Effects of physical nonequilibrium conditions on calibration and interpretation of TDR for use in solute transport studies

by D. Mallants, M. Vanclooster, J. Diels, and J. Feyen
Institute for Land and Water Management, K.U. Leuven, Belgium

Table of contents

Abstract
Introduction
Material and methods
Results and discussion
Conclusions
References

A solute transport experiment was carried out on 1-m long and 30-cm diameter undisturbed saturated soil columns. Prior to the analysis of the BTCs, three different calibration methods which relate impedance, measured with TDR (Time Domain Reflectometry), to resident solute concentration, were compared. The three procedures were compared for estimating the impedance, Z_o, associated with the tracer concentration of the inlet solution, C_o, and evidence for their validity for some particular conditions is given. The first calibration method comprises the application of a solute pulse for a long enough time upon the assumption that the solute will be distributed uniformly in the entire profile within that time: C/t = 0 and C = C_o everywhere. For the second method, the response to a pulse function input is convolved numerically to yield the response to a step function input from which Z_o can be readily obtained. The third method determines Z_o based on an experimentally determined EC_a-EC_w- relationship on repacked soil. All methods compared favorably well at the first observation depth (x = 5 cm). Deeper in the soil profile, physical nonequilibrium effects were dominating the transport process with long equilibration times necessary to diffuse the solutes from the mobile to the immobile water regions. As a result, the first calibration method was only valid at shallow depths. The second calibration procedure could be applied throughout the whole soil profile upon the assumption that flow was homogeneous. The procedure based on the empirical EC_a-EC_w- relationship gave surprisingly good predictions of Z_o for the upper horizon, although the simple model did not account for the current flow through large continuous pores that were present in the soil profile.

Introduction

Investigations on solute transport in subsurface porous media require numerical models and experimental data. Although a vast amount of complex mathematical flow and transport models exist, reliable predictions of flow and transport processes in natural, heterogeneous soils can only be made if appropriate values for the flow and transport parameters are available. To date, the limiting step in our understanding of field-scale solute transport is a lack of reliable and sufficient data (Knight, 1988).

In the past, collection of tracer data has been accomplished by the analysis of the column effluent using a variety of tracers (e.g., van Genuchten and Wierenga, 1977; Seyfried and Rao, 1987), by the analysis of the soil water extracted by means of solution samplers (Wierenga and van Genuchten, 1989), or by soil coring and subsequent sampling of the soil water (Bresler and Laufer, 1974; Bond et al., 1982). A major drawback of solution samplers is the disruption of the flow path of the dissolved chemical at high suction (van der Ploeg and Beese, 1977), their limited use at low water contents due to the air entry pressure of the ceramic cups, and the fairly small sampling volume which increases the variability of the measurements (Hansen and Harris, 1975). Furthermore, the concentration profiles derived from solution samplers are believed to represent flux concentrations, although it may also represent resident concentrations or anything in between (Parker and van Genuchten, 1984). Erroneous interpretation of the concentration mode may lead to gross under prediction or over prediction of the solute behavior. Also, the soil water that is collected by solution samplers most probably represents mobile water whereas water in immobile water regions may not be detected (van Genuchten and Wierenga, 1977). As opposed to solution samplers, solute concentrations obtained with soil coring undoubtedly represent resident concentration. Unfortunately, soil coring is destructive, time consuming, and provides only a limited temporal resolution of the tracer distribution.

Recently, several authors have discussed the large potentials of TDR for measuring tracer movements in laboratory soil columns as well as in field conditions (Kachanoski et al., 1992; Wraith et al., 1993; Vanclooster et al., 1993; Mallants et al., 1994a; Ward et al., 1994). There are many potential advantages of using TDR. Since the thickness of the TDR probes usually is only a few millimeters, it is essentially a non-destructive monitoring technique and the flow path of the tracer is not or only minimally disturbed. TDR measures total resident concentration from both mobile and immobile water regions for a sampling volume with a well defined geometry. TDR allows data collection of both water content and salt concentration at a high spatial and temporal resolution. Automation of the TDR has made it even more powerful for use in the laboratory and even more so in field applications at remote sites (Heimovaara and Bouten, 1990). Possible disadvantages of TDR include: only applicable to non-reactive tracers and low electrical conductivity soils; for horizontally installed probes the calibration may be problematic even in steady-state flow conditions (this paper).

