Soil Science Society of America Journal 64:1244-1252 (2000)
© 2000 Soil Science Society of America
DIVISION S-1-SOIL PHYSICS
Impacts of the Real and Imaginary Components of Relative Permittivity on Time Domain Reflectometry Measurements in Soils
G.C. Toppa,
S. Zegelinb and
I. Whitec
a Crop Production, Eastern Cereal and Oilseed Research Centre, Agriculture and Agri-Food Canada, 960 Carling Ave., Ottawa, Canada, K1A 0C6
b Land and Water Commonwealth Scientific and Industrial Research Organization, G.P.O. Box 1666, Canberra, ACT 2601, Australia
c Water Research Foundation of Australia, Centre for Resources and Environmental Studies, Australian National Univ., Canberra, ACT 2601, Australia
toppc{at}em.agr.ca
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ABSTRACT
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Time domain reflectometry (TDR) is widely used for routine field monitoring of water content and salts in soils. Most estimates of water content assume the TDR-measured apparent relative permittivity, 
a, is a good approximation for the real component, 'r, of the soil's complex relative permittivity with the magnitude of 'r being determined primarily by water content. We examine this assumption and show that a is influenced by both the real and imaginary components of the relative permittivity. Increases in a resulted from the dc conductivity and dielectric loss arising from the presence of ions in solution and clay content. At water contents above 0.15 m3 m-3 in soils with high clay content and/or salt, specific calibrations are needed for precise determinations of water content from TDR. We use the wave propagation equations to separate the real and imaginary component contributions to a. The Giese and Tiemann interpretation for dc conductivity was again shown to be within 10% of that from a conductance meter and this fact was used to propose a method using only TDR data to separate real and imaginary components of the relative permittivity. It was found that the dielectric losses and conductive losses did not differ according to the source of conductivity, whether from clay content in the soil matrix or electrolyte in the soil solution.
Abbreviations: EC, electrical conductivity, TDR, time domain reflectrometry
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INTRODUCTION
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ROUTINE MONITORING of water content and electrical conductivity (EC) in soils is now widely used in agricultural and environmental management, waste disposal, and mining. Time domain reflectometry has provided a powerful tool for real-time, simultaneous measurement of soil water content and bulk electrical conductivity on the same in situ soil sample. Problems arise, however, with the technique in materials with significant EC.
Analyses of the TDR wave form for water content use only the travel time, t, of the TDR voltage signal in a probe immersed in soil (Fig. 1)
(Topp et al., 1980). Bulk soil EC is estimated from the amplitude of the TDR signal (Fig. 1) (Baker and Spaans, 1993; Dalton et al., 1984; Dalton and van Genuchten, 1986; Dalton, 1992; Heimovaara, 1992; Nadler et al., 1991; Spaans and Baker, 1993; Topp et al., 1988; Zegelin et al., 1989). Current methods for interpreting TDR output rely on the assumption that the effects of water content and conductivity are completely non-interacting, allowing separable analyses. In this work we examine this assumption.
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Fig. 1 Schematic diagram of time domain reflectometry system (left), idealized trace (upper right), and voltage reflection pattern (lower right)
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The most reliable estimates of direct current conductivity, 
0, from TDR are based on the Giese and Tiemann (1975) equation which uses of the amplitude of the TDR signal at long times. The Giese and Tiemann approach agrees well with other low frequency measurements of EC (Topp et al., 1988; Zegelin et al., 1989; Heimovaara, 1992; Baker and Spaans, 1993). Dalton (1992) and Heimovaara (1992) have indicated that at times much longer than the TDR pulse rise-time, the signal returning from the soil probe contains only low frequency contributions and thus the signal amplitude is a measure of the low frequency conductivity. Direct measurement of EC using TDR has found significant applications in tracking of solute movement in soil and waste sites (Kachanoski et al., 1992).
In contrast to the long-time analyses, Topp et al. (1988) and Zegelin et al. (1989) used a multiple reflection model (Yanuka et al., 1988) to estimate EC which differed from that given from Giese and Tiemann (1975). Their calculations (Topp et al., 1988; Zegelin et al., 1989) were based on the magnitude of signal return after only one round-trip of the reflected signal in the transmission line (Fig. 1). In both studies the shorter-time estimates of EC were high compared to measurements using a conductivity bridge or the Giese and Tiemann (1975) long-time analysis. Topp et al. (1988) suggested that the discrepancy arose because the shorter-time analysis includes both dc and high frequency contributions to the conductive losses. If this is so then comparison of the shorter-time and long-time analyses of EC may provide a way of examining the relative importance of dc conductivity and high frequency dielectric loss in TDR signals.
