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DIVISION S-1-SOIL PHYSICS

Estimation of Soil Solution Electrical Conductivity from Bulk Soil Electrical Conductivity in Sandy Soils

Univ. of Minnesota, Dep. of Soil, Water, and Climate, St. Paul, MN 55108 USA

jbaker{at}soils.umn.edu

	ABSTRACT

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

 
Studies of solute transport through soil and attendant environmental impacts are hampered by the lack of methods for continuous monitoring of solute concentration. Measurement of bulk soil electrical conductivity (EC_b) using time domain reflectometry (TDR) is a promising technique, but it is indirect, and estimation of solute concentration from such measurements requires a model relating soil solution electrical conductivity (EC_w) to EC_b. Several models of varying complexity exist, but further testing is required to determine their relative merits and applicability. This study was conducted to determine the efficiency of various models that use different methods of estimating the tortuosity factor, F_g, in order to estimate EC_w from EC_b. All models assume that the ratio of EC_b/EC_w is proportional to soil water content, , with F_g as the coefficient of proportionality. In this study, two types of models were compared, those in which F_g is obtained from soil hydraulic properties and those in which F_g is estimated as it is in gas diffusion models, except with rather than porosity as the independent variable. Measurements were conducted in a sandy soil, across a range of EC_w from 0.10 to 0.56 S m^-1. The models in which F_g is obtained from soil hydraulic properties did not perform as expected. The results with the gas diffusion analog models were variable; the most successful of these was based on the 1959 model of Marshall, in which F_g is a power function of , ^b. Optimal results were obtained with , not far from Marshall's suggested value of 0.5 for gas diffusion. We conclude that there is no benefit to the use of soil hydraulic properties in estimating EC_w from EC_b measurements, at least for sandy soils, where simpler relationships appear to provide superior results.

Abbreviations: BVG, Burdine–van Genuchten model • EC_b, bulk soil electrical conductivity • EC_w, solution electrical conductivity • F_g, tortuosity factor • F_g(MF1), first F_g prediction method of the Mualem–Friedman model • F_g(MF2), second F_g prediction method of the Mualem–Friedman model • MVG, Mualem–van Genuchten model • PIM, Pulse Input Method • SIM, Step Input Method • TDR, time domain reflectometry • %Clay, percentage clay

	INTRODUCTION

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

 
THE IMPACT OF AGRICULTURAL PRACTICES on groundwater quality requires studying solute transport through soils. This is a difficult research problem because solute concentrations in soil water are not easy to measure. Solution samplers are often employed, but their use is limited to the matric potential range of 0 to perhaps -0.1 MPa, and they provide temporally discrete rather than continuous data, so that critical periods are easily missed.

The development of TDR as a method for automated, in situ measurement of EC_b offers the promise of improved temporal resolution in tackling solute movement. However, estimation of concentration of conservative solutes from EC_b requires either determination of a direct relationship between EC_b and the concentration, or an intermediate step of secondary calibration such that concentration can be determined from EC_w. Under specific conditions of constant and temperature, concentration of soil solution can be directly determined from TDR-measured EC_b (Kachanoski et al., 1992) by assuming a linear relationship between EC_b and EC_w. Techniques like the Step Input Method (SIM) (Ward et al., 1994; Mallants et al., 1996), and the Pulse Input Method (PIM) (Ward et al., 1994; Kim et al., 1998) make use of this approach and directly estimate solute concentration from EC_b. However, both the SIM and PIM calibration techniques are site specific, and therefore it is necessary to obtain independent calibrations for individual soils.