Applications with TDR in the area of contaminant hydrology have been reported for vertically (Kachanoski et al., 1992; Elrick et al., 1992) as well as for horizontally (Vanclooster et al., 1993; Mallants et al., 1994a; Ward et al., 1994, Vanclooster et al., 1995) installed probes. Most of these studies were carried out on sandy or loamy sand soils with a low percentage of clay and silt and without distinct macropores. These relatively favorable conditions allowed the authors to adopt simple hypotheses for the water flow and solute transport and also for the calibration. For instance, in the study of Ward et al. (1994), calibration constants for all horizontally installed TDR probes were based on the numericalconvolution of a measured pulse response with a theoretical step function input to obtain the theoretical step response. This approach assumes that all the mass injected could be traced back with the TDR probes which implies an almost perfect mass recovery. Within the soil volume of interest, i.e. the soil column, flow was relatively homogeneous such that the sampling volume of the TDR probe represents the average resident solute concentration at a fixed depth. Consequently, the requirement of complete mass recovery could be fulfilled. An exception is the study by Mallants et al. (1994) where a large number of macropores was present in a sandy loam soil containing 13% clay in the upper Ap horizon. This study showed that for macroporous soils the TDR sampling volume may be too small to accurately measure the average concentration across the soil column. As a result, the convalution procedure applied by Ward et al. (1994) could not be adopted. The heterogeneity of the flow field within the soil column required the use of an alternative calibration methodology. Appropriate calibration constants were obtained by the addition of a second, step function input until C = C_o at the detection volume. This is a prerequisite for relating the TDR impedance readings, Z, to resident solute concentrations. For instance, when the solute is applied continuously as a step function input, than the TDR reading Z = Z_o can be equated to the known solute concentration C_o at time t when the solute front has moved below the TDR probes. However, if zones of low permeability and stagnant water are present within the sampling volume of the TDR probe, the solute may require a long time before it has spread uniformly, hence requiring a very long (thus impractical) application time of the solute. The success or failure of the TDR technique to accurately predict solute concentrations therefore heavily depends on the appropriateness of the calibration procedure used. In fact, this is also true for the EC_a measurements made using conventional four-electrode salinity probes (Rhoades et al., 1989).

In the present study we will compare three different methods for relating TDR impedance readings to solute concentrations based on data measured at six different depths in l-m long and 30-cm diameter saturated undisturbed soil columns. First, the accuracy of the numerical integration procedure to estimate calibration constants from a pulse function input of tracer (method proposed by Ward et al., 1994) will be evaluated. Next, the validity of an independently measured relationship between the bulk soil electrical conductivity (EC_a) and the electrical conductivity of the water phase (EC_w) for the prediction of solute concentrations in undisturbed soil will be examined. Values for the calibration constants, Z_o, obtained with these two methods will be compared with impedance data collected for a solute application time that was long enough to satisfy the condition C/t = 0 for at least one observation depth (third method). The effects of calculating inappropriate values for the calibration parameters on solute BTCs will be illustrated for one extreme case.

Material and methods

Experimental design

Flow and solute transport processes were examined on 30 undisturbed soil columns taken one meter apart at the Bekkevoort experimental field, east of Leuven (Belgium). The field plot was located in an orchard and the transect was chosen in between two rows of trees. The surface in between the trees was covered with grass. Within the first meter of the soil profile, three different horizons were identified. The thickness of the layers remained fairly constant along the transect. The average thickness of the Ap horizon is 25 cm whereas the mean thickness of the Cl and C2 horizons is 30 and 45 cm, respectively, with a sharp boundary between all soil layers. Physical and chemical properties of each soil horizon are listed in TABLE 1. Clay content increased from 12.7% in the Ap horizon (0-25 cm) to 16.7 % in the C1 (25-SScm) and 21.8% in the C2 (SS-IOO cm) horizon. The Ap and Cl are pedogenetically identical, i.e. colluvial material, whereas the C2 is an old textural B horizon. The soil was classified as an Udifluvent (Eutric Regosol), with a large number of macropores throughout the profile. The macropores consisted mainly of decayed root channels and earthworm holes. The columns were one meter long and 30 cm in diameter. Collection of the soil columns was done by excavating the soil gradually in such a way that a pedestal of soil could be isolated, its diameter slightly larger than the polyvinyl chloride (PVC) cylinder. PVC cylinders with 30-cm I.D., the inner side greased and the bottom end sharpened, were hydraulically driven around the soil pedestals. The bottom of the soil column was cut off by means of a steel plate, sharpened at one side. The plate was driven pneumatically under the PVC cylinder, isolating the soil column from the underlying soil. Next, a PVC end cap was placed on both ends of the cylinder. This construction was lifted hydraulically onto a truck and was transported to the laboratory.

