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Published in Vadose Zone Journal 4:79-88 (2005)
© 2005 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA

ORIGINAL RESEARCH

Spatial and Temporal Dynamics of Preferential Bromide Movement towards a Tile Drain

J. Maximilian Köhnea,* and Horst H. Gerkeb

a Department of Biological & Agricultural Engineering, Texas A&M University, Scoates Hall, College Station, TX 77843-2117
b Institute of Soil Landscape Research, Leibniz-Centre for Agricultural Landscape and Land Use Research (ZALF), Müncheberg, Germany
* Corresponding author (mkoehne{at}cora.tamu.edu)

Received 20 October 2003.



   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
A tracer experiment was conducted to study the spatial and temporal dynamics of preferential Br– movement toward a 1-m-deep subsurface tile drain. Potassium bromide solution was sprayed onto the soil surface on a 0.30- by 10-m strip located at 1 m distance (parallel) to a drain, followed by irrigation of the plot area of 11.8 by 10 m between two adjacent drains for 4 h at 2 mm h–1. Because irrigation intensity was too low to initiate preferential flow, the Br– application was repeated 3 mo later with two 7 mm h–1 irrigations, each lasting 4 h, with a 12-h break in between. During the second irrigation, a concentration peak containing Br– mainly from the first application was observed in the drain effluent. Resident Br– concentrations were measured at 42 locations in a 1.1- by 1-m trench excavated across one end of the Br– strip before the second application, and at 108 locations in a 5.9- by 1-m trench at the opposite end of the strip at the end of the experiment. The spatial Br– concentration distributions suggested predominantly diagonal Br– transport from the application strip toward the tile drain. The experiment was numerically simulated with a two-dimensional Richards' and convective–dispersive model (CDM) and with a two-dimensional mobile–immobile model (MIM). Model analysis of Br– concentrations in the drain effluent revealed preferential flow since the main peak was reproduced with the MIM but not with the CDM. The MIM analysis of the spatial Br– distribution in the soil showed that physical nonequilibrium transport was limited to periods of high intensity irrigation and rainfall, while convective–dispersive transport was prevalent at other times. This study showed that preferential flow as reflected by effluent concentrations from tile-drained field soils cannot be fully understood without considering two-dimensional spatial flow dynamics.

Abbreviations: BC, boundary condition • CDM, convective–dispersive model • MIM, mobile–immobile model • TDR, time domain reflectometry


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
A WELL-DEVELOPED soil structure in agricultural field soils can provide preferential flow pathways for water that bypasses the majority of the soil matrix, thereby potentially leaching surface-applied pesticides and nutrients into groundwater (Jabro et al., 1991; Czapar et al., 1994; Brown et al., 1995). Subsurface drained agricultural fields can be regarded as field-scale lysimeters that facilitate studies of preferential flow and transport at the field scale (Richards and Steenhuis, 1988; Gerke and Köhne, 2004). In their review of a large number of pesticide and other transport experiments, Kladivko et al. (2001) indicated that subsurface tile drainage generally increases infiltration and reduces surface runoff, especially during heavy rainstorm events. Total pesticide losses from a field may sometimes be reduced by installing a subsurface drainage system. This effect can be explained by the occurrence of less reduced erosive runoff containing surface-applied adsorbing pesticides, whereas total losses of the nonadsorbing NO3 from the field may increase due to increased infiltration (Kladivko et al., 2001). Numerous tracer experiments have been performed on tile-drained agricultural fields to study preferential flow and solute transport processes in macroporous soils (Villholth et al., 1998; Villholth and Jensen, 1998; Elliott et al., 2000; Petersen et al., 2002; Kung et al., 2000a, 2000b). In most of these studies, conclusions about preferential flow were derived primarily from tracer breakthrough concentrations in the tile drainage effluent. By comparison, relatively few studies combined information from both the tile drainage effluent and the soil (e.g., Bronswijk et al., 1995b; Mohanty et al., 1998; Zehe and Flühler, 2001; Stamm et al., 2002). We hypothesize that analyses of tracer concentrations in both the drainage effluent and the soil are required for a comprehensive understanding of preferential flow in a tile-drained field soil.

At the Bokhorst site (Northern Germany), solute transport was found to be strongly affected by preferential flow (Wichtmann et al., 1998; Lennartz et al., 1999). Preferential tracer movement at Bokhorst was thought to reduce mass transfer between the transport pathways and the porous soil matrix in the dual-permeability soil system (Gerke and Köhne, 2004). Kamra et al. (1999) suggested that solutes at Bokhorst are mostly transported horizontally along the interface between the plow layer and the subsoil until they reach the back-filled drain trench, where they subsequently move vertically down to the subsurface drain. However, previous tracer experiments conducted at Bokhorst did not investigate the spatial aspects of solute transport as affected by both preferential flow and tile drainage.

