Reprinted from the Soil Science Society of America Journal

Volume 60, no. 3, May-June 1996
677 South Segoe Rd., Madison, WI 53711 USA

Comparison of Three Methods to Calibrate TDR for Monitoring Solute Movementin Undisturbed Soil
D. Mallants,* M. Vanclooster, N. Toride, J. Vanderborght, M. Th. van Genuchten, and J. Feyen
ABSTRACTTime domain reflectometry (TDR) is rapidly becoming a popularmethod for measuring solute concentrations in the laboratory as wellas in the field. Success or failure of TDR to represent solute resident
concentrations depends on the accuracy of the invoked calibration.
In this study, we compared three commonly used calibration methods
that relate the impedance, Z+ as measured with TDR, to the soluteconcentration such as the inlet concentration, C O. The comparison
was carried out using solute transport data obtained from l-m-long,
0.3-m-diam. undisturbed saturated soil columns. The first method
comprised the application of a long enough solute pulse such that theconcentration in a soil column became equal to the input concentration.
The second method involved numerical integration of the observed
response to a tracer pulse input function from which ZO could beobtained. The third method determined & using an independently
measured relationship between the impedance and the solute concentration. The three calibration methods gave approximately the same
results for the first observation depth at x = 0.05 m. However,the presence of heterogeneous transport processes involving solute
diffusion from mobile to immobile water regions predicated the useof excessively long solute pulses in order to equilibrate the entire soilcolumn to the input concentration. The first method hence w a s useful
only for the shallower depths. The second method could be applied
throughout the soil profile, provided impedance measurements weremade for a reasonable time period, especially in the case of nonequilibrium transport. The procedure using an independently measured
Z-C relationship underpredicted Z.O in about 50% of the cases, presumably because of the use of repacked soil in the calibration.

have recently demonstrated the potential of TDR for measuring solute transport inSlaboratory soil columns as well as field soil profiles (e.g.,
EVERALL STUDIES

Kachanoski et al., 1992; Wraith et al., 1993; Vanclooster
et al., 1993, 1995; Mallants et al., 1994; Ward et al.,1994). Potential advantages of TDR have been discussed
D. Mallants, M. Vanclooster, J. Vanderborght, and J. Feyen, Inst. forLand and Water Management, KULeuven, Vital Decosterstraat 102, 3000
Leuven, Belgium; N. Toride, Dep. of Agricultural Sciences, Saga Univ.,
840 Saga, Japan; and M.Th. van Genuchten, USDA-ARS, U.S. Salinity
Lab., 450 W. Big Springs Road, Riverside, CA 92507 CA. Received 3
Mar. 1995. *Corresponding author (dirk.mallants@agr.kuleuven.ac.be).
Published in Soil Sci. Soc. Am. J. 60:747-754 (1996).

at length in the above literature, and are not repeated
here. A possible disadvantage of TDR is its usefulness
primarily for nonreactive tracers and low EC soils.
Success or failure of TDR to accurately measure soluteconcentrations depends strongly on the appropriatenessof the calibration procedure being used. The assumed
calibration is also important for EC measurements using
conventional four-electrode salinity probes (Rhoades etal., 1989). Since TDR measures the total resistance or
impedance, Z, of a soil to the flow of electromagnetic
energy, solute concentrations can be inferred from impedance readings if a particular value of the impedance,
ZO, can be related to a known value of the concentration,such as the concentration of the inlet solution, C O. A
linear relationship between Z and C has been observedfor instance by Ward et al. (1994) for different valuesof water content, 8, although at higher values of 8 somenonlinearity exists for low concentrations. By meansof such Z-C relationships, impedance distributions cansubsequently be translated back to solute distributions.
The three most commonly used calibration methods are:
TDR measurement of a continuous solute application
until some constant value ZO is obtained (referred tohereafter as Method l), TDR measurement of a pulsetype solute application using the concept of convolution(Method 2), and determination of an independent Z-C
calibration using disturbed or undisturbed soil (Method
3). Any of these three methods works well for relatively
homogeneous sandy soils or repacked soil columns(Kachanoski et al., 1992; Vanclooster et al., 1993; Ward
et al., 1994). However, calibrations may become problematic for soils exhibiting small-scale heterogeneities
due to the presence of macropores, immobile water
regions, or low-permeability zones. This problem wasdemonstrated by Mallants et al. (1994), who used TDR
to measure solute concentrations in a sandy loam soil
containing a large number of macropores. They showedthat the TDR sampling volume for their macroporous
soil may have been too small to yield accurate values
Abbreviations: TDR, time domain reflectometry; EC, electrical conductivity; PVC, polyvinyl chloride; BTC, breakthrough curve.