Kraus (1984) and Yanuka et al. (1988) have included explicitly the dielectric loss and the dc conductivity in their formulation of the electromagnetic (em) wave propagation constants. In this work we use these more complete formulations to estimate the effect of both dc conductivity and dielectric losses on the measured apparent relative permittivity, a, by changing both soil electrolyte and surface conduction at a range of soil water contents. We also reassess the Giese and Tiemann (1975) method for using the attenuation of the TDR signal to determine dc conductivity.
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Methods
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Methods for Time Domain Reflectometry Signal Analysis
Wave Propagation Constants
When fluctuating electric and magnetic fields travel through wet porous materials, energy dissipation or dielectric loss occurs by two processes. This first results from the fact that constituent dipolar molecules require a finite time, the relaxation time, to adjust to the changing field strength of the pulsating electric and magnetic fields (Debye, 1929). This polarization or relaxation process gives rise to a phase lag between the imposed field and the material's response to it. This phase lag is a function of the angular frequency, 
, of the imposed field. Because of this lag, relative permittivity must be represented as a complex quantity, r, with a real (in-phase), 'r (), and imaginary (out-of-phase), ''r (), components (see notation list in Appendix A).
The second energy dissipation process arises from the EC, , of the media. This conduction can be both surface conduction as a result of electric charges on the surfaces of the solids and liquid phase ionic conduction due to dissolved electrolytes in the water phase. The contribution of both polarization and conductivity to ris represented by (Kraus, 1984)
 | (1) |
where
, 0 is the zero frequency (dc) EC of the bulk sample, 0 is the permittivity of free space and tan
is the loss tangent defined as
 | (2) |
The loss tangent, thus, lumps together all dielectric and conductive losses. Losses due to dipolar relaxation effects become important as the frequency of the imposed signal increases, and Eq. [1] shows that dc conduction losses are more significant as frequency decreases. The fundamental assumption in most applications is that TDR measurements occur in the range between these frequency limits where losses can be ignored. We examine that assumption below.
A TDR trace is usually displayed as voltage amplitude, V, or reflection coefficient, 
, as a function of time, t (Fig. 1). Soil water content is inversely related to propagation velocity, v, and thus has a direct relationship with signal travel time, t. Travel-time measurements give the apparent relative permittivity, a (Topp et al., 1980),
 | (3) |
where c is the velocity of propagation of light in free space. Eq. [3] can be written in terms of v as
 | (4) |
The dielectric loss and the EC of the soil, , determine the attenuation, 
, of the voltage, V, during its propagation and can be found from measurements of V. Propagation coefficients, and v, for electromagnetic waves have similar form (von Hippel, 1954; Yanuka et al., 1988):
 | (5) |
The denominator of Eq. [4] and [5] is 
and if tan << 1, the above equations simplify to
 | (6) |
 | (7) |
and
.
Analysis of TDR traces for both water content and EC have generally assumed that tan <<1. We show below, however, that ''r and 0 increase with salinity of wetting solution, clay content and soil water content, and tan may be non-negligible sometimes.
Calculation Procedure
When tan is not small, the TDR calculations are more complex. The initial aim is to solve Eq. [4] for 'r even when tan cannot be ignored. This is achieved by making successive approximations for 'r starting with Eq. [6] to give a first approximation for 'r. An independent estimate of the dc conductivity, 0, is required (here measured with a conductivity meter). Estimates of and ''r are needed to determine tan in Eq. [2] to provide an improved estimate of 'r using Eq. [4]. Estimates for can be based on the rise time of the reflected signal as described below. We set
as an initial approximation. The resulting value of 'r may yet be an overestimate because we have not included any dielectric loss. The effects of conductivity and dielectric loss act together to attenuate the signal. Yanuka et al. (1988) and Topp et al. (1988) provide a method which allows ''r and 0 to be estimated separately. The estimate of ''r gives the next estimate of tan which is used to give the improved estimate of 'r.
The separation of ''r and 0 makes use of the multiple reflection analyses (Yanuka et al., 1988). Topp et al. (1988) identified the quantity (0 ''r + 0) as the effective conductivity measured by TDR. This "effective conductivity" can be calculated from Eq. [5] using TDR traces
 | (8) |
where YZT is the effective conductivity from multiple reflections analyses given by Yanuka et al. (1988), L is the length of the TDR probe, is the reflection coefficient at the soil surface (Fig. 1), Vf is the final voltage of the TDR trace after all multiple reflections have disappeared and V0 is the magnitude of the applied voltage step. The quantities, 'a, , Vf and V0, on the right-hand side of Eq. [8] can be calculated from the TDR trace. With 0 is available from the conductivity meter measurements, Eq. [8] gives the imaginary component as
.