The objectives of this study were (i) to assess the contribution of preferential flow to Br– transport and (ii) to analyze the spatial Br– transport patterns in a tile-drained field. The two tasks were pursued by conducting a field tracer experiment in which Br– was applied onto a strip, located at a 1-m offset from a tile drain, followed by irrigation and natural rainfall and by simulating the experimental data (i.e., tile drainage discharge rates, Br– concentrations in tile drainage effluent and in the soil). The simulations were performed using the standard two-dimensional Richards' and convective–dispersive equations as solved with HYDRUS-2D (Simunek et al., 1999) and with a variably saturated MIM (Simunek et al., 2003), as implemented in an extended version of HYDRUS-2D (Simunek, unpublished data, 2003; see Acknowledgments).


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Bokhorst Field Site
The Bokhorst tile-drained agricultural field site is located south of Kiel in northern Germany. Figure 1 shows a schematic of the 5000-m2 field site, along with groundwater elevations as estimated from a large number of groundwater observation wells in the area (Fig. 1). The central four out of six tile drains, installed at an average of 1 m deep and a spacing of 11 to 14 m, were routed to a monitoring station with a Venturi flume and an automated water sampler (Fig. 1 and 2) . For the present study, a plot 10 m long (parallel to the drains) and 11.8 m wide (between drains) was selected for the tracer application and irrigation. Adjacent to the plot a weather station was installed consisting of a tipping bucket rainfall gauge, a humidity sensor, and a temperature probe. Tensiometers at distances of 1, 3, and 5 m from a tile drain recorded pressure heads in the Ap horizon at the 0.15- and 0.3-m depths and in the subsoil at the 0.4-, 0.6-, and 0.8-m depths, while time domain reflectometry (TDR) probes monitored water contents at the 0.3- and 0.6-m depths (Fig. 2b). Three piezometers near the southeastern end of the plot measured the water levels at 1 m depth below soil surface. The soil surface at and near the site had a small slope of 1 to 2% directed southeast toward the monitoring station. Winter wheat (Triticum aestivum L.) was growing on the field during the experiment. Soil types ranged from Stagnic Calcaric Regosols to Stagnic Luvisols according to the FAO classification scheme (i.e., Calcaric or Eutric Epiaquent and Argillic Epiaqualf of the U.S. system), with the most abundant soil type being a poorly drained Dystric Gleysol with about 20% clay and 30% silt in the cultivated Ap horizon (0–0.3 m soil depth). The clay content generally decreased with depth down to about 10% at the 0.7- to 1.1-m depth. Soil structure changed from subangular (0–0.3 m) over angular blocky (0.3–0.95 m) to coherent (below 0.95 m). A plow-compaction pan was present at a depth of 0.3 to 0.35 m. Further details regarding the Bokhorst field site can be found in Lennartz et al. (1999) and Gerke and Köhne (2004).



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  		Fig. 1. (a) Schematic of the Bokhorst experimental plot, including interpolated groundwater elevations in m above sea level on 25 Mar. 1997. Symbols: piezometer or well location (cross), drain-pipe connected to monitoring station (thick line), drain-pipe ending in trench (hatched line). (b) Time table of the experiment.

 


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  		Fig. 2. Schematic of the experimental plot: (a) top view, (b) cross-section view.

 
Bromide Application and Analysis
One month before Br– application, samples of the tile drainage effluent were taken and analyzed (see below) to determine the background concentration of Br– from previous experiments (initially 5 mg L–1). The Br– concentration in the experimental plot was assumed to be initially zero since the plot was located in an area of the Bokhorst field where no Br– had been applied previously, and since Br– was not a natural constituent in the soil.

A time schedule of the experiment is given in Fig. 1b. The first tracer application (Application 1) occurred on 18 Dec. 1996 (Day 0) when 3 L (1 mm) of a solution containing 333 g L–1 Br– (1.5 kg KBr dissolved in 3 L of water) were sprayed on a strip (10 by 0.3 m) located at a horizontal distance away from a tile-line of between 0.85 and 1.15 m (Fig. 2). Immediately after Br– application, the plot area was irrigated with a backpack sprayer at 2 mm h–1 during 4 h. At that time the winter wheat was in an initial growing phase, classified according to the Eucarpia-Scale as growth stage 10. A frost period between Day 2 (20 Dec. 1996) and Day 39 (26 Jan. 1997) produced only minor episodic drain discharge. In February 1997 a total of 71 mm of rain during several low intensity events resulted in drainage outflow without causing any Br– breakthrough. For this reason we decided to repeat the tracer application and irrigation.

