Published online 8 March 2006
Published in Vadose Zone J 5:412-418 (2006)
DOI: 10.2136/vzj2005.0019
© 2006 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
ORIGINAL RESEARCH
Solute Transport Measurement Under Transient Field Conditions Using Time Domain Reflectometry
K. Noborioa,
R. G. Kachanoskib,* and
C. S. Tanc
a Iwate Univ., Morioka, Iwate 020-8550, Japan; present address, School of Agriculture, Meiji Univ., Kawasaki, Kanagawa 214-8571, Japan
b Third Floor University Hall, Univ. of Alberta, Edmonton, AB, Canada T6G 2J9
c Greenhouse and Processing Crops Research Centre, Agriculture and Agri-Food Canada, Harrow, ON, Canada N0R 1G0
* Corresponding author (gary.kachanoski{at}ualberta.ca)
Received 7 February 2005.
 |
ABSTRACT
|
|---|
Measurement of transport properties of field soil remains a challenge. Time domain reflectometry (TDR) has been used for rapid and nondestructive measurement of the movement of conservative tracers in controlled laboratory and field experiments. Measuring transport under transient conditions in the laboratory using TDR has also been reported, but obtaining appropriate calibration relationships remains a challenge. We present a method for rapid and nondestructive measurement of field transport of an electrolytic tracer (applied to the soil surface) under transient rainfall and evapotranspiration conditions with net drainage using TDR without any a priori calibrations. The method uses TDR probes in plots with and without a tracer applied. The simultaneous TDR measurements of apparent impedance and dielectric constant in the paired plots were used to calculate the relative solute mass remaining to a given depth (i.e., TDR probe depth) as a function of time during a 270-d field experiment under natural rainfall and evapotranspiration conditions of net drainage. The measurements give relative solute mass flux that is equivalent to the solute travel time probability density function.
Abbreviations: CDE, convective–dispersive transport • CLT, convective lognormal transport • DOY, day of year • pdf, probability density function • TDR, time domain reflectometry
|
INTRODUCTION
|
|---|
THE POLLUTION of surface and groundwater resources by agrochemicals (e.g., pesticide, and nitrate) continues to be a public concern. New farm-based soil and water management practices (i.e., best management practices) to maintain environmental quality as well as crop production have also been introduced with success (e.g., Tan et al., 1993; Gaynor et al., 2002). There is, however, still much to be learned about the movement and management of agrochemicals in soil.
Characterization of water and solute transport in field soils is not a trivial task. A large number of measurements are required because of significant spatial variability of soil properties and boundary conditions controlling transport. A common method of in situ determination of transport properties is to apply a conservative tracer and follow its transport through the soil profile with time. Transport properties of soil can be estimated by fitting output from appropriate models to measured data. Coring soil is often used as a direct technique for measuring the movement of the tracer in soil. However, soil coring techniques are very labor intensive, destructive, and time-consuming. Using a ceramic suction cup is another direct technique to obtain soil solution samples with time when soil water matric potential is higher than about –30 kPa (Rhoades and Oster, 1986).
Ward et al. (1988) developed a method of simultaneously measuring solute tracer concentration, c, and soil water content, 
, using TDR. The method was based on the work of Dalton et al. (1984), who used TDR to simultaneously measure and soil bulk electrical conductivity, 
b, which have well-studied relationships with the electrical conductivity of soil water, w (Rhoades et al., 1976; Mualem and Friedman, 1991). Ward et al. (1988) determined a priori the -b–w-c relationship, and subsequently used TDR to measure transient water flow and solute (tracer) transport in the laboratory during three-dimensional flow from a point drip source. For a conservative tracer applied instantaneously to the soil surface under steady water flow conditions, Kachanoski et al. (1992) developed a field method for rapid, nondestructive measurement of solute tracer mass flux (i.e., the solute travel time probability density function) using vertically installed TDR probes. The method does not require a priori knowledge of the -b–w-c relationship, but is limited to steady water flow conditions. The studies of Ward et al. (1988) and Kachanoski et al. (1992) were followed by a number of studies, both in the laboratory (Vanclooster et al., 1993; Ward et al., 1994; Mallants et al., 1996; Comegna et al., 1999) and in the field (Kachanoski et al., 1994; Ward et al., 1995) under steady-state water flux conditions. Using horizontally installed TDR probes, breakthrough curves of solute transport have been made under steady-state water flux condition (Vanclooster et al., 1993; Wraith et al., 1993; Mallants et al., 1994; Vanderborght et al., 1996) and under transient-water flux conditions with known -a–w-c relationships (Risler et al., 1996; Persson, 1997; Nissen et al., 1998). Lee et al. (2001) successfully used a vertically installed TDR probe in the laboratory to estimate preferential flow parameters, which were comparable to the results from effluent data, for an undisturbed and structured soil.
