Predicting the accumulation of mercury-contaminated sediment on riverbanks—An analytical approach



[1] Mercury was introduced into the South River, Virginia, as a result of industrial use from 1929 to 1950. To guide remediation, an analytical model is developed to predict the mercury inventory resulting from deposition of mercury-contaminated sediment on subhorizontal surfaces adjacent to the river channel from 1930 to 2007. Sediment cores and geomorphic data were obtained from 27 sites. Mercury inventories range from 0.00019 to 0.573 kg m−2. High mercury inventories are associated with frequent inundation by floodwaters, forested riparian vegetation, and (at only four sites) unusually high sediment accumulation. Over the 10 km study reach, mercury inventories do not vary with downstream distance. The frequency of inundation at each coring site is determined from hydrologic data and a streamtube stage-discharge model. Water levels are exponentially distributed. A simple parameterization represents the enhanced ability of forested vegetation to trap mercury-contaminated sediments compared to nonforest vegetation. The calibrated model explains 62% of the observed variation in mercury inventories; 15 of the 27 predicted values are within a factor of 1.8 of the observed values. Calibration indicates a mercury deposition rate during inundation of 0.040 kg m−2 yr−1 (95% C.I. 0.032–0.048), that forested areas accumulate mercury-contaminated sediment 3.05 (95% C.I. 2.43–3.67) times faster than nonforested areas, and that floodwaters deeper than 0.98 (95% C.I. 0.45–1.53) m do not accumulate suspended sediment or mercury. At four sites, floodplain accumulation of 0.8–1.2 m occurred over a period of 39 (95% C.I. 22–56) years, while sedimentation is negligible (mean: 0.1 m, median: 0.03 m) at other sites.

1. Introduction

[2] Many river systems have been contaminated by industrial releases of metals and other contaminants [Miller and Orbock Miller, 2007]. Where contaminants are adsorbed to particles, floodplains and other storage compartments along river valleys can sequester these contaminants long after their release. Stored sediments can be remobilized through geochemical processes and fluvial erosion, providing a continuing source of contamination to fluvial ecosystems that can last for millennia [Coulthard and Macklin, 2003; Malmon et al., 2002].

[3] Mercury was introduced into the South River from 1929 to 1950 when it was used as a catalyst for producing rayon acetate fiber at a manufacturing facility in Waynesboro, Virginia. The contamination was discovered in 1976, leading to a fish consumption advisory for 160 km below Waynesboro. Unfortunately, mercury levels in fish tissue have failed to decrease through natural attenuation [Wang et al., 2004]. Recent studies have implicated erosion of mercury-contaminated bank sediments as an important ongoing source of mercury to the South River's food web [Rhoades et al., 2009]. Because the residence time of floodplain sediments along the South River is thousands of years [Pizzuto et al., 2011a; Jackson et al., 2005], remediation planning necessarily includes measures to control rates of bank erosion.

[4] To design a remediation scheme to reduce mercury loading from eroding banks, it would be helpful to know the average annual rate of mercury loading from bank erosion as a function of distance downstream of Waynesboro. This information is key for targeting the most important sources of mercury loading to the river for remediation, and could be used in combination with other information to prioritize site selection ( Mercury loading from bank erosion processes can be estimated from knowledge of mercury concentrations and erosion rates of riverbank soils. However, these variables cannot be directly measured along many miles of river channel, and as a result, predictions of mercury loading must rely on a suitable computational model calibrated with field observations.

[5] This paper describes a method for predicting the inventory of mercury in riverbank deposits adjacent to a river channel, as these are the most likely sources of mercury that could be mobilized by bank erosion. Mercury accumulation is treated as a sedimentation process, recognizing that mercury is mostly transported adsorbed to suspended particles. A simple analytical equation is derived for the mercury inventory. Parameters are estimated by calibrating the equation to data from sediment cores. Results presented here demonstrate that simple models of long-term sedimentation processes can be readily calibrated using appropriate field measurements. After calibration, the analytical model can predict the spatial distribution of sediment thicknesses and contaminant concentrations along the margins of a river channel.

2. Study Area

[6] The South River is located in the Blue Ridge and Valley and Ridge physiographic provinces of Virginia [Bingham, 1991] (Figure 1). It flows through a valley consisting of alluvium, fluvial terraces, alluvial fans, with frequent outcrops of folded and faulted Paleozoic clastic and carbonate sedimentary rocks [Gathright et al., 1977, 1978]. The region has a humid temperate climate.

Figure 1.

Location of the study area. Coring sites indicated by black dots in a. Multiple cores were taken at some of the sites (indicated by numbers in a).

[7] The study area encompasses about 10 km of South River's valley, starting from about 4 km north (downstream) of Waynesboro to Crimora, Virginia. Here the South River is a single-thread, gravel bed bedrock river [Turowski et al., 2008)] with an average slope of 0.0013, a bankfull width and depth of about 26 and 1.9 m, respectively, and an average sinuosity of 1.4 [Narinesingh, 2010]. The bedrock exposures and forested riparian zone limit channel migration rates to only a few cm per year [Rhoades et al., 2009]. In 1937, 13 colonial-age mill dams impounded the river from Waynesboro to its confluence with the North River in Port Republic, Virginia. All of these dams except one were breached by 1957, with the sole remaining dam breached by 1974 [Pizzuto and O'Neal, 2009].

