Methods

Study site—Site S10C-N is located in the Water Conservation Area-1 (WCA-1), approximately 200 m north of control structure S10-C on Levee 39, also referred to as the Hillsboro levee (Fig. 1). Site S10C-S is located approximately 50 m south of the tailwater canal on the south side of Levee 39, in Water Conservation Area-2A (WCA-2A). Because of water conservation practices, a difference in water level of ~0.3-1 m often occurs between these two sites. As a result of this potentiometric head difference, groundwater recharge is known to occur at S10C-N and groundwater discharge is known to occur at S10C-S (Harvey et al. 2002). Site U3 is located in the interior of WCA-2A, 12 km away from the levee, and the head difference at the levee has a much smaller effect on the groundwater movement at this site. Harvey et al. (2002) showed that the long-term average vertical flux of groundwater at site U3 is small (~0.06 cm d^-1), though instantaneous rates can sometimes be as large as ±0.5 cm d^-1.

Fig. 1. Map showing the location of sites S10C-N, S10C-S, and U3. [larger image]

Samples were collected from sites S10C-N and S10C-S on 5 April 2001 and 30 April 2001. Samples were collected from site U3 on 25 September 2001. All sites are in undisturbed sediment and vegetation. The peat layer is approximately 1 m thick at these sites, and the bottom of the peat is well defined with either carbonate or siliceous sediments lying directly beneath it. Above the peat is an unconsolidated detrital layer, commonly called the "floc" layer, which is easily disturbed and resuspended into the overlying surface water.

Measurements of dissolved radium—Temporary wells were installed at various depths in the sediments to collect water for measurements of dissolved radium. These wells consisted of either (1) 3/8-inch (0.95 cm) stainless steel drivepoints with vertical slots near the bottom end measuring 0.010 inch (0.025 cm) wide and 2 cm in length or (2) 1/2-inch (1.27 cm i.d.) schedule-40 polyvinyl chloride (PVC) pipes with 5 cm of slotted screen (0.010 inch) near the bottom. The wells were installed in an array to sample at 10-20 cm vertical resolution, making sure that the screened sampling intervals of individual wells were no closer than 50 cm from each other in any direction. Between 0.5 and 2 liters of pore water was pumped at rates <100 ml min^-1 and filtered through 0.45-µm (actual) pore size filters, then passed through Mn-fiber to concentrate the radium isotopes (Moore 1976). ²²³Ra and ²²⁴Ra were analyzed by delayed coincidence counting of the Mn-fiber (Moore and Arnold 1996). Subsamples of the filtered water were also analyzed for chloride by ion chromatography.

Radium distribution—In saturated sediments, a significant fraction of exchangeable radium is dissolved, but most is adsorbed to particles. This partitioning is commonly described as a simple, linear, sorption isotherm (Ra_Adsorbed = K_D x Ra_Dissolved), which can be rearranged to solve for K_D, the Ra distribution coefficient.

Ra_Adsorbed is the mass of radium per gram dry weight of peat and Ra_Dissolved is the mass of radium per mass of pore water.

K_D is often measured in the laboratory either by leaching the exchangeable radium from the sediment using high-ionic strength solutions, or by adding a radium spike or tracer to a sediment slurry and determining the amount taken up in the liquid and solid fractions (e.g., Rama and Moore 1996; Krest et al 1999). However, by treating a sample with dilute hydrogen peroxide, Rama and Moore (1996) demonstrated that oxidation of the sediment during transport and analysis might free up binding sites in the sediment and artificially increase the value of K_D. Sun and Torgersen (1998) provided an improvement on these methods whereby the dissolved and adsorbed phases are quickly separated and measured directly from the water or solid, but some oxidation of the sample can still occur before separation unless great care is taken.

Because of the low radium activities in the Everglades’ peat sediments and pore water, K_D could not be measure with good precision using Sun and Torgersen's (1998) method. Instead, K_D was determined for each site by dividing the production rate of the exchangeable radium by the dissolved radium activity according to Eq. 1. This calculation was performed only on data from upper portions of the peat cores, where an equilibrium relationship between the production rate and dissolved activity was demonstrated. Because the dissolved fraction is collected in situ and the production measurement gives total exchangeable radium, oxidation problems are not a concern with this method.

Sediment analyses—Sediment cores 10.2 cm in diameter were taken at each site for measurements of radium production rates, porosity, and dry bulk density. Cores were sectioned in 5- or 10-cm intervals, and interval depths were corrected for compression as measured at the time of coring. Each interval was homogenized, and one fraction was taken to determine the average density of the sediment particles, the average porosity, and the dry bulk density (Lambe 1951). Another fraction of sediment was aged to ensure equilibrium between the radium isotopes and their respective parents, dried, disaggregated in a blender, and analyzed for the production rates of exchangeable ²²³Ra and ²²⁴Ra by delayed coincidence counting of the remoistened sediment (Sun and Torgersen 1998).