An alternative method of obtaining solute concentration from EC_b is a two-step process. First, EC_w is obtained from EC_b using some type of functional relationship between the two; then concentration is estimated from EC_w. Relating EC_w to EC_b requires an independent calibration. Conceptual models, such as those developed by Rhoades et al. (1976) and Nadler (1982), relate EC_b to EC_w using empirical constants. These models require preliminary measurements of EC_b, EC_w, and to obtain the empirical constants. Others use physical parameters that can be determined from other measurable soil parameters, such as soil hydraulic properties in the form of tortuosity factors, F_g (Mualem and Friedman, 1991; Heimovaara et al., 1995). It is easier to use these latter models with soils for which the hydraulic parameters have already been measured, eliminating the need for an independent experiment. The third method is the three-pathway model (Rhoades et al., 1989), which partitions soil water into mobile and immobile fractions and makes use of these fractions to relate EC_b to EC_w. There is theoretical merit in this third method, but there remain practical limitations in estimating the mobile and immobile water fractions accurately. Despite the difficulties encountered in developing precise functional relations between EC_b and EC_w, conceptual models impose fewer practical restrictions and thus can be used under more typical field conditions, for example, variable (Persson, 1997).

The soil liquid and solid fractions both contribute to the total soil EC. The contribution of the solid fraction depends on the number of exchangeable ions adsorbed to the surfaces of clay and organic matter (Nadler and Frenkel, 1980). This contribution tends to depend on (Rhoades et al., 1989) because a reduction in results in increased Coulomb interactions, due to attractions between the free ions and the solid particles. Polarization, dispersion, and the arrangement of water molecules close to the clay surfaces (Cremers et al., 1966) have influence on the EC of soil solids. The combined effects of these interactions make the contribution of the solid fraction to EC_b complex. The contribution of EC_w to EC_b can also depend on the concentration of the soil solution, but generally the two are assumed to be linearly related for EC_w above 0.1 S m^-1 (Rhoades et al., 1989), with F_g acting as a proportionality factor. Models differ in the way they estimate tortuosity factor and its effects on EC_b.

At present, use of these models is constrained by uncertainty about their accuracy and their applicability to different soil types. The objectives of this study were (i) to test the various models used to express EC_b as a function of F_g, , and EC_w; and (ii) to suggest the model that best estimates EC_w at least for the particular soil used.

	Theory

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

 
Conceptual Model with Empirical Parameters
In a two-pathway model (Rhoades et al., 1976), electrical conduction is assumed to take place along two parallel conducting paths. The predominant path is through the soil solution, EC_w, also known as pore water electrical conductivity. The contribution of the solid fraction, EC_s, takes place along the continuous films of exchangeable cations residing on the surface of the solid particles. According to this model, EC_b at constant is linearly related to EC_w

(1)

The geometric factor , where the empirical constants a and b show some degree of dependence on the arrangement and size of the soil particles. The two constants can be estimated by fitting EC_b against measured under conditions of constant EC_w (Rhoades et al., 1976). Substitution for F_g in Eq. [1] gives

(2)

For a constant EC_w, EC_b can be explained as a function of alone. This technique of keeping EC_w constant is used in the determination of the two constants, a and b. Under field conditions, however, EC_w is rarely constant because of changes in due to evaporation, drainage, or infiltration. According to Eq. [2], EC_s is assumed to be independent of , and it can be determined by curve fitting. It can also be estimated from the clay percentage (%Clay) using the relation

(3)

The constants, c and d are obtained from a linear plot of EC_b of oven-dry soil measured under the same packing geometry against %Clay. Rhoades et al. (1989) obtained and for EC_s measured in decisiemens per meter. These values are site specific and are expected to vary among soils depending on the percentages and types of clay minerals.