[8] Water discharge of the South River is gauged by the U.S. Geological Survey at three locations. At Waynesboro (period of record 1952–2011) the South River has a drainage basin area of 330 km2, a mean annual discharge of 4.2 m3 s−1, and a mean annual flood of 117 m3 s−1. At the South River near Dooms (period of record 1974–2011) the South River has a drainage basin area of 385 km2, a mean annual discharge of 5.9 m3 s−1, and a mean annual flood of 157 m3 s−1. At Harriston (period of record 1925–2011) the South River has a drainage basin area of 550 km2, a mean annual discharge of 7.3 m3 s−1, and a mean annual flood of 216 m3 s−1.

[9] Sites for model calibration were selected based on geomorphic characteristics and availability of data (Figure 1; Table 1). Sites with exposed bedrock or engineering works were avoided. Sites where sandy sediments are deposited as a result of lateral channel migration (point bars, for example) were not successfully parameterized by our model, and these sites are not included.

Table 1. Location, Geomorphic Setting, Data, and Computed Values for the Coring Sites
Distance Downstream of Waynesboro (km)aBankGeomorphic SettingForest (F) or Pasture (P)Hg Inventory (kg m−2)Slopeλ (m−1)pdf Correlation Coefficientbzcf (m)zc0(m)Sediment Accumulation 1929–2007 (m)c
  • a

    From the footbridge across the South River at the Invista Plant.

  • b

    From regression analysis to determine λ.

  • c

    Inferred from Hg inventory (see text).

4.75RAccreting benchF0.2050.000511.5780.9751.160.00NA
5.63LAccreting BenchF0.0980.00222.6660.9871.230.03NA
5.92LAccreting benchF0.5730.00721.8810.9890.840.00NA
13.84RAccreting benchP0.1270.000531.6210.9960.940.00NA

[10] Three coring programs in 2007 provided useful data. Many cores were obtained to document mercury contamination of the floodplain throughout the study area. A few of these cores were close enough to the river channel to be useful for model calibration. Most cores (19) were located within 10 m of the river's low flow shoreline, with three located at distances of 10–20 m, two at distances of 20–30 m and 30–40 m, and one at a distance of 40–50 m. Samples were obtained at depths of 0–0.15 m and 0.15 – 0.75 m. Another coring effort focused on eroding banks. Here samples were obtained at 0–0.15 m and at subsequent intervals of 0.3 m throughout the entire height of the bank. A third set of cores were obtained at sites where deposits dating from 1929–1950 were likely to have been preserved near the channel; these cores were sampled at the same intervals as the eroding river banks. The samples were processed as part of a very large floodplain sampling program administered by URS Corporation (unpublished data), who was responsible for all quality control measures.

3. Methods

3.1. Field and Laboratory Methods

[11] Sediment for mercury analyses was sampled using a bucket auger, an Eikjelkampf peat corer, or (in the case of eroding banks) a trowel. Samples were sent to Lancaster Laboratories, who measured the concentration of total inorganic mercury concentrations using SW-846 method 7471A of the U.S. Environmental Protection Agency.

[12] Topographic data were also obtained at each sampling site. A single cross section was surveyed using a TOPCON Total Station to supplement 0.6 m contour maps constructed from an aerial LiDAR survey completed in April 2005. The water surface was also surveyed between sites located 4.1–8.7 km downstream of the footbridge at the Invista Plant in Waynesboro. The reach from 5.2 to 8.7 km was surveyed on 30–31 March 2010, when the water level was approximately halfway to bankfull stage. The reach from 4.1 to 5.2 km was surveyed at a lower stage on 20–21 April 2010. At other sites farther downstream, the water surface slope was estimating from the 0.6 m contour maps.

3.2. Documenting Significant Sedimentation

[13] Floodplain sediment accumulation rates along the South River are remarkably low, with typical values of only a few cm per 100 years [Pizzuto et al., 2011b]. At these rates, it is a reasonable approximation to treat the elevation of most coring sites as constant from 1929 to 2007.

[14] However, at four sites, significant floodplain sedimentation seemed to be occurring on the insides of slowly migrating river bends. Diverse sources of data proved useful in documenting the extent of sedimentation. First, Skalak and Pizzuto [2009] reconstructed mercury concentrations on suspended sediment carried by the South River from 1929 to present. Their results indicate that concentrations greater than about 100 mg kg−1 were typical from 1929 to 1970, and thus high mercury concentrations in depth profiles from cores can be used to detect the sediments deposited during this period (within the resolution of sampling, bioturbation, and other sources of error). Lateral migration was detected from historical aerial photographs from 1937 and 2005 [Rhoades et al., 2009].

