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Modeling decadal timescale interactions between surface water and ground water in the central Everglades, Florida, USA

3. Methods

Study Area
Figures, Tables & Equations
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The primary data needed for the present study were measurements of an environmental tracer in ground water that preserves information about ground-water residence time at various depths in ground water. Tritium is a naturally occurring, radioactive isotope of the hydrogen atom that decays by beta emission and has a half-life of 12.43 years. Prior to thermonuclear bomb testing, only the background level of tritium was present in the precipitation that recharged aquifers. Bomb testing in the mid and late 1950s and early 1960s increased tritium in precipitation to much higher levels (peaking in 1963) that 'labeled' ground water that was recharged at that time with relatively high tritium values. Now that more than 40 years has elapsed since bomb testing was stopped on a global scale, tritium in precipitation has declined to levels close to background again (IAEA/WMO, 2001). In order to distinguish relatively 'young' ground water (decades) from ground water that is much older (i.e. 'tritium-dead' ground water), it is particularly important to establish an accurate minimum detection limit for a given set of groundwater samples using a particular laboratory analysis. Even with the best available techniques for tritium analysis, there often remains considerable uncertainty about the age since recharge of a particular groundwater sample.

Improved dating of young ground water recently has developed through exploitation of the fact that radioactive decay of 3H produces the noble gas helium-3 (3He). Use of a measurement of tritogenic 3He in addition to 3H aids in defining what the initial input signature of tritium was to a ground-water sample, which has helped considerably in estimating the age of ground water following recharge in a number of aquifer types (Schlosser et al., 1988, 1989; Solomon et al., 1992). Price et al. (2003) used 3H/3He ratios to estimate that years to decades have elapsed since shallow ground waters in the Surficial aquifer of the southern Everglades were recharged. That study was one of the first investigations to estimate groundwater residence times in the Everglades using isotopes.

3.1. Measurement locations in Water Conservation Area 2A

Tritium was measured in ground water at seven wetland sites in WCA-2A (Fig. 1A). Six of the sites (F1, F4, E1, E4, U3, and S7-E) were located in the interior areas of the wetland. Research wells at each of the six interior sites had been emplaced in the underlying limestone and sand aquifer. Each site had 2-6 wells with depths ranging from 2 to 37 m below the ground surface. Site S10-C, with wells at three depths, differed from the other sites in the wetland interior by being located on the levee at the northern boundary of WCA-2A.

3.2. Well emplacement, ground-water sampling, and chemical analysis

Initial sets of exploratory shallow wells were drilled at five of the six interior sites in WCA-2A to depths of 2 and 8 m below ground surface by USGS-Geologic Discipline. A portable tripod drill rig with rotary coring capabilities (Shinn et al., 1984) was used to emplace those wells. Only surface water was used as the drilling fluid in that operation by pumping it down the annular space with hydraulic pumps. The depth of drilling under these conditions was limited by 'running sands' in the aquifer, the flow of which eventually equaled the flushing capacity of the pump and ended drilling. Upon completion of the borehole, a 3.8-cm (1.5-in. nominal) diameter PVC well with a 0.6-m long section of slotted (0.025-cm) screen at the bottom.

Additional boreholes were drilled at three wetland interior sites and one levee site using a more traditional mud-rotary method that was mounted conventionally on a truck trailer or on a specialized floating drilling barge. At sites in the wetland interior, two wells were emplaced in each borehole, resulting in one pair of shallow wells (4.5 and 9 m) and one pair of deeper wells (18 and 37 m) in addition to preexisting wells emplaced at 2 and 8 m. Three boreholes were drilled at the S10C levee site (9, 18, and 27 m), and four wells were emplaced (4.5, 9, 18, and 37 m) at the new site in the wetland interior referred to as S7-E. The new wells were 5.1-cm (2-in. nominal) diameter PVC with a 0.6-m section of slotted (0.025-cm) screen at the bottom. Details of drilling, core recovery, logging, well construction, and development of the wells are given in Harvey et al. (2002). All told, 25 monitoring wells were emplaced between 1997 and 2000 in WCA-2A.