Estimation of Tortuosity Factor from Soil Hydraulic Properties
Estimation of F_g becomes more complicated when F_g is dependent on the geometry of soil in addition to . The real challenge in using conceptual models is therefore finding a relation between F_g and without using empirical constants. One such approach, the Mualem–Friedman model (Mualem and Friedman, 1991) theorizes that F_g can be derived from the ratio of hydraulic conductivity of water in soil to that of capillary bundles with identical water retention, and is expressed as

(4)

where K_s() and K_c() represent hydraulic conductivities of the soil and the corresponding capillary bundle, respectively. The two hydraulic conductivities can be derived from the matric potential function, h, using the equation

(5a)

and

(5b)

where is the relative saturation, and - _r represents the effective water content, _eff, with _s and _r symbolizing saturation and residual water contents, respectively (Mualem, 1976). The integrals in Eq. [5a] and [5b] can be solved if the relationship between h and S_e is known. One such relation is a power-function relation between h and S_e

(6)

where h_cr represents the bubbling pressure and the fitting parameter, is a constant also known as pore-size distribution index (Brooks and Corey, 1964). Substituting Eq. [6] in Eq. [5a] and [5b], and solving Eq. [4] gives

(7a)

where

(7b)

The latter equation can be approximated to unity for coarse-textured soils with large (Mualem and Friedman, 1991), thereby simplifying the relation between EC_b and EC_w to the form

(8)

The expression in parentheses is the new tortuosity (geometric) factor with the _eff exponent, ß + 1, representing the saturation index. If EC_b is expressed solely as a function of _eff and EC_w, the total power of _eff will be ß + 2. The constant ß is the same parameter used in the hydraulic conductivity formulation for which Mualem (1976) obtained values ranging from -1.0 to 2.5, with 0.5 applicable to most soils. This value of 0.5 is observed when F() is constrained to unity (Kelly and Kalinski, 1993). F_g obtained from Eq. [7a] with is hereafter referred to as F_g(MF1) to indicate that it is the first F_g prediction method of the Mualem–Friedman model.

A better estimation of the soil water retention parameters can be obtained using van Genuchten's formulation

(9)

where n and m are parametric constants known as soil water retention parameters, and is the reciprocal of the bubbling pressure, h_cr, used in Eq. [6] (van Genuchten, 1980). A problem in solving Eq. [5a] and [5b] with S_e expressed as in Eq. [9] is the difficulty in finding solution to both integrals using the same parameter m. Thus, Heimovaara et al. (1995) used two different values of m estimated using two different models in order to solve the integrals in the numerator and the denominator separately. The two models are the Mualem–van Genuchten (MVG) model in which the parameters n and m are related as m = 1 - 1/n and the Burdine–van Genuchten (BVG) model with (U.S. Salinity Laboratory Staff, 1994). Solving the numerator and the denominator of Eq. [4] using water retention parameters obtained using MVG and BVG, respectively, gives

(10a)

where

(10b)

with the same parametric constant, ß, as the one used in Eq. [8]. The expression of F_g in this case is similar to that of Eq. [7a], with F(m) playing the role of F(). F_g obtained using Eq. [10a] is hereafter referred to as F_g(MF2) to indicate that it is the second form of expression of F_g obtained by the Mualem–Friedman model. Using this F_g form, EC_b can finally be expressed as

(11)

Equation [11] requires three constants, m, m*, and ß (two if ß is fixed to 0.5), which in turn require three (two water retention and one hydraulic conductivity) models to estimate EC_w from EC_b (Heimovaara et al., 1995). Note that the exponent of _eff in Eq. [11] increased from ß to ß + 1 due to the additional _eff dependency of EC_b besides F_g. The constant ß may either be fixed to 0.5 or else its precise value for a specific soil can be obtained from

(12)

using predetermined values of saturated hydraulic conductivity, K(_s), and water retention parameter m (van Genuchten, 1980).

Estimating F_g Using Diffusion Models
Another method by which the tortuosity factor is obtained is from the models of gas or liquid diffusion in soil. The drift of ions in porous media is influenced by tortuosity, reduction in the effective fluidity of water near solid (especially clay) particles, and reduction in the mobility of ions due to electrical interaction between the solid particles and the ions (Low, 1962). Although electrical interaction, polarization, and dispersion effects on ionic movement may not be fully represented as tortuosity effects alone (Cremers et al., 1966), tortuosity factors based on gaseous diffusion models may incorporate them better than factors estimated from soil hydraulic conductivity parameters. In the past, attempts have been made to estimate diffusion constants using electrical conduction techniques (Shainberg and Kemper, 1966), and the technique of using diffusion models for estimation of tortuosity factor is similarly reasonable.