3.3. Hydrology and Hydraulics

[15] Predicting the frequency of flood inundation of coring sites is essential for our model. This requires estimates of (1) the recurrence intervals of different discharges, and (2) water levels for each discharge at all of our sampling sites. Recurrence intervals for all mean daily discharges were determined for the three U.S.G.S. gauging stations (some 15 min data are available, but not for the entire period of record, so these higher resolution data were not used). For each recurrence interval, the corresponding discharges increase in a downstream direction from Waynesboro to Harriston. At our sampling sites, discharges for each recurrence interval were interpolated from the gauging station data as linear functions of the downstream distance (measured along the channel centerline).

[16] A streamtube hydraulic model is used to estimate the water surface elevation of different discharges (Figure 2). (This approach was developed because an existing HEC-RAS model was based on low resolution topographic data, and it did not provide the necessary resolution to predict inundation of the coring sites.) The discharge qi in each streamtube of Figure 2 is

display math

where hi and Pi are defined in Figure 2, θi is the angle (measured from horizontal) of element i of the channel perimeter, g is the acceleration of gravity, S is the slope, Cf is a friction coefficient, and R is the hydraulic radius defined by hi cos(θi). Constant values of Cf are used for the channel and the floodplain, with a threshold elevation (determined by field observations) used to discriminate between the two (Figure 2). The values used for Cf are equivalent to Manning's n of 0.03 for the channel and 0.08 for the floodplain [determined by calibrating a HEC-RAS model to measured rating curves (URS Corp, unpublished data)]. The water discharge Q is determined by adding up the values of qi for all the streamtubes in the cross section.

Figure 2.

Definition diagram for streamtube stage-discharge model.

[17] To determine the water surface elevation for a given discharge Q, the streamtube model must be solved iteratively. Starting with an initial guess for the water surface elevation, successive water surface elevations are determined until the discharge calculated using the streamtube model is close enough to the discharge required to determine the water surface elevation to within 0.01 m. At each site, water surface elevations were computed for flows with frequencies of 50, 20, 10, 4, 2, 1, 0.5, 0.2, and 0.1 yr−1. For analytical convenience the results were then fit to an exponential water surface elevation probability density function distribution p(zw):

display math

where zw is the water surface elevation (in meters) (Figure 3) and λ has units of m−1. The datum for the water surface elevation is the elevation of a flow that is equaled or exceeded on average 50 times per year at each site. Equation (2) ignores all flows below this datum; it is written so that the probability of a flow equaling or exceeding zw = 0 is 1. To account for the known occurrence of lower average daily discharges during the remaining 315 days per year, probabilities from (2) are multiplied by a constant kw = (50/365):

display math
Figure 3.

Schematic cross section illustrating characteristic landforms for model application and defining variables for model development. The water surface elevation of the flow that is equaled or exceeded 50 times per year is the datum for measuring elevations. An overbank flow provides an example inundation event.

4. Model Development and Calibration

4.1. Classification of Sites

[18] Before attempting to develop a quantitative model, the primary controls on mercury inventories are identified (data are presented in Table 1). These include riparian vegetation, the elevation of the coring site relative to the adjacent stream channel, and the extent of sedimentation since 1929 (Figure 4).

Figure 4.

Boxplots showing mercury inventories for sites classified according to riparian vegetation (forested or nonforest), elevation relative to the adjacent stream channel (i.e., levees at relatively high elevation and benches at relatively low elevations), and whether significant sedimentation (“accreting”) has occurred at the site since 1929.

[19] Some sites along the South River have well developed forests adjacent to the stream channel, while others are in pasture (no cores were taken along sections of the river that were actively tilled). Riparian vegetation may change with time so evidence was obtained from aerial imagery from 1937, 1956, 1974, and 2005. A site was identified as “forested” if a well-developed forest was present on any of these images. Mercury inventories in forested areas are higher than those in nonforested areas (Figure 4).

[20] The term “levee” will be used here to indicate areas adjacent to the stream channel whose elevation is similar to that of the surrounding alluvial valley. Levees are landforms that have developed on the “active floodplain.” “Benches” are approximately horizontal surfaces lower in elevation than levees (Figure 3). Benches are inundated by floodwaters more frequently than levees, and along the South River, benches have higher mercury inventories than levees (Figure 4).

[21] At four sites (Table 1) we observed evidence (presented below) of significant sediment accumulation. Mercury inventories at these four sites are significantly higher than those at sites without significant sedimentation (Figure 4).

4.2. Conceptual Modeling Framework

[22] To develop a simple analytical model to predict mercury inventories, it is helpful to reduce the dimensions of the problem. Accordingly, variations in mercury inventories related to downstream distance are neglected, and time-dependent factors that influence mercury accumulation (temporal variations in the frequency of high discharges, mercury concentrations on suspended sediment, sediment concentrations, riparian vegetation, and so on) are greatly simplified.

[23] Figure 5 demonstrates that mercury inventories do not vary significantly with distance downstream of the Invista plant in Waynesboro (a regression analysis of these data yields correlation coefficients less than 0.01, regardless of the model equation used). Nonetheless, inventories range over almost four orders of magnitude, suggesting that variables other than downstream distance significantly influence mercury accumulation. If a longer study reach is used, then some correlation with downstream distance emerges. However, the model developed here will only be used in the section of the river covered by Figure 5.

Figure 5.

Mercury inventory for levee, bench, and accreting sites as a function of distance downstream measured from the footbridge crossing the river to the Invista plant in Waynesboro, Virginia.

[24] The concentration of mercury on particles in the South River was as high as 900 mg kg−1 during the period of mercury use at the plant, and has decreased nearly two orders of magnitude to present values of around 10 mg kg−1 [Skalak and Pizzuto, 2009; Flanders et al., 2010]. Furthermore, high flows are episodic, and their frequency may have increased during the last 77 years [Jurk, 2012]. However, these temporal variations do not need to be explicitly modeled to account for the variations in mercury inventories of our study reach. The model relies on the distribution of water levels averaged through time and a time-averaged mercury accumulation rate during periods of inundation that is quantified by model calibration.

[25] The model reflects the hypothesis that variations in mercury inventory between sites are primarily controlled by local factors that influence the accumulation of mercury-contaminated particles. These include (1) the probability of a coring site being inundated by floodwaters, and (2) the factors that enhance the accumulation of particle-bound mercury during inundation. The latter include riparian vegetation and (at four sites only) the creation of accommodation space by slow lateral migration. No effort is made to account for spatial variations in the nature of the particles transported by the river, or for geochemical processes such as desorbtion, methylation, volatization, or atmospheric deposition. While geochemical processes are of great importance to contamination of the South Rivers riverine ecosystem [Eggleston, 2009], physical drivers probably represent the most significant control on the enormous mass of mercury that has accumulated in the valley of the South River during the last 78 years [Flanders et al., 2010].

[26] Cross sections of the South River document a variety of landforms, including the channel bed, steeply sloping banks, levees, and benches (Figure 3). Mercury-contaminated particles accumulate on all of these surfaces when they are inundated by floodwaters. Generally, particles that are deposited on steeply sloping surfaces have a high probability of being re-eroded, while those that are deposited on nearly horizontal benches and levees have a lower probability of being re-eroded. Because the sites available to us for model calibration are all located on gently sloping benches and levees, and to avoid having to represent complex processes of cohesive particle erosion from sloping river banks, model development is focused on these areas. As a result, the model only predicts mercury contamination on nearly horizontal surfaces adjacent to the channel where gravitational (i.e., slope-related) processes that enhance erosion may be neglected. Of course, horizontal surfaces may be eroded by lateral migration of the stream channel, so this limitation does not restrict the ability of the model to contribute to predictions of mercury loading from eroding banks.

4.3. Mathematical Development

[27] The rate of accumulation of mercury dMHg/dt (kg m−2 yr−1) on a floodplain surface of elevation zc is

display math

where DHg is the mass deposition rate of mercury (kg m−2 yr−1) when a surface is inundated by high flows, and P[ ] is the probability of the water surface reaching an elevation interval between zc and zc + h. For most of our sites, the surface elevation zc is treated as a constant, but in general zc may increase through time as a result of sedimentation. The variable h is included because deposition may not occur during higher floods (i.e., those with inundation depths > h) when turbulence keeps particles in suspension (the value of h is determined through calibration). The total inventory of mercury deposited during a time period tf is obtained integrating (4):

display math

[28] While DHg could be simply quantified by model calibration, it is useful to explicitly relate it to sedimentation because this approach allows the model to reflect influence of riparian vegetation on the accumulation of mercury-contaminated sediment. It will also allow calibrated values to be compared with measurements from the literature, a useful aid in interpreting the results. The mercury deposition rate DHg is related to sedimentation by introducing the density of suspended sediment ρs (kg m−3), the concentration of mercury on suspended particles CHg, and the volumetric sedimentation rate Dt (m3 m−2 yr−1) during overbank flows:

display math

[29] Sedimentation onto vegetated surfaces can be parameterized in a variety of different ways. For simplicity (and also because it proves effective), sediment deposition is represented as a process of trapping sediment onto plant stems (rather than by particle settling) [Mariotti and Fagherazzi, 2010]:

display math

In (7)Cs is the concentration of suspended sediment, u is the downstream overbank flow velocity, ds is the stem diameter, ηs is the stem density per unit bed area, hs is the stem height, and ε is the sediment trapping efficiency of stems. Substituting (7) into (6):

display math

Equation (8) contains too many variables to parameterize using a small data set, and vegetation is represented by categories rather than by continuously varying parameters. So, all the vegetation parameters are grouped into a single constant X that can have two values, one for forest and one for pasture (grass). Equation (8) is reduced to

display math

where σ, the ratio of Xforest to Xgrass, is a multiplier that represents ability of forested vegetation to enhance sedimentation. It is further assumed that the velocity of overbank flow is only weakly dependent on flow depth [Harvey et al., 2009; Smith, 2004] and that the other variables can be represented by constants, so that equation (8) is reduced to

display math

where the mercury deposition rate parameter Φ is defined by

display math

The parameter Φ (determined by calibration) is treated as a constant for all sites, with the added influence of riparian forests represented by the multiplier σ (note that the calibrated value of σ may implicitly include differing hydraulic roughness as well as other variables; these and other simplifications are addressed further in the discussion).