Before sampling ground water for chemical constituents, all wells were purged at rates ranging from 2 to 12 l min-1 until three well borehole volumes had been pumped, or longer if necessary for measurements of water quality parameters (temperature, pH, specific conductivity, oxidation-reduction potential, and dissolved oxygen) to stabilize in a flow cell attached to the discharge line. After purging, ground-water sampling began by pumping at a rate of approximately 1 l min-1 with a peristaltic pump through pre-cleaned 6-m sections of flexible tubing.

Unfiltered ground-water samples for tritium analysis were collected in 500 or 1000 ml glass bottles with polyseal caps from all wells on five sampling dates (September 1997, January 2000, April 2000, September 2000, and September 2001). Tritium samples were sent for analysis by the Tritium Laboratory at Rosenstiel School of Marine and Atmospheric Science (RSMAS), University of Miami. Tritium was measured at the RSMAS laboratory by internal gas proportional counting of H2-gas followed by electrolytic enrichment and liquid scintillation counting. Accuracy of these low-level tritium measurements is approximately 0.1 TU (0.3 pCi per liter of 3H2O). The average standard deviation of replicate measurements reported by RSMAS for our samples was approximately 0.3 TU. For the present study, we used the sum of accuracy and average uncertainty (0.4 TU) as the best estimate of a tritium minimum detection limit (MDL). The MDL for tritium is important because it separates field measurements into two classes, those with greater than 0.4 TU have a high probability of containing relatively young ground water with measurable tritium while those with less than 0.4 TU have a dominant component of older, 'tritium-dead' ground water. Further details of tritium analysis and interpretation are available from the RSMAS Tritium Laboratory.

Several ground-water samples were collected for 3H/3He age-dating in September 1997. Those ground-water samples were sent for analysis of 3H/3He by the Lamont-Doherty Earth Observatory, New York. Details of sample collection, handling, and analysis are available from the USGS Reston Chlorofluorocarbon Laboratory. Samples were processed and interpreted with regard to ground-water age, i.e. time elapsed since recharge, by the contract laboratory. Although the results of 3H/3He analysis provided much more specific information about the residence time of the water sample in the aquifer, the collection of samples for measurement of 3H/3He ratios was potentially subject to more errors than collection for tritium alone. Samples with problems such as natural degassing processes in the aquifer or bubble capture in the sample were rejected and corrections were made for factors such as the input of terrigenic 3He to the sample (Schlosser et al., 1998). For the present study, there were four useable results from a collection of ten samples that were analyzed for 3H/3He ratio.

3.3. Coupled model of surface-water and ground-water flow

The purpose of the tritium measurements and transport modeling was to estimate average (decadal timescale) recharge and discharge fluxes of water in the interior wetlands of WCA-2A. Tritium was generally only detectable in a shallow layer of fresh ground water near the top of the Surficial aquifer. The layer of ground water that is actively exchanged with surface water on a decadel timescale is referred to as 'interactive' ground water. It lies above a thicker layer of relict sea water in the lower part of the aquifer that dates from an earlier geologic period of higher sea level stand (Harvey et al., 2002). The model considers the depth of water storage and average residence time of ground-water layer in the 'interactive' layer of the aquifer, as well as several other parameters (tritium concentration in rainfall, and average water depth, velocity, and longitudinal dispersion in surface water). Average recharge and discharge fluxes over the 50-year simulation period are calculated from modeling results.

The USGS numerical code OTIS (One-dimensional Transport with Inflow and Storage) (Runkel, 1998) was used for the tritium transport simulations. Although developed for streams, the OTIS code is general enough to be applied anywhere that surfacewater transport characteristics are significantly affected by mass transfer into and out of storage reservoirs. For example, OTIS was recently used to simulate transport through waste water treatment wetlands in Florida (Martinez and Wise, 2003) and solute transport through wetlands of Everglades National Park (Harvey et al., 2005). For the present case, the model simulates transport and decay of tritium in surface water in WCA-2A and exchange of tritium with ground water that occurs as a result of recharge and discharge. Characteristics of longterm averaged average surface-water flow velocity and depth, along with measurements of the vertical distribution of tritium in an aquifer with known porosity, along with the well known decay rate of tritium, are the principal constraints that allow recharge and discharge to be determined.