The reflection coefficient, , is related to the characteristic impedance of the TDR probe (transmission line) according to (Kraus, 1984; Yanuka et al., 1988)
 | (9) |
where Z0 is the characteristic impedance of the probe and Zi is the output impedance of the instrument. We obtained Z0 from a calculation given by Bill Wedemeyer (personal communication, 1994) that yielded 126.8 
for the probes used in this experiment. Others have used measurements in water as a known medium to determine Z0 (Zegelin et al., 1989).
The Giese and Tiemann expression for conductivity, GT, reliably estimates 0 based only on TDR signal estimates (Baker and Spaans, 1993),
 | (10) |
where all variables are obtainable from the TDR trace, as in Fig. 1. Thus TDR measurements alone provide a method for estimating both 0 and ''r.
The above equations employ a particular angular frequency, . TDR spans a broad band of frequencies (from 10–1000 MHz when using the Tektronix cable tester). The relative permittivity of soil depends on frequency in this frequency range (Campbell, 1990; Heimovaara, 1994). An estimate of the effective frequency is needed in Eq. [4] and [5]. It has been suggested (Bill Hook, personal communication, 1995) that it is possible to estimate the maximum frequency of the TDR reflected signal from its first reflection from the end of the probe (see Fig. 2)
. This is effectively treating the soil as a low pass filter and estimating its frequency bandwidth limit value. Based on this, the maximum frequency was estimated following the procedure given in the Tektronix Application Note, Appendix C (Tektronix Metallic TDRs for Cable Testing).
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Fig. 2 Time domain reflectometry trace showing the way in which travel time, t1, rise time, tr, of the return refelection were estimated for use in the calculations. This trace resulted from a 0.15-m-length probe in B horizon soil wetted with tap water
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In brief, the procedure for calculating the real and imaginary components is:- Equation [3] gives a as a first approximation for 'r, from the travel time.
- The effective frequency, , is estimated as shown in Fig. 2 and described above.
- Equation [8] is used to estimate YZT (the combined effect of conductivity and dielectric loss) for substitution in Eq. [2] along with and the first approximation for 'r to provide the estimation for tan.
- tan is used in Eq. [4] to solve explicitly for 'r. This results in the improved estimate of 'r intended.
- We estimate ''r in a similar way:
- 0 is given as GT using Eq. [10] or from direct conductivity bridge measurement.
- 0, a, and are used in Eq. [8] to calculate ''r.
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Materials
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The TDR measurements were made in a 20°C laboratory using soils that had been air-dried, crushed, and sieved to approximately 
2 mm. The soil samples were taken in New South Wales from cereal, pasture, and oilseed growing regions near Temora. The soil had approximately 20% clay in the A horizon and 55% in the B horizon. The clay consisted of approximately equal parts mica, kaolin, and smectite. The soil samples were wetted using two solutions of differing salt content: tap water, with minimal but sufficient salt content to prevent dispersion of the soils, and 0.05 M KCl solution. The EC of any one soil sample was altered by changing water content or changing salt content. Differing clay content of the soil samples also contributed to differences in the EC.
Soil samples, whether air-dried or wetted, were sieved and packed by hand into a cylindrical plastic container, 0.25 m long by 0.15 m diam. The sieved soil was added to the container in 350 mL increments and each increment was hand-packed by tamping with a 30-mm-diam. rubber tamper. When full the container held approximately 8 kg of soil. The wetting sequence used was from initial air dry to fully wetted with a series of incremental additions of tap water. After measurements were completed at the wettest condition, the soil was spread to allow air drying, crushed and sieved before re-wetting again but using 0.05 M KCl instead of tap water. This sequence was repeated until the soil became so saline that signal reflection was undetectable in the TDR trace. Wetting of the soil was carried out incrementally by adding approximately 250 mL of tap water or KCl solution to the soil spread evenly on a tray and about 3-cm deep. Soil and liquid were mixed thoroughly in the tray and passed through a series of sieves to break into about 2-mm sized particles and packed uniformly as described above. The upper limit on volumetric water content (
0.35) was determined by the limit on manipulation and mixing of the wetted soil.
