well-screen depth. Averaged data are shown in Fig. 5B. Tritium data for individual wells along with the spatially averaged tritium concentrations and standard deviations for four well-screen depth ranges (0-4.5, 4.5-9, 15-18, and 34-37 m) are shown in Fig. 5B. As explained earlier, tritium measurements beneath the S10C levee were not included in the spatial averages.
The first important observation about spatially averaged tritium data is that reliable detections of tritium (O0.4 TU) were almost entirely restricted to wells less than 8 m deep (Fig. 5B). Average groundwater tritium concentrations were 1.8 TU in the shallowest depth range (0-4.5 m), 0.63 TU in the next deepest depth range (4.5-9 m), and below the MDL in the two depth ranges in deeper ground water (15-18 and 34-37 m) (Fig. 5B). Relatively high rates of ground-water flow beneath levees is a well studied phenomena (Swayze, 1988; Meyers et al., 1993; Genereux and Slater, 1999; Bolster et al., 2001; Sonenshein, 2001; Nemeth and Solo-Gabriele, 2003) that was also characterized locally in WCA-2A (Krest and Harvey, 2003; Harvey et al., 2004). Since the present goal was to quantify recharge and discharge in the interior areas of WCA-2A, tritium data beneath the levee were not used in modeling analysis. In an upcoming section we justify the assumption that horizontal flow of tritium in ground water from levee boundaries was not important to our analysis.
4.1. Estimating tritium concentration and water storage in interactive ground water
In order to determine the average tritium concentration throughout the top 8 m of interactive ground water, the depth-distribution of tritium and porosity must be taken into account. Tritium concentrations clearly decrease with increasing depth in the aquifer, but the exact form of the decline in tritium concentration is difficult to specify. The best method of depth averaging was presumed to be computing a depth and porosity-weighted average of tritium concentrations based on average tritium concentration at the midpoints of the two depth classes of wells. The shallow depth class ranged between 0 and 4.5 m with a midpoint of 2.25 m, and the deeper class ranged between 4.5 and 8 m with a midpoint of 6.75 m, respectively. The average concentration for each well class was assigned to all depths within the corresponding depth range. Furthermore, depths in the top 1 m (peat) of the aquifer were assigned a porosity of 0.98 to represent peat, while the layer between 1 and 8 m (sandy limestone) were assigned a porosity of 0.3 (Harvey et al., 2002). The total storage depth of water that resulted from those calculations was 3.1 m in the top 8 m of the aquifer. Approximately one-third of the water storage (0.98 m) was accounted for by water storage in peat. The resulting estimates of average tritium concentration in the 8-m layer of interactive ground water was 1.5 TU. It should be noted that this estimate of average tritium concentration is uncorrected for mixing that may have occurred with deeper, tritium-dead ground water. Vertical mixing between those waters would cause both residence time (tGW) and the depth (dGW) of the relatively young component of ground water to be overestimated. The reasons for overestimation are that upward transport of tritium-dead water dilutes the average tritium concentration of young ground water with tritium free water, leading to overestimation of residence time for the component of young ground water. At the same time, downward transport of young ground water with tritium increases the apparent depth of interactive ground water. The approach we chose was to proceed with the modeling and accept the possible overestimation of tGW and the dGW. Even if vertical mixing was later shown to be important, we relied on the fact that mixing would probably have little effect on estimates of recharge and discharge. That is because (1) the total mass of tritium in ground water remains unaffected by vertical mixing, (2) both residence time and depth are simultaneously overestimated if vertical mixing with tritium-dead water occurs, and (3) since water storage depth and residence time in the interactive ground-water layer appear in ratio in the calculation of exchange flux (Eq. (3)), it is probable that vertical mixing would have little or no overall effect on our estimate of exchange flux. A later evaluation of the effect of vertical mixing was made possible by comparison of model estimated residence times with residence times estimated using measurements of 3H/3He ratios in several wells. Significant vertical mixing with tritium-dead water would be evident in shorter residence times estimated from 3H/3He ratios compared with model-estimated residence times obtained by fitting to tritium data. The results of the residence time comparison and the resulting interpretation of the importance of vertical mixing are discussed later in this paper.
4.2. Determination of average recharge and discharge fluxes
Tritium transport was simulated using fixed values of surface-water velocity, surface-water depth, and longitudinal dispersion in surface water (values given in Table 2). Fig. 6 shows a range of simulation results using the following values of ground-water residence time, tGW = 1, 3, 10, 30, 100, 300, and 1000 years. Fig. 7 compares the results of those simulations with measurements of tritium in ground water categorized by well depth class. Although, there is wide variation in residence times associated with ground waters of a specific depth class, there is a tendency for shallow ground waters (<4.5 m) to be associated with younger ages (<100 years), while deeper ground waters (>15-m) are consistently associated with modeled residence times greater than 100 years. The 'best fit' simulation to the average ground-water tritium concentration was determined to have a ground-water residence time of 90 years. The best fit simulation is not shown, but the close fit of the simulation with 100 year residence time is apparent in Fig. 7. Dividing the water storage depth in the layer of aquifer with interactive ground water that was determined earlier (3.1 m) by 90 years results in an exchange flux of 0.01 cm d-1. As explained earlier, the values of spatially averaged recharge and discharge fluxes associated with the exchange flux are also 0.01 cm d-1.
We suspected that the residence time of 90 years for shallow interactive ground water might be overestimated due to vertical mixing with deeper, tritium-dead ground water. Independent data were needed to gain further perspective and substantiate a final interpretation. Alternative estimates of ground-water age come from the few analyses of tritium-helium-3 ratios (3H/3He) that were possible for the sampled wells. There is a practical reason why 3H/3He may be a better tracer of residence time when available. It provides a better estimate of only the young component of ground water, without being affected by dilution with much older ground water. This is a consequence of using the parent/daughter isotopic ratio as the tracer, because the ratio 3H/3He is not diluted by upward mixing of tritium-dead ground water. Consequently the residence time is not overestimated. However, the samples are more difficult to collect without corruption and more expensive to analyze. As a consequence, our 3H/3He measurements were limited to four samples.
The average residence time of shallow ground water indicated by three of the 3H/3He analyses was 25 years (Table 3). The fourth analysis was from levee site S10C collected from the shallowest well (C) at a depth of 9 m. That water had a much younger age (approximately 2 years), which reflects the much higher driving forces for recharge on the up gradient side of the levee near the S10C site that drives rapid ground-water flow beneath the levee (Harvey et al., 2002). This sample was collected too close to a levee to be representative of interior wetlands and was omitted from the calculation of average residence time.
It is important to emphasize once more that the estimates of recharge and discharge from tritium modeling are considered reliable even though modeling of tritium overestimated ground-water residence time. That is because both ground-water residence time and water storage depth are simultaneously overestimated if vertical mixing occurs (i.e. the total mass of tritium in ground water is unaffected by vertical mixing). Thus, the resulting overestimates of water storage depth and residence time in the interactive ground water will tend compensate one another in the calculation of exchange flux (Eq. (3)), with minimal effect on resulting estimates of recharge and discharge.
U.S. Department of the Interior, U.S. Geological Survey
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