Under natural field conditions, the flux of water and solute in the soil profile is variable because of temporal fluctuation in rainfall and evapotranspiration. Under these transient conditions, TDR can be used to measure the movement of an applied tracer, but the calibration relationships of -b–w-c for the undisturbed field soil must be determined, which is not a trivial task. Recently, Malicki and Walczak (1999) and Hilhorst (2000) developed novel methods to estimate w directly from the measurement of the bulk dielectric constant of soil, 
b, and the bulk electrical conductivity of soil, b. They assumed that b– and b– relationships are of similar forms, which eliminates the need for individual determination of those relationships.
The objective of our study was to develop a rapid, nondestructive method to measure the relative solute mass transport of a conservative electrolytic tracer, under the transient field conditions with net drainage. The method is an extension of the method presented by Kachanoski et al. (1992) for steady water flow conditions and utilizes the procedure of Hilhorst (2000) and the experimental boundary conditions to determine in situ the required calibration relationships (b-b–-c) for the undisturbed field soil, and the TDR cell constants.
|
MATERIALS AND METHODS
|
|---|
The approach used here is similar to that given by Kachanoski et al. (1992). The TDR probes are inserted vertically into soil from the surface to some depth L. For the case of constant application of water at the soil surface, steady-state soil water content, L (m3 m–3), and a pulse of applied electrolytic tracer with specific mass, ML (kg m–2), within the measurement depth, L (m), the following relationship can be given (Kachanoski et al., 1992; Eq. [5])
 | [1] |
where w0 is the electrical conductivity of soil water measured before any electrolytic tracer is added, w is the electrical conductivity of soil water measured after the specific mass of tracer has been applied but before any tracer has moved past the ends of the TDR probes, and 
a calibration constant specific for the tracer. Under transient conditions where both soil water content, L(t), and specific solute mass, ML(t), vary with time, Eq. [1] becomes
 | [2] |
where w0(t) is the electrical conductivity of soil water varied with time measured where no electrolytic tracer is added, w(t) is the electrical conductivity of soil water varied with time measured after the specific mass of tracer has been applied.
Electrical conductivity of soil solution, w (S m–1), may be expressed as a function of the apparent dielectric constant, b, and the bulk electrical conductivity, b (S m–1), of soil (Hilhorst, 2000) as
 | [3] |
where p is the dielectric constant of soil solution (
80), b is the bulk dielectric constant of soil, b is the bulk electrical conductivity of soil, and 0 the bulk dielectric constant of soil at b = 0. Equation [3] is only valid for soil water content and associated b values that are greater than a minimal soil water content min defined by the value of 0. The values of min and associated 0 are soil specific, but it has been suggested that in general min > 0.10 m3 m–3 (Hilhorst, 2000). The requirement that min > 0.10 m3 m–3 for estimating w from b and is similar to the value, > 0.1 m3 m–3 suggested by Rhoades et al. (1976), but smaller than the value, > 0.2 m3 m–3 suggested by Malicki and Walczak (1999). Persson (2002) validated Eq. [3] using three sandy soils moistened with various concentrations of salt solution. Values of b can be expressed with the impedance, R (
), measured at a distance from the end of a TDR probe on the display of a TDR instrument such as the model 1502C of Tektronix (Beaverton, OR) (Nadler et al., 1991; Ward et al., 1994; Heimovaara et al., 1995):
 | [4] |
where fT is the temperature correction factor, K is the cell constant (m–1) depending on the configuration of a TDR probe, R is the impedance load () of the TDR probe measured at a fixed location along the TDR trace after multiple reflections cease in a manner similar to Nadler et al. (1991) and Ferré et al. (1998), and 
is an empirical constant accounting for resistances due to connectors, a cable, and/or others. The temperature correction factor is expressed (Heimovaara et al., 1995) as
 | [5] |
where T is the temperature of soil water (°C), assuming that it equilibrates to soil temperature, as a function of time, t. As long as w is constant, whereas b, and thus , vary with time, b and R–1 have a linear relationship, which is derived by substituting Eq. [4] into Eq. [3] and rearranging for fTR–1, as
 | [6] |
When no tracer is added in soil, it can be assumed that w tends to be constant for a long time. Equation [6] would be valid because the spatial sensitivities to b and b are the same for low-loss conditions as demonstrated by Ferré et al. (2003).