On Day 68 (February 24), the entire plot was covered with plastic sheet to prevent further infiltration of natural rainfall. A 1.1-m-long, 1-m-deep trench (Transect 1) was excavated between the strip and (perpendicular to) the nearby tile. A total of 42 undisturbed soil samples (100 cm3) were taken at six depths (0.15, 0.3, 0.4, 0.55, 0.7, and 0.85 m) and seven dislocations (0.1, 0.25, 0.4, 0.55, 0.7, 0.85, and 1 m) from the drain. Bromide concentrations of the pore solutions were determined by extracting 50 g of dry soil with 50 cm3 of H2O by shaking for 1 h. The batch samples were rotated in a centrifuge and the supernatant solution was analyzed for Br–. Bromide concentrations of the pore solutions and the tile drain effluent were measured using an ion-chromatography system with a conductivity detector (GAT, Bremerhaven, Germany) with anion exchanger (Wescan Anion R-10 µm, Alltech, Deerfield, IL). The solid phase of the detector was a 0.1-m-long anion cartridge (Super-Sep 6.1009.000, Methrom, Herisau, Switzerland) together with a 0.02-m guard-cartridge (part 6302137, Bischoff chromatography, Leonberg, Germany). The mobile phase was a 2.5-mM phthalic acid eluant (pH 4.2) that was flowing at 1.5 mL min–1 and was degassed via an automatic on-line solvent degasser (Degasys, Chrom Tech, Apple Valley, MN). The detection limit of the system was 0.2 mg L–1 Br–.

The plastic sheets were removed from the plot on Day 97 (25 March), and 6.4 kg of KBr salt (4.3 kg Br–) was applied as solid grains to the strip (Application 2). The solid form of KBr was chosen to avoid disturbances of the natural flow field as caused by application of a large volume of KBr-saturated solution to the strip. Immediately after Application 2, the plot area (with the strip) of 10-m length by 11.8-m width (between two tile lines) was irrigated at 7 mm h–1 for 4 h, followed by a 12-h break and another 7 mm h–1 for 4 h on Day 98 (26 March). The irrigations represented typical rainstorms in terms of intensity and duration for this part of northern Germany. Two 10- by 5.5-m parts of the plot (one part covering the tile line and nearby application strip and the other part flanking the opposite tile drain) were irrigated one after another in 30-min turns. The irrigations were performed using a 5.5-m-long mobile spray-line sprinkler (Fig. 2a, 2b) equipped with 15 regularly spaced nozzles operated at a pressure of 0.2 MPa (2 bars) at a height of 0.5 m above soil surface. The KBr salt had completely dissolved by the end of the 4-h irrigation on Day 97.

At the end of the experiment on Day 140 (May 7), 108 soil samples were taken from a trench wall of 5.9-m length (half drain-spacing) and 1-m depth (Transect 2) at six depths (0.15, 0.3, 0.4, 0.55, 0.7, and 0.85 m) and at 18 horizontal positions separated by 0.3-m intervals between 0.1 and 5.5 m from the drain. Resident Br– concentrations in the solution extracted from the soil samples were determined as described above using ion chromatography.

Numerical Analysis
The finite element numerical model HYDRUS-2D (Simunek et al., 1999) was used to simulate the field data. HYDRUS-2D assumes the following form of the Richards' equation for variably saturated water flow in a two-dimensional vertical cross section of an isotropic porous medium:

[1]
where {nabla} is the vector differential operator ({partial}/{partial}x, {partial}/{partial}z), {theta} is the volumetric water content (L3 L–3), h is the pressure head (L), x is the horizontal and z the vertical coordinate (positive upward) (L), t is time (T), and K is the hydraulic conductivity function (L T–1). The relationships between {theta}, h, and K were defined using van Genuchten–Mualem functions (van Genuchten, 1980). Nonreactive solute transport during transient water flow was described with the convection dispersion equation as

[2]
where c is the solute concentration (M L–3), q is the water flux density (L T–1), and Dij is the dispersion coefficient tensor (L2 T–1) evaluated according to Bear (1972) as

[3]
where De is the molecular solute diffusion coefficient (L2 T–1), |q| is the absolute value of the water flux (L T–1), {delta}ij is the Kronecker delta function ({delta}ij = 1 if i = j, and {delta}ij = 0 if i != j), DL and DT are the longitudinal and transverse dispersivities (L), and {tau} is a dimensionless tortuosity factor calculated with the formula of Millington and Quirk (1961):

[4]

Alternatively, to simulate physical nonequilibrium (preferential) tracer transport, a dual-porosity medium was assumed where the total soil water content is partitioned into mobile, {theta}m (L3 L–3), and immobile, {theta}im (L3 L–3), regions (van Genuchten and Wierenga, 1976) as follows:

[5]
Variably saturated water flow in the MIM dual-porosity medium was simulated similarly as done by Simunek et al. (2003) for the one-dimensional Richards' equation by extending Eq. [1] as follows:

[6a]

[6b]
where the indices "m" and "im" refer to the mobile and immobile regions, {Gamma}w is the rate of water transfer between the mobile and immobile regions, {alpha}w (T–1) is a first-order water transfer coefficient, and Sem and Seim are effective saturations of the mobile and immobile regions given by, respectively,

[7a]

[7b]
where {theta}m,s, {theta}m,r ({theta}im,s, {theta}im,r) are the saturated and residual mobile (immobile) water contents (L3), respectively. The relationships between {theta}m, hm, and Km for the mobile region were defined by van Genuchten's (1980) soil hydraulic functions.