748

SOIL SCI. SOC. AM. J

of the average concentration across the soil column.
Mallants et al. (1994) subsequently employed Method
1 by adding a very long solute pulse so that the conditions
that C = CO (or Z = ZO) at the detection volume wassatisfied. This method, however, also has problems if
zones of low permeability and/or stagnant water arepresent within the sampling volume of the TDR probe;
the solute may then require an inordinate amount of timein order to spread uniformly by diffusion across theentire cross-section of the column.
In this study we compared these three calibration methods for relating TDR impedance readings to solute concentrations using data measured at six different depths
in 1 -m-long, 0.3-m-diam. water-saturated undisturbed
soil columns. First, we evaluated the accuracy of Method
1 to calibrate the Z-C relationship from a very long
tracer pulse, i.e., until Z becomes constant and equal to
ZO. Second, the results from a numerical convolution of
the solute pulse response was investigated (Method 2).
Next, we examined the applicability of an independently
measured relationship between the bulk soil EC (EC,)
and the EC of the soil liquid phase (EC,) as a functionof the soil water content, 8 (Method 3). Values for thecalibration constant, ZO, obtained with Methods 2 and3 were compared with impedance data obtained using
Method 1.
MATERIALS AND METHODS
Solute transport processes were examined on 30 undisturbed
soil columns taken 1 m apart at the Bekkevoort experimental
field, east of Leuven, Belgium. Details of the experimental
design and the transport experiments can be found in Mallants
et al. (1995, unpublished data). Soil water contents, 0, andbulk soil electrical conductivities, EC, were monitored bymeans of TDR probes installed horizontally at six different
depths (0.05, 0.15, 0.30, 0.45, 0.60, and 0.80 m) underconstant temperature conditions. Time-averaged water contents
based on all 30 columns were 0.37, 0.34, 0.33, 0.33, 0.33,
and 0.35 m3 mm3 for the six observation depths mentioned
above. Standard errors of observed 8 are very small ranging
from 0.002 to 0.004, which is within the range of TDR
instrument variability. The mean water flux was 0.0078 m h-‘,with a standard deviation of 0.0064 m h-‘. After establishingsteady-state saturated flow using solute-free water, longduration solute pulses containing 7 X 10m3 M CaCl* wereapplied in order to “saturate” the soil column with the applied
tracer solution (i.e., until C = Co in the columns). Solute
application times (to) ranged from 79 h for 14 columns to morethan 660 h. Measurements were made with a Tektronix cable
tester (Tektronix 1502B, Beaverton, OR) and the channels
were multiplexed manually. Values of Z were obtained for
0.25-m-long two-rod TDR probes (0.005-m diam. and 0.02-m
spacing). The travel time of the electromagnetic wave and theimpedance Z were taken from the screen of the cable tester.
Values of Z are calculated by taking the reflection coefficient,p, at long times (f-03) on the reflected wave form (see Fig.
1). The impedance where the wave form has reached a stablelevel, Z, is calculated from:z =z(l+Pm)
03[1]
Yl - Pm)
where Zc is the impedance of the coaxial cable (50 Sz), andpm is the reflection coefficient at long times (Fig. 1).

VOL. 60, MAY-JUNE 1996

-1.2

+-- /
40

0

I

I

80

,
120

Time (ns)Fig. 1. Typical wave form of a two-rod TDR probe without balun
inserted in demineralized water and tap water (electrical conductivity = 0.75 dS m-‘) at 20°C. Values of the reflection coefficient atlong times, pm, were obtained by positioning the screen cursor atlong times when all multiple reflections had disappeared.

