Discussion

The one-dimensional models derived to explain the advective (Eq. 5a) or dispersive (Eq. 5b) transport of shortlived radium isotopes through pore water are based on a number of implicit assumptions. It is important to keep in mind that these simple models require the radium production rate and the radium distribution coefficient (K_D) to be constant through the sediment layer being studied. If these assumptions are not met, more detailed geochemical terms will be needed in the governing equation to account for these additional complexities (e.g., Cochran 1980; Sun and Torgersen 2001).

Testing the assumption of constant radium production was simplified recently by Sun and Torgersen's (1998) elegant method of measuring the emanation of ²²⁰Rn from a column of moistened sediment to determine the amount of exchangeable ²²⁴Ra in the sample. This method quickly and easily determines the amount of ²²⁴Ra adsorbed to the sediment particles, and this surface-bound radium is the fraction subjected to the processes of adsorption, desorption, and transport in the dissolved phase. Using samples that have been aged to ensure ²²⁴Ra is in equilibrium with its ²²⁸Th parent allows us to determine the production rate of surface-bound ²²⁴Ra. We also determined the production rate of the surfacebound ²²³Ra in the peat samples by applying the same theory to the ²²⁷Ac–²²³Ra–²¹⁹Rn decay series. Figure 2b shows that the ²²³Ra and ²²⁴Ra production rates are constant through the peat layer but become more variable in the deeper sediments. Our assumptions for modeling vertical transport of radium through the peat are therefore reasonable, but variability in production rates below the peat mean that vertical transport in the sand and limestone layers are too complicated to be accurately described by our simplified transport models.

A gradient in the radium distribution coefficient (K_D) could similarly cause an apparent dissolved radium gradient in the pore water. Therefore, good knowledge of K_D through the sediment layer is essential. Sun and Torgersen (1998, 2001) measured K_D directly from the sediment samples and the pore water extracted from the sediment intervals. However, because of the low radium concentrations in the Everglades peat and pore-water samples, our estimates of K_D could be determined experimentally only from certain sediment and pore-water samples collected far enough from the interface to ensure an equilibrium relationship between the dissolved radium and its production rate. There is excellent agreement between the average dissolved radium activity in samples collected away from the interface () and the model-derived estimate of the production rate of the dissolved radium (P), giving us confidence that equilibrium has been reached between production, decay, and exchange in this interval (Table 2).

Because of the significant potential for error in estimating K_D in freshwater sediments, small trends of variation in K_D as a function of depth might not be noticed in the data even though they could have large effects on the dissolved radium activities. Because the strongest control on the radium distribution coefficient in homogeneous portions of the sediment is likely to be the ionic strength of the solution (Copenhaver et al. 1993; Webster et al. 1995) and because chloride concentration is the overwhelming contributor to the anion side of the charge balance, the constancy of the chloride concentration with depth was used as a first-order approximation of the constancy of K_D (Fig. 3a).

Furthermore, radium activity shows no correlation to the chloride concentration at any site, except possibly in the most surficial samples at site S10C-S (Fig. 3b). This slight correlation is not of concern in this study because pore-water radium concentrations in the upper part of the peat are all very similar and have little or no bearing on the radium distribution in the bottom of the core where the concentration gradient is being modeled.

Radium profiles at S10C-S are consistent with groundwater discharge, with a modeled advective velocity (averaged for the results of the two radium isotopes) of 1.5 ± 0.7 cm d^-1. The model result for the advective velocity is not very sensitive to the boundary conditions; the analytical uncertainty of the radium activity and production rate boundary conditions adequately cover the spread of radium activities in the pore-water profiles (Fig. 4). An advantage of this model is that the activity gradient being modeled occurs deep within the peat, away from the surface of the peat where mechanical disturbances to the system could easily distort the signal.

The radium profile at site U3 is very similar to the profile at the groundwater discharge site, S10C-S. Fitting the advective transport model to the U3 data results in an advective velocity of 2.3 ± 0.5 cm d^-1, which is slightly higher than the velocity calculated for S10C-S, although not statistically different. The issue of whether the primary transport mechanism is advective or dispersive cannot be resolved by measuring the flux to the surface water: for advective transport, the radium flux (J) is roughly calculated as the average radium pore-water activity in the upper part of the core multiplied by the velocity (Berner 1980).

In the case of dispersion, the maximum flux is a function of the dispersion coefficient and the decay constant (Krest et al. 1999).

J = A

(7)

A can be approximated in this case as the difference between the pore-water and the surface-water radium activities. On the basis of the values for v and D calculated from the radium pore-water profiles, radium fluxes to the overlying surface water at site U3 should be the same without regard as to whether the primary transport is modeled as a function of advection or dispersion (Table 3).

Modeling the radium pore-water profiles as described in this paper determines limits for the flux of radium to surface water and can be used as an important test in mass balance models for surface-water radium. Furthermore, results of the solution of these one-dimensional vertical models will also be useful for estimating the transport rates of nutrients and other solutes into or out of the pore water and can be used to quantify solute storage and release rates and biogeochemical cycling. One of the key advantages of this technique is that dispersion and upward advection are measured at depth in the sediment column, away from mechanical disturbances to the surficial sediment. In an environment with consistent radium production rates in deeper sediment layers, this advantage would hold true for recharge measurements as well. These techniques can be adapted for any wetland systems that have well-defined layers (sedimentary or sediment/surface-water transition) creating distinct discontinuities in the radium production rate, but they must be used with caution in environments where there are uncertainties in the constancy of lithology or ionic strength within layers. For those situations, more data and a more detailed model representation will be required.