A triple pronged TDR probe (Zegelin et al., 1989) with 6.35-mm-diam. stainless steel rods, and a 50 mm center-to-center rod spacing was used for measurements. Lengths of probe were 0.1, 0.15, and 0.2 m. The TDR measurement was made and controlled through custom software operating on a portable PC which retrieved the traces from a Tektronix model 1502B TDR cable tester. The software included algorithms to analyze the TDR trace to give apparent relative permittivity, a, magnitude of the applied voltage step (V0) and magnitude of the final voltage (Vf) (Fig. 1). These values were used for calculations in the equations given above.
A low frequency ac conductivity bridge (Radiometer, CDM3) was used to provide a direct measure soil EC for comparison with the TDR measured EC (Zegelin et al., 1989). Cell constants for each length of TDR probe were determined in a series of reference KCl solutions, following the procedure outlined by Zegelin et al. (1989). Conductivity bridge readings were taken at the same time and under the same conditions as the TDR determinations.
After each TDR measurement and the conductivity bridge measurement, the total mass of the full cylinder of soil was obtained by weighing and duplicate 40 g subsample were taken for the determination of the bulk density and gravimetric water content.
The frequency for each TDR measurement was estimated from the shape of the rising part of the curve indicating the returning reflection (Fig. 1). On the printed TDR trace, a line was drawn to approximate the rise time of the return reflection, tr (Fig. 2). From Appendix C, Tektronix Application Note, Fmax was estimated as 0.35/tr and
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Results
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The results are tabulated in Appendix B showing the probe lengths, the measured 
, a, and 0 together with the estimated values Fmax, 'r, ''r, GT, and YZT. The measured data are presented in Fig. 3a as typical TDR calibration curves (a vs. ) along with the calibration curve suggested by Topp et al. (1980) (dotted curve). A solid line curve is also shown in Fig. 3 which would result if the soil water had relative permittivity equal to that of free water. The data fall below the two curves for a < 10 and to go above the curves for a > 10. The data from samples with increased salt and increased clay tend to lie at the extremes of the deviations from the two curves. Figure 3b shows the estimated 'r and ''r as a function of as resulting from calculations involving Eq. [4] and [5]. At water contents <0.14, 'r is unchanged from a and ''r values are negligible. At higher water contents, 'r drops considerably below the Topp et al. curve and that for pure water, especially for those samples having added salt or clay content. For > 0.15, ''r increases very steeply with water content, equalling or exceeding the magnitude of 'r in conditions of high salt and high water content. When values of a values are plotted against the corresponding 'r values (Fig. 4)
, the effect of salt and clay can be identified. For the A horizon soil (Fig. 4a) wetted with water (open triangle), the differences between a and 'r are negligible for a < 15. When wetted with the KCl solution, the differences become detectable for a > 7 (Fig. 4a). In the higher clay B horizon soil (Fig. 4b), a > 'r for a > 7 when tap water was used as the wetting solution. When the KCl solution was used, the differences between a and 'r were measurable for a > 5. As the water content increased, the differences between a and 'r also increased. The amount that a is above the 1:1 in Fig. 4 indicates the effect of dielectric and conductive losses arising from either surface or soil solution conductivity. There are missing values in Fig 4 at some of the highest water contents. In the conductive soil conditions at these higher water contents, the returning TDR reflection is difficult to determine, especially in longer probes. Also Vf/V0 decreases so that the argument in the ln function in Eq. [8] becomes negative and the function is indeterminate. In Fig. 4a the missing open triangles are from the 0.15 and 0.2 m probes. In Fig. 4b, data from 0.15 and 0.2 m probes for KCl wetted B horizon (hour glass symbol) were indeterminate at
. Essentially this is the limiting conditions for TDR measurement in this B horizon. The high conduction of the wet clayey soil with added salt resulted in attenuation of the TDR signal so that there was barely sufficient signal reflection for TDR analyses. In the A horizon soil with its lower clay content the readable limit was at higher water content and up to twice as much added salt.