[30] Substituting equation (11) into equation (5):

display math

The probability P[zw] can be obtained by integrating equation (3) between the specified limits:

display math

Substituting (13) into (12):

display math

Further progress requires a model for floodplain accumulation due to overbank sedimentation that defines the function zc(t). Generally, floodplains accrete at a gradually decreasing rate as their elevation increases, because the frequency of flood inundation decreases with time (Figure 6). Here this trend is approximated with a linear function of increasing floodplain elevation with time from t = 0 to t = t1, followed by a period of constant floodplain elevation:

display math

where zc0 is the elevation of the floodplain surface at t = 0, and zcf is the elevation of the floodplain surface at t = t1 (and thereafter).

Figure 6.

Decreasing floodplain sedimentation rate versus time and an approximation by two linear functions.

[31] Substituting (15) into (14) and expanding into two separate integrals:

display math

Integrating (16):

display math

For sites without floodplain sedimentation, there is no time period of linear increase in floodplain elevation, and thus t1 = 0. Under these conditions, the term at the far right of (17) vanishes.

4.4. Model Calibration

[32] Equation (17) contains nine variables: Φ, σ, kw, λ, h, tf, t1, zcf, and zc0. The duration of mercury accumulation at our field sites tf began in 1929 and ended when the time cores were collected in 2007. The water level probability distribution parameter λ is determined from rating curves developed at each site, and kw is a known constant. The elevations of the coring sites in 1929 and 2007 (zc0 and zcf) are determined from field data (Table 1).

[33] The remaining four variables (Φ, σ, h, and t1) are determined by calibrating the model using data from the 27 field sites. I used the MATLAB routine nlinfit (nonlinear least-squares regression) to fit the data to equation (17), and MATLAB routine nlparci (confidence intervals for parameters in nonlinear regression) to determine the 95% confidence intervals of the fitted parameter values. To ensure that all the parameters contribute significantly to the final regression result, terms containing each parameter were added one at a time (the order of adding parameters was varied in several ways, but only one of these is presented here for brevity). For example, an initial first regression model only includes the variable Φ, so the regression only considered equation (17) in the form of MHg = kwΦ. Another regression model includes both Φ and the probability of flood inundation, with equation (17) in the form math formula. The third model adds the riparian forest multiplier σ, and so on. Each model is evaluated by computing the root mean square error Erms of the 27 predicted and measured mercury inventories for each site:

display math

Values of Erms were used to demonstrate the relative contribution of each variable to improving the correlation between observed and predicted mercury inventories.

4.5. Sensitivity Analysis

[34] A simple approach was used to illustrate the sensitivity of predicted mercury inventories to variations in parameter values. First, typical base values were selected for all parameters. Then, each parameter was varied by ±25% while keeping the remaining parameters constant. The sensitivity was quantified by

display math

where “parameter” refers to the base value chosen for each parameter and the notation MHg (parameter) refers to the mercury inventory computed from equation (17) using the parameter value indicated in the closed parentheses.

5. Results

[35] Mercury profiles in cores document sedimentation at four sites (Figure 7). These data, combined with analysis of bank line movements from aerial imagery, provide the basis for determining values of zc0 (Table 1). The results indicate total accumulations of 1.16, 1.20, 0.84, and 0.94 m. At all of these sites, the elevations of the coring sites were close to base flow water level in 1929, so zc0 is approximated by the water surface elevation of the flow that reoccurs 50 times per year (i.e., zc0 = 0).

Figure 7.

Reconstructed topography in 1929 at four coring sites based on mercury profiles in cores and bank line positions on historical aerial photographs. Sites are located (a) 4.75 km, (b) 5.63 km, (c) 5.92 km, and (d) 13.84 km downstream of Waynesboro.

[36] Probability density functions of water surface elevations are well described by the exponential distribution of (2) (Figure 8). Correlation coefficients range from 0.973 to 0.996, while values of λ range from 1.395 to 2.666 m−1 (Table 1).

Figure 8.

Probability density function of water surface elevations at the coring site located 4.10 km downstream of Waynesboro. Symbols represent elevations determined using the streamtube hydraulic model, and the solid line is the exponential distribution (equation (2)) fit to the data using linear regression.

[37] Root-mean square errors obtained by increasingly complete versions of the model are summarized in Table 2. The term in the model that quantifies the probability of flood inundation (included in model 2) provides the greatest reduction in root-mean square errors. Accounting for vegetation type (via the parameter σ in model 3) and sedimentation (included in model 5 only) provides important, and approximately equal, decreases in root-mean square errors. Including a maximum water depth of inundation (via h in model 4) apparently does not improve model predictions significantly. A visual examination of predicted and observed mercury inventories obtained using the complete calibrated version of equation (17) (Figure 9) suggests that the model errors (represented by the deviation of the data about the solid line of perfect agreement) are larger for lower mercury inventories than for higher mercury inventories. Six of the seven largest deviations from the line of perfect agreement are overpredictions from forested sites. This may indicate some uncertainty in the vegetation classification, or there may be another (as yet unknown) explanation for these errors. The median absolute error (represented by the dashed lines of Figure 9) represents predictions of mercury inventories within a factor of 1.85 of observed inventories. The envelope defined by the median absolute error includes 15 of the 27 sites.

Figure 9.

Predicted and observed mercury inventories for the complete calibrated model. The solid line represents perfect agreement between observations and predictions. Dashed lines indicate the envelope defined by the median absolute error, a factor of 1.85.

Table 2. Root-Mean-Square Errors Associated With Adding Each Term to the Model
ModelParameters IncludedErms (kg m−2)Difference in Erms
  • a

    t1 = 0 for models 2–4.

1. math formulaΦ0.1128NA
2. math formulaΦ0.08010.0327
3. math formulaΦ, σ0.06870.0114
4. math formulaΦ, σ, h0.06730.0014
5. Equation (17) completeΦ, σ, h, t1a0.05650.0108

[38] The calibrated parameter values provide some insights into the controls on mercury accumulation in near bank regions of the South River (Table 3). The average rate of mercury accumulation during periods of inundation is 0.04 kg m−2 yr−1 (95% C.I. 0.032–0.048). Forested riparian zones increase the rate of mercury accumulation by a factor of 3.05 (95% C.I. 2.43–3.67) compared to nonforested riparian zones. Mercury only accumulates when flood waters are less than 0.98 m deep (95% C.I. 0.45–1.53), though this result does not appear to greatly improve model predictions. The time scale for floodplain sedimentation (t1) is 39 years (95% C.I. 22–56).

Table 3. Parameter Values and 95% Confidence Intervals Determined During Model Calibration
ParameterValue95% Confidence Interval
Φ (kg m−2 yr−1)0.0400.032–0.048
h (m)0.980.45–1.53
t1 (yr)3922–56

[39] The sensitivity of predicted mercury inventories to ±25% variation in parameter values (computed using equation (19)) are summarized in Table 4. Of the parameters evaluated through calibration, results are most sensitive to Φ and σ: MHg varies in linear proportion to these parameters, so the sensitivity is 0.50. Predicted mercury inventories are only slightly less sensitive to t1 (0.41), while MHg is not sensitive to the maximum inundation depth for sedimentation (h), whose sensitivity is only 0.17. Of the measured parameters, results are most sensitive (−0.63) to the inundation frequency parameter λ. Predicted mercury inventories are relatively insensitive to tf, zc0, and zcf, with sensitivities of 0.09, −0.18, and −0.22, respectively.

Table 4. Sensitivity of Predicted Mercury Inventories to a ±25% Variation in Parameter Values
ParameterCalibrated (C) or Measured (M)Base ValueSensitivity
Φ (kg m−2 yr−1)C0.040.50
h (m)C0.980.17
t1 (yr)C390.41
λ (m−1)M2−0.63
tf (yr)M780.09
zc0 (m)M0.2−0.18
zcf (m)M2−0.22

6. Discussion

[40] The calibrated model appears reasonably successful in reproducing observed mercury inventories. A regression analysis of the predicted mercury inventories as a function the observed inventories values yields the power function y = 0.32x0.58, with a correlation coefficient (r2) of 0.62 and a p value of 1.2 × 10−6. These results indicate that (1) the model “explains” 62% of the variance in observed mercury inventories, and (2) the model tends to overpredict low mercury inventories (as indicated by the exponent of 0.58 and the coefficient of 0.32). The unexplained variance of 38% could be caused by (1) errors in estimating the frequency of inundation, (2) inaccuracy in parameterizing or classifying vegetation, (3) systematic changes in sediment grain sizes deposited at different sites (and the related ability of different sizes to adsorb mercury), (4) variation in mercury inventories or sedimentation related to distance from the stream channel, and a host of other variables. Poor results may be obtained for very low mercury inventories simply because background variability (“noise”) may swamp these small values.

[41] The calibrated model is only useful if it can provide detailed predictions of mercury inventories along an entire reach, which for the South River would imply essentially continuous predictions along the banks for 15 km. Equation (17) is well-suited for this. The required data include flow duration curves, detailed topographic data, and a vegetation classification (forest or nonforest) for all locations in the study area. For most regions, the hydrologic data are easily obtained (as described for the South River above), the necessary topographic data can be obtained from high resolution LiDAR surveys, and vegetation can be classified from aerial photographs. Though not reported here, equation (17) has been already used to estimate mercury inventories for the entire 15 km South River study reach.

[42] Table 2 indicates that the most important process considered that controls accumulation of mercury along the South River is inundation by floodwaters. Forested vegetation increases mercury accumulation by a factor of 3, and significant sedimentation increases mercury accumulation at 4 of the 27 coring sites.

