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DIVISION S-1-SOIL PHYSICS

Solute Transport for Steady-State and Transient Flow in Soils with and without Macropores

Institute for Land and Water Management, Katholieke Universiteit Leuven, Vital Decosterstraat 102, 3000 Leuven, Belgium

jan.vanderborght{at}agr.kuleuven.ac.be

	ABSTRACT

TOP ABSTRACT INTRODUCTION Materials and methods Results and discussion Summary and conclusions Appendix REFERENCES

 
The effect of flow rate and flow regime on solute transport in two soils, a sandy-loam (Glossudalf) and loam (Udifluvent), was investigated. For each soil type, leaching experiments were carried out in two large undisturbed soil columns (0.3-m i.d., 1-m length) for three different steady-state flow rates and three (sandy loam), or two (loam) transient flow regimes. Solute concentrations were measured in the drain water, c^f, and in situ, c^r, using time domain reflectometry (TDR). In order to approximate the transient by a steady-state flow transport process, a solute penetration depth coordinate, , was used. Breakthrough curves (BTCs) of c^r and c^f were used to optimize parameters of the convection–dispersion equation (CDE). In the sandy loam, the CDE described transport for steady-state and transient flow conditions well and relevant CDE model parameters could be derived from BTCs of c^r. In the loam soil, due to the activation of macropores, lateral solute mixing decreased with increasing flow rate, which resulted in an increase of dispersivity with increasing depth for higher flow rates. Since bypass flow and transport through macropores is barely apparent in time series of concentrations measured in situ, c^r, CDE parameters derived from BTCs of c^r were inconsistent with parameters derived from BTCs of c^f when bypass flow was important. The dispersivity increased with increasing flow rate in both soil types and an effective or flux-weighted average flow rate rather than a time-averaged flow rate was used to derive the relation between the dispersivity and the flow rate.

Abbreviations: BTC, breakthrough curve • CDE, convection–dispersion equation • EC, electrical conductivity • PVC, polyvinyl chloride • TDR, time domain reflectometry

	INTRODUCTION

TOP ABSTRACT INTRODUCTION Materials and methods Results and discussion Summary and conclusions Appendix REFERENCES

 
TO DESCRIBE SOLUTE TRANSPORT in undisturbed soils, several transport models that conceptualize the transport process in different ways have been presented. Which transport model is most appropriate to describe transport depends on the soil type, the scale on which transport is described, and the flow rate. Transport in repacked and homogeneous soils is well described by the CDE, which assumes complete macroscopic lateral mixing of the replacing solution with the initial soil solution. The dispersion of the displacement front resulting from variations in advection velocities at a microscopic scale is described as a diffusion process. In heterogeneous soils, local variations in advection velocity that are persistent across a macroscopic scale lead to an incomplete lateral mixing of the initial soil solution with the applied tracer solution. When the velocity does not change along the trajectory of a solute, transport can be described as a stochastic-convective process (Simmons, 1982). In some soils, field-scale (e.g., Jury et al., 1982; Butters and Jury, 1989) and lysimeter-scale (e.g., Vanclooster et al., 1995; Vanderborght et al., 1997) transport was well described as a stochastic–convective process, whereas a convective–dispersive model was more appropriate for other soils (Roth et al., 1991; Vanderborght et al., 1997). An alternative transport conceptualization that accounts for incomplete lateral solute mixing is the two (multiple)-region model approach (e.g., Coats and Smith, 1964; van Genuchten and Wierenga, 1976; Jarvis et al., 1991; Gerke and van Genuchten, 1993; Gwo et al., 1995; Durner and Flühler, 1996). The pore domain is divided into different subdomains in which transport occurs with different advection velocities. Solutes are exchanged between flow domains due to advective and diffusive fluxes between the domains. The simplest two-region model, which considers only two pore domains, advective transport in one pore domain, and a first-order rate exchange of solutes between the two domains, is the mobile–immobile model (MIM; van Genuchten and Wierenga, 1977). This model better describes the asymmetric solute BTCs that are observed in structured soils with large interaggregates or macropores (e.g., van Genuchten and Wierenga, 1976; De Smedt and Wierenga, 1984).