It is assumed that L(t), and thus b(t), fT, and K, are identical between adjacent probes (with and without tracer added). Substituting Eq. [3] and [4] into Eq. [2] results in
 | [7] |
where R(t) is the impedance load () of a TDR probe at a plot where a tracer is applied, R0(t) is the impedance load () of a TDR probe at a plot with no tracer applied, and b(t) is the bulk dielectric constant of soil at time t. As long as the tracer remains in the soil from the surface to the end of the probe length L, then the mass applied is conserved. Therefore, Eq. [7] can be rearranged by replacing ML(t) with 
MT to obtain an 0 value as follows:
 | [8] |
 | [9] |
where MT represents the mass applied. All the variables on the left-hand side and b(t) on the right-hand side in Eq. [8] are measured with TDR and temperature probes. If the theory and proposed method are valid, then there should be a linear relationship between the left-hand term versus b(t), and the correlation coefficient of the linear relationship should be a good indicator of the validity. The value of the only unknown parameter, 0, is then easily obtained as the ratio of the intercept to the slope of the linear relationship. All TDR measurements for testing whether or not a linear relationship exists (and for calculating 0) are taken under transient conditions after the tracer has been applied, but before any tracer has moved past the ends of the TDR probes. Thus, the value of MT is constant for all of these measurements.
The procedure for measuring tracer mass flux beyond the ends of the TDR probe is obtained by dividing Eq. [7] by MT, which gives the relative specific mass of applied tracer, MR(t), located from the surface to the TDR probe length, L, at any time t
 | [10] |
where ß is the slope of the linear relationship in Eq. [8]. As indicated in Eq. [10], the value of MR(t) depends on simultaneous TDR measurements of impedance, R, bulk dielectric constant, b, and soil water content, L, which is a function of b. Simultaneous measurements of R(t), b(t), and L(t) with TDR are straightforward.
The relative mass remaining measurements, MR(t), can be used to estimate a solute travel time density function, fL(t), for depth L (Kachanoski et al., 1992):
 | [11] |
where MR,L(t) is estimated relative mass remaining in the TDR probe length, fL(t) the solute travel time probability density function (pdf), L is the depth (m), and t is time (d). Transfer function models for fL(t) can be obtained by assuming either effective convective–dispersive (CDE) transport or convective lognormal transport (CLT) (Jury and Roth, 1990). For the CDE
 | [12] |
where D is the dispersion coefficient, and v the solute velocity. For the CLT
 | [13] |
where and µ are parameters for the lognormal pdf.
Equations [12] and [13] were substituted into Eq. [11] and then curve fitted to the measured MR(t) data expressed by Eq. [10]. The curve fitting gave nonlinear least square estimates of D and V for the CDE model, and µ and for the CLT model.
Experiment
The experiment was conducted at the Eugene F. Whelan Exp. Farm, Agriculture and Agri-Food Canada near Woodslee in southwestern Ontario, Canada (42°12'37''N, 82°44'42''W). Two "nests" of two-wire TDR probes (0.2 m long and 0.04 m apart), made of 0.002-m-diameter stainless-steel rods, per plot were vertically installed in the Ap horizon of Brookston (fine-loamy, mixed, superactive, mesic Typic Argiaquoll) clay loam, which is a swelling soil with 27.2% sand, 34.5% silt, and 38.3% clay (Reynolds et al., 2003). Sixteen nests in total were installed for eight experimental strips, 15.0 by 67.0 m each. The two nests were 8 m apart from each other in each experimental plot. A pulse of KCl tracer solution (60 g Cl– L–1), which was a readily detectable concentration by TDR in the Brookston soil, was applied to a 1.5 by 1.5 m area over one nest of the TDR probes. The same amount of tracer-free water was applied to a similar area over the other nest of the TDR probes. Careful installation made it possible to produce similar cell constant values for adjacent probes. Each probe was connected to a 200- shielded TV antenna cable and to a metallic cable tester (model 1502C, Tektronix) via an impedance matching transformer. Dielectric constant and impedance of soil were measured twice weekly during 1996. Values of b were determined from TDR measurements of travel time; then was determined using the calibration proposed by Topp et al. (1980). Triplicates of undisturbed soil cores (2.3-cm diam.) per probe were taken to the 45-cm depth around the TDR probes during the experiment for Cl– analysis. The soil cores were dissected into 5-cm-long sections, and the Cl– mass within each section was determined. Daily rainfall was measured at an automated weather station located about 200 m northwest of the experimental site. The experimental site was managed using no-till practices, with a soybean [Glycine max (L.) Merr.]–corn (Zea mays L.) rotation. A pulse of KCl tracer and tracer-free water were applied on Day of Year (DOY) 115, 13 d after installation of the TDR probes. Corn was planted on DOY 150.