In the same field, undisturbed 20-cm long and 20-cm diameter columns were also collected in between the l-m long soil columns in the upper Ap soil horizon. We alsocollected 5.3-cm long and 5-cm diameter soil cores next to the 20x20-cm columns for the Ap horizon (60 in total). For the C1 and C2 horizon, 5.3x5-cm soil cores (60 samples for each horizon) were taken exactly below the 5.3x5-cm cores' sampling locations for the Ap horizon, at depths of 50 and 90 cm, respectively. Solute transport experiments using 20-cm long columns were carried out to investigate the applicability of TDR for measuring transport behavior at the shallow depth (Mallants et al., 1994a). Water content at zero pressure and bulk density were determined using the 5.3x5-cm soil cores.

Once in the laboratory, a perforated plate was attached to the bottom end of the 1-m long columns. On top of the perforated plate we glued a nylon-type mesh which allowed the application of a suction up to 70 mbar (FIGURE 1). This assembly was attached to the bottom of the column together with an enclosed drainage system. Drainage water from this system could be collected in small sampling bottles via a poly-ethylene (PET) tube. The system also allowed to maintain a watertable at the bottom of the column or to regulate suction at the bottom of the column, while increasing of the water level allowed to mimic a water table inside the soil column. Water could be applied at the top of the columns by means of a constant rate drip irrigation system. To reduce crust formation on the soil surface, a 1-cm thick fiberwool cover was put on top of the soil surface. The maximum depth the water was allowed to pond was 1 cm. A second independent drip irrigation line was constructed for the application of the tracer. In this way, we could easily switch from solute free water to the tracer solution.

Water content, , and bulk soil electrical conductivity, EC_a, of the soil were monitored by TDR probes whereas pressure head was measured with tensiometers. Both devices were installed at six different depths (5, 15, 30, 45, 60, and 80 cm, see also FIGURE 1).

Transport experiments

Solute transport processes were monitored in saturated conditions. The soil columns were saturated from the bottom by gradually increasing the water level in the drainage tube in order to minimize the inclusion of air pockets. When the columns were completely saturated, solute free water was applied through the drip irrigation system at a rate large enough to generate ponding. The groundwater level was again established at the bottom of the soil column. As soon as steady state flow conditions were obtained, the application of solute free water was interrupted and the remaining water allowed to infiltrate. Next, a 7x10^-3 M CaCl₂ solution was applied for a period of at least 79 hr until the whole soil column was saturated with the applied solution. Then, solute free water was applied again to the surface until the initially measured impedance, Z_i, was again reached. The motivation for using such a long application time for the pulse function input was the evaluation of different calibration procedures. Only if the column could be saturated with the tracer solution at all observation depths, i.e. C = CO (which is equivalent to C/t = 0) at z = 5, 15, ..., 80 cm, then the necessary conditions for evaluation would be fulfilled. For several soil columns. application of the tracer solution for 79 hr was not sufficient to obtain a constant concentration (C = C_o everywhere), even at 5 cm depth. For these columns, the solute was applied until C/t = 0 at x = 5 cm, unless the application time became practically infeasible. For some extreme cases, solute had to be applied for 664 hr. Therefore, the application time of the solute was different for different columns, except for those where the application time to = 79 hr. Throughout the experiment, water content and bulk soil electrical conductivity were measured with TDR. We used a TEKTRONIX cable tester (TEKTRONIX, 1502B, BEAVERTON, OREGON, USA) and multiplexed the different channels manually. The travel time of the electromagnetic wave and the impedance Z were taken from the screen of the cable tester. Values of Z were taken at a far distance on the reflected wave form (t ).