Besides the soil type, the flow rate and the flow regime also have a large impact on the extent to which lateral solute mixing occurs and on the solute dispersion. In soils with macropores, the transport process depends largely on whether these pores are activated or not (Bouma, 1991; White, 1985). Both solute dispersion and bypass flow increase drastically with the flow rate when these pores are activated. In contrast to transport in macroporous or well-structured soils, lateral solute mixing tends to decrease with decreasing flow rates in sandy soils with coarse-textured layers (Ju and Kung, 1997). The flow regime also greatly influences lateral solute mixing and solute dispersion. Under intermittent flood irrigation, the solute dispersion was considerably larger than under continuous flood or drip irrigation (Bowman and Rice, 1986; Jaynes et al., 1988; Jaynes and Rice, 1993). Due to wetting front instability, intermittent infiltration may result in less lateral solute mixing and hence larger solute dispersion in water-repellent soils (Ritsema et al., 1993) or soils with a coarse texture (e.g., Kung, 1990a, 1990b). In well-structured soils, the soil water content at the start of an infiltration influences the occurrence of preferential flow (Flury et al., 1994). More water infiltrates in the soil matrix and less preferential flow through macropores occurs when the soil is dry.

The main objective of this study was to evaluate the effect of flow rate and flow regime on solute transport in two soil types, a relatively structureless sandy loam and a loam with macropores. The displacement of the initial soil solution by a tracer solution in undisturbed soil monoliths was observed at several depths in the soil profile using TDR and using concentration measurements in the drain water. The time series of concentrations or BTCs were used to estimate the average solute particle velocity and the dispersion coefficient of the BTC. From the change of the dispersion coefficients with depth, the extent of lateral solute mixing was derived.

Time domain reflectometry has been shown to be a very practical technique to measure in situ concentrations with great temporal resolution under both steady-state (e.g., Vanclooster et al., 1993; Wraith et al., 1993; Mallants et al., 1994; Ward et al., 1994) and transient flow conditions (Risler et al., 1996; Vogeler et al., 1996). However, in situ-measured or volume-averaged concentrations may differ substantially from flux-averaged concentrations, which are measured in the drain water. Since the latter concentration mode is important to assess the pollution load to the groundwater, our second objective was to investigate if easy to measure in situ solute concentrations can be used to calibrate transport models that can subsequently predict solute fluxes.

	Materials and methods

TOP ABSTRACT INTRODUCTION Materials and methods Results and discussion Summary and conclusions Appendix REFERENCES

 
Experimental Setup
Two soil types were selected for the transport experiments: a sandy loam with a highly degraded illuvial clay horizon (Arenic Glossudalf; Soil Survey Staff, 1994) and a loam, which consists of colluvial material with only a weak horizon development overlying a buried illuvial clay horizon (Udifluvent on top of Hapludalf). The main characteristics of the two soils and their horizons are listed in Table 1 . For the loam field site an exhaustive data set on soil hydraulic and transport parameters at the local and field scale has been collected in the past (Mallants, 1996; Mallants et al., 1996a, 1997a, 1997b; Jacques et al., 1998). For the sandy loam field site, transport parameters have been determined from leaching experiments in large lysimeters (0.8-m i.d., 1-m length) (Vanderborght et al., 1997).