|
RESULTS AND DISCUSSION
|
|---|
Water contents in the KCl-applied and control plots were averaged to estimate L and b. After DOY 172, L along the TDR probes decreased consistently due to evapotranspiration, until DOY 252, when frequent rainfall events caused L to increase (Fig. 1A
and 1B). Average water content in the top 0.2-m layer changed between 0.15 and 0.5 m3 m–3. Average soil temperature increased from 5 to 25°C from DOY 100 to 170, and it remained as high as 25°C for the summer, when L coincidently remained low (Fig. 1C). After DOY 250, average soil temperature decreased to 0°C.
View larger version (21K):
[in this window]
[in a new window]
|
Fig. 1. Temporal changes in (A) daily precipitation, (B) volumetric soil water content measured with vertically installed 0.2 m-long TDR probes, and (C) average soil temperature between 0.05 and 0.3m deep. Bars in (B) indicate ± one standard deviation with n = 16.
|
|
Measured L between the KCl-applied and control plots were linearly related (P < 0.001) as shown in Fig. 2
. The slopes and intercepts of the regression lines were not significantly different (P < 0.01) from 1.0 and 0.0, respectively. This relationship confirmed the assumption, made in the theoretical section for Eq. [7], stating that L values obtained in the adjacent sites were identical.
View larger version (18K):
[in this window]
[in a new window]
|
Fig. 2. An example of comparing TDR-measured water content at the control and KCl-applied plots. Dotted lines represent the boundaries of ±90% confidence interval.
|
|
The b–w– relationship by Rhoades et al. (1976) and others is described as
 | [14] |
where a and b are constants and s is the surface conductivity—these values may change little for a specific soil for a long time. As seen in Eq. [14], changes in b, and thus R–1, are contributed only by changes when the concentration of solute in soil water is constant. Hysteresis in drying and wetting cycles of soil may not affect the b–w– relationship, as Bottraud and Rhoades (1985) reported little evidence of hysteresis in the –a relationship. We established the b–R–1 relationship from readings of TDR probes in the control plot located adjacent to those at the KCl-applied plot. A linear relationship of b against R–1, as expressed in Eq. [8], with the temperature correction factor involved, was highly significant (P < 0.001) in the control plot, whereas this was not the case for the relationship with no temperature correction factor (Fig. 3
). Before any KCl application, assuming that the concentration of soil water, w, was identical both in the control and KCl-applied plots, the b–R–1 relationship for the KCl-applied plot was closely scattered along the relationship for the control plot. The need for a temperature correction is evident by the deviation in the linear relation between b and R–1. When the temperature correction factor was applied, the assumption for Eq. [7] that K values for the control and KCl-applied plots are identical is justified. All of the TDR probes used showed results similar to Fig. 3, which are also very similar to the relationship in Fig. 1C of Malicki and Walczak (1999), although they used b instead of R–1.