Calibration of the solute concentration-impedance relationship

Solute concentrations can be deduced from TDR-based estimates of the bulk electrical conductivity as was shown by a number of authors (Kachanoski et al., 1992; Wraith et al., 1993). A linear relationship is generally observed between the resident solute concentration, C (g/cm³), and the bulk soil electrical conductivity, EC_a, for water contents ranging from dry to saturation and salinity levels from 0 to 50 dS/m (Diels et al., 1994; Ward et al., 1994):

where a and b are calibration constants. The bulk soil electrical conductivity at ° C, EC_a,25 (dS/m), can be related to the impedance of an electromagnetic wave, Z (), that travels through the soil, following Nadler et al. (1991):

where K_c is the cell constant of the TDR probe (m^-1), and f_t a temperature correction factor. Once we accept EQUATIONS 1 and 2, i.e., C ~ Z^-1, the calibration is in fact not a unique problem for TDR, but a general problem for any EC measurement device, whether TDR, electrical conductivity probe or electromagnetic induction method. The relative solute concentration, c(x,t), can be expressed as:

where C_o is a reference concentration such as an input concentration and C_i is the background concentration. Inserting EQUATION 1 into EQUATION 3 and using EQUATION 2 results in:

where Z_i> is the impedance before application of the tracer solution and Z_o, is the impedance associated with the concentration of the inlet solution, C_o. As can be seen from EQUATION 4, all constants drop out and a solute BTC could be derived if appropriate values of Z_x,t, Z_i, and Z_o can be obtained. Values for the background impedance, Z_i, and the impedance throughout the course of the transport experiment, Z_x,t, can be readily obtained. Values of Z_o can be obtained in a number of ways. For homogeneous soils, values of Z_o can be related to C_o as described below:

1. Continuous solute application

This is a most commonly used calibration method. For a continuous solute application, Z_o can be easily related to the input solution concentration C_o after a long enough time when solutes are distributed uniformly in the soil profile. A disadvantage of this technique is that for solute applications in long soil columns or in the field, an impractically large amount of tracer solution may be required. Previous applications with this methodology have been reported by Rhoades (1981) and Rhoades et al. (1989) to establish EC_a-EC_w- relationships for field soils using four-electrode salinity probes.

2. Pulse function input

When a single pulse of input of duration time t_o is applied to the surface, C is less than C_o for relatively small t and large x. Integrating EQUATION 4 from t = 0 to t = for a pulse function input leads to

As long as Z_i is known, Z_o can be determined by evaluating the area of measured impedance (Vanclooster et al., 1993; Ward et al., 1994). Note that this method assumes that the TDR detects the same amounts of solutes as those applied on the soil surface.

3. Experimentally determined EC_a-EC_w relationship

Based on EQUATION 2, the TDR measured soil impedance, Z, can be used to calculate the bulk soil electrical conductivity, EC_a, provided the cell constant for the TDR probe, K_c, is known. The next step is to relate EC_a, to the electrical conductivity of the water phase, EC_w, for a given soil water content, . The most simple form of this relation is

with and empirical parameters. It has been shown (Rhoades et al., 1976) that the parameter represents the electrical conductivity of the solid phase of the soil (EC_s), and the parameter is equal to T_w (T a transmission coefficient equal to the fraction of "mobile" water, i.e. the large pore system, and _w, the total soil water content). A more physically based model (the "three-pathway model") was proposed by Rhoades et al. (1989) taking into account the current carrying capacity of the solid phase (EC_s), the small pores and intraped pores (EC_ws) and the larger or continuous pores (EC_wc or simply EC_w). For a comparison between empirical EC_a-EC_w relationships and predicted EC,-ECW relationships based on the "three-pathway" model of Rhoades (1989), the reader is referred to Diels et al. (1994). The EC_a-EC_w relationship used in this study was determined for repacked Bekkevoort sandy loam soil, taken from the same transect as our soil columns. Diels et al. (1994) used linear regression analysis to obtain intercept and slope of EQUATION 6 for sets of EC_a-EC_w data for three different water contents (0.12, 0.24 and 0.36 cm³cm^-3) and eight different salt concentrations. Linear relationships were found for all three water contents for salinity levels from 0 to 50 dS/m, with r² ranging from 0.81 ( = 0.12) to 0.99 ( = 0.36). The data analyzed by Diels et al. (1994) did not show any significant curvilinearity for low concentrations (EC_w ~ 0.5 dS/m) of the electrolytes in the soil solution. In the same study, values for the cell constant K_c were derived in a way similar to Heimovaara (1993). Based on the previously determined EC_a-EC_w relationships, we derived a continuous EC_a-EC_w- surface (FIGURE 2). Based on these EC_a-EC_w- relationships we can determine EC, and through EQUATION 2 also Z (or Z_o), for any combination of EC_o and .

Although all of the above three methods have both advantages and disadvantages when applied to undisturbed soil, we applied these procedures to the TDR measurements made in 1-m long undisturbed soil columns in order to find appropriate calibrations for undisturbedsoils.