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Fig. 3 Relative permittivity as a function of water content. In (a) is the apparent relative permittivity estimated directly from time domain reflectometry based on Eq. 3. In (b) are the real (filled symbols) and imaginary (open symbols) components of the relative permittivity estimated from the use of Eq. [4] and [5]. In the legends, the first letter indicates the soil horizon (A or B), the next symbol(s) indicate the wetting solution (W = water, S1 = KCl solution once and S2 = KCl solution twice). The dotted curve was given by Topp et al. (1980). The solid curve assumes the water in soil has a relative permittivity of 80
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The short-time analyses of Yanuka et al. (1988) and the long-time technique of Giese and Tiemann (1975) provide a way of separating the high frequency (dielectric loss) and low frequency (conductivity) effects in TDR measurement. Figure 5
shows the comparison between the calculated short- and long-time conductivities and the conductivity-bridge measured 0. Clearly there is excellent agreement between the Giese-Tiemann technique and direct measurements. In contrast, the short-time analysis over estimates EC as has been found before (Topp et al., 1988; Zegelin et al., 1989). The portion of the TDR measured EC above the 1:1 line in Fig. 5 represents the relative magnitude of the dielectric loss or ''r effects. The portion below that line is the dc contribution. Examination of the data shows that, regardless of the source of the increased EC, the dielectric loss contribution is about 1.5 times the dc conductivity measurements. The correspondence between the data from the A and B horizons is surprisingly close, also indicating that it is EC, not clay content that determines the magnitude of the dielectric losses. This is an unexpected result.
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Discussion
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We have suggested here that direct TDR measurements can be used to estimate the real and imaginary components of the relative permittivity of wet soils. Based on this we have derived these components using the wave propagation velocity and attenuation to get successive approximations. This approach requires an estimate of the dc conductivity and the characteristic frequency of the first return pulse from the end of the probe. We used an independently measured EC but, as we have shown, could equally well have used the long-time Giese and Tiemann (1975) for the TDR itself to get 0. The values we have found for the real and imaginary components are plausible and consistent with those published by Heimovaara (1994) and Wyseure et al. (1997).
One motivation for this work was the hypothesis that separation of the real and imaginary components would remove the complication of conduction, whether from electrolytes or from surface conduction on clay colloids, from the TDR calibration curve. Although the calibration (Fig 3a) for these soils is not greatly different from the Topp et al. (1980) curve, Fig 3b shows that the real component of the relative permittivity is also affected by EC and that conduction still influences the TDR calibration. This could be interpreted as both clay and solute causing similar changes in the polarization and a commensurate decrease in the in-phase component of the relative permittivity (Hoekstra and Delaney, 1974). If so, would different electrolytes and clays with different charge densities differ?
Our analysis here has assumed that we can use a single characteristic frequency, determined from the shape of the first reflection (see Fig. 2), to separate real and imaginary components. TDR involves a wide range of frequencies which are attenuated at different rates as the TDR pulse sweeps through the immersed probe. The validity of this approach needs to be tested. Alternative methods in the frequency domain would be valuable to test these analyses and to examine independently the effects of clay and salts.
The conductivity results in Fig. 5 are intriguing. They suggest that it is a matter of indifference to the propagating wave if losses arise from surface conduction or ionic conduction in the soil water phase. Our results suggest that only bulk EC is important. This has implications for the mechanism of dielectric relaxation of water in the presence of charge surfaces or ions. The results warrant further study.
We have again shown that GT is a good measure of 0 (Fig. 5). These and additional data are shown in more detail in Fig. 6
, to include those from wetting the A and B horizon samples with water, wetting the A horizon twice with 0.05 M KCl and wetting the B horizon once with the KCl solution. Table 1
presents the regression coefficients for these data, where m (conductivity bridge measurement) was the independent variable (X) and GT was dependent variable (Y). The regressions show that data from both A and B horizons wetted with water were represented well by linear relationships with a slope close to 1. Wetting the A horizon with KCl solution resulted in decreasing the slope by 4%. By contrast, the KCl solution wetting the B horizon increased the slope by 11%. The differing effect of salt solution in the two soil horizons remains unexplained. Similar small deviations (±10%) were found by Zegelin et al. (1989). In spite of these differences in response, the results here confirm earlier conclusions that GT is a useful estimate of 0 (Zegelin et al., 1989; Baker and Spaans, 1993; Heimovaara, 1992; Topp et al., 1988). The partially compensating effect of salt and clay on the relationship between GT and m indicates that a single 1:1 relationship can be used to estimate 0 to within 10%. If improved precision is required, however, a specific calibration should be made for the particular soil and condition. The high r2 values in Table 1 indicate excellent linearity and low data scatter of the relationship, implying the adequacy of a two point calibration to specify the relationship.
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Fig. 6 Giese-Tiemann (GT) electrical conductivity vs. the conductivity bridge measurement for the Temora soil. The line is 1:1. In the legend, A and B refer to horizons of Temora soil. W refers to soil wetted with tap water. S refers to soil wetted with 0.05 M KCl solution
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Conclusions
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- The imaginary component of the relative permittivity, which includes high and low frequency contributions, can be estimated from TDR analysis and can have a measurable effect on 'r. The estimated 'r values are not a unique function of water content indicating that dissolved salts and clay lower the real component of the relative permittivity of the water present within the soil.