View larger version (21K):
[in this window]
[in a new window]
|
Fig. 3. An example of relationship between bulk dielectric constant, b, and reciprocal impedance, R–1, before KCl solution application in the control and KCl-applied plots with and without a temperature correction factor.
|
|
The value of 0 in Eq. [3], [7], and [10] was estimated using Eq. [8] for each nest of probes. This is the only calibration needed for this procedure. Figure 4
shows an example of the relationship between b and (R–1 – R0–1) measured between DOY 116 and 149, for which we assumed that all of the applied tracer mass remained in the soil from the surface to the bottom of TDR probe. The high correlation coefficient (r > 0.85) suggests the proposed theory and method work well under transient conditions. Average 0 values for Brookston clay loam were found as 13.3 ± 1.62 (N = 8) and 11.5 ± 1.78 (N = 8) for the temperature correction factor involved and no temperature correction factor involved, respectively. Malicki and Walczak (1999) found that b 0, when b < 6, in the linear relationship of b–b for different w. Hilhorst (2000) reported the average 0 value of 4.1 for several soils. The slightly higher estimates of 0 in this study are attributed to the higher clay content of the soil. Temperature affected 0 estimates by increasing the values of (R–1 – R0–1) due to a soil temperature rise during the period of calibration. The reasonably small variation in 0 for the different TDR probes also suggests that the theory and proposed method work well for transient conditions.
Temporal changes in relative solute mass remaining in the soil from the surface to the depth of the TDR probes calculated using Eq. [10] are shown in Fig. 5A
for the case with no temperature correction and in Fig. 5B for the case with a temperature correction factor. In both cases relative solute mass estimated using TDR agreed well with that from soil cores. An immediate increase in the relative solute mass by applying the KCl solution on DOY 115 was well detected in both cases. The relative solute mass estimated was more or less equal to unity until DOY 130, after which it gradually decreased as the tracer moved downward beyond the end of the probe. The results indicated that the center of mass of the applied tracer [when MR(t) = 0.5] took about 85 d to move from the surface to the 0.2-m depth (Fig. 5). During the summer growing season (DOY 180–250), the soil water content was low (Fig. 1B) and the TDR-measured b was less than the detection limit (0) for calculating the relative solute mass MR,L(t), so no measurement of solute mass flux was possible. This is a limitation of the method that is dependent on the soil specific value of 0 and climate conditions. In practice this may not be a problem because periods with low soil water contents likely coincide with periods of very slow downward water movement. At this site very little of the applied tracer mass moved deeper than L = 0.20 m (TDR probe length) during the dry period from DOY 180 to 250. At the end of the growing season (DOY > 250) measurements of relative solute (tracer) mass MR,L(t) were once again possible because higher precipitation combined with lower crop water use resulted in higher soil water contents (Fig. 1B and 5). Solute mass flux also increased again with the measurements, indicating the applied tracer was rapidly leached past the end of the TDR probe (L = 0.20 m). Temperature effects on the estimated relative tracer mass were evident, especially when R–1 values were high. The TDR measurements without the temperature correction tended to overestimate the relative mass of tracer.
View larger version (27K):
[in this window]
[in a new window]
|
Fig. 5. Temporal changes in relative solute mass along L = 0.2 m TDR probes (A) with a temperature correction factor and (B) without a temperature correction factor. Bars indicate ± one standard deviation with n = 8. A KCl solution was applied on Day of Year 115.
|
|
Fitted curves for the CDE and CLT transfer functions are shown in Fig. 5A and 5B. The values of µ and for the CLT model were determined as 4.35 and 0.816 for the temperature-corrected data, and as 4.49 and 0.687 for the uncorrected data, respectively. For the CDE model, D = 1.58 x 10–4 m2 d–1 and v = 1.88 x 10–3 m d–1 were found for the temperature-corrected data, and D = 1.03 x 10–4 m2 d–1 and v = 1.79 x 10–3 m d–1 for the uncorrected data. As expected, the CDE and CLT curves were very similar. Using the µ and values for the CLT model and the D and v values for the CDE model, breakthrough curves were estimated by differentiating Eq. [12] and [13] with respect to time, t (Fig. 6
). The CLT and CDE functions, with and without the temperature correction, fit the measured data well. The center of the tracer mass estimated with data without the temperature correction factor was about 20 d slower than the estimate with the temperature correction factor.