Results and discussion

All three calibration procedures were applied to the measured Z vs. time data in order to find the most appropriate calibration for our particular soil which would lead to meaningful resident concentration distributions. As will be shown in the following sections, each calibration method has its particular difficulties when applied to data obtained from undisturbed soil.

Application of a tracer solution for a long enough time until C = C_o everywhere seems a very simple and attractive method for the determination of the calibration constant Z_o. Analysis of the impedance vs. time data, Z_x,t, revealed that saturation of the soil with the tracer solution was difficult to obtain, especially for the deeper depths. Although we found a quick drop of the impedance after the start of the solute application, even so at deeper observation depths, the remaining part of the Z versus time curve often showed long tailing (FIGURE 3). The fast decrease of Z is probably due to the existence of macropores (see also Mallants et al., 1993; Mallants et al., 1994a) which allow the tracer to move quickly downward, bypassing soil zones that are still solute free. The subsequent tailing of the Z_x,t, curve is presumably caused by physical nonequilibrium effects in the transport process: the solute slowly diffuses from the higher concentration zones, usually the larger pores, to the low concentration zones, mostly the smaller pores, dead-end pores and the less permeable soil matrix (recall that clay percentage in the lower C2 horizon is approximately 22%). These nonequilibrium effects can be very extreme, as can be seen in FIGURE 4. For an observation depth of 80 cm, the impedance decreases from approximately 140 to 65 in about 7 to 8 days. For the next 20 days, however, Z drops only up to 55 . It is clear that even after almost 30 days of solute application, the solute concentration has not yet reached the concentration of the inlet solution, or C < C_o. This shows that the diffusion of solute from the mobile water region to the immobile or stagnant water region can be very slow. It waspractically impossible to apply the solute for all columns for more than 30 days. For this reason, we could not use the final impedance values for Z to estimate Z_o at the deeper observation depths, since C < C_o. For the extreme case of nonequilibrium transport such as the example shown in FIGURE 5, the BTCs can be very susceptible to values of Z_o that are incorrectly measured, i.e. Z < Z_o. To illustrate this effect, the extreme case of FIGURE 5 will be discussed. At a depth of 5 cm, it took 664 hr to completely saturate the soil with the tracer solution, i.e. C/t = 0, for which the final impedance was Z_o = 56 . At t = 400 hr, Z = 57.2 , a value close to Z_o, while at t = 300 hr Z = 58 and for t = 200hr Z = 61.2 . These values were selected to show the effects of cutting off the Z vs time curve too soon, which is equivalent to applying tracer solution for a too short time. FIGURE 6 shows the BTCs based on EQUATION 4 for the reference value Z_o = 56 and the three "error" values of Z_o. Cutting off the Z_x,t data too soon results in earlier breakthrough and less tailing. The effect of less tailing of the BTC on the solute transport parameters can be evaluated by fitting solutions of the transport equation to the observed data (not shown here).

An alternative calibration method consisted in the numerical integration of the response to a long pulse function input in order to derive Z_o according to EQUATION 5. To test this calibration procedure, estimates of Z_o following EQUATION 5 were compared with measured values of Z_o for those locations where C/t = 0. The results given in TABLE 2 illustrate that estimates of Z_O using the numerical convolution procedure only minimally deviate from the presumed correct value of Z_o.

Since it is reasonable to assume that the flow processes become more homogeneous at larger depths, the estimates of Z_o presumably will not become less accurate for greater depths. We therefore decided that for all those depths were C/t 0, the numerical integration of the pulse input function is a valid procedure to estimate values of Z_o. We note again that this procedure assumes that all the mass is recovered at the detection volume of the TDR. In a similar study using a set of 20x20 cm columns, Mallants et al. (1994; 1995) indicated that the presence of preferential flow paths in soil columns may force the solute to bypass the detection volume of the TDR probes and the condition of mass recovery might not be met. If such flow phenomena are suspected to occur in the soil being investigated, the first calibration method has to be used. The problem of a too small detection volume is related to the theory of a Representative Elementary Volume (REV). In macroporous soil, the sample volume of the TDR probes may not contain a representative amount of the local variations in the flow properties. Sampling volumes for TDR probes can be calculated in the following way. Consider TDR probes consisting of two parallel waveguides, with the distance between the center of the rods, 2d, equal to 2.5 cm (see inset FIGURE 1). When the diameter of the stainless steel rods, B, equals 0.5 cm, the effective sampling volume of the TDR probe can be estimated from (see Knight, 1992):