Different approaches were used to estimate the scaling factor that relates gaseous and liquid diffusions to porosity and water content, respectively. Penman (1940) considered gaseous diffusion to be dependent on porosity, , as , where D_e and D are diffusivities in soil and in air, respectively. The coefficient, a, accounts for tortuosity effects and hence may serve as a surrogate for F_g. Penman experimentally obtained a value for a of 0.66, whereas De Vries (1950) and van Bavel (1952) obtained 0.62 and 0.58, respectively. Others (Marshall, 1959; Millington, 1959; Millington and Quirk, 1961) have considered a to be a power function of porosity. Considering the viscous flow of fluids in the presence of obstructing effects of solids, Marshall theoretically obtained an approximate estimate for a to be , where the pore size factor is neglected. Using the factor as a gives . Millington (1959) found the D_e/D to be ^4/3, which gives a porosity factor of ^1/3 serving as the coefficient (instead of a) in Penman's relation. Millington and Quirk (1961) used for diffusion in pores partly filled with water that gives a porosity factor of ^7/3/². Sallam et al. (1984) found a better fit when the exponent 10/3 was replaced with 3.10.

Estimates of the parameter a based on porosity work relatively well to model gas flow in porous media. By analogy, tortuosity effects in unsaturated soil should be dependent on (Ryan and Cohen, 1990). Common to the different diffusion models mentioned so far is that the porosity remains a factor, while the factor a may be expressed in any one of the above forms, with the bulk soil EC expressed as

(13)

F_g may assume the form F_g(P) = constant, , or . Uses of Eq. [13] with these F_g forms are referred to as diffusion analog models. F_g(P), F_g(M), and F_g(MQ) stand for tortuosity factors estimated by Penman, Marshall, and Millington and Quirk models, respectively.

	Materials and methods

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The soil used in this experiment was sampled from the C₂ horizon (at 120-cm depth) of Verndale sandy loam, a frigid Typic Argiudolls obtained from the Central Minnesota Agriculture Experiment Station, Staples, MN. The soil at this depth consisted of 96.5% sand, 2.5% silt, and 1% clay.

Soil Column Preparation
Six Tempe cells with ceramic plates of 47.2-cm² cross-sectional area and 0.5-cm plate thickness were used for the soil columns, contained in polyvinyl chloride pipe of 7.75-cm i.d. and 15-cm length. The upper acrylic portion of each Tempe cell cover was drilled at 1.5 cm off center to make a hole sufficient to allow the passage of a bayonet connector and cable. A rubber stopper was used to plug the hole and silicone was applied to seal the interstice made to accommodate the cable. Two-wire TDR probes of 10-cm length, 0.2-cm diam., and 1.57-cm spacing were used in this experiment.

Each column was packed to 11.85-cm depth with oven-dried and mechanically mixed soil to a uniform bulk density of 1.5 Mg m^-3. A small space of 3 cm was left above the soil surface to allow centering of the waveguide before the top cover was set in place and tightly secured with butterfly nuts (Fig. 1) .

View larger version (30K): [in this window] [in a new window]   Fig. 1 Setup of soil column experiments showing waveguide orientation and connections of drain test tubes used to collect effluent