- The dielectric loss contributions to the imaginary component of the relative permittivity were estimated from TDR to be approximately 1.5 times the dc conductivity and both resulted from increases in amounts of clay, salt, and/or water.
- Methods are given for removing dc conductivity and dielectric loss contributions from a to give improved estimates of 'r using only the TDR trace. In a like manner an estimate of ''r can also be determined from the same data.
- The Giese-Tiemann calculation for electrical conductivity is linearly related to the dc conductivity and the slope of the relationship is unity but may deviate from this by as much as 10%. This means that the relationship is soil dependent, requiring specific calibration information where precise determinations are needed.
- Frequency domain measurements of the impacts of surface and soil-water ionic conduction on real and imaginary components of the relative permittivity in wet clay soil with added electrolyte would be valuable.
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ACKNOWLEDGMENTS
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In-depth consultation with Bill Wedemeyer was of great assistance to provide a direct calculation for the characteristic impedance of multi-wire transmission lines. We gratefully acknowledge Bill Hook for suggesting the frequency correction procedure and for helpful discussion of the frequency effects with David Gregson and Ron McFarlane. Three anonymous reviewers, one of whom was particularly helpful, and the associate editor contributed to the improvement of this paper.
Received for publication April 19, 1999.
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Appendix A
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A Notation List
- r the complex relative permittivity.
- 0 the permittivity of free space (F m-1).
- a the TDR-measured apparent relative permittivity.
- 'r, ''r the real and imaginary components, respectively, of the complex relative permittivity.
- the bulk electrical conductivity (S m-1).
- 0 the zero frequency (dc) electrical conductivity (S m-1).
- GT the electrical conductivity from an analysis based on Giese and Tiemann (1975) (S m-1).
- YZT the electrical conductivity from an analysis based on Yanuka et al. (1988) (S m-1).
- m the electrical conductivity measured by conductance meter (S m-1).
- i is
.
- the coefficient of attenuation.
- tan the loss tangent, pertaining to the phase lag during em wave propagation.
- the voltage reflection coefficient.
- the angular frequency of the imposed electromagnetic field.
- Fmax the maximum frequency of a reflected em signal (s-1).
- t travel time of the propagating signal (s).
- tr the rise time of the returning or reflected em signal (s).
- L the length of the transmission line (m).
- v the velocity of em wave or signal propagation (m s-1).
- c the velocity of light or em wave propagation in free space (m s-1).
- V the voltage amplitude of a TDR trace (V).
- V0 the voltage amplitude of the transmitted em signal (V).
- Vf the voltage amplitude of the em signal after all reflections have occurred (V).
- volumetric water content of soil (m3 m-3).
- Z0 the characteristic impedance of the soil probe or transmission line (ohm).
- Zi the instrument's output impedance (ohm).
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Appendix B. Measured data and calculated numerical results from Temora soil
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APPENDIX B Measured data and calculated numerical results from Temora soil.
Probe length
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Grav. WC
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a
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Meas. 0
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Fmax
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'r
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''r
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GT
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YZT
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| cm |
m3 m-3 |
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S m-1 |
s-1 |
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S m-1
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Temora A horizon soil wetted with tap water
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| 10 |
0.019 |
2.7 |
9.60 x 10-6 |
4.00 x 108 |
2.7 |
0.0 |
0.00 x 100 |
0 |
| 15 |
0.019 |
2.8 |
1.24 x 10-5 |
3.32 x 108 |
2.8 |
0.0 |
0.00 x 100 |
0 |
| 20 |
0.019 |
3.0 |
5.17 x 10-6 |
3.78 x 108 |
3.0 |
0.0 |
0.00 x 100 |
0 |
| 20 |
0.059 |
3.6 |
0.00 x 100 |
3.12 x 108 |
3.6 |
0.2 |
1.71 x 10-3 |
5.13 x 10-3 |
| 15 |
0.059 |
3.5 |
9.41 x 10-4 |
3.41 x 108 |
3.5 |
0.0 |
7.56 x 10-4 |
1.33 x 10-3 |
| 10 |
0.059 |
3.2 |
7.35 x 10-4 |
3.57 x 108 |
3.2 |
0.0 |
0.00 x 100 |
0 |
| 10 |
0.096 |
3.8 |
2.73 x 10-3 |
3.32 x 108 |
3.8 |
0.2 |
3.31 x 10-3 |
7.22 x 10-3 |
| 15 |
0.096 |
4.4 |
2.50 x 10-3 |
3.18 x 108 |
4.4 |
0.0 |
1.50 x 10-3 |
2.01 x 10-3 |
| 20 |
0.095 |
4.5 |
2.84 x 10-3 |
2.78 x 108 |
4.5 |
0.2 |
3.30 x 10-3 |
7.08 x 10-3 |
| 10 |
0.104 |
5.1 |
5.22 x 10-3 |
3.22 x 108 |
5.0 |
0.4 |
6.56 x 10-3 |
1.45 x 10-2 |
| 15 |
0.107 |
5.7 |
6.15 x 10-3 |
2.88 x 108 |
5.6 |
0.5 |
7.37 x 10-3 |
1.61 x 10-2 |
| 20 |
0.106 |
5.5 |
6.10 x 10-3 |
2.93 x 108 |
5.5 |
0.3 |
5.60 x 10-3 |
1.08 x 10-2 |
| 10 |
0.131 |
4.8 |
5.25 x 10-3 |
3.04 x 108 |
4.8 |
0.2 |
4.45 x 10-3 |
8.13 x 10-3 |
| 15 |
0.133 |
5.6 |
5.84 x 10-3 |
2.91 x 108 |
5.6 |
0.4 |
6.00 x 10-3 |
1.22 x 10-2 |
| 20 |
0.133 |
5.9 |
7.17 x 10-3 |
2.51 x 108 |
5.9 |
0.4 |
6.21 x 10-3 |
1.16 x 10-2 |
| 10 |
0.140 |
7.6 |
1.03 x 10-2 |
2.94 x 108 |
7.5 |
0.6 |
9.93 x 10-3 |
1.96 x 10-2 |
| 15 |
0.142 |
6.8 |
1.00 x 10-2 |
2.71 x 108 |
6.8 |
0.6 |
9.17 x 10-3 |
1.78 x 10-2 |
| 20 |
0.144 |
7.4 |
1.17 x 10-2 |
2.62 x 108 |
7.3 |
0.9 |
1.16 x 10-2 |
2.41 x 10-2 |
| 10 |
0.171 |
7.0 |
9.54 x 10-3 |
2.98 x 108 |
7.0 |
0.7 |
1.01 x 10-2 |
2.10 x 10-2 |
| 10 |
0.188 |
11.5 |
2.11 x 10-2 |
2.92 x 108 |
11.4 |
1.3 |
2.10 x 10-2 |
4.26 x 10-2 |
| 15 |
0.207 |
12.2 |
2.48 x 10-2 |
2.46 x 108 |
11.9 |
2.1 |
2.55 x 10-2 |
5.48 x 10-2 |
| 20 |
0.197 |
10.1 |
2.00 x 10-2 |
2.23 x 108 |
9.9 |
1.8 |
1.98 x 10-2 |
4.27 x 10-2 |
| 15 |
0.263 |
14.3 |
3.21 x 10-2 |
2.37 x 108 |