[43] Confidence in the accuracy of the model can be at least partly assessed by relating calibrated model parameters to measurements in the literature. For example, Xgrass can be defined from equation (7) as the product dsηshsε; physically it represents the frontal area of vegetation exposed to the flow per unit bed area, times the efficiency of sediment trapping on stems. Values of these parameters have been measured by Pizzuto et al. [2008], Smith [2004], Harvey et al. [2009], and Palmer et al. [2004] in diverse environments ranging from Montana floodplains to the Everglades. Values of Xgrass derived from these data vary by more than three orders of magnitude (Table 5).

Table 5. Xgrass Computed as dsηshsε Using Literature Valuesa Compared With the Value Obtained From Calibrated Model Parameters and Equation (11)
Sourceds (m)ηs (m−2)dsηs (m−1)hs (m)Xgrass
  • a

    The efficiency ε is 0.1 [Palmer et al., 2004].

  • b

    Value of dsηs is the lowest of a range of three orders of magnitude.

Pizzuto et al. [2007]0.002424NA0.54E−02
Smith [2004]0.04100NA1.345E−01
Harvey et al. [2009]bNANA2E−030.61E−04
This StudyNANANANA2E−04

[44] Equation (11) provides a means of relating the calibrated value of Φ to an implied value of Xgrass. I adopt an overbank flow velocity through vegetation of 0.1 m s−1 [Pizzuto et al., 2008; Smith, 2004], a density of 2000 kg m−3 for suspended particles, an average suspended sediment concentration of 0.0001 [Eggleston, 2009], and an average concentration of mercury on suspended sediment of 0.000239 based on the historical reconstructions of Skalak and Pizzuto [2009]. The resulting order of magnitude estimates of Xgrass and Xforest are 2 × 10−4 and 5 × 10−4, respectively. These values are on the very low range of the derived values in Table 5, lower than the two estimates from Montana floodplains but within the range of values derived from Harvey et al.'s [2009] data from the Everglades. While these results cannot either validate or repudiate the model results (and further analysis is hardly warranted given the complexity of the problem and the paucity of available observations), they at least indicate that one calibrated model parameter is physically reasonable.

[45] In developing the model, sedimentation at all but four sites was assumed to be negligible. This assumption can be tested if equation (6) is reinterpreted to represent the average deposition rate from 1929 to 2007. Then, the mercury mass accumulation rate (per unit area) is simply the measured mercury inventory IHg sampled from cores (because it accumulated over the entire period 1929–2007) and the mass sedimentation rate per unit area can be converted to the thickness of sediment deposited Tt using the bulk density of floodplain soils ρb:

display math

In equation (20), CHg:1930–2007 represents the average concentration of mercury on suspended particles transported by the South River from 1919 to 2007; it is (as noted above) 0.000239. The summation terms on the right-hand side of equation (19) illustrate how the mercury inventory is computed from n intervals in a core, each with mercury concentration Csoil Hgi and thickness Ti. The soil bulk density is treated as a constant with depth, and as a result it cancels from equation (20). This is useful because the bulk density was not measured as part of the floodplain sampling program.

[46] Applying equation (20) to the 23 sites assumed to be without net deposition yields a mean sediment accumulation of 0.1 ± 0.13 (standard deviation) m (Table 1). At half of these, accumulation is less than the median accumulation of 0.03 m. These values indicate that the assumption of negligible sedimentation is well justified at nearly all the sites, particularly in light of likely decimeter-scale errors in estimating the stages of varying stream discharges (and hence frequencies of flood inundation). At two of the sites where cores were obtained from low-lying benches, the total accumulation is 0.40 and 0.46 m, perhaps high enough to underestimate mercury accumulation at these two sites.

[47] In future studies it would be useful to verify sediment accumulation rates determined from mercury inventories using fallout radionuclides such as 137Cs and 210Pb. Fallout radionuclides have not been widely used to quantify floodplain deposition in the mid-Atlantic region, possibly because useful vertical profiles of activity cannot be resolved at the very low sediment accumulation rates that are typical of the area [Bain and Brush, 2005; Walter and Merritts, 2008]. Methods based on analyzing the full inventory (rather than the depth distribution of activity) of fallout radionuclides could prove useful, however [Mabit et al., 2008].

[48] The model presented in this paper is highly generalized. While the model is process based, it relies on simple equations that can be calibrated using data obtained from cores. The strength of this approach is that the model is calibrated using data representing the entire historical period of floodplain mercury accumulation: the model is fit by the observed accumulation that actually occurred from 1929 to 2007, without requiring any monitoring data. There is, however, a cost to this approach. The physical processes represented in the model are somewhat vague. For example, the parameter Φ represents the rate of deposition of mercury-contaminated particles, but its definition does not clarify the extent to which deposition is related to particle settling on the bed or to entrapment of particles on plant stems and leaves (the process represented by equation (7)). Similarly, floodplain sedimentation is treated in a very cursory manner, though it is clearly important in some locations. Erosion is entirely neglected.