Measurements and Computations of Soil EC_b and
Before commencement of EC_b and measurements, the upper cover of each soil column was connected to a common regulated pressure system (Fig. 1). A copper-constantan thermocouple was connected to the surface of one of the columns and temperature was measured with a data logger (CR10, Campbell Scientific, Logan, UT). A 1502C metallic Tektronix cable tester (Tektronix, Beaverton, OR) was interfaced to a PC to control the TDR, retrieve data, and display the waveforms. The program developed by Baker and Allmaras (1990) and later modified by Spaans and Baker (1993) was used to retrieve values of soil conductance and pulse travel times and to view the waveforms on the computer screen. Measurements were conducted under the faster, more convenient transient flow conditions with varied by applying step-wise increases in pressure to the soil columns. The TDR measurements of soil conductance and pulse travel time commenced with the soil at saturation at atmospheric pressure. Pressure at the inlet ends was then gradually increased up to 0.1 MPa (1021-cm H₂O), and measurements were taken by sequentially connecting each waveguide to the TDR. Effluent of 5 mL was collected in each test tube prior to changing the pressure to the next level. The collected effluent was weighed to counter-check TDR-measured and a small part of the sample was also reserved to measure EC_w. Effluent EC_w was measured using the Horiba B-173 twin conductivity meter (Cole-Parmer Inst., Vernon Hills, IL). The measured EC_w was used to check the variability of solute concentration during the draining process and to compare with the concentration of the initial solution prepared for saturation.

Separate experiments were conducted to obtain water characteristic curves from which water retention parameters were estimated using the MVG and BVG models (U.S. Salinity Staff, 1994).

Each measured travel time (t_s) of a signal in soil was first converted to apparent dielectric permittivity of the soil, , using the relation , where L and c_o symbolize TDR probe length and the speed of light in air, respectively. Volumetric soil water content was then obtained from using the Topp et al. (1980) empirical relation

(14)

A separate calibration of vs. for this soil showed very good agreement with Eq. [14]. Measured total electrical conductance (1/R_tot) was converted to EC_b using the relation

(15)

is the probe constant obtained from probe dimensions s and d representing probe separation and probe diameter, respectively. R_c is the cable resistance with its measured value of 0.4 subtracted from R_tot to improve estimation of EC_b (Heimovaara et al., 1995).

Temperature Calibration of EC_b
A separate experiment was conducted to measure the dependence of EC_b on temperature. A soil column was prepared by packing it with oven-dried soil to a bulk density of 1.5 Mg m^-3, then saturating it with 0.01 M KCl solution. A two-wire TDR probe of 10-cm length was vertically inserted into the column; then the top and bottom of the column were completely covered to minimize evaporative losses and to maintain a constant . A copper-constantan thermocouple was inserted in the soil to monitor temperature. Measurements of EC_b, , and temperature were taken as the soil temperature was raised from 12 to 50°C by gradually heating the column in an oven set at 60°C. Then the measurements were repeated as the soil was gradually cooled to 2°C. The thermal coefficient () was then determined using the relation

(16)

and by plotting EC_b against T - 25 from which a bulk soil electrical conductivity normalized to 25°C, EC²⁵_b, was obtained as an intercept, and EC²⁵_b as the slope.

	Results and discussion

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

 
Maintaining Constant EC_w during the Transient Flow Experiment
It is generally not easy to monitor EC_w during a transient flow experiment. For this experiment, a uniform EC_w was created by repeatedly saturating the soil with solution of known concentration and draining it until the concentration of the effluent equaled the concentration of the initial solution. The number of pore volumes required to bring the soil to equilibrium concentration was determined by subsequent measurement of effluent EC_w after every pore volume addition of solution, and it varied with the residence time of the solute. As many as five to six pore volumes were required to attain equilibrium concentrations when saturation was followed by draining, whereas two to three pore volumes were enough when the residence time of the salt solution in the soil was increased. This was achieved by stopping the drainage for 12 h or longer after every saturation. Longer residence time gave the solutes more time to diffuse from the mobile region of the soil to the immobile region.