For the sandy loam columns, one of the soil monoliths (Column 1) was placed on a ceramic plate (ref. no. 606D11-B1M1, Soilmoisture, Santa Barbara, CA) and a suction of -50 kPa was applied under the ceramic plate by a vacuum pump to create a negative pressure head at the bottom of the soil monolith during the leaching experiments. Due to the low hydraulic conductivity of the ceramic plate (0.3 mm d^-1), the suction exerted on the soil water during a leaching experiment was considerably smaller. The other soil monolith (Column 2) was placed on a perforated PVC plate and no suction was applied. From the transport experiments in the sandy loam columns it became clear that the ceramic plate somewhat obstructed water flow during transient flow experiments. Therefore, in the loam lysimeters, the ceramic plate was replaced by two glass-fiber wicks (1 cm [3/8 inch], high density, no. 10-864KR-02, Amatex Corp., Norristown, PA), which have a much higher hydraulic conductivity. The bottom end of the wicks was at 1.15 m below the bottom of the soil column to create negative pressure heads under the loam lysimeters. The procedure of Rimmer et al. (1995) was used to select the optimal wick type, number of wicks per soil column, and wick length on the basis of the hydraulic properties of the wicks (Knutson and Selker, 1994) and of the soil (Mallants et al., 1996a). To ensure good contact between the soil and the wicks, the soil columns were placed on perforated PVC plates, which were entirely covered by the twisted top ends of the glass-fiber wicks.

For all transport experiments, an input CaCl₂ solution having a different electrical conductivity (EC) than the initial soil solution at the start of the transport experiment was applied by a peristaltic pump until the initial soil solution was completely replaced by the input solution. In the steady-state flow leaching experiments, the input flow rate was constant. For the transient flow experiments, solution was applied at a constant flow rate during a short time period. The time interval between successive applications and the application time were constant, resulting in a periodic flow. A cloth on top of the soil surface assured a homogeneous horizontal redistribution of the applied solution. A summary of the water fluxes, solute concentrations, and electrical conductivities used in the different experiments and duration of the leaching experiments is given in Table 2 . For the steady-state leaching experiments, the leaching solution was added after the soil water contents had reached a constant value. For the transient leaching experiments, the leaching solution was added when the water content course during infiltration–drainage cycles did not change between subsequent cycles, that is, when quasi-steady-state conditions were obtained.

View this table: [in this window] [in a new window]   Table 2 Information on leaching experiments.

Soil bulk electrical conductivities ECa (^-1 L^-1) and water contents were measured using horizontally installed TDR probes (2-rod probes: 0.25-m-long, 0.005-m-diam., 0.025-m-spaced stainless steel rods). In each soil column, 13 TDR probes were alternated along three vertical transects. The first probes were installed at 0.05 m below the input surface and subsequent probes were installed at 0.075-m depth intervals except the deepest probes in the sandy loam soil, which were installed at 0.93 m below the input surface.

All TDR measurements were carried out using a Tectronix 1502B cable tester (Tectronix, Beaverton, OR). A computer-controlled multiplexing system (Heimovaara and Bouten, 1990) was used to retrieve, store, and analyze TDR wave forms. The apparent dielectrical permittivity, Ka, of the soil around a TDR probe was derived from the travel time of an electromagnetic wave along the TDR rods, ts (T) as:

(1)

with c (L T^-1) the velocity of light in free space, and L the probe length. was derived from Ka using the empirical relation of Topp et al. (1980). When the soil columns were dismantled, two soil samples (5.1 cm long, 5-cm diam.) of 100 cm³ were taken in the proximity of each TDR probe. The water contents in these samples, which were determined gravimetrically, were used to improve the estimation of by adjusting the intercept of the Ka– relation of Topp et al. (1980) for each TDR probe.

The ECa (^-1 L^-1) at a reference temperature of 20°C was derived from the TDR-measured impedances at long times Z () (Heimovaara et al., 1995) as:

(2)

with f_T a temperature correction factor, Kp the cell constant (L^-1), and R_cable () the series DC resistance of the cable tester, coaxial transmission line, and switches. Kp (2.78 m^-1) and R_cable (1.25 ) were determined from Z measurements in solutions with known EC. f_T was determined indirectly from Z measurements at different temperatures in a calibration sample with constant solute concentration and water content.