Physical nonequilibrium two-dimensional transport of a nonreactive solute during variably saturated flow was described by extending the two-region model of Simunek et al. (2003) to two dimensions

[8a]

[8b]
where cm (cim) is the concentration in the mobile (immobile) region (M L–3), {Gamma}s is a first-order solute transfer term (M L–3 T–1) (Gerke and van Genuchten, 1993) containing both a diffusive and an advective component (Eq. [8b]), and {alpha}s (T–1) is a first-order solute mass transfer. Equations [1] through [8] were solved with the Galerkin finite elements method using a fully implicit time weighting scheme for the transport calculation (Simunek et al., 1999). The model domain finite element grid of 806 nodes represented a vertical cross section through the experimental plot of 5.9-m width (half-distance between tiles) by 2-m depth. To obtain a numerically accurate yet time-efficient solution, small nodal distances (0.01–0.03 m) were selected near the node representing the tile drain, near the soil surface, across the topsoil–subsoil transition, and below and adjacent to the 0.3-m-wide tracer application strip. Nodal increments elsewhere in the model domain increased up to 0.2 m. Small mass balance errors of <1% for water and solute indicated that accurate numerical solutions were obtained.

All boundaries of the domain, except the soil surface and the node representing the tile drain (details are given below), were assumed to be impervious by imposing a boundary condition (BC) of zero flux for both water and solute. Imposing zero fluxes at the sides of the domain was justified due to symmetry of the tile-drained flow field. The lower boundary was located deep below (1 m) the tile drain to keep boundary effects on the simulated flow field minimal. Based on water budget calculations, the assumption of zero deep drainage across the lower boundary was deemed to be a reasonable approximation for the Bokhorst site. At the upper boundary, a specified water flux (Cauchy type) BC was imposed using measured rates of irrigation and daily rainfall, and monthly values of actual evapotranspiration estimated as follows. First, monthly average values of potential evapotranspiration were calculated from the field observations of temperature and relative humidity according to Haude (1955). Monthly averages of actual evapotranspiration rates were estimated from these data using information of the water budget (i.e., evapotranspiration = rainfall – drainage – change in soil moisture storage) for the duration of the experiment. Relatively low actual evapotranspiration rates (3–45 mm mo–1) were obtained, as was expected for the experimental period covering winter and spring months.

The tile drain was represented by means of a single numerical node at the 1-m depth on one side of the model domain. A program controlled (system dependent) drainage BC was imposed with zero water flux at an unsaturated drain node and a zero pressure head at a saturated drain node. Hydraulic conductivities at the nodes adjacent to the model drain node were adjusted according to Fipps et al. (1986) to represent hydraulic entry resistances of the drain (Simunek et al., 1999). The drainage BC required the effective drain diameter as input parameter, which was estimated to be equal to 0.02 m based on the number and sizes of small openings in the drain tube (Mohammad and Skaggs, 1983). A zero-gradient solute BC was prescribed at the drain node. The Br– application strip was represented by a third-type solute BC with prescribed Br– concentrations of the water flux. The Br– concentration of the first application was 333 g L–1, applied with 1 mm of water (3 L of water per strip area of 3 m2) during 30 min. For the second application, the Br– concentration of the infiltrating irrigation water was calculated based on the observation that KBr was completely dissolved after 4 h at the end of the first irrigation. Assuming a constant dissolution rate during 4 h, the Br– concentration (47.8 g L–1) was set equal to the ratio of applied Br– mass (4.3 kg) to the volume of irrigation water (90 L) applied to the strip during Day 97. The initial Br– concentration in the soil of the plot before Application 1 was assumed to be zero. The initial pressure head distribution represented a static equilibrium profile with the groundwater table located at the 1-m depth at drain level.

For inverse parameter identification in the CDM and MIM approaches, the Levenberg–Marquardt optimization algorithm was used to minimize the weighted squared deviations between observations and simulated values (Simunek et al., 1999):

[9]
where m is the number of different sets of measurements, n represents the number of observations in a particular measurement set, Oj(z,ti) are observations at time ti at location z (such as tile drainage water fluxes, Br– concentrations of the tile drainage effluent, and resident Br– concentrations of the soil), Ej(z,ti,b) are the corresponding estimated space–time variables for the vector b of optimized parameters (for both soil horizons b consisted of {alpha}, n, Ks, {lambda}, for CDM, and {lambda}, {alpha}w, and {alpha}s for MIM), and vj and wi,j are weighting factors associated with a particular measurement set or point, respectively. We assumed that the weighting coefficients wi,j in Eq. [9] were equal to one, which is similar to assuming equal variances of the errors within a particular measurement.