[49] A more precise and inclusive physically based model could have been developed. Early versions included parameterizations of erosion, and also related sedimentation to boundary shear stress, a parameter that is often included in sediment transport models [Garcia, 2007]. However, these more complex models could not be successfully calibrated using the field data. It might have been possible to calibrate more complex models using a combination of short-term field monitoring and laboratory tests. The resulting models would necessarily have more parameters (creating increased uncertainty) than the simpler approach described here, and they would have to represent diverse field conditions very different from those that occurred during calibration. For example, the density and nature of the riparian vegetation along the South River varies dramatically seasonally as annuals grow in the spring and decline in winter. These differences have no doubt influenced the accumulation of mercury-contaminated sediment, but it would be exceedingly difficult to obtain the necessary data required to capture these controls explicitly in a modeling scheme covering the last 78 years.

[50] Including grain size effects would be an obvious improvement to include in future efforts because of mercury's well-documented affinity for smaller particle size fractions [Flanders et al., 2010]. However, trying to include these factors in a depositional model for the South River is not really warranted. There is no available grain size information for suspended sediment, so predicting the concentration of suspended silt or clay size fractions is impossible. Within the study reach, floodplain deposits do not systematically vary in grain size with distance downstream or distance from the river channel (Pizzuto, unpublished data). Finally, though it is possible to demonstrate that mercury is preferentially associated with smaller particles in individual cores from the South River, a general statistical relationship between mercury concentration and measures of particle size does not seem to exist [Skalak, 2009]. Either the appropriate metric of particle size has not been measured, or mercury concentrations are controlled by additional factors that confound any attempt to create a generalizable relationship. All of these complicating factors lead to the decision to neglect particle size variations for developing the present version of the model.

7. Conclusions

[51] The accumulation of mercury-contaminated sediment onto subhorizontal surfaces adjacent to the channel of the South River from 1929 to 2007 is represented by a simple analytical model calibrated using data from 27 cores. Mercury accumulation is strongly influenced by the frequency of flood inundation, which is quantified using an exponential distribution of water surface elevations. Forested riparian areas increase mercury accumulation by a factor of 3 compared to accumulation in nonforested areas. While changes in the elevation of floodplain surfaces through time may be ignored at most of our sites, mercury accumulation is greatly enhanced at four sites where 0.8–1.2 m of sediment accumulated from 1929 to 2007.

[52] The calibrated model can be used to estimate the extent of historic mercury accumulation along near-channel riparian areas of the South River in our study area, information that is helpful for remediation planning. Model predictions require detailed knowledge of floodplain morphology (channel cross section and longitudinal slope), a flow duration curve, and mapping of the riparian vegetation into categories of forest and nonforest. Only 15 of 27 predicted mercury inventories are within a factor of 1.8 of measured mercury inventories, so the model predictions are best used as a screening tool to guide further sampling and analysis.

[53] The approach described in this paper should be useful for any river where sediment and contaminants accumulate on river banks. However, in many settings (including longer sections of the South River) longitudinal variations in mercury concentrations must be explicitly considered. It would not be difficult to include this in the model, but a numerical solution would probably be required, and its use would involve specifying an upstream boundary condition representing the history of loading from the original source of mercury (in this case, the plant at Waynesboro). This information is often unavailable.

[54] The calibrated model is not only useful for predicting the accumulation of mercury: it can also be used to predict the accumulation of sediment if the time-averaged mercury concentration on suspended sediment can be estimated. This highlights the utility of using sediment-borne contaminants as tracers for long-term sedimentation processes that are otherwise exceedingly difficult to measure.


friction coefficient.


concentration of mercury on suspended particles.


volumetric suspended sediment concentration.


stem diameter, m.


mass deposition rate of mercury per unit surface area, kg m−2 yr−1.


volumetric sediment sedimentation rate, m3 m−2 yr−1.


root-mean-square error of predicted vs measured mercury inventory, kg m−2.


acceleration of gravity, m2 s−1.


water depth, m.


stem height, m.


measured mercury inventory, kg m−2.


= 50/365.


average vertical floodplain sediment accumulation rate, m yr−1.


mass of mercury per unit surface area, kg m−2.


probability density of water surface elevations, m−1.


length of the channel boundary at the base of a streamtube, m.


probability of exceeding water surface elevation z.


water discharge in a streamtube, m3 s−1.


water discharge in the entire channel, m3 s−1.


hydraulic radius of a streamtube computed as h cos(θ), m.


time, yr.


time when a core is taken, yr.


time required for linear floodplain sedimentation, yr.


thickness of sediment deposition, m.


downstream overbank flow velocity, m s−1.


sedimentation parameter for grass.


sedimentation parameter for forest.


elevation of a coring site, m.


elevation of a coring site at the time of coring, m.


elevation of a coring site at t = 0, m.


water surface elevation, m.


sediment trapping efficiency of stems.


water surface elevation probability distribution parameter, m−1.


stem density per unit bed area, m−2.


mercury deposition rate parameter, kg m−2 yr−1.


bulk density of floodplain soils, kg m−3.


density of suspended sediment, kg m−3.




angle of the channel boundary at the base of a streamtube relative to horizontal.


[55] Funding was provided by the DuPont Company. Members of the South River Science Team ( provided very helpful guidance, support, and access to data. Dajana Jurk, Stephanie Stotts, and Suzann Pomraning assisted with field mapping.