Tritium transport was modeled along a 12-km transect of unit width that extends from the northern boundary of WCA-2A and WCA-1 (near site S10C) into the center of WCA-2A. The transect is roughly oriented parallel with the principal surface-water flow path which is towards the southwest in WCA-2A (Harvey et al., 2002). Fig. 2B illustrates the major components of the model schematically. The governing equations for the present study are presented below. Note that the variables of a typical application of the OTIS model in a stream (Runkel, 1998) are recast following a derivation that uses 'exchange flux' in the formulation of the mass transfer terms between surface-water and the storage zones (Harvey et al., 1996). The equations for stream and storage zone are as follows

equation 1   D

equation 2   D

where Q is the average volumetric flow rate of surface water through the wetland [L3 t-1]; t is time [t]; x is distance [L]; C is the concentration of tritium [TU] in surface water; CGW is the concentration of tritium [TU] in interactive ground water layer defined as the layer of shallow ground water that undergoes exchange with surface water due to alternating periods of recharge and discharge; D [L2 t-1] is the longitudinal dispersion coefficient in surface water; w [L] is the width of the modeled cross-section in surface water and ground water; d [L] is the average depth of the surface water; dGW [L] is the average depth of water storage in the layer of interactive ground water; lambda [t-1] is the first-order coefficient for radioactive decay of tritium in surface water and ground water (1.8x10-9 s-1 or 5.6% per year); and qE [L2 t-1] is the coefficient describing bi-directional exchange that occurs between surface water and ground water by vertical fluxes (recharge and discharge) across the ground surface. The units of exchange flux can be interpreted physically as a volume of water exchanged per unit time, per unit length along the model domain in the direction of surface-water flow.

Application of the model involves adjusting the parameters of the model to fit measured tritium data. Among the ground-water parameters, calibration is simplified because depth of ground water storage, dGW, is independently specified from the tritium observations. Note that ground-water residence time is uniquely related to depth of water storage (multiplied by transect width) and divided by a water exchange flux

equation 3   D

As a result, the residence time is the only groundwater parameter that need be adjusted to fit observed tritium data. Average recharge and discharge fluxes (in units of L3 L-2 t-1 or simply L t-1) are both estimated by dividing the exchange flux by the transect cross-sectional width, w, as shown

equation 4   D

Note that for the present model of flow through central WCA-2A that the flow system is wide enough that transport can be assumed to be invariant with small to moderate changes in width. A 'transect' model of unit width (w = 1) is therefore appropriate, which results in estimates of recharge and discharge that are both equivalent to the water exchange flux, qE.

3.4. Model initial and boundary conditions

The simulation started in 1953, just before significant bomb testing began and when tritium in precipitation was relatively low. The initial and boundary conditions that were needed include specification of an upstream boundary condition for tritium in surface water, and specification of the initial concentration of tritium throughout surface water and shallow interactive ground-water at the start of the simulation. In the mid-1950s, tritium levels increased substantially in precipitation worldwide due to the advent of nuclear bomb testing. Tritium peaked in precipitation in 1963 and has decreased slowly ever since. The upstream boundary condition for our simulation (tritium concentration in surface water at the upstream location where water inflow occurs to the wetland transect) was prescribed on the basis of estimates of tritium in precipitation at Miami, FL. The initial conditions for the simulation were determined by initializing all surface-water and ground-water concentrations with the tritium concentration in precipitation in 1953, and then following the procedure of Runkel (1998) by running the model until steady concentrations were achieved at all locations.

Tritium data were available for Miami from 1964 to 1991 and from 1996 to 2001 (IAEA/WMO, 2001). Because ground water with a decadal-scale residence time would not be expected to reflect the monthly variations in tritium concentrations that affect precipitation, the tritium data for precipitation were averaged annually (weighted by monthly precipitation) to smooth the data record. For years without tritium measurements in Miami, the values were calculated based on a linear regression approach using the longer record of measurements from Ottawa, Canada (IAEA, 1981). Tritium values used for the years 1963-1991 and 1996-2001 were the annual averaged of the monthly measured values in Miami (Fig. 3). Annual mean values shown in Fig. 2 for the years prior to 1963, and the years 1992-1994 were determined from a regression of Miami tritium on tritium data from Ottawa (log [Miami tritium] = 0.9826[Ottawa tritium] - 0.8920, r2 = 0.96). Tritium was not measured in either city in 1995, so the 1995 tritium value for Miami was estimated by linear interpolation between estimates for 1994 and 1996 (value for 1995 shown in Fig. 3 as an x).

graph of tritium in precipitation for Miami, Florida
Fig. 3. Tritium in precipitation for Miami, Florida. Annual mean tritium values were computed directly from monthly measurements in Miami when available. When Miami tritium data were unavailable, tritium was computed from a linear regression of Miami tritium data (monthly weighted annual means) on similarly weighted tritium data from Ottawa, Canada. [larger image]

3.5. Model sensitivity analysis

Before applying the model to simulate the field data, a 'base' simulation was needed with rough, order-of-magnitude estimates of parameters, for the purpose of exploring model behavior and sensitivity. Results of sensitivity analyses would be important for testing assumptions of the model and guiding the final simulations to quantify recharge and discharge. An average surface-water velocity (0.5 cm s-1) and depth of surface water (0.3 m) were selected to represent long-term average values for the base simulation (Harvey et al., 2002; Rybicki et al., 2002). A preliminary estimate of the depth of water storage in the interactive layer of the aquifer was based on observed depths of the layer of freshwater that overlies the much older relict seawater in the aquifer (Harvey et al., 2002). An initial estimate of exchange flux was calculated (using Eq. (3)) to be consistent with a modeled ground-water residence time on the order of decades. Table 1 contains the initial parameter estimates used in the base simulation for sensitivity analyses.

Table 1
Parameter estimates used in the base simulation
Parameter Value
Surface-water velocity, v 0.5 cm s-1
Depth of surface water, d 0.30 m
Longitudinal dispersion in surface water, D 0.01 m2 s-1
Depth of shallow interactive ground water, dGW 1.9 m
Water exchange flux across ground surface, qE 0.2 cm d-1
Tritium decay rate, lambda 1.8x10-9 s-1

Sensitivity of the model results to individual parameters was tested by adjusting parameters of the base simulation one at a time by a factor of 2 and rerunning the model. Fig. 4 shows an example of how tritium concentrations in ground water are affected by varying the exchange flux across the ground surface. Overall results of the sensitivity analysis are summarized in Table 2. The root mean squared error (RMSE) of tritium concentrations in the interactive ground-water zone was calculated for each new simulation with relation to the base simulation. The RMSE is a measure of the absolute difference in the base simulation and new simulation results caused by the parameter change. The results show that the modeled tritium concentrations in shallow interactive ground water were primarily sensitive to two parameters, dGW and qE (Table 2). The sensitivity to surface-water velocity and longitudinal dispersion in surface water are minor in comparison. Since dGW is constrained by the observations of tritium and since this parameter only appears in the model in ratio with qE, only the model ground-water residence time (tGW = dGWw/qE), needed be adjusted to achieve a final model fit to tritium data because all other parameters were either relatively insensitive (surface-water velocity v and longitudinal dispersion D), or fixed (w = 1).

Table 2
Sensitivity of tritium concentrations in ground water to factor of 2 changes in the input parameters
Parameter Root mean squared error (from base simulation)
Increase parameter Decrease parameter
Depth of shallow interactive ground water, dGW 236 235
Water exchange rate across ground surface, qE 231 233
Surface-water velocity, v 3 6
Longitudinal dispersion of surface water, D 2.8x10-4 1.4x10-4
The root mean squared error (RMSE) was computed relative to the base simulation.

graph showing sensitivity of model to changes in the exchange flux between surface water and the layer of interactive ground water
Fig. 4. Sensitivity of model to changes in the exchange flux between surface water and the layer of interactive ground water, qE. [larger image]

3.6. Justification for model simplifications

One of the most important model simplifications is that temporally and spatially averaged recharge must equal discharge. This simplification is reasonable if (1) temporal averaging is long enough that changes in water storage in the wetland are negligible, and (2) if all water that is recharged across the wetland ground surface is eventually discharged across the same surface. With regard to assumption (1), temporal averaging of the water balance in WCA-2A over decades is almost certainly long enough that changes in water storage in the wetland can be ignored. With regard to (2), there is thought to be a small 'net recharge' flux over the long-term in WCA-2A due to very slow transport to ground-water areas outside WCA-2A, but that flux is thought to be mainly important near the eastern boundary of WCA-2A and, when averaged over WCA-2A as a whole, the net flux is thought to represent only a small difference between the much larger recharge and discharge fluxes across the wetland ground surface (Harvey et al., 2002).

Our use of a model that does not allow for horizontal flow in ground water also needs to be justified. Also needing justification is the decision to average parameters spatially along the transect even though the model allows for horizontal spatial variation in ground-water storage, residence time, and water exchange flux parameters. For example, the choice was to either account for horizontal spatial variation in parameters by implementing 'sub-reaches within the model, each with different parameters. Or, if spatial variation is minimal or is random, reach-averaged values of the parameters could be determined for a single reach. The second choice was selected as being most reasonable for this model of surface-water and ground-water interactions in WCA-2A. Several considerations were important, including a consideration of the timescales of the various processes and the form of the spatial variability. Those considerations are summarized as follows: (1) horizontal ground-water velocities in WCA-2A (~0.02 cm d-1) from Harvey et al. (2002) indicate that the residence time of horizontally flowing ground water in WCA-2A is on the order of hundreds of thousands of years, which is extremely slow relative to the timescale of tritium decay (12.43 years), the residence time of surface water along the transect (approximately 30 days), and also the timescale of significant changes in the tritium concentration of precipitation (years); and (2) horizontal variation in the water exchange flux (based on variability of observed tritium profiles in ground water) do not appear to vary systematically along the transect.

We addressed the question of what is the appropriate level of simplification of our model by evaluating the sensitivity analysis results (Table 2) and also evaluating variability of tritium measurements. It appears safe to ignore the effects of horizontal ground-water flow based on the relative timescales of surface-water and ground-water flow, tritium variation in precipitation, and horizontal movement of ground water. Also due to the relative timescales of flow and tritium decay, no longitudinal gradient is expected to develop in surface-water tritium. These comparisons explain the insensitivity of the model to the average velocity and longitudinal dispersion coefficient in surface water (Table 2). The question of whether to represent longitudinal variability in ground-water parameters in sub-reaches, or simply average that variability in a single reach, rested on the evaluation of measured tritium profiles in ground water; these data are presented in the next section. It is sufficient to say here that the evaluation supported use of a one-reach model with (horizontally) spatially averaged parameters. It is important to note that the model's complexity could easily be expanded as needed for modeling other data sets.

Is further simplification of the model possible? Since the model is generally insensitive to average characteristics of surface-water flow and transport, and because spatial variation in the measured tritium profiles can be appropriately averaged, the problem of estimating recharge and discharge in the central Everglades potentially reduces even further to the simple calculation presented in Eq. (3). Use of Eq. (3) instead of the full model depends on having independent estimates of average ground-water residence time and depth of water storage in the interactive layer of the aquifer. This simple procedure to calculate recharge and discharge fluxes will be especially useful for data such as that presented by Price et al. (2003), where numerous independent estimates of ground-water residence time and depth of the interactive layer were determined by measurement of 3H/3He ratios in ground water in Everglades National Park. It should be emphasized that use of such a simple calculation as Eq. (3) to compute recharge and discharge in the Everglades is justified only because we demonstrated that tritium transport and decay in the interior areas of the Everglades are insensitive to rates of horizontal transport of ground water, as well as the insensitive to surface-water velocities and rates of longitudinal dispersion. Application in areas of the Everglades closer to its boundaries, or application with different tracers could invalidate use of Eq. (3).

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