Experimentally Determined F_g
EC_b was first corrected to a temperature of 25°C using a thermal coefficient, , of 0.019 mS m^-1 °C^-1. This value, obtained from the slope and intercept of a linear fit between the plot of EC_b against T - 25, as indicated in Eq. [16], agreed well with the result obtained by Heimovaara et al. (1995). Plots of temperature-corrected EC_b, EC²⁵_b, against give families of curves corresponding with a constant EC_w (Fig. 2) . With the superscript in EC²⁵_b dropped, EC_b hereafter represents temperature-normalized EC. By fitting each of these curves with a second-order polynomial, it is possible to obtain F_g using as indicated in Eq. [2]. Theoretically, the intercepts of the curves give EC_s, but occasionally we observed negative intercepts (Fig. 2) for this soil with a clay content of only 1%. These small negative intercepts may not have much practical significance. Figure 2 shows a nearly identical critical water content at which EC_b becomes zero. Essentially the soil becomes a nonconductor below this critical water content.

View larger version (29K): [in this window] [in a new window]   Fig. 2 Quadratic fit between temperature corrected ECb and soil water content, , depicted for eight different values of ECw. The curves intersect at a single point at slightly larger than 0.03 m3 m-3 and their r2 values range between 0.9986 to 0.9999

View larger version (26K): [in this window] [in a new window]   Fig. 3 Changes in temperature corrected ECb with ECw evaluated from curve-fit of Fig. 1 shown for eight arbitrarily selected water contents. The solid lines represent linear regression lines

View this table: [in this window] [in a new window]   Table 1 Fg of sandy soil expressed as linear and power functions of water content, . ECb is in units of S m-1

Dependence of EC_s on Soil Water Content and Estimation of _eff

View larger version (15K): [in this window] [in a new window]   Fig. 4 Dependence of soil solid electrical conductivity treated here as, ECim, on soil water content, . All of the ECim were determined from the intercepts of Fig. 3. The curve intersects the horizontal axis at = 0.032 m3 m-3 evaluated from the curve-fitted equation and corresponds with the relatively common intersection point of all the curves shown in Fig. 2

View larger version (24K): [in this window] [in a new window]   Fig. 5 Experimentally determined geometric factor, Fg(expt), shown with Fg predicted using the following models: Mualem–Friedman Method 1, Fg(MF1) = (eff)(ß+1)/(s - r); Mualem–Friedman Method 2, Fg(MF2) = F(m)(eff)ß, with ß = 0.5; Marshall's method, Fg(M) = (eff)b, with b = 0.5; Millington and Quirk's method, Fg(MQ) = (eff)c/(s - r)2, with c = 10/3; and Penman's method, Fg(P) = 0.66

View larger version (24K): [in this window] [in a new window]   Fig. 6 Experimentally determined geometric factor, Fg(expt), shown with Fg estimated using optimized values of powers of eff in the following models: Mualem–Friedman Method 1, Fg(MF1) = (eff)(ß+1)/(s - r); with ß + 1 = 1.356; Mualem–Friedman Method 2, Fg(MF2) = F(m)(eff)ß with ß = 0.068; and Marshall's method, Fg(M) = (eff)b with b = 0.58

	Summary and conclusions

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

 
Three conceptual models relating EC_b, EC_w, and were tested using a sandy soil. All of them assume that the ratio of EC_b/EC_w is proportional to , with the coefficient of proportionality typically called a tortuosity factor, F_g. The best fit to the measured data was obtained with a model that assumes the tortuosity factor is a power function of , ^b. This model was derived from a model for gas diffusion in soil (Marshall, 1959) on the assumption that electrical conduction and diffusion are analogous processes. The commonly used model of Rhoades et al. (1976), which describes the geometric or tortuosity factor as a transmission factor, also fits the data quite well but not as close as ^b. The two models that attempt to estimate the tortuosity factor using soil hydraulic properties did not show satisfactory results when the hydraulic parameters were included in the models.Millington Quirk 1959

	ACKNOWLEDGMENTS

 
The authors would like to thank the Fulbright and MacArthur Programs for the financial support necessary to carry out this research.

Received for publication February 21, 2000.

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