Calibration of the Solute
Concentration-Impedance RelationshipAs shown by several researchers (e.g., Kachanoski et al.,1992), solute concentrations may be deduced from TDR-based
estimates of the EC,. A linear relationship is generally observed
between the resident solute concentration, C, and EC, forconstant water contents ranging from relatively low to saturation, and for salinity levels ranging from 0 to approximately
50 dS mm’ (Diels et al., 1994, unpublished data; Ward et al.,1994):

C=a+BEC,[2]where a and b are calibration constants. The EC, (dS m-l)
can be related to the impedance, Z (Sz), of an electromagnetic
wave that travels through the soil using (Topp et al., 1988
and references herein; Heimovaara et al., 1995):

EC, =

K
Z - Zcable[3]

where Kc is the cell constant of the TDR probe (mm’), andZcable (a) is the resistance associated with cable, connectors,
and cable tester. For salinity levels less than ~0.3 S m-l,
Zcahle << Z in Eq. [3] and is therefore omitted in the following
discussion. When the cable resistance, Zcable = 0.2 Sz, wasaccounted for (using a 50 D coaxial cable of approximately
2 m), a perfect linear relationship was found between solution
EC and TDR-measured EC, with the slope Kc = 2.937 m-’(see Fig. 2). It is evident from Fig. 2 that TDR measurements
not corrected for cable resistance underestimate conductivity
when EC > -0.3 S m-l. The cell constant Kc was obtainedby measuring Z when immersing the TDR probe in five different
salt solutions of known conductivity ranging from 0 to 1.2 S
mm’ (see also Nadler et al., 1991; Heimovaara et al., 1995).
Electrical conductivity measurements were carried out with alaboratory four-electrode EC meter (WTW, Weilheim, Germany, LF 92 conductivity meter with TetraCon 96 measurement cell). We note here that calibrations based on Eq. [2]and/or [3] are not a unique issue for TDR, but a general

MALLANTS ET AL.: COMPARISON OF TDR CALIBRATION METHODS

749

Z. was obtained when such a step increase of tracer solution
was compared with the convolution of a pulse application(Method 2) with the same concentration Co.

corrected for Zcebte

Method 2: Convolution Method

ii?
g

0.6

/

I

/

ifi2

When a continuous tracer solution (todoo) is applied during
steady-state flow to a soil profile having background concentration C,, the local concentration C in the soil can remain lessthan CO for relatively long periods of time, especially at large
depths in structured soils exhibiting nonequilibrium transport.
Rather than assuming that C = Co at a TDR detection point,
Method 2 assumes mass conservation of a solute pulse (t,,finite) passing through the detection volume for a uniform
velocity field, i.e., the amount of solute passing the detection
volume should be equal to the amount (Cot,) applied to thesoil surface. Integrating Eq. [5] between times 0 and 00 yields,
for a linear system:
1
cO~O=zo’ _Z;l I 0- (Z:; - Z,Ti’)dr

0.0

0.2

0.4

0.6

0.6

1.0

1.2

EC (conductivity meter) (S m-t)

Fig. 2. Electrical conductivity, EC, measured with a conductivity
meter vs. EC calculated from two-rod TDR probes in five different
KCl solutions. Open circles represent TDR measurements corrected
for cable resistance.
problem for any EC measurement device, whether TDR, anelectrical conductivity probe, or electromagnetic induction.
Relative solute concentration, c(x,t), can be expressed asc - c,

c(x,t) = ~co - Cl

where CO is a reference concentration such as the input concentration during miscible displacement, and C, is the backgroundconcentration. Inserting Eq. [2] into Eq. [4] and using Eq.
[3] leads toz;; - Z;’

CW) = z$, _

[6]

1.4

z;l

where Z, is the impedance before application of the tracer
solution, and Zo is the impedance associated with the reference
concentration, CO. Equation [5] shows that, under steady flow
conditions (i.e., constant soil water content) the relative soluteconcentration c at a particular depth, x, and time, t, can bederived from the measured impedance Z,,t if appropriate valuesof Z, and ZO are available. In this study, values for Zi and Z.
were determined for each depth and column separately becauseof local variations in water content and soil texture. Values
for the background impedance Z, at concentration C, are readily
obtained from the initial condition while, for homogeneous
soils, values for Zo can be related to the reference concentration
C, using one of the following three methods.