The following sequential inverse modeling strategy was used. First, measured and simulated tile discharge rates were included in the objective function of the CDM inverse approach. The van Genuchten (1980) parameters n, {alpha}, and Ks were simultaneously estimated for both soil layers, whereas {theta}r and {theta}s were fixed at measured laboratory values (Table 1). Next, flux concentrations of the drainage effluent during 140 d, and the resident concentrations at 10 locations in the two transects at 67 and 140 d were included in the objective function of the CDM inverse approach. This approach allowed us to inversely estimate the longitudinal dispersivities, {lambda}L, of the two layers, while keeping the hydraulic parameters fixed. To limit the number of estimated parameters for the MIM approach, values for n and {alpha} were assumed to be the same as those for the CDM inverse simulation. The saturated mobile water content, {theta}m,s, and immobile water content, {theta}im,s, were determined based on measured values for {theta}s (Table 1) as explained below.


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  		Table 1. van Genuchten (1980) and solute transport parameters used in the model simulations of the Bokhorst Br– transport experiment: parameters of the convection–dispersion model (CDM) determined independently (CDM-forward) and by inverse parameter identification (CDM-inverse), respectively, and parameters of the mobile–immobile model (MIM) with inverse parameter identification of the water transfer coefficient, {alpha}w, and solute transfer coefficient, {alpha}s. Fixed parameters: transversal dispersivity, {lambda}T = 0.1 cm, molecular diffusion coefficient of Br–, D0 = 1.797 cm2 d–1.

 
Previous dye tracer experiments performed on Bokhorst soil columns showed that average dye stained soil fractions of 0.1 and 0.05 for the topsoil and subsoil, respectively (Köhne, 1999). Accordingly, {theta}m,s was set equal to 0.1 {theta}s for the topsoil and to 0.05 {theta}s for the subsoil, with {theta}s being the measured value. The respective values for {theta}im,s were obtained using Eq. [5]. The residual mobile water contents were assumed to be zero. The longitudinal dispersivity, {lambda}L, was assumed to be equal to an average of 0.5 cm as estimated by Meyer-Windel (1998) from laboratory Br– transport experiments using Bokhorst Ap soil columns. Only the {alpha}w and {alpha}s values for both horizons were estimated by inverse MIM simulation.

Additionally, to assess the applicability of measured soil hydraulic properties for flow and Br– transport modeling, hydraulic model parameters were estimated using combined field and lab data. Tension-infiltrometer measurements were performed adjacent to the application strip at imposed pressure heads of 0, –10, –30, and –100 mm, both on the soil surface and on the subsoil at the 33-cm depth after removing the Ap layer. Hydraulic conductivities at the different imposed pressure heads were calculated from steady-state infiltration rates according to the method of Ankeny et al. (1991). Intact soil cores were taken at the same locations by driving metal rings (0.075 m in diam. and height) into the soil. The drying soil moisture characteristic curve was determined on the soil cores by applying suctions between 0 and –2 m using the hanging water column method. The soil moisture characteristic data of the soil cores and the hydraulic conductivities of the tension-infiltrometer measurements were simultaneously fitted using RETC (van Genuchten et al., 1991) to estimate the van Genuchten (1980) soil hydraulic parameters (Table 1). A forward CDM simulation of Br– transport was performed with the hydraulic parameters fixed at their measured values and again assuming {lambda} = 0.5 cm.

The irrigated plot area comprised only 120 m2 of the total field site of 5000 m2. Since the observed tile drainage flux was small and constant before the irrigations, and since no rainfall occurred during the irrigations, it was possible to separate the plot area drainage flux, qPlot (L T–1), from experimentally observed drainage stemming from total field site drainage. During and after periods of irrigation (until onset of natural rainfall) qPlot was calculated as

[10]
where Q is the volumetric tile drainage experimentally observed after onset of irrigation (L3 T–1), Q0 is the volumetric tile drainage observed before irrigation (L3 T–1) (i.e., constant total field site drainage), and APlot is the plot area. During periods without irrigation, drainage fluxes from the plot area, qPlot, and from the total field site area, q, were assumed to be identical.

Simulated Br– concentrations in tile effluent were multiplied by a time-dependent dilution factor F to approximately account for dilution by water resulting from regional (total field site) drainage.


[11a]

[11b]

During periods with large contributions of plot area drainage due to high-intensity irrigation, F reached values of up to 0.85 (F ≤ 1). After the irrigations, F eventually tended toward a value of zero and was then set equal to the plot-to-field site area ratio, Aplot/A = 0.024 (Eq. [11b]). No attempt was made to include in Eq. [11] the effects of (variable) low Br– background concentrations of regional drainage water.

The resident tracer concentrations of the field plot were assumed not to be affected by dilution from regional subsurface flow entering the plot. This assumption was based on the presence of only a very small groundwater hydraulic gradient (<0.005 m m–1) directed toward the plot, as compared with much higher lateral hydraulic gradients directed toward the tile drains.


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
CONCLUSIONS
 REFERENCES
 
Figure 3 shows rates of precipitation, irrigation, and drain water discharge (Fig. 3a), groundwater levels in selected wells (Fig. 3b), and Br– concentrations (Fig. 3c). Before Day 40 and after Day 120, drain discharge was very small due to a frost and a drought period, respectively. Figure 3a shows that drain discharge responded quickly to larger rainfall events, but did not respond to rainfall having an intensity of <0.5 cm d–1. Notice that the drain responded quickly to the second irrigation during Days 97 and 98 (Fig. 3a). The groundwater table as measured in wells (Fig. 3b) was initially near the tile drain level, such that only little outflow occurred from the tile drains until 50 d (Fig. 3a). Starting at Day 50, the groundwater table rose by 1 m within a few days in response to several rainfall events (Fig. 3b). The groundwater table between 60 and 70 d was fairly constant and then slowly declined after Day 70 (Fig. 3b). The Br– background concentrations of around 5 mg L–1 (fluctuating between 1 and 15 mg L–1) resulted from previous tracer experiments performed outside of the plot (Fig. 3c). There was no obvious response of the Br– concentration to Application 1. By contrast, Application 2, with irrigations during Days 97 and 98, caused a small increase in the Br– tile effluent concentration on Day 97 and a sharp increase to 130 mg L–1 on Day 98, yielding the highest observed Br– concentration throughout the experiment. Just before a major natural rainfall event occurred on Day 100, Br– concentrations dropped to 5 mg L–1. Between 100 d and the end of the experiment at 140 d, Br– concentrations fluctuated around the background level of 5 mg L–1 (Fig. 3c).



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  		Fig. 3. Time series of experimental observations: (a) natural rainfall (open bars) and tile drain discharge rates (line), (b) groundwater levels as observed in selected wells, and (c) Br– concentrations in tile drain effluent, and second irrigation events.

 
Due to the variable background Br– concentrations originating from prior Br– tracer experiments, only an upper limit for Br– recovery could be calculated. The tile drain effluent during the experiment contained a total of 2.5 kg of Br (including background Br–) as compared with 1 and 4.3 kg applied. This means that <45% of both Br– applications was recovered in the drain effluent and suggests that the bulk Br– mass still resided in the soil at the end of the experiment. The single high peak between 98 and 100 d accounted for 300 g Br– lost to tile drainage, equivalent to 30 and 5.7% of the applied mass of the first and both applications, respectively.

For the irrigation on Day 97, Fig. 4 shows pressure heads recorded with tensiometers installed at 1 m (Fig. 4a) and 5 m (Fig. 4b) lateral distances from the tile, respectively. The pressure heads at a distance of 5 m showed an earlier response to the irrigation than at a distance of 1 m (Fig. 4b). At both locations, the response of the pressure heads at the 0.15-m depth was followed, after a certain time lag, by almost simultaneous reactions of the pressure heads at the 0.3-, 0.4-, and 0.6-m depths (Fig. 4). Positive pressure heads at a lateral distance of 5 m from a tile drain (Fig. 4b) indicated that complete saturation of the subsoil was reached within 2 h. Moreover, pressure heads were rising to more positive values at a distance of 5 m than at 1 m, which points to a locally higher groundwater table between the tile drains (Fig. 4a, 4b). Water contents at the 0.3- and 0.6-m depths as measured with TDR probes at 1 and 5 m from the drain are shown in Fig. 5 . Water contents at 0.6 m in the subsoil were close to saturation from the beginning and showed a small increase only at 1 m near the drain (Fig. 5).



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  		Fig. 4. Pressure heads in soil at different depths below the application strip as recorded with tensiometers during the irrigation on Day 97 (25 Mar. 1997), (a) at 1-m lateral distance from the drain and (b) at 5-m lateral distance from the drain.

 


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  		Fig. 5. Water contents in soil at different depths and distances from the tile drain as recorded with TDR probes during irrigation on Day 97 (25 Mar. 1997). Legend: 1 m; 0.3 m denotes horizontal offset from the drain (1 m) and depth (0.3 m), respectively.

 
The observed spatial distribution of Br– concentrations on Day 68 in soil transect 1 is shown in Fig. 6 . The spatial interpolation was accomplished by means of ordinary point-kriging using a linear variogram model fitted to the experimental variogram calculated with Surfer 8 (Golden Software Inc., 2002). The spatial Br– concentration pattern indicates diagonal transport of a dispersed Br– plume from the application strip toward the drain (Fig. 6), with maximum concentrations of about 500 mg L–1 in the soil solution.



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  		Fig. 6. Spatial distribution of measured Br– concentrations (mg L–1) on Day 68 (24 Feb. 1997) in Transect 1.

 
The time series of tile drainage discharge was fairly well matched by the forward and inverse CDM approaches and the inverse MIM (Fig. 7a) . The high peaks of 2.7 cm d–1 (Fig. 3a) caused by irrigations on Days 97 and 98 were overestimated with the MIM (9 cm d–1, beyond range of Fig. 7a) and underestimated with the CDM approaches (<1 cm d–1). The CDM predicted that part of the irrigation water was lost to surface runoff (not shown). Cumulative tile discharge was described well using all approaches (Fig. 7b). Measured and simulated Br– effluent concentrations are compared in Fig. 7c. The observed short-term Br– peak around Day 98 could be matched only with the MIM, while the inverse and forward CDM approaches gave gradually rising concentrations (Fig. 7c). The comparison between the simulated mobile concentration (in the tile drainage water) and immobile concentration (in the pore solution at the drain node) in Fig. 7d suggests that during periods with high flow rates, considerable physical nonequilibrium occurred, whereas the mobile and immobile concentrations converged during periods of little or no drainage, thus indicating equilibrium transport. Figure 7d additionally shows results for a forward MIM simulation based on parameters and boundary conditions of the inverse MIM approach, except that only the first Br– application was used as the boundary condition. This simulation resulted in a smaller Br– peak around 98 d. Hence, the MIM simulations suggest that the observed peak contained Br– from both the first and the second application. This can only be explained by transport through preferential flow paths. The plot irrigation of 60 mm (30 mm each on Days 98 and 99) at 7 mm h–1 intensity must have initiated the preferential flow process. By comparison, the first irrigation of 8 mm water on 18 December at an intensity of 2 mm h–1 caused no Br– breakthrough. From this we infer that the amount and intensity of the second irrigation triggered the preferential flow, whereas the first irrigation was insufficient to initiate preferential flow.



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  		Fig. 7. Data and model results using the mobile–immobile model (MIM), the convection dispersion model without (CDM-forward) and with (CDM-inverse) inverse parameter estimation: (a) drain discharge rates, (b) cumulative drain discharge, (c) Br– concentration of the drain effluent during the entire experimental duration, and (d) from 97 to 99 d, as simulated with the MIM for the mobile region (MIM, mobile), immobile region (MIM, immobile), and for the mobile region when only the first Br– application [MIM, mobile (first application)] was considered.

 
To illustrate the spatial dynamics of simulated mobile–immobile Br– movement in a dual-porosity soil, Fig. 8 shows the spatial distribution of Br– concentrations as simulated with the MIM approach at different times. Until Day 97 just before Application 2, concentration patterns were essentially the same in the mobile and immobile regions (compare Fig. 8a, 8b with 8e and 8f). This simulated pattern markedly changed in response to Application 2 within a few hours after the onset of high-intensity irrigation. Bromide in the mobile region resulting from Application 2 traveled far below the previous simulated peak from Application 1. Bromide peak concentrations in the immobile region were lower than in the mobile region and were mainly confined to the top soil layer. The physical nonequilibrium situation during rapid transport in the mobile region was caused by relatively little exchange of Br– between the mobile and immobile regions as reflected by the small interregion water and solute mass transfer coefficients of the subsoil (Table 1). Note that the simulated nonequilibrium between the spatial concentration distributions in the mobile and immobile regions coincided with the simulated nonequilibrium between the mobile and immobile Br– concentrations in the tile drain effluent (Fig. 7d). Convective–diffusive transfer into the immobile region already caused lower Br– concentrations after 101 d in the mobile region. This apparent dilution explains the low observed and simulated (MIM) Br– concentrations in the tile drainage water after Day 100 (Fig. 7c). Additionally, dilution of drainage water may have been caused by infiltrating rainfall that bypassed the Br– plume. We note that this latter dilution effect cannot be considered in one-dimensional dual-porosity models, which are frequently used for analysis of preferential solute transport in tile-drained fields. Also, it would have been difficult to conclude from an analysis of Br– concentrations of the drainage effluent only, whether or not the main Br– peak had leached from the profile after 101 d, while analysis of the simulated and observed (see below, Fig. 9) spatial Br– concentration distribution clearly shows that the bulk of Br– of both applications still resided in the soil.



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  		Fig. 8. Spatial Br– concentration distributions in the mobile and immobile regions as obtained with the MIM simulation at different times after the first tracer application.

 


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  		Fig. 9. Bromide concentrations of the soil solution on Day 140 (7 May 1997) of Transect 2 for (a) observations, (b) forward simulation results for the convection–dispersion model (CDM-forward), and c) inverse simulation results for the convection–dispersion model (CDM-forward).

 
Finally, Fig. 9 shows the resident tracer concentrations in Transect 2 at the end of experiment on Day 140 (6 wk after Application 2). The concentration profiles represent measured values (Fig. 9a) and model simulation results for the forward CDM (Fig. 9b), the inverse CDM (Fig. 9c), and the MIM (Fig. 9d) approaches starting on Day 0 and including both applications. Results for the MIM (Fig. 9d) represent the mobile region; however, Br– concentrations in the immobile region (not shown) were almost the same due to concentration equilibrium. The measured spatial Br– concentration distribution showed a diagonal trend toward the drain (already observed after 68 d, Fig. 6), which was not fully reproduced by any of the models. The diagonal trend was approximated only with the MIM, which showed a considerably more diagonal transport during periods of fast flow (Fig. 8c). The observed spatial patterns of the resident concentration were generally matched fairly well with all models (Fig. 9), compared with the relatively poor agreement between data and CDM simulation for the flux concentrations of the drain effluent (Fig. 7c). This discrepancy between relatively good CDM description of spatial concentration patterns and poor CDM descriptions of Br– peaks in the tile effluent suggests that Br– displacement at the Bokhorst field site followed most of the time a convective–dispersive transport process, except during high intensity storms that triggered preferential transport. This conclusion was corroborated by the MIM simulation results showing pronounced nonequilibrium between Br– concentrations in the mobile and immobile regions only after the high-intensity irrigations (Fig. 8c, 8g), which produced the high Br– peak in drainage outflow (Fig. 7c, 7d). Note that Jaynes et al. (2001) also found that a CDM could reasonably well approximate resident Br– concentrations in a fine loamy glacial till soil relatively similar to the Bokhorst soil, but failed to reproduce Br– concentrations in the tile drainage effluent.

The strong lateral spreading for the forward CDM and the inverse CDM approaches was a result of different processes. For the forward CDM approach, small values of the hydraulic conductivity function as calculated using the independently obtained van Genuchten parameters (Table 1) caused the saturated zone during rainfall events to rise up to 40 cm below the upper boundary, this producing lateral hydraulic gradients in the periodically saturated zone and leading to lateral Br– transport. For the inverse CDM approach, the soil hydraulic parameters allowed the groundwater table to rise only to about 0.8 m below the surface; solute spreading in this case was caused by large estimated longitudinal dispersivity values of 0.3 m for the topsoil (its upper constraint, Table 1) and 0.13 m for the subsoil.


   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
REFERENCES
 
The two-dimensional numerical MIM analysis of tile outflow, effluent Br– concentrations, and spatial distributions of resident Br– concentrations allowed a consistent interpretation of flow and solute transport processes at the Bokhorst site. The distinct peak in the tile effluent Br– concentrations accounted for 300 g or 5.7% of applied Br– lost to tile drainage. The fact that this peak could be reproduced with the MIM, but not with the CDM, suggests that the peak was caused by preferential flow. On the other hand, the CDM reproduced the spatial distribution of measured resident Br– concentrations in a soil transect at the end of the experiment relatively well. The MIM simulation of the time evolution of the spatial Br– concentration pattern revealed that Br– was transported during physical equilibrium conditions, except for periods of heavy rainfall that triggered preferential flow involving physical nonequilibrium. Our study hence suggests that different chemical transport mechanisms are active at the Bokhorst site at different times depending on the rainfall intensity: convective–dispersive transport through the unsaturated zone prevailed most of the time, except after storm events triggering preferential flow and physical nonequilibrium transport. We also found a rarely reported transport process involving diagonal tracer transport in the unsaturated zone toward the tile drain, whereas model results suggested mainly vertical (only slightly diagonal) movement in the vadose zone and lateral movement in the saturated zone toward the tile. This study shows that the spatial dynamics of transport toward tile drains is important for understanding the exact mechanisms causing preferential flow in tile drained field soils.


   ACKNOWLEDGMENTS
 
This study was financially supported by the Deutsche Forschungsgemeinschaft (DFG) under grant DFG Wi-671/9. We are grateful to Bernd Lennartz, Sigrid Köhne, and two excellent anonymous reviewers for their valuable comments and suggestions. For their assistance during field work, we thank Hans-Jürgen Voß and Harald Grehl. Special thanks to Jirka Simunek for providing us with an extended HYDRUS-2D code for inverse simulation of mobile–immobile solute transport during transient flow in a two-dimensional dual-porosity medium.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 




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