Simulating dispersive mixing in large peatlands

Journal of Hydrology 242 (2001) 103–114 www.elsevier.com/locate/jhydrol

Simulating dispersive mixing in large peatlands A.S. Reeve a,*, D.I. Siegel b, P.H. Glaser c a

Department of Geological Sciences, University of Maine, Orono, ME 04469, USA b Department of Earth Sciences, Syracuse University, Syracuse, NY 13244, USA c Limnologic Research Center, University of Minnesota, Minneapolis, MN 55455, USA Received 16 February 2000; revised 31 August 2000; accepted 20 October 2000

Abstract Numerical simulations indicate that mechanical dispersive mixing can be the dominant mass transport mechanism in large peatlands. Dispersive mixing driven by lateral flow can drive solute fluxes from the mineral soil upward to the peat surface and thereby explain observed patterns of bog and fen in large peatlands. Longitudinal and transverse dispersivities of only 0.5 and 0.05 m, respectively, were sufficient to supply solutes to the peat surface in the absence of upward ground-water flow. Incorporation of hydrodynamic dispersion in peatland systems explains apparent contradictions in solute migration in peatlands, allowing the simultaneous downward flux of labile carbon (i.e. root exudates) produced at the peat surface and upward migration of inorganic solutes from the underlying mineral soil. Previous models of peatland hydrogeochemistry that rely on advection alone as the dominant process for solute transport may therefore be inadequate to explain fully the hydrology, geochemistry, and evolution of large peatlands. 䉷 2001 Elsevier Science B.V. All rights reserved. Keywords: Peatland; Solute transport; Ground-water; Bogs; Dispersion; Simulation

1. Introduction Solute transport is the fundamental process that governs most geochemical and ecosystem functions in large peatlands. The mass transport of inorganic solutes from mineral sources, for example, determines both the abundance and distribution of vegetation in large peatlands (Glaser et al., 1981). Solute transport also supplements the supply of nutrients and simple carbon substrates to microbial communities within the deeper peat strata and regulates the loss of dissolved organic carbon (DOC) to runoff and ground-water recharge (Waddington and Roulet, 1997). These processes directly affect carbon cycling in the largest peatlands that are large reservoirs in the global carbon cycle. * Corresponding author.

Advection and diffusion are generally assumed to be the dominant mechanisms for solute transport in peat. However, peat deposits usually contain complex sequences of strata that have highly variable botanical, physical, and hydraulic properties (Chason and Siegel, 1986). This high degree of spatial heterogeneity should enhance mechanical dispersion as solutes are advected through any given peat profile. Although mechanical dispersion has been identified as a potentially important transport mechanism in small peatlands (Hemond et al., 1987), its effects have yet to be considered for the largest peatlands that form the bulk of the global peat deposits. Mechanical dispersion is produced during fluid advection by heterogeneities that generate variations in ground-water velocities. These flow variations occur at different scales ranging from microscopic pores to regional landforms (Domenico and Schwartz,

0022-1694/01/$ - see front matter 䉷 2001 Elsevier Science B.V. All rights reserved. PII: S0022-169 4(00)00386-3

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1990; Bear, 1972). In general, dispersive mixing tends to increase with higher flow velocities, longer transport distances, and greater heterogeneity. Dispersion is also stronger parallel to the direction of flow (longitudinal dispersion), than in orientations that are perpendicular to flow (transverse dispersion). Dispersive mixing has been extensively analyzed for spreading tracers and contaminant plumes by two and threedimensional (2D and 3D) numerical models (Leij and Dane, 1991; Frind and Germain, 1986; Schwartz, 1975). These models can also be applied to large peatlands if the model domain is modified to adjust for the effects of: (1) a constant solute-source in the underlying mineral deposits; and (2) water-table mounds within the raised bogs. Conceptual numerical models were developed to evaluate mass transport mechanisms in large peatlands incorporating both longitudinal and transverse dispersion. These models differ from previous solute transport studies by including a constant solute-source at depth and ground-water mounds within the model domain. This study focuses on mass transport within the large peat basins of North America, such as those found in the Glacial Lake Agassiz region and the Hudson Bay Lowland. These peat basins contain an average peat thickness of 2–3 m and cover over 100,000 km 2 (Gorham, 1991). Although detailed analyses of peatland hydrology have been made for these peatlands, less effort was made to assess solute transport processes.