where = r/d the dimensionless radius of the cylindrical sampling volume, = B/d, and q is defined as:

where p the proportion of the electromagnetic energy. For = 0.4, we can calculate that for p = 0.95, 95% of the energy is within a cylinder of radius 3.3d. For the configuration used in this study, we find a cylinder of influence with diameter 6.6 cm. We note that this theory was applied to measurements of water content, (Knight, 1992). We assume, at this point, that it also holds for measurements of electrical conductivity, EC. For TDR probes that are 25 cm long (this study), the cross-sectional sampling area is 165 cm² or 23% of the total cross-sectional area. Thus, in the study presented here, almost one fourth of the total potential cross-sectional flow area could be sampled. For the 1-m long columns investigated here, this seems sufficient to trace the complete solute pulse. Unlike the severe preferential flow effects for short columns in the study of Mallants et al. (1994), longer columns tend to reduce the effects of preferential flow because macropores most likely will not be continuous from top to bottom of the column. As a result, lateral spreading of solute is enhanced and flow becomes more homogeneous throughout the profile, as was already demonstrated by Mallants et al. (1994b). This allows the application of calibration methods such as the numerical convolution discussed here.

The third calibration method tested was based on experimentally determined EC_a-EC_w relationships for different water contents, . The expected calibration constant, Z_o for a known concentration of the inlet solution, C_o, was obtained by first computing EC_a, for a given EC_w (for a given temperature, unique relationships exist between EC_w and the concentration of a solute, say C_o). Next, values of EC_a are transformed to impedance, Z (or Z_o if C = C_o) following EQUATION 2. Results are illustrated in TABLE 3 for one column where, in addition, values of Z_o obtained with the two other calibration methods are also presented.

It is remarkable that, at least for the first two observation (5 and 15 cm), differences between values for Z_o are small. For the other depths, differences between method (2) and (3) increase. Since the EC_a-EC_w- relationship was determined only for the soil representative for the upper Ap horizon (0-25 cm), it is reasonable to find discrepancies for soil layers that have other physico-chemical properties. As the clay content increases from 13% in the Ap horizon to 22 % in the C2 horizon (see TABLE 1), the intercept of the EC_a-EC_w curve will also increase. This is because the intercept can be interpreted as being equal to EC_s, the electrical conductivity of the solid phase (Rhoades et al., 1989). We evaluated the effect of increasing clay content on EC_s following FIGURE 5 from Rhoades et al. (1989):

i.e., EC_s = 0.278 dS/m for the Ap and 0.485 dS/m for the C2 horizon, respectively. One can doubt about the validity of EQUATION 9 for soils with completely different mineralogy and texture than the ones used to derive the relationship, but at least the relation between EC_s and clay percentage indicates that soil horizons with different clay content will have a different EC_s. The value of EC_s obtained from regression analysis (which is in fact equivalent to the parameter from EQUATION 6 was 0.363 dS/m (for = 0.36 cm³ cm^-3. Owing to the typical shape of the EC_a-EC_w curves (see for instance FIGURE 8 from Rhoades et al., 1989), the relative contribution from EC_s to EC_a is larger for lower values of EC_w. Because we used rather low concentrations (the electrical conductivity of the tracer solution was approximately 2.3 dS/m), effects of changing EC_s might have been important enough to partly explain the observed differences between Z_o from method (2) and (3). Another explanation for the discrepancies might be the differences in bulk density (1.42 g/cm³ for Ap vs. 1.52 g/cm³ for C2), since the electromagnetic wave travels mainly via the large, continuous pores, at least at normal levels of water content (Rhoades et al., 1989). However, the surprisingly good agreement between Z_o at x = 5 and x = 15 cm (TABLE 2) for both methods suggests that soil structure (the complicated arrangement of interconnected macropores and micropores and the direct particle to particle contact) does not seem to be so important if we want to relate EC_a to EC_w. To further test the performance of the EC_a-EC_w- relationship for predicting Z_o for a given C_o, we computed Z_o for those columns that reached an equilibrium condition at the first observation depth (x = 5 cm), i.e. C = C_o. TABLE 2 lists values of Z_o according to the three calibration procedures. At least nine out of eighteen values are close to or relatively close to the measured value of Z_o. This proves that at least for a subset of the date the EC_a-EC_w- relationship is capable of giving reasonable accurate predictions of Z_o for a given C_o, although the relationship has been determined on repacked soil.