For the steady-state leaching experiments, relative solute concentrations c(z,t) at time t and depth z were derived from ECa measurements as:

(3)

with C_in the initial concentration in the soil solution, C₀ the concentration of the leaching solution, ECa_in(z) the initial soil bulk EC at a depth z, and ECa₀(z) the soil bulk EC at a depth z when the initial soil solute concentration was completely replaced by the leaching solution. Equation [3] assumes a linear ECa–c or ECa–ECw (with ECw the electrical conductivity of the soil solution) relation. In Fig. 1 , we plotted ECa measured in the loam soil for different steady-state flow experiments vs. ECw of the initial and input concentrations. This plot shows that for small concentrations, this relation is not strictly linear (Rhoades et al., 1989). However, this deviation from linearity is minor and does not have a large influence on the calculated c. The scatter on the ECa–ECw plot reflects the spatial variability of the ECa–ECw relation in the soil profile due to local variations in volumetric water content, clay content, and soil structure (Mallants et al., 1996b). However, for the transport experiment, all ECa measurements were rescaled using site-specific ECa₀ and ECa_in measurements (Eq. [3]) and the spatial variability of the ECa–ECw–C relation had no impact on the calculated relative concentrations, c. Since the ECa–c relation is highly dependent on , this relation will change during the transient flow experiments. The water application during the transient experiments was periodic and after quasi-steady-state flow was obtained, , with t the period of the infiltration–drainage cycle, n the number of infiltration–drainage cycles before the current cycle, and t' the time since the beginning of the current infiltration–drainage cycle. As a consequence, the ECa–c relation is periodic when quasi-steady-state conditions are obtained and is given as:

(4)

View larger version (8K): [in this window] [in a new window]   Fig. 1 Soil bulk electrical conductivity ECa in the loam soil for the steady-state flow experiments vs. the conductivity of the soil solution Ecw

Solute concentrations in the drain water were derived from the drain water EC that was measured using a laboratory EC meter (LF92 WTW, Weilheim, Germany). Concentrations derived from TDR measurements represent in situ-measured, volume-averaged or resident concentrations, c^r, whereas the concentrations measured in the drain water represent flux-averaged concentrations, c^f.

Estimation of Convection–Dispersion Equation Transport Parameters
The general formulation of the one-dimensional CDE is:

(5)

with C (M L^-3) the solute concentration, D (L² T^-1) the dispersion coefficient, and v (L T^-1) the average solute velocity. In general, D, v, and are functions of both t and z. For steady-state flow conditions and a uniform soil profile, D, v, and are constants and Eq. [5] is reduced to:

(6)

The parameters D and v were obtained from fitting the analytical solutions of Eq. [6] to BTCs observed during steady-state flow leaching experiments using a least-squares optimization procedure (proc NONLIN; SAS Institute, 1989). The analytical solutions for a third-type inlet boundary were considered for the c^r BTCs, whereas a first-type inlet boundary condition was used for the c^f BTCs (Parker and van Genuchten, 1984).

It should be noted that in the derivation of Eq. [6] from Eq. [5], it was assumed that the soil profile was uniform. If the water content profile is not uniform, the changes of with z are reflected in the estimates of D and v using Eq. [6]. Using time moment analysis of BTCs, it is readily shown that (Appendix, Eq. [A4]):

(7)

with J_w the flow rate. If we assume that the dispersivity, , is constant in the soil profile, the fitted dispersivity to a BTC at z, (z), is related to as (see Appendix, Eq. [A4]):

(8)

with CV() the coefficient of variation of the water content with depth. Since for the steady-state flow experiments, CV() < 10%, it follows from Eq. [8] that the fitted (z) overestimates the real only by 1%. As a consequence, the estimated dispersivities are merely influenced by relatively small changes of with depth.