surface-water is generally similar to that of local precipitation, with minor deviations due to biological activity and evaporative concentration (Shotyk, 1988). Gorham and Pearsall (1956) also note that specific conductance of peatland surface-waters is indicative of peat landform, with fens having conductivities of 70–100 mS cm ⫺1 and bogs typically having conductivities of less than 50 mS cm ⫺1. The contrast between the bog-water chemistry and that of groundwater is sharpest in the large peat basins of boreal America that are underlain by calcareous bedrock or glacial deposits. The chemistry of the fen waters is more similar to that of ground-water, although it becomes more dilute with increasing distance from a mineral source because of mixing with precipitation. Two conceptual hydrologic models have been proposed to explain the occurrence of bogs and fens within a peatland (Reeve et al., 2000):

2. Background

The primary difference between these models is the assumption regarding vertical flow. The surface-water model assumes that the lower peat layers insulate the surface peat from the mineral soil whereas the groundwater model assumes that the deeper peat has sufficient permeability to allow a significant amount of vertical flow. Reeve et al. (2000) have shown that both of these models may apply in different hydrogeologic settings and that the permeability of the mineral soil below the peat column is an important factor influencing the vertical penetration of flow cells in large peatlands. Several studies have shown that seasonal and long term climate variation are important controls on the vertical movement of solutes in peat columns (Waddington and Roulet, 1997; Siegel et al., 1995; Romanowicz et al., 1993). It should be noted

Peatlands are divided into two classes based on their surface-water chemistry and vegetation. Bogs are topographic domes that contain acidic (pH ⬍ 4.2) surface-waters with low concentrations of inorganic solutes (e.g. Ca ⬍ 2 mg kg ⫺1) (Shotyk, 1988; Gorham et al., 1985; Glaser et al., 1981). Bog vegetation generally contain few species and are dominated by Sphagnum. Fens, in contrast, have a flat or gently sloping surface. The higher pH (⬎4.2) and greater solute concentrations (Ca ⬎ 2 mg kg ⫺1) in fen surface-waters supports more diverse plant communities with feather mosses as the dominant bryophyte (Shotyk, 1988; Gorham et al., 1985; Glaser et al., 1981). The inorganic geochemistry of bog

1. Solutes are supplied to peatlands by surface run off from mineral uplands. This run off cannot reach the elevated bog domes and they only receive inorganic solutes from precipitation (surface-water model) (Ingram, 1983). 2. Local ground-water flow cells that form under the bog domes flush dilute recharge, derived from precipitation, downward under bog domes and these flow paths emerge in the fens after dissolving solutes from the underlying mineral soil (groundwater model) (Glaser et al., 1997; Siegel and Glaser, 1987; Siegel, 1983)

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Conc. Gradient=0

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990

ET Conc=0

Pea t Min

Drains Conc.=Cell Conc.

era

l So

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Con

c. =

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985

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995

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105

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980

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low

970 Distance (km) 0

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Fig. 1. Model grid and boundary conditions. Note the extreme vertical exaggeration. The upper six layers represent peat with the upper layer having a thickness of 0.5 m and the remaining layers having equal thicknesses. Total peat thickness ranged from 3 m to about 3.9 or 4.8 m, depending on the assumed mound size. The lower six layers of the model represent mineral soil and have a thickness of 0.5 m in layer 7 and successively increase by a factor of 1.75 with depth.

that these hydrologic models have been proposed primarily to explain general differences in chemical gradients in peat pore-water. Solute transport studies in peatlands have been limited primarily to the application of one-dimensional models to describe concentration profiles in peatlands (Romanowicz et al., 1995; Price and Woo, 1988; Siegel, 1988; Hemond et al., 1987; Siegel and Glaser, 1987). We are aware of only one published attempt to create a 2D solute transport model of a peatland (Price and Woo, 1990). In this study, Price and Woo (1990) argue that ground-water velocities in peatlands will be very low and therefore, mechanical dispersion is insignificant. Their view is based on the assumption that the characteristic length of dispersion is equal to the grain size of a porous media, about 10 ⫺6 m in their study area. Laboratory experiments done on peat columns (Ours et al., 1997; Hoag and Price, 1997) indicate longitudinal dispersivities in saturated humified peat are however, in the order of millimeters to centimeters, suggesting dispersivities are much larger than the humified peat pore size.

Furthermore, longitudinal dispersivities measured in laboratory column experiments are more than an order of magnitude lower than longitudinal dispersivities measured at larger scales (typically from 1 to 100 m) (Gillham et al., 1984). 3. Methodology Numerical simulations were run in two steps: first, ground-water flow rates were calculated for selected peatland settings using the computer program Modflow (Harbaugh and McDonald, 1996), and second, solute transport was simulated using a finitedifference computer program we developed. 3.1. Ground-water flow simulations Ground-water flow models were constructed as 2D arrays with one row, 100 columns, and 12 layers (Reeve et al., 2000). We selected two hydrogeologic extremes (Fig. 1) based on Reeve et al. (2000): (1) a scenario with a 1.8 m high bog mound and mineral

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Table 1 Summary of depth dependent parameters used in numerical models Layer

1

2

3

4–5

6

7–12

KH m s ⫺1 KH:KV Porosity

10 ⫺2 10 0.6

10 ⫺4 10 0.4

10 ⫺5 10 0.3

10 ⫺5 10 0.2

10 ⫺6 20 0.1

10 ⫺4 or 10 ⫺7 100 0.1

soil with a high hydraulic conductivity (10 ⫺4 m s ⫺1) that generates vertical flow penetrating deep into the mineral soil; and (2) a scenario with a 0.9 m high bog mound and mineral soil with a low hydraulic conductivity (10 ⫺7 m s ⫺1) that is dominated by lateral flow (Reeve et al., 2000). Parameters in each of these simulations are described in Fig. 1 and were selected based on the hydrogeologic framework of major circumboreal peatlands (Glaser, 1989, 1987). Recharge was supplied to the upper layer of the model at a rate of 3 × 10 ⫺8 m s ⫺1 and an evapotranspiration rate of 2.9 × 10 ⫺8 m s ⫺1 with an extinction depth of 0.5 m. Constant head boundaries were established in columns 1 and 100 of the model and drains were set at the model surface to simulate the removal of water due to surface runoff (Reeve et al., 2000). Horizontal hydraulic conductivities in the layers representing the peat range from 10 ⫺2 m s ⫺1 at the peat surface to 10 ⫺6 m s ⫺1 in the basal peat (Table 1). These values are based on hydraulic conductivities measured in large boreal peatlands (Reeve et al., 2000; Waddington and Roulet, 1997; Chason and Siegel, 1986) and used in previous hydrogeologic peatland models (Siegel et al., 1995; Winston, 1994). Vertical hydraulic conductivities were 20 times lower than horizontal hydraulic conductivities (Chason and Siegel, 1986). 3.2. Solute transport simulations A solute transport program was prepared using Python, a rapid development interpretive computer language (Lutz, 1996), with selected pieces implemented in Fortran. Dispersive and advective fluxes were split and calculated sequentially. Solute transport calculations were performed using the explicit QUICKEST scheme (Leonard, 1988, 1979) to simulate advection and an implicit finite-volume method to simulate mechanical dispersion and diffusion. This scheme is similar to the methods described by Haefner et al. (1997) and includes their front limiting method.

During a single time step, the following methods were applied to numerically solve for concentration in a model cell. 1. The dispersion tensor (D) at each cell face was calculated utilizing the equations for an isotropic aquifer (Bear, 1972) that are widely adopted in mass transport programs (Konikow et al., 1996; Zheng, 1990). The dispersion tensor was calculated based on ground-water velocities previously calculated with Modflow (Harbaugh and McDonald, 1996) and longitudinal and transverse dispersivities (a L and a T). The diffusion term in the dispersion tensor is calculated by multiplying the homogeneous liquid diffusion rates by porosity squared, resulting in an estimate of a diffusion rate through tortuous pores within the porous media (Boudreau, 1996). 2. Dispersive fluxes (F) at each cell face with a specified cross-sectional area (A) and porosity (n) were estimated using a finite-difference approximation for the concentration gradient (e.g. dC/dx).   dC dC dC ⫹ Dxy ⫹ Dxz …1† Fx ˆ ⫺nA Dxx dx dy dz Porosities and cross-sectional areas for cell faces were based on arithmetic means of the values assigned to cells adjacent to the cell face. Similar approximation were made for all cell faces and the sum of the fluxes equaled the change in solute mass due to dispersion within a cell over some time (Dt), X

F ˆ nV

DC Dt

…2†

These equations were created for each cell and the equations were solved for concentration using a fully implicit method. 3. Advective solute fluxes across each cell face were calculated using the explicit QUICKEST scheme (Leonard, 1988, 1979). This method is a third order

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Fig. 2. Concentration profile for mass transport simulations that incorporate strong ground-water flow cells. The regional slope is 0.006, the peat mound has a height of 1.8 m, and the mineral soil has a hydraulic conductivity of 10 ⫺4 m s ⫺1. Numbers labeling concentration isopleths correspond to the percentage of ground-water mixed with recharge. Note that the diagram shows only the central portion of the model domain.

upstream weighting scheme that incorporates the concentration variation over time at a cell face, in effect interpolating concentration over the length of a streamline that crosses the cell face during a time step. A complete description of this method is presented by Leonard (1988). This method accurately tracks sharp concentration fronts with minor oscillations. Over and under-shoots are handled with a front limiter that ensures that the concentration assigned to a cell face Ccf is between or equal to the concentrations in the adjacent cells (Haefner et al., 1997). Ccf ˆ min…max…Cb ; Cf †; max…min…Cb ; Cf †; Ccf;Q †† …3†

The cell face concentration Ccf,Q on the right hand side of this equation is that determined through the QUICKEST method. The Ccf will equal Ccf,Q if Ccf,Q lies between the concentration in the cells adjacent to the cell face, suppressing numerical oscillations. The concentration change in a cell due to advective fluxes is calculated by summing the advective solute fluxes across each cell face and dividing by the volume of water in that cell. P …qACcf † …4† DC ˆ Vn

All mass transport simulations were run until

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5 10 20 80 40 99

10 60

988

80

6

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10 12 Distance (Km)

14

Fig. 3. Concentration profile for mass transport simulations that incorporate weak ground-water flow cells. The regional slope is 0.006, the peat mound has a height of 0.9 m, and the mineral soil has a hydraulic conductivity of 10 ⫺7 m s ⫺1. Numbers labeling concentration isopleths correspond to the percentage of ground-water mixed with recharge. Note that the diagram shows only the central portion of the model domain.

steady-state conditions were achieved. Simulation results presented in this paper were all run for 1000 years. Changes in the concentrations based on visual inspection of contour plots, were no longer apparent after about 200 years of simulated mass transport, indicating that our models had achieved steady-state conditions. Dispersivity and effective porosity of peat have been measured in column experiments, yielding longitudinal dispersivities of 2 mm to 10 cm and effective porosities that decrease with depth from about 0.6 to about 0.1 (Hoag and Price, 1997; Ours et al., 1997). This range of effective porosity has been incorporated into all mass transport simulations while longitudinal dispersivities were varied from 0.01 to 0.5 m. The ratio of a L to a T was set to 10. Diffusion Do was set at 10 ⫺9 m 2 s ⫺1.

Boundary conditions in the model were assigned as follows (Fig. 1): water added or removed across the top of the model through recharge or evapotranspiration was assigned a concentration of zero, water removed from cells across the top of the model by drains and advected across the left and right edges of the model was assigned the current concentration of water in the respective cell. The concentration gradient at the sides (column 1 and 100) was set to zero and constant concentration boundary conditions (C ˆ 100) were set in the mineral soil below the peat layer. Initially, peat concentrations were set to zero (C ˆ 0 at time ˆ 0 in the peat layers). Concentrations in all simulations can be considered the percent of ground-water that has mixed with recharge from precipitation. These boundary conditions assume

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Fig. 4. Percentage of ground-water that mixes with recharge in the upper layer of mass transport models. Top and bottom figures contain concentrations from simulations with a strong (Fig. 2) and weak (Fig. 3) ground-water flow cells, respectively. Letters correspond to results from models with different longitudinal dispersivities (A ˆ 0.001 m, B ˆ 0.1 m, C ˆ 0.5 m, and D ˆ 1.0 m).

that the peat itself does not supply solutes to the water and that the mineral soil maintains a continuous and uniform concentration through time. The grid defining the cells was telescoped in the vicinity of the peat mound, which was the primary area of interest. The outer 10 columns were sequentially increased in width by a factor of about 1.3 with all other cells having a column width of 100 m. The six layers used to represent the peat column were of equal thickness in each column and ranged from 0.5 m away from the bog mount up to 0.72 m in the column at the center of the bog mount. The thickness to the layers in the mineral soil was 0.5 m adjacent to the peat layer and increased in thickness sequentially by a factor of 1.75.

4. Results Numerical simulations (Figs. 2 and 3) indicate that mechanical dispersion has a strong effect on solute transport in large peatlands. Both models simulate lateral flow through sloping fens with local recharge of varying intensity under a peat mound. The most striking result was the consistent rise in solute concentrations (i.e. % ground-water) from the base of the peat profile to the surface within areas of lateral flow. Simulations that incorporated a high peat mound and highly permeable mineral soil (Fig. 2) contain sharp concentration gradients around the margins and base of the peat mounds when dispersivity was

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Fen Hi

Bog Specific Conductance pH

Low

Mixing

Solutes from Mineral Soil

Mixing

Mixing

Labile Carbon produced in Acrotelm

Acrotelm Catotelm

Dispersive Mixing Model

Mineral Soil Fig. 5. A conceptual model of solute dynamics in peatlands that explains the surficial pore-water chemistry in peatlands. Dilute recharge that moves downward under bog domes flush solutes from the shallow peat. Alkaline ground-water in the mineral soil mixes into the peat column through dispersion, supplying inorganic solutes to the fen surface and labile carbon produced at the peat surface mixes downward into the peat column.

low. These concentration gradients are reduced as dispersivity increases. In all cases, the model simulated deep penetration of recharge with low solute concentrations directly under the mound and upwelling of ground-water (with high solute concentrations) at the margins of the mound. In contrast, simulations with a low peat mound and low hydraulic conductivity mineral soil produce solute isopleths that were generally oriented parallel to the sloping peat surface except for slight upward bulges under the upslope margin of the mound (Fig. 3). While downward ground-water flow under the peat mound and upward ground-water flow at the margins of the dome are present in these simulations, recharge at the apex of the bog mound does not penetrate into the mineral soils and is primarily confined to the upper peat layers. In both models, a significant fraction of groundwater from the base of the profile was transported to the surface by mechanical dispersion (Fig. 4). The fraction of ground-water that was transported to the peat surface (0–0.5 m) ranged from 0.1% groundwater at the apex of the peat mounds to 7 and 47% ground-water at the margins of the low and high peat mounds, respectively. The maximum concentrations at the peat surface increased with increasing dispersivity but the location of maximum solute concentration in the surficial peat remained similar in each simulated hydrogeologic setting.

5. Discussion The large peatlands of North America contain complex patterns of bogs and fens (Glaser et al., 1981; Heinselman, l963; Sjors, 1963). Field studies consistently confirm that bog pore-waters contain lower concentrations of inorganic ions than fen pore-waters (Reeve et al., 1996; Shotyk, 1988; Gorham et al., 1985). Using calcium values as indicators of ground-water and focusing on the large peatlands found in the glaciated areas of North America, we make the following broad generalizations: • ground-water from carbonate-rich sediments will have a calcium concentration of 100 mg kg ⫺1; • pore-water in the shallow peatland surface will have calcium concentrations of less then 2 mg kg ⫺1 in bogs and greater values in fen areas. Although these parameters are dependent on the mineralogic composition of the underlying geologic materials, inputs from precipitation, and other factors, these generalizations are consistent with published values (Shotyk, 1988; Gorham et al., 1985; Glaser, 1983; Gorham and Pearsall, 1956) and our own measurements in North American peatlands. Using these generalizations, and assuming that rain water has a calcium concentration of about 1 mg kg ⫺1 and a specific conductance of about 10 mS cm ⫺1 (Hem,

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1985), the relative proportions of ground-water (FGW) in peat surficial pore-water can be calculated through a simple mixing model from the ground-water concentration (CGW), rainwater concentration (CR), and peat pore-water concentration (C). FGW ˆ

C ⫺ CR CGW ⫺ CR

…5†

Using the generalizations for calcium concentration in peat pore-water and Eq. (5), we calculate that surficial peat pore-waters in bogs and fens contains about 1 and 10% ground-water, respectively. Similar estimates for ground-water contribution to peatland runoff were obtained by Siegel (1983). These results raise a fundamental question in peatland ecosystems: how are solutes supplied to the surficial peat layers and why are they distributed as observed (Fig. 5)? The same mass transport issues will also affect the subsurface movement of dissolved carbon in peatlands, recently identified as a significant component of the peatland carbon budget (Waddington and Roulet, 1997). Simulations with a strong ground-water flow cell under the bog and low dispersivities produce localized high concentration zones in the fens adjacent to the bog dome, associated with upwelling ground-water (Figs. 2 and 4). Glaser (1989) suggested that spring fens at the margins of bogs in the Hudson Bay Lowland, form in ground-water discharge zones. However, we are unaware of any detailed geochemical transects collected across the margin of a bog with this sharp concentration gradient and localized high concentration zone. In scenarios with weak ground-water flow cells and negligible dispersive mixing, concentrations at the peat surface are dilute, less than 1% of ground-water, across most of the simulated peat surface, including fens (Fig. 4). If this occurred naturally, large peatlands would not contain their complex patterns of bog and fen. Note that the solutes supplied to the peat surface are rapidly diluted downgradient from locations with high concentrations, suggesting that any local surficial source would also be rapidly diluted. This result needs to be evaluated further by coupling ground-water and surface-water flow models. Simulations with a strong ground-water flow cell under the bog and modest dispersivities (a L ˆ 0.5 to 1.0 m) are similar to simulations with lower dispersiv-

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ities. Increasing dispersivities in the simulations smoothes the vertical concentration gradients, providing a more reasonable vertical concentration distribution through the peat column (Fig. 2). The results of these simulations still fail to reproduce the surficial pore-water concentration distributions that are typically found in large peatland settings (Fig. 4), where solute concentrations typically increase with distance from the bog dome into the fen (Shotyk, 1988; Malmer, 1986; Glaser et al., 1981). In simulations that include a large bog mound and modest dispersivities, concentrations were highest at the edge of the bog dome. When modest dispersivities (a L ˆ 0.5 to 1.0 m) are included in a mass transport scenario with a weak ground-water flow cell, the concentration distribution within the model cross-sections better reflect field observations. Concentrations are lowest at the bog dome and increase hydraulically downgradient from the bog dome into the fen, as observed in field data (Shotyk, 1988; Malmer, 1986; Glaser et al., 1981). The low concentrations hydraulically upgradient of the bog dome are unrealistic, and indicate that our model may be too simple, perhaps requiring a 3D model. When the peat dome is small, even very small dispersivities (a L ˆ 0.1 to 0.5 m) can significantly affect the pore-water concentrations in the peat profile (Fig. 3). Incorporating small values for dispersivity into simulations with a small peat mound provides a mass transport mechanism that is capable of supplying solutes that can sustain fen surface-water chemistry and the accompanying vegetation. The small rate of downward ground-water flow under the bog in this hydrogeologic scenario prevented solutes supplied from the mineral soil from reaching the surface of the bog. This effect can also be seen upgradient from the bog (0 to 5 km region) where model boundary conditions force ground-water flow downward. These models indicate that transverse dispersion, driven by lateral flow, can supply sufficient solutes to the fen surface in the absence of upward ground-water movement or runoff from adjacent mineral uplands. The transport of solutes from underlying mineral soils to the peat surface by transverse dispersion alone can act relatively quickly; according to simulations, steady-state profiles were effectively reached in about 100 years (Fig. 3).

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The rate of dispersive mixing is sufficiently slow to allow short-term temporal changes in hydrology to impact water chemistry, but fast enough to contribute to the unexpectedly young radiocarbon dates of methane and carbon dioxide recovered at depth in peatlands (Chanton et al., 1995; Charman et al., 1994; Aravena et al., 1993). These data provide evidence for the downward transport of simple carbon compounds (i.e. root exudates) that are released from plant roots near the peat surface. Dispersive mixing in peatlands can simultaneously explain upward movement of inorganic solutes derived from the mineral soil and the downward movement of this labile carbon generated at the peat surface by green plants. This two-way process can occur when different concentration gradients exist for different solutes because the concentration gradient is the driving force behind dispersive mixing. Dispersion will result in the mixing of alkaline ground-water with labile carbon at depth in the peat column, producing an environment that is favorable for microbial activity and creating areas where methane production can proceed at depth in the peat profile, as previously observed (Waddington and Roulet, 1997; Chanton et al., 1995; Romanowicz et al., 1995; Charman et al., 1994; Aravena et al., 1993). Dispersion has previously been suggested as a controlling factor in gas concentration profiles within peatlands (Hemond et al., 1987). Short-term changes in peat pore-water chemistry, cannot be explained by this process unless lateral peat pore-water velocities are higher than those used in our simulations or dispersivities are larger than the range used in this paper, a possibility that we find doubtful based on current measurements of dispersivity (Hess et al., 1992; Freyberg, 1986; Gelhar and Axness, 1983). Therefore, short-term changes in pore-water chemistry are probably controlled by shifts in ground-water flow patterns (Waddington and Roulet, 1997; Siegel et al., 1995). Increased chemical concentrations through the peat column of a bog during a drought cycle have been attributed to discharge driven by regional flow (Siegel et al., 1995). We suggest that current conceptual models used to explain the distribution of vegetation and surficial pore-water chemistry should be

modified to incorporate dispersive mixing. In this modification of current conceptual models, solutes are supplied to fens by transverse dispersive mixing driven by lateral flow. Water-table mounds sustained by precipitation drive weak ground-water flow cells that flush solutes from the bog peat. 6. Conclusions Numerical simulations suggest that dispersion is an important process in peatlands and explains many of the chemical patterns observed in peat pore-water. Dispersive mixing provides a mechanism for the supply of inorganic solutes to the peat surface in the absence of strong vertical hydraulic gradients or nearby mineral uplands. Dispersion also explains the presence of labile carbon produced at the peat surface at depth in peatlands. We believe that dispersive mixing, coupled with downward hydraulic gradients at bog domes, can account for observed inorganic concentrations, as well as observed distributions of labile carbon generated at the peat surface. Bogs will form where horizontal ground-water velocities are low enough to limit dispersion. In settings were the ground-water velocity drives significant amounts of transverse dispersion, upward fluxes of mineral nutrients and base-rich ground-water will preclude the formation of bogs. In addition, this model provides a mechanism for the relatively rapid production of greenhouse gases, such as methane, in deeper portions of the peat column through the relatively rapid dispersive fluxes of alkaline ground-water from the mineral soil and labile carbon compounds from the peat surface. Acknowledgements We thank Dr N. Roulet and an anonymous reviewer for their comments on this paper. This work was funded by the National Science Foundation under Grant 9615429. References Aravena, R., Warner, B., Charman, D., Belyea, L., Mathur, S.,

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