Models of vertical transport through peat—Background: The peat layer has different production rates for ²²³Ra and ²²⁴Ra than the surface water or underlying sediments, so profiles of the isotopes near the upper or lower interface can be modeled to determine the advective or dispersive flux across the interface. Water that crosses the interface from one layer to the next will initially have a radium concentration greater than or less than that supported by the local production rate, and as that water parcel continues to travel through the new layer, this dissolved concentration will eventually come into equilibrium with the new production rate. Similarly, at the surface of the peat, profiles can be used to determine the gain or loss due to groundwater recharge if the surface-water activities are different from the supported radium activities in the pore water.

The one-dimensional advection and dispersion models presented below are an appropriate simplification for freshwater systems of the detailed one-dimensional, advective-diffusive transport model recently formulated by Sun and Torgersen (2001). Because of the estuarine system they were working in, their model required considerations for changes in the adsorbed/dissolved radium partitioning coefficient (K_D) and a subjective assignment of separate zones of physical and biological mixing without explicit correlation to pore-water geochemistry or sediment morphology.

Model derivation: ²²³Ra and ²²⁴Ra are produced from the decay of their respective thorium parents. Thorium is extremely particle reactive (K_D = 10⁴-10⁵), so the primary source of these radium isotopes is in and on sediment surfaces. Because radium is much less particle reactive than thorium (K_D 10²–10³ in freshwater), an appreciable fraction is dissolved in pore water. As a dissolved ion, radium is transported with pore fluids, and its gain or loss near sediment/sediment or sediment/water interfaces can be modeled in saturated sediments as a balance of its production, decay, advection, dispersion, and exchange with particles (Berner 1980).

(2)

D

where t is time, Z is depth below the peat surface, C is the number of dissolved radium atoms per volume of water, C* is the number of adsorbed radium atoms per mass of dry sediment, D is the hydrodynamic dispersion coefficient in units of (length)² per time, v is the pore-water advective velocity in units of length per time, is the production rate of exchangeable radium (dissolved plus adsorbed) from its respective parent isotope in atoms per time, per mass of bulk sediment, is the pore water density in mass per volume, f is the mass of dry sediment per mass of bulk sediment, K_D is the radium distribution coefficient (Eq. 1), and is the respective decay constant (0.189 d^-1 for ²²⁴Ra; 0.0606 d^-1 for ²²³Ra).

When conditions are at steady state, and in areas where advective fluxes greatly exceed dispersive fluxes, Eq. 2 can be simplified and solved for the concentration of radium at any depth in the peat (C(Z)).

(3)

D

Here, C_I is the radium concentration at an interface defined by the investigators as the depth of a transition between sedimentary layers or the depth of the sediment/surface-water interface. Z is calculated as the difference between the depth of the interface and the sample depth so that Z = 0 at the interface and is positive upward. The boundary conditions are C(Z = 0) is equal to the measured C_I, and C(Z = ) is equal to P. P is equal to /(f K_D + (1 - f ))—the fraction of the exchangeable radium production that will enter the pore water—and is analogous to the supported, dissolved radium activity at equilibrium.

In some areas of the Everglades, vertical velocities are slow and often reverse directions so that the average advective velocity approaches zero (Harvey et al. 2002). In these areas, it might be more appropriate to model dispersion as the dominant transport process. The steady-state solution to Eq. 2 for the case where dispersion dominates over advection is shown in Eq. 4.

(4)

D

The absolute value of the distance from the interface (|Z|) is needed in Eq. 4 to allow for the most general case where Z could be a positive or negative distance from the interface in this coordinate system.

It would have been preferable to solve for advection and dispersion simultaneously, but at very low pore-water velocities, it is unlikely that analytical uncertainties will allow us to separate these variables. At low velocities, the advective and dispersive terms are usually similar in magnitude, occur as a ratio in solution and cannot be independently estimated. Indeed, model curves produced from Eqs. 3 and 4 are nearly identical, and the choice of one over the other depends primarily on our knowledge of the hydraulics and geochemistry of the system.

It must be noted that the radium production rate has been described as a constant through the sediment layer being studied. In relatively homogeneous sediments, this assumption should be valid but should be tested for individual systems. In this freshwater system, we are assuming that K_D is constant through each layer of sediment as long as we can demonstrate that the ionic strength of the pore water does not change appreciably with depth. Because K_D is constant and we are modeling for steady-state conditions, retardation of radium is not a factor (Berner 1980; Tricca et al. 2001).

Because radium is generally measured and discussed in terms of its activity (A) rather than its concentration, we multiply both sides of Eqs. 3 and 4 by (A = C). The vertical profile of dissolved radium is therefore described by Eqs. 5a and 5b.

(for advection)

(5a)

D

or

(for dispersion)

(5b)

D

A_I is the dissolved radium activity at the interface and A(Z) is the dissolved radium activity as a function of depth.