For the transient experiment, Eq. [5] was also reduced to a similar form as Eq. [6] making certain simplifications. A solute penetration depth coordinate, (t), is introduced (De Smedt and Wierenga, 1978; Eq. [12] in Vanderborght et al., 2000):

(9)

with _a the soil water that is accessible for solutes and a dummy integration variable. We assumed that all water is accessible to the applied solutes.

Assuming that J_w and do not change drastically with depth for the narrow region around the solute displacement front and replacing the time coordinate by the solute penetration depth coordinate , Eq. [5] is reduced to a similar form as Eq. [6] (Eq. [14] in Vanderborght et al., 2000):

(10)

with . Assuming that the water content did not change considerably with depth for the narrow region around the solute displacement front, (t) was calculated for the period that the solute front passes z_i as:

(11)

with Using Eq. [11], (t) can be approximated for depths larger than the length of the soil column.

If is a function of the flow rate, () is not a constant during a transient flow leaching experiment. Vanderborght et al. (2000) found that a BTC at a depth z_i can be described reasonably well using a constant, effective dispersivity, _eff(z_i) (Eq. [18] in Vanderborght et al., 2000). To derive the soil specific relation (J_w), _eff(z_i) can be coupled to an effective flow rate _{w eff}(z_i) (Eq. [23] and [24] in Vanderborght et al., 2000):

(12)

with

(13)

J_{w eff}(z) or flux-weighted average flow rate corresponds with the flow rate at which most of the water crosses depth z in the soil profile, and J_w is the time-averaged flow rate across an infiltration–drainage cycle (Fig. 1 in Vanderborght et al., 2000).

If the solution of Eq. [10], with () replaced by _eff(z_i), is fitted to a BTC as a function of , only _eff(z_i), which defines the spreading of the BTC at z_i, can be optimized. The mean position of the BTC on the (t) axis is fixed and defined by the flow rate during an infiltration–drainage cycle and the soil water content at the beginning of the infiltration–drainage cycle in the soil layer above the observation depth z_i. (Eq. [9] and [11]). However, due to horizontal redistribution of water in the soil column, the cumulative amount of water that drained per unit area from the cross-sectional area of the TDR detection volume at z_i, (z_i,t), may be quite different from I(z_i,t), which represents the spatial average of the cumulative drainage across the entire cross-sectional area of the soil column (Vanderborght et al., 1997). As a consequence, the measured BTC at z_i may arrive earlier [(z_i,t) > I(z_i,t)] or later [(z_i,t) < I(z_i,t)] than predicted from the solute penetration depth coordinate (t), which is calculated from I(z_i,t). Also (z_i,t) is measured in the detection volume of the TDR probe only. But, since the spatial variability of water content measurements is in general much smaller than the spatial variability of water fluxes (Jury, 1985), it is reasonable to assume that the water content measurements at z_i are representative for the entire cross section of the soil column at z_i. If (z_i,t) I(z_i,t), we can define a solute penetration depth (t;z_i) that describes the solute front arrival and solute breakthrough observed in the TDR detection volume at z_i Postulating leads to:

(14)

whereby _z is the depth-averaged water content for the interval z, and (0,t;z_i) is the cumulative infiltration depth at the soil surface that leads to a solute penetration depth (t;z_i). (0,t;z_i) is related to the actual infiltration depth at the soil surface as:

(15)

with A(z_i) the cross-sectional area of the TDR detection volume and A₀ the capture area on the soil surface where streamlines that go through A(z_i) originate, and I(a,t) the infiltration depth at a on the capture area A₀.

Replacing (t) in Eq. [10] by leads to:

(16)

with (z_i) an additional fitting parameter that defines the average position of the BTC at z_i on the axis. _eff(z_i) and (z_i) are obtained by fitting the analytical solution of Eq. [16] to a BTC as a function of at z_i. For c^r BTCs, the analytical solution for a third-type inlet boundary condition is used, whereas the solution for a first-type inlet boundary condition is considered for the c^f BTCs. It should be noted here that when the water flux and the solute concentrations in the TDR detection volume are not representative for the cross section of the soil column, the fitted is different from one. However, a fitted different from one does not necessarily result from nonrepresentative concentrations and water fluxes in the TDR detection volume. As we will discuss below, it may also be caused by using the convection–dispersion model to interpret resident concentration BTCs and to link resident concentrations to solute fluxes, which define the solute travel time distribution, in cases when the convection–dispersion equation does not appropriately describe the transport process.

To compare BTCs observed during transient and steady-state flow leaching experiments at z_i, we replaced the solute penetration depth coordinate, , with a transformed time coordinate t*(z_i) (T):

(17)

with J_w defined in Eq. [13]. Replacing in Eq. [16] by t*(z_i), a comparison between Eq. [6] and [16] reveals that:

(18)

can be considered as the velocity of the solute displacement front during the transient flow displacement experiment. v*(z_i) for (z_i) = 1 corresponds with the piston flow velocity v_p*(z_i), which predicts the average transformed travel time t* of a solute front from the inlet surface to depth z_i when all initial soil water is accessible to the applied tracer solution.

	Results and discussion

TOP ABSTRACT INTRODUCTION Materials and methods Results and discussion Summary and conclusions Appendix REFERENCES

 
In Table 3 , depth-averaged , , are listed. For the transient experiments, in Table 3 corresponds with the depth-averaged , that is, at the beginning of the infiltration drainage cycle. Also, the depth-averaged maximum water content, _max, observed during an infiltration–drainage cycle is listed in Table 3. For the steady-state experiments, decreased with decreasing flow rate, especially for the sandy loam soil but less for the loam soil. The difference between _max and decreased for both soil types with increasing depth (results not shown) and increasing flow rate. For the sandy loam columns, there was a clear difference in the water content depth profile for the two soil columns, which reflects the different bottom boundary condition. When no suction was applied (Column 2), was clearly higher and hardly influenced by the flow rate at the top of the soil column. For the loam soil, at the bottom of the soil column was also little influenced by the flow rate and the difference was minimal. This could indicate that the glass-fiber wicks did not apply sufficient suction to create negative pressures at the bottom of the loam lysimeters during the leaching experiment.

View this table: [in this window] [in a new window]   Table 3 Depth–averaged water contents, . For the transient experiments, the depth-averaged water content at the beginning of an infiltration–drainage cycle is shown. The depth averaged maximum water content during an infiltration drainage cycle, max, is given in parentheses.

View larger version (24K): [in this window] [in a new window]   Fig. 2 Soil bulk electrical conductivity (a) ECa and (b) relative concentrations cr vs. time t and vs. transformed time t* (Eq. [17]) in the sandy loam soil at the 0.125- and 0.725-m depths during a transient flow leaching experiment (Exp. 4)

View larger version (18K): [in this window] [in a new window]   Fig. 3 Water content and cumulative drainage depth I, initial soil bulk electrical conductivity ECain, and the soil bulk electrical conductivity when the initial soil solution is completely replaced by the leaching solution ECa0, during an infiltration–drainage cycle in the sandy loam soil (Exp. 4) at the 0.125- and 0.725-m depths

View larger version (24K): [in this window] [in a new window]   Fig. 4 Relative concentrations, cr, at two depths in the sandy loam and loam soils (0.125 and 0.725 m) during a steady-state (Exp. 3) and a transient flow (Exp. 4) leaching experiment with a similar time averaged flow. For the transient experiment, cr is plotted vs. the transformed time coordinate t* (Eq. [17])

View larger version (21K): [in this window] [in a new window]   Fig. 5 Relative flux concentrations, cf, measured in the drain water, relative concentrations measured in the drain water that was collected during one infiltration–drainage cycle, cfcum, and relative resident concentrations cr measured in situ at the bottom of the soil column during steady and transient flow experiments with similar time-averaged flow rates in the loam soil. The concentrations are plotted vs. time, t

View larger version (15K): [in this window] [in a new window]   Fig. 6 Methylene blue stained area at various depths in the loam soil profile

View larger version (33K): [in this window] [in a new window]   Fig. 7 Average solute particle velocity v (steady-state flow), v* (transient flow) derived from convection–dispersion equation fits to breakthrough curves of cr and cf, and the piston flow velocity vp (steady-state flow, Eq. [7]) and v*p (transient flow, Eq. [18]) in the sandy loam soil

View larger version (29K): [in this window] [in a new window]   Fig. 8 Average solute particle velocity v (steady-state flow), v* (transient flow) derived from convection–dispersion equation fits to breakthrough curves of cr and cf, and the piston flow velocity vp (steady-state flow, Eq. [7]) and v*p (transient flow, Eq. [18]) in the loam soil

View larger version (27K): [in this window] [in a new window]   Fig. 9 Dispersivity derived from convection–dispersion equation fits to breakthrough curves of cr and cf in the sandy loam soil. (For transient flow, .)

View this table: [in this window] [in a new window]   Table 4 Dispersivities ( = D/v) derived from flux concentrations cf (or resident concentrations cr measured at the bottom of the soil column) and the flow rate Jw in the different transport experiments. The flow rate in parentheses is the effective flow rate during an infiltration drainage cycle, w eff (Eq. [12] and [13]), at the bottom of the soil column.

View larger version (26K): [in this window] [in a new window]   Fig. 10 Dispersivity derived from convection–dispersion equation fits to breakthrough curves of cr and cf in the loam soil. (For transient flow, .)

Effect of Flow Rate on
In Fig. 11 , (_eff) are plotted vs. J_w (_weff). For the loam soil, only the dispersivities derived from BTCs of c^f are shown since derived from in situ-measured BTCs increased with depth and for transient flow conditions the interpretation of BTCs of resident concentrations using a CDE model led to false predictions of the solute travel time distribution. In both sandy loam and loam soil columns, increased with increasing flow rate. On a log-log plot, the relationship can be approximated by a linear relation, which is of the form:

(19)

View larger version (18K): [in this window] [in a new window]   Fig. 11 (eff for the transient flow leaching experiments) vs. the flow rate Jw (effective flow rate, w eff (Eq. [14]), for the transient flow leaching experiments)

According to Skopp and Gardner (1992) can be related to the product of a flux-weighted pore length and a k factor that is related to the variability of the solute velocity distribution (Eq. [30] in Skopp and Gardner, 1992). When wider pores are activated at higher flow rates, the variability of the solute velocity and the k factor increase due to higher solute velocities at the center of these pores. When longer pores are activated at larger flow rates, an increase in flow rate results in an increase of effective flux-weighted pore length . Both mechanisms result in an increase of with increasing flow rate. However, based on the increase of with increasing z at higher flow rates, we may conclude that for the loam soil preferentially longer continuous pores were activated with increasing flow rate. A larger flux-weighted pore length results in an increase of across a larger range of depths (Skopp and Gardner, 1992). Since such an increase of with increasing z was not observed in the sandy loam soil, we may conclude that wider pores, but not necessarily longer pores, were activated with increasing flow rate in this soil.

	Summary and conclusions

TOP ABSTRACT INTRODUCTION Materials and methods Results and discussion Summary and conclusions Appendix REFERENCES

 
Under steady-state flow conditions, solute transport in the sandy loam soil was well described by the CDE model. For the loam soil, the transport process shifted from a convective–dispersive ( was independent of z) at lower flow rates to a stochastic–convective process ( increased with increasing z) at higher flow rates, which indicates that lateral solute mixing decreased with increasing flow rate in this soil.