View larger version (17K):
[in this window]
[in a new window]
|
Fig. 6. Breakthrough curves estimated as derivatives of the convective–dispersive transport (CDE) and convective lognormal transport (CLT) models fitted to the TDR-measured data with and without a temperature correction factor.
|
|
The fitted transfer functions are a convenient way to characterize the solute travel time probability for the particular growing season monitored. The parameters of the transfer functions reflect a combination of soil and climate conditions. The proposed method could be easily automated and combined with meteorological monitoring locations for estimating average solute travel-time probability from multiple years.
|
CONCLUSIONS
|
|---|
We presented a new method for nondestructive measurement of the transport of an applied tracer in soil under transient field conditions of net drainage. The method uses vertically installed TDR probes that require no a priori calibration and gives an estimate of the solute travel time probability density function. The validity of the method can be tested by a simple correlation procedure using early time data taken immediately after tracer application. The method requires measurement of soil temperature and a temperature correction of the TDR measurements of impedance. The proposed method is easily automated and may be a useful and effective tool to measure the transport properties of soil under transient conditions
|
ACKNOWLEDGMENTS
|
|---|
The authors are grateful to Dr. Dan Reynolds and Mr. Don Pohlman, Greenhouse and Processing Crops Research Centre, Agriculture and Agri-Food Canada, for reviewing the first manuscript draft and for technical assistance on data acquisition, respectively.
|
REFERENCES
|
|---|
- Bottraud, J.-C., and J.D. Rhoades. 1985. Referencing water content effects on soil electrical conductivity-salinity calibrations. Soil Sci. Soc. Am. J. 49:1579–1581.[Abstract/Free Full Text]
- Comegna, V., A. Coppola, and A. Sommella. 1999. Nonreactive solute transport in variously structured soil materials as determined by laboratory-based time domain reflectometry (TDR). Geoderma 92:167–184.[CrossRef][ISI]
- Dalton, F.N., W.N. Harkelrath, D.S. Rawlins, and J.D. Rhoades. 1984. Time-domain reflectometry: Simultaneous measurement of soil water content and electrical conductivity with a single probe. Science (Washington, DC) 224:898–990.[Abstract/Free Full Text]
- Ferré, P.A., H.H. Nissen, J.H. Knight, and P. Moldrup. 2003. Transverse sample area of two- and three-rod time domain reflectometry probes: Electrical conductivity. Water Resour. Res. 39:1261–1269.[CrossRef]
- Ferré, P.A., J.D. Redman, D.L. Rudolph, and R.G. Kachanoski. 1998. The dependence of the electrical conductivity measured by time domain reflectometry on the water content of a sand. Water Resour. Res. 34:1207–1213.[CrossRef]
- Gaynor, J.D., C.S. Tan, C.F. Drury, T.W. Welacky, H.Y.F. Ng, and W.D. Reynolds. 2002. Runoff and drainage of atrazine, metribuzin and metalochlor in three water management systems. J. Environ. Qual. 31:300–308.[Abstract/Free Full Text]
- Heimovaara, T.J., A.G. Focke, W. Bouten, and J.M. Verstraten. 1995. Assessing temporal vacations in soil water composition with time domain reflectometry. Soil Sci. Soc. Am. J. 59:689–698.[Abstract/Free Full Text]
- Hilhorst, M.A. 2000. A pore water conductivity sensor. Soil Sci. Soc. Am. J. 64:1922–1925.[Abstract/Free Full Text]
- Jury, W.A., and K. Roth. 1990. Transfer function and solute movement through soil. Theory and application. Birkhauser Verlag Publishers, Basil, Switzerland.
- Kachanoski, R.G., E. Pingle, and A. Ward. 1992. Field measurement of solute travel time using time domain reflectometry. Soil Sci. Soc. Am. J. 56:47–52.[Abstract/Free Full Text]
- Kachanoski, R.G., J.L. Thony, M. Vauclin, G. Vachaud, and R. Laty. 1994. Measurement of solute transport during constant infiltration from a point source. Soil Sci. Soc. Am. J. 58:304–309.[Abstract/Free Full Text]
- Lee, J., R. Horton, K. Noborio, and D.B. Jaynes. 2001. Characterization of preferential flow in undisturbed, structured soil columns using a vertical TDR probe. J. Contam. Hydrol. 51:131–144.[CrossRef][ISI][Medline]
- Malicki, M.A., and R.T. Walczak. 1999. Evaluating soil salinity status from bulk electrical conductivity and permittivity. Eur. J. Soil Sci. 50:505–514.[CrossRef]
- Mallants, D., M. Vanclooster, M. Maddahi, and J. Feyen. 1994. Estimating solute transport in undisturbed soil columns using time-domain reflectometry. J. Contam. Hydrol. 17:91–99.