Method 1: Continuous Solute Application
The impedance, Za, can be immediately related to the input
solution concentration CO by applying a long enough (continuous) solute pulse until the solutes have distributed uniformly
throughout the soil profile. This method is most commonlyused for TDR calibration. The procedure was previously usedby Rhoades (1981) and Rhoades et al. (1989), among others,
to establish relationships between ECa, ECw and 8 of fieldsoils using four-electrode salinity probes. Ward et al. (1994)
found for their loamy sand that essentially the same impedance

where T is time. As long as to and Z, are known, Zu can be
determined from the convolution integral in Eq. [6] using themeasured impedance curve Z(t) (see also Ward et al., 1994).
Strictly speaking, the above equation is valid for flux-averaged
concentrations (Kreft and Zuber, 1978) whereas TDR detects
total resident concentrations. We assume, however, that thedifference between resident and flux-averaged concentrations
is relatively minor compared with the mass balance error due
to local fluctuation of flow velocity. Equation [6] is incorrectwhen the pore-water velocity at the TDR detection point isdifferent from the inflow velocity.

Method 3: Experimentally Determined
EC,-EC,-8 Relationship
Equation [3] shows that the EC, may be calculated directlyfrom the TDR-measured Z if the cell constant for the TDR
probe, K,, and Zcabre are known. In order to relate Z with C,
it is further necessary to describe EC, as a function of theEC, and 8. This is because 8 was found to fluctuate between
the soil columns used for our transport experiments, as well
as vs. depth within some of the columns. For a given 8, therelation between EC, and EC, may be given in a linear form
(Rhoades et al., 1976):[7]
in which EC,’ is apparent electrical conductivity of the solid
phase of the soil, and T is a transmission coefficient accounting
for the tortuosity of the current flow. In a more recent study,
Rhoades et al. (1989) interpreted T as the mobile water fraction(soil water in the large pores). The EC-EC, relationship forthis study was determined using repacked sandy loam soil
taken from the upper Ap horizon (O-O.25 m) of the sametransect as used for the soil columns. Particle-size distributionof the soil is 12.65% clay, 13.10% silt, and 74.25% sand.
Calibration experiments were carried out by mixing dry soilmaterial with known volumes of water containing eight different
concentrations of CaC12 (ranging from 0 to 32 g L-‘). The
soil packed into PVC boxes (0.32 m long, 0.25 m wide, and0.21 m high) had a uniform bulk density of 1.4 Mg mm3 with
8 of 0.12, 0.24, and 0.38 m3 m-3. Calibration experiments
were carried out for eight different concentrations of CaC12(ranging from 0 to 32 g L-l). Upon application of Eq. [3],all readings of Z were transformed to ECa, using a previously
determined value for K,.
EC, = EC; + T6EC,

750

SOIL SCI. SOC. AM. J

0.25

1

VOL. 60, MAY-JUNE 1996

and 32 g L-‘) were determined using linear regression
analysis (Diels et al., 1994, unpublished data). Linear
relationship between EC, and EC, were found for all
three water contents using salinity levels from 0 to 50
dS m-l, with r* ranging from 0.81 (0 = 0.12) to 0.99
(0 = 0.38). The estimated values for the intercept T0
were used to relate the transmission coefficient T to 8
by using the expression T = d3 + b. Best-fit parameters
were a = 1.421 and b = -0.146 (r* = 0.997). Figure
3 is a plot of TO vs. 8 using the estimated values of aand b, together with curves obtained by Rboades et al.
(1976) for a variety of soils. Estimated values for theintercept of Eq. [7], ECs', were found to increase withwater content. Although originally Rhoades et al. (1976)
reported that EC,’ was essentially independent of watercontent, their later model (Eq. [5] from Rhoades et al.,1989) shows a dependency of the intercept on the watercontent:

Te=[ae+b]eRhoades et al. (1976)
-*

0.10

,:’

“Bekkevoort” sandy loam

0.20

:’

0.30

0 . 400.50

EC a =

volumetric water content, 8 (msm-3)

8,(es + ews)2 E C + Te EC[

Fig. 3. Relation between the slope of Eq. [7], 7’6, vs. volumetric soil
water content, 0.

s

a

[8]

where EC, is electrical conductivity in the solid phase,8, is the volumetric content of the solid phase, and 0,,
is water content in the fine pores. The latter parameteris a linear function of the total soil water content, 0 (seeFig. 6 and 7 of Rhoades et al., 1989). Thus, the increasing
values of the intercept of Eq. [7] as observed in thisstudy are due to increasing values of fl,, when total soil

RESULTS AND DISCUSSION
The intercept and slope of Eq. [7] for three different
water contents (0.12, 0.24, and 0.38 m3 mm3) and eight
different salt concentrations (0, 0.5, 1, 2, 4, 8, 16,1

0 . 4 0

0.0

0.4

0.6

1.2

1.6

2.0

2.4

2.0

3.2

EC, [dS/m]
Fig. 4. Bulk soil electrical conductivity, EC., of Bekkevoort sandy loam soil as a function of the water content, 6, and the electrical conductivityof the soil water, EC,.

751

MALLANTS ET AL.: COMPARISON OF TDR CALIBRATION METHODS

should reach the input concentration, CO, when the impedance achieves a constant minimum value, 20. Notice,
however, that the observed Z in Fig. 5 keeps decreasing
during the application period for al cases except theshallower 0.05-m depth location. As discussed by Mallants et al. (1994), the relatively quick and early decreasein Z is most likely due to the presence of macropores,
which cause solutes to move quickly downward while
bypassing much of the soil matrix liquid phase. Concomitant tailing is caused by slow diffusion of solutes fromthe larger pores to the less permeable soil matrix. Severalof our soil columns could not be quickly saturated with thewater content increases. A linear relationship of the form
A + B9 was used to relate ECs' to 8. The data wasrepresented well for A = -0.1094 and B = 1.249(r2 = 0.981). The resulting EC,-EC,-8 relationship thus
obtained was used to construct a smooth EC,-EC,-8
surface as shown in Fig. 4.
The continuous solute application Method 1 is very
simple and attractive as long as the soil can be equilibrated
with the input solution within a relatively short time
period. Figure 5 shows typical distributions of the impedance vs. time at six depths following the application of
a 79-h solute tracer pulse. The soil solution concentration
150 ,
140
130
120
110
100
90
80

I. .

‘_.~ i i _ __+._ t__+____+++-2- ~

zi.<

,t

._

1.. --) _ ;)“‘--‘.-;

J& _ _ ._)-_ *-

-..I

A.

d

2

+

-5cm

3

15cm

cm)

70
60
50 !
0

100

I
300

200

4

150 ,

1

120 -Ii
110

//

-If

I
30cm

-

II

45cm

A

100
90
80
70
60

,_”

_,a-_ H_r-_aw-*~--+--k--x-_-+.I.-..

.~-‘TI_.~_ 1, ~_ T_

r__w--T-_v
Y/

110 - %'

loo- 7,90- ; y+

80-

:

70-

*

*’
#

+,

Y

'
"&=/

,.v-

I

+

I I/

60 -

:I
N+v(

50 I
0

100

_--- +

IT
7’

x

60cm

v 80cmI;'

I

Zo(60 cm)

Z, (80 cm)

I
200

300

1

4 10

Time (h)Fig. 5. Impedance vs. time readings at six depths in one soil column measured with TDR for a solute application where to = 79 h.

752

SOIL SCI. SOC. AM. J., VOL. 60, MAY-JUNE 1996

140 c

I

v

130 P:

.
.
.

50 /
0

20
Time (d)

10

30

.

1

.

.