Under transient flow conditions, using a transformed time coordinate, t*, which was derived from the solute penetration depth, , produced BTCs that had a shape similar to BTCs measured under steady-flow conditions except for the BTCs of c^f that were measured in drain water of the loam soil. In the sandy loam soil, the CDE described transport under transient flow conditions fairly well and v* derived from c^r was close to the piston flow velocity v^*_p. For the loam soil, considerable bypass flow and transport occurred during the transient flow leaching experiments through macropores that are continuous for the entire length of the soil column. This resulted in a nonmonotonic increase of the flux concentration BTCs, with peak concentrations in the drain water at times when the flow rate was high. Since bypass flow occurred in only a small fraction of the total pore volume, the bypassing solutes were merely detected in BTCs of in situ-measured, volume-averaged or resident concentrations, c^r. Therefore, bypass flow resulted in an underestimation of v^*_p by v* when v* was derived from CDE fits to BTCs of c^r. The bypass flow most likely also resulted in underestimation of derived from BTCs of c^r.

In both sandy loam and loam soils, the dispersivity increased with the flow rate. In the sandy loam soil, an increase in flow rate probably resulted in the activation of wider pores in which local solute velocities were considerably higher. Since transport was well described by the CDE, the solution in the newly activated pores was well mixed with the solution in the narrower pores. This indicates that the flux-weighted pore length in the sandy loam soil was relatively small, which is consistent with the weak structure of this soil in which no strongly developed aggregates and long, interaggregate pores were observed. For the loam soil, the solution in the newly activated pores was less mixed with the solution in the smaller pores so that the transport at higher flow was better described by a stochastic–convective model. This is in agreement with the assumption that long, continuous macropores were activated at higher flow rates, which was further evidenced by the results of the dye experiment in this soil.

Since depended on the flow rate, an effective flow rate, which defines the flow rate at which most of the water flows through the soil, should be considered to interpret the solute dispersions observed under transient flow conditions.De Smedt Wierenga 1978

	ACKNOWLEDGMENTS

 
The authors would like to thank the Belgian Fund for Scientific Research (F.W.O.) and the Research Fund of the Catholic University of Leuven. The corresponding author was a research assistant of the Belgian National Fund for Scientific Research (F.W.O.) and a postdoctoral research assistant at the Catholic University of Leuven.

The authors are also grateful to David Elrick for his helpful discussion on our work. We would like to thank the anonymous reviewers for their inspiring comments on an earlier version of the paper.

Received for publication September 4, 1997.

	Appendix

TOP ABSTRACT INTRODUCTION Materials and methods Results and discussion Summary and conclusions Appendix REFERENCES

 
The effect of vertical variation of on solute transport is evaluated using time moment analysis of c^f BTCs predicted by a CDE. For a dirac pulse application of tracer solution at the soil surface, the time moments of c^f BTCs can be interpreted as the moments of the solute travel time probability density function (Jury and Roth, 1990). The first temporal moment of c^f(z), E(z,t), is the average solute travel time, whereas the second centralized moment, var(z,t), is the variance of solute travel times from the soil surface to depth z. For a homogeneous soil profile, E(z,t) and var(z,t) are related to v and as (Jury and Sposito, 1985):

(A1)

The average and variance of solute travel times in a soil layer from z to z + dz is:

(A2)

The average solute travel time from the soil surface to depth z is the sum of the average travel times for each depth increment dz. Since for a convective–dispersive transport process, the travel times of a solute particle from z - dz to z and from z to z + dz are not correlated, the variance of solute travel times from the soil surface to depth z is the sum of travel time variances for each depth increment dz. As a consequence, when (z) changes with z:

(A3)

If v(z) and (z) are derived from a c^f BTC at z assuming a vertically homogeneous soil profile, inverting Eq. [A1] and using Eq. [A3] yields:

(A4)

	REFERENCES

TOP ABSTRACT INTRODUCTION Materials and methods Results and discussion Summary and conclusions Appendix REFERENCES

 

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