- Mallants, D., M. Vanclooster, N. Toride, J. Vanderborght, M.Th. van Genuchten, and J. Feyen. 1996. Comparison of three methods to calibrate TDR for monitoring solute movement in undisturbed soil. Soil Sci. Soc. Am. J. 60:747–754.[Abstract/Free Full Text]
- Mualem, Y., and S.P. Friedman. 1991. Theoretical prediction of electrical conductivity in saturated and unsaturated soil. Water Resour. Res. 27:2771–2777.[CrossRef]
- Nadler, A., S. Dasberg, and I. Lapid. 1991. Time domain reflectometry measurements of water content and electrical conductivity of layered soil columns. Soil Sci. Soc. Am. J. 55:938–943.[Abstract/Free Full Text]
- Nissen, H.H., P. Moldrup, and K. Henriksen. 1998. Time domain reflectometry measurements of nitrate transport in manure-amended soil. Soil Sci. Soc. Am. J. 62:99–109.[Abstract/Free Full Text]
- Persson, M. 2002. Evaluating the linear dielectric constant-electrical conductivity model using time-domain reflectometry. Hydrol. Sci. J. 47:269–277.
- Persson, M. 1997. Soil solution electrical conductivity measurements under transient conditions using time domain reflectometry. Soil Sci. Soc. Am. J. 61:997–1003.[Abstract/Free Full Text]
- Reynolds, W.D., X.M. Yang, C.F. Drury, T.Q. Zhang, and C.S. Tan. 2003. Effects of selected conditioners and tillage on the physical quality of a clay loam soil. Can. J. Soil Sci. 83:381–393.
- Rhoades, J.D., and J.D. Oster. 1986. Solute content. p. 985–1006. In A. Klute (ed.) Methods of soil analysis. Part 1. 2nd ed. Agron. Monogr. 9. ASA and SSSA, Madison, WI.
- Rhoades, J.D., P.A.C. Raats, and R.J. Prather. 1976. Effects of liquid-phase electrical conductivity, water content, and surface conductivity on bulk soil electrical conductivity. Soil Sci. Soc. Am. J. 40:651–655.[Abstract/Free Full Text]
- Risler, P.D., J.M. Wraith, and H.M. Gaber. 1996. Solute transport under transient flow conditions estimated using time domain reflectometry. Soil Sci. Soc. Am. J. 60:1297–1305.[Abstract/Free Full Text]
- Tan, C.S., C.F. Drury, J.D. Gaynor, and T.W. Welacky. 1993. Integrated soil, crop and water management system to abate herbicide and nitrate contamination of the Great Lakes. Water Sci. Technol. 28:497–507.
- Topp, G.C., J.L. Davis, and A.P. Annan. 1980. Electromagnetic determination of soil water content: Measurements in coaxial transmission lines. Water Resour. Res. 16:574–582.[CrossRef]
- Vanclooster, M., D. Mallants, J. Diels, and J. Feyen. 1993. Determining local-scale solute transport parameters using time domain reflectometry (TDR). J. Hydrol. (Amsterdam) 148:93–107.
- Vanderborght, J., M. Vanclooster, D. Mallants, J. Diels, and J. Feyen. 1996. Determining convective lognormal solute transport parameters from resident concentration data. Soil Sci. Soc. Am. J. 60:1306–1317.[Abstract/Free Full Text]
- Ward, A.L., R.G. Kachanoski, and D.E. Elrick. 1994. Laboratory measurements of solute transport using time domain reflectometry. Soil Sci. Soc. Am. J. 58:1031–1039.[Abstract/Free Full Text]
- Ward, A.L., R.G. Kachanoski, A.P. von Bertoldi, and D.E. Elrick. 1995. Field and undisturbed-column measurements for predicting transport in unsaturated layered soil. Soil Sci. Soc. Am. J. 59:52–59.[Abstract/Free Full Text]
- Ward, A.L., R.G. Kachanoski, A.P. von Bertoldi, I.J. van Wesenbeeck, and C.J. Hamlen. 1988. Solute transport during three-dimensional unsaturated water flow: Axisymmetric measurements using time domain reflectometry. p. 192. In Agronomy abstracts. ASA,CSSA, and SSSA, Madison, WI.
- Wraith, J.M., S.D. Comfort, B.L. Woodbury, and W.P. Inskeep. 1993. A simplified waveform analysis approach for monitoring solute transport using time-domain reflectometry. Soil Sci. Soc. Am. J. 57:637–642.[Abstract/Free Full Text]
TOP
ABSTRACT
INTRODUCTION