13.8 |
2.7 |
3.14 x 10-2 |
6.72 x 10-2 |
| 20 |
0.258 |
13.3 |
2.99 x 10-2 |
2.17 x 108 |
12.8 |
3.0 |
2.89 x 10-2 |
6.55 x 10-2 |
| 10 |
0.358 |
19.7 |
5.07 x 10-2 |
1.94 x 108 |
18.4 |
5.5 |
5.12 x 10-2 |
1.10 x 10-1 |
| 15 |
0.347 |
18.8 |
4.89 x 10-2 |
1.84 x 108 |
17.2 |
6.8 |
4.98 x 10-2 |
1.19 x 10-1 |
| 17 |
0.351 |
23.7 |
4.75 x 10-2 |
2.24 x 108 |
22.9 |
4.9 |
4.63 x 10-2 |
1.07 x 10-1 |
Temora A horizon soil first wetting with 0.01 M KCl
|
| 10 |
0.094 |
4.0 |
1.96 x 10-3 |
3.05 x 108 |
4.0 |
0.1 |
2.19 x 10-3 |
4.61 x 10-3 |
| 15 |
0.094 |
5.0 |
2.77 x 10-3 |
2.65 x 108 |
5.0 |
0.3 |
3.72 x 10-3 |
8.40 x 10-3 |
| 20 |
0.096 |
4.9 |
3.02 x 10-3 |
2.36 x 108 |
4.9 |
0.2 |
2.77 x 10-3 |
5.31 x 10-3 |
| 10 |
0.098 |
4.7 |
2.67 x 10-3 |
3.19 x 108 |
4.7 |
0.1 |
2.19 x 10-3 |
3.89 x 10-3 |
| 10 |
0.137 |
6.3 |
1.09 x 10-2 |
3.18 x 108 |
6.2 |
0.7 |
1.11 x 10-2 |
2.27 x 10-2 |
| 15 |
0.137 |
6.6 |
1.05 x 10-2 |
2.71 x 108 |
6.6 |
0.7 |
1.00 x 10-2 |
2.00 x 10-2 |
| 20 |
0.138 |
6.7 |
1.16 x 10-2 |
2.23 x 108 |
6.5 |
1.1 |
1.21 x 10-2 |
2.57 x 10-2 |
| 10 |
0.180 |
9.2 |
2.71 x 10-2 |
2.85 x 108 |
8.9 |
1.8 |
2.71 x 10-2 |
5.64 x 10-2 |
| 15 |
0.183 |
9.2 |
2.91 x 10-2 |
2.34 x 108 |
8.6 |
2.6 |
2.85 x 10-2 |
6.27 x 10-2 |
| 20 |
0.179 |
9.1 |
2.66 x 10-2 |
2.26 x 108 |
8.6 |
2.5 |
2.50 x 10-2 |
5.67 x 10-2 |
| 10 |
0.209 |
11.2 |
4.53 x 10-2 |
2.55 x 108 |
10.1 |
4.3 |
4.75 x 10-2 |
1.08 x 10-1 |
| 15 |
0.217 |
11.8 |
4.47 x 10-2 |
2.38 x 108 |
10.5 |
5.3 |
4.50 x 10-2 |
1.15 x 10-1 |
| 20 |
0.211 |
11.7 |
4.54 x 10-2 |
1.97 x 108 |
8.8 |
10.7 |
4.30 x 10-2 |
1.61 x 10-1 |
| 10 |
0.199 |
9.4 |
3.36 x 10-2 |
2.65 x 108 |
8.8 |
2.6 |
3.40 x 10-2 |
7.27 x 10-2 |
| 15 |
0.201 |
9.5 |
3.21 x 10-2 |
2.20 x 108 |
8.7 |
3.4 |
3.23 x 10-2 |
7.42 x 10-2 |
| 20 |
0.202 |
9.6 |
3.55 x 10-2 |
1.98 x 108 |
8.2 |
5.3 |
3.36 x 10-2 |
9.20 x 10-2 |
| 10 |
0.260 |
15.4 |
6.69 x 10-2 |
2.29 x 108 |
13.2 |
7.6 |
6.85 x 10-2 |
1.65 x 10-1 |
| 15 |
0.268 |
15.3 |
7.56 x 10-2 |
2.14 x 108 |
Nd |
Nd |
6.99 x 10-2 |
Nd |
| 20 |
0.266 |
15.7 |
7.46 x 10-2 |
1.71 x 108 |
Nd |
Nd |
7.15 x 10-2 |
Nd |
Temora A horizon soil second wetting with 0.01 M KCl
|
| 10 |
0.054 |
3.4 |
4.56 x 10-4 |
3.83 x 108 |
3.4 |
0.2 |
2.25 x 10-3 |
6.31 x 10-3 |
| 15 |
0.054 |
3.4 |
5.46 x 10-4 |
2.83 x 108 |
3.4 |
0.1 |
7.54 x 10-4 |
1.72 x 10-3 |
| 20 |
0.055 |
3.7 |
6.40 x 10-4 |
2.50 x 108 |
3.7 |
0.1 |
1.12 x 10-3 |
2.72 x 10-3 |
| 10 |
0.099 |
4.7 |
6.30 x 10-3 |
3.23 x 108 |
4.7 |
0.4 |
6.63 x 10-3 |
1.36 x 10-2 |
| 15 |
0.100 |
5.0 |
6.47 x 10-3 |
3.26 x 108 |
4.9 |
0.3 |
5.87 x 10-3 |
1.12 x 10-2 |
| 20 |
0.098 |
5.2 |
7.27 x 10-3 |
2.25 x 108 |
5.2 |
0.6 |
7.21 x 10-3 |
1.46 x 10-2 |
| 10 |
0.140 |
6.7 |
1.98 x 10-2 |
2.68 | |
TOP
ABSTRACT
INTRODUCTION