I
50

40

Fig. 6. Measured impedance vs. time at 0.80-m depth in one soilcolumn for the tracer pulse (to) of 664 h.

applied solution, even after continuing ponded infiltration
with the tracer solution for 600 h. This is demonstrated
in Fig. 6, which shows that the impedance Z at x =0.80 m in one soil column still decreased after applying
the tracer solution for 664 h. Hence, the solute concentration in this soil remained less than C O, and the final
impedance Z0 could not be determined accurately.
Applying long-duration (large to) solute pulses to structured soils exhibiting nonequilibrium transport is important since TDR-measured breakthrough curves are very
susceptible to the value of the reference impedance, ZO,
assumed in the calibration process. Figure 7 shows anexample Z(t) curve obtained at x = 0.05 m for 664 h.
In this example it took 664 h to completely equilibrate
the soil with the input solution, leading to a final Z0 of
56 Sz. By comparison, the impedance after 400 h was
57.2 0, a value close to ZO, while after t = 300 and
200 h, the impedance values were 58 and 61.2 0, respectively. Note that water content is constant throughout
the experiment (0 ranged from 0.312 to 0.317, which
is within the range of measurement error of TDR). Using
these values for ZO in Eq. [5] reveals the significanceof the effects of having incorrectly estimated Z. values
on the “measured” BTCs. Results in Fig. 8 show that
o’35

200

400

! 0.3
600

400

600

Time (h)Fig. 8. Effect of incorrectly determined values for impedance &I (Fig.
4) on calculated solute breakthrough curve (& = 56 12 is thereference value).

cutting off the Z(t) distribution too early (i.e., before
equilibrium is reached) leads to roughly the same early
breakthrough times, but with considerably less tailingin the BTC. Using inaccurately measured BTCs in turnwill lead to incorrect transport parameter values when
the TDR data are subsequently analyzed with transportmodels. For instance, Table 1 gives estimated parametersv (pore water velocity) and D (dispersion coefficient) forthe convection-dispersion equation obtained for the four
BTCs and Fig. 8. The parameter values for the referencecase are considerably different in comparison with thethree other cases (representing inappropriate calibrations) .
The alternative calibration Method 2 avoids the needfor solute concentrations to reach the final equilibrium
value, ZO. We tested this calibration procedure for 18
soil columns by comparing estimates of ZO based on Eq.
[6] with values of Z0 measured at 0.05 m where the soil
had already equilibrated with the applied solution. The
results in Fig. 9a show that estimates of Z. obtainedwith Method 2 only minimally deviate from ZO values
based on Method 1, with a coefficient of determination,r’, of 0.994. Method 2 is based on the assumption thatthe convolution of the TDR-measured impedance equals
Cot0 (Eq. [6]). Therefore, Method 2 requires that measurement times are long enough to ensure that all solute
passing the measurement window of the TDR probe will
be detected. This is especially true at larger depths in
structured soils where long equilibration times to capture
the low-concentration tails can be very extreme.
Furthermore, pore-water velocity needs to be homogeTable 1. Estimated convection-dispersion equation transport parameters for different values of impedance ZO.
.%ITime (h)Fig. 7. Measured impedance vs. time readings at 0.05-m depth fora tracer pulse (to) of 664 h; vertical arrows indicate different impedance (Z+) values used for calibration purposes. Triangles represent TDR-measured water content and dashed line is mean watercontent.

200

0

Y

cm h-’

56t
57.2
58
61.2

6.2

t Considered as reference value.

D
cm2 h-’
3790
zz
897

r2
0.992
0.987
0.985
0.987

MALLANTSET AL.: COMPARISON OF TDR CALIBRATION METHODS

80

60

60

Z,observed

80

100

80

100

80

60

40

60

Z,observed

Fig. 9. Observed (Method 1) vs. estimated values for impedance ZO
based on (a) Method 2 and (b) Method 3. The solid line represents
perfect agreement. Also shown are linear regression lines (dashed)
and the coefficient of determination (r*).

neous to ensure proper mass recovery for Method 2. As
discussed by Mallants et al. (1994), the TDR sampling
volume might be too small compared to the spatial variation of pore-water velocity in undisturbed soils. In thiscