Results

Test of model assumptions—The one-dimensional advective and dispersive transport models defined above require that certain conditions or assumptions be reasonably well met. The principal conditions are that (1) the pore-water radium activity near the sediment/sediment or sediment/surface-water interface is out of balance with the activity that would be expected as a function of the radium production rate in the sediments and the partitioning of radium between the dissolved and adsorbed phase and that this disequilibrium can be described as the result of either advective or dispersive transport across the interface; (2) the sedimentary layers are relatively homogeneous chemically and physically, and the interface between the layers is well defined; (3) the radium production rates are constant through each layer, but significantly different between the two layers; and (4) the partitioning of radium between the dissolved and adsorbed phase is constant through each layer. The first condition we already addressed using our knowledge of the vertical hydraulic gradient in Everglades peat. We will address the remaining three conditions here.

The Everglades' peat layer is relatively homogeneous in bulk sediment properties (Fig. 2a). For example, at site S10C-N porosity of peat is very high (0.93 ± 0.02), the density of peat is relatively low (1.34 ± 0.08 g cm^-3), and the dry bulk density of peat is also very low (0.09 ± 0.02 g cm^-3). The base of the peat is well-defined and is characterized at all the sites by a distinct change from the high-porosity, low-density peat sediments to high-density, lowporosity silicate or carbonate sediments. The underlying silicates or carbonates are reasonably homogeneous in terms of their physical characteristics, but not their chemical characteristics (Fig. 2b). The production rates of ²²³Ra and ²²⁴Ra are constant through the peat layer, but much more variable in the sediments below the peat.

Fig. 2. Physical and chemical characteristics of the sediments. (a) The base of the peat is readily apparent by the decrease in porosity and the increases in the average density of the sediment grains and the dry bulk density at site S10C-N. (b) Production rates of 224Ra and 223Ra are constant through the peat layer, but then increase below the peat. This increase is most apparent in sediment samples taken from a 1.8-m core at site S10C-N where the production rates initially increase exponentially below 0.9 m and then become irregular with variations in sediment lithology (compare with dry bulk density profile in panel a). Solid horizontal lines in panels a and b indicate the base of the peat layers. [larger image]

Table 2. Radium distribution coefficients (KD) in Everglades peat. nd, not determined; dpm, disintegrations or atoms per minute.   S10C-S S10C-N U3 224Ra 223Ra 224Ra 223Ra 224Ra 223Ra (dpm kg-1) 21.2 0.49 25.5 0.66 34.9 0.91 (dpm [100 L]-1)* 8.42 0.34 10.2 0.29 20.2 0.55 P (dpm [100 L]-1)† 7.60 0.40 nd nd 17.0 0.60 KD (using ) 250 144 250 230 170 160 KD (using P) 280 120 nd nd 210 150 * is the average of the dissolved radium activities between 10 and 50 cm in the peat. † The value for P is determined from the model (see text and Table 3).

K_D values were determined from the relationship between the exchangeable radium and dissolved radium (Eq. 1). The dissolved radium was approximated as the average of the dissolved radium samples between 10 and 50 cm depth in the peat (). Dissolved activities in this interval were all very similar, suggesting equilibrium had been reached between production, decay, and exchange. The total exchangeable radium was estimated from the production rate of the exchangeable radium, again assuming that equilibrium conditions existed for this interval. K_D values ranged from 120 to 280 for the peat sediments (Table 2).

Fig. 3. (a) Concentrations of dissolved chloride are plotted as a function of depth to show the lack of variation through the peat and underlying sediment. (b) 224Ra shows no correlation with chlorinity below a few centimeters in the core, supporting the assumption that KD is constant through the homogeneous sediment layers (see text). The trend for 223Ra is similar and is not shown here. [larger image]

In homogeneous sediments, changes in K_D would most likely result from changes in the ionic strength of the pore water. Because chloride can be measured with much greater precision than K_D, chloride concentration was used as a proxy of ionic strength to test the constancy of K_D in the peat and aquifer sediments. Figure 3a shows chloride concentration as a function of depth, and Fig. 3b shows porewater radium activity as a function of chloride concentration. There is little or no correlation between chloride concentration and depth or between radium activity and chloride concentration, suggesting that K_D is constant in the peat layer. Unfortunately, we cannot extend this relationship below the base of the peat because of the confounding effects of changing sediment characteristics.

Quantify rates of exchange—Figure 4a,b shows pore-water ²²⁴Ra and ²²³Ra activities in the peat layer at site S10C-S. The activities are highest near the base of the peat as a result of upward transport from below. Activities decrease exponentially to a constant value in the upper portion of the peat as the excess radium decays away and the activity of the dissolved plus adsorbed fraction approaches equilibrium with the production rate. Overlying the data in Fig. 4a,b are model-derived lines for upward advection of radium and pore fluids based on Eq. 5a. For all data sets, the "best fit" parameters v or D, A_I, and P were determined using a curve-fitting routine that maximized the log of the likelihood function using a Nelder–Mead simplex algorithm and assuming a Poisson distribution. The center line in each panel of Fig. 4 shows the best fit simulation, modeled using the parameters identified by the fitting routine. The two outside lines indicate the 95% confidence intervals (mean ± 2 SE) for combined uncertainty in the velocity or coefficient of dispersion (v or D), radium activity at the interface (A_I), and the production rate in the peat (P). Based on the ²²⁴Ra and ²²³Ra model fits, the advective velocity at site S10C-S is 2.4 ± 0.6 cm d^-1 or 0.50 ± 0.25 cm d^-1, respectively.

Fig. 4. Pore-water radium activities as a function of depth. (a) 224Ra and (b) 223Ra activities at site S10C-S are highest at the base of the peat, indicated by a solid horizontal line, and decrease upward as the excess radium in discharging groundwater decays to a level supported by its equilibrium production and exchange with the adsorbed fraction. (c) 224Ra and (d) 223Ra activities at S10C-N are elevated only in the upper portion of the peat, suggesting that recharge occurs at this site. (e) 224Ra and (f) 223Ra profiles at site U3 are similar to profiles from S10C-S but have been modeled for dispersive transport because of independent observations that recharge and discharge alternate at this site. Model curves in panels a, b, e, and f indicate the best fit to the data along with 95% confidence intervals based on the uncertainty of the three parameters (v or D, AI, and P). The central model curves in panels c and d indicate the upper limit of our estimate for the magnitude of the recharging velocity (v) with the best estimate for the boundary conditions, AI and P. The outer model curves in panels c and d use the same value for v as the central line and their spread is based on the analytical uncertainty of the boundary conditions. [larger image]

Data from site S10C-N are modeled in Fig. 4c,d using Eq. 5a. Activities are nearly constant through the peat but are slightly higher at the very surface of the peat. The activity gradient near the surface and the lack of a gradient at depth, despite an increased production rate in the sand beneath the peat, indicate that groundwater is recharging at this site. Sampling intervals were not adequate to precisely determine the activity gradient at the top of the peat, but model fits are useful to constrain the possible maximum rate of advective transport. The ²²⁴Ra profile indicates that magnitude of the recharge is less than 0.9 cm d^-1. The ²²³Ra profile constrains the magnitude of recharge to less than 0.43 cm d^-1. Because the radium production rate is not constant in the sediments below the peat, we are unable to further constrain the rate of recharge at site S10C-N by modeling the radium profiles below the peat.

Figure 4e,f shows the result of fitting the dispersive transport model (Eq. 5b) to pore-water ²²⁴Ra activities at site U3, resulting in coefficient of dispersion values of 60 ± 18 cm² d^-1 and 23 ± 5 cm² d^-1 from ²²⁴Ra and ²²³Ra profiles, respectively. Model results for all sites are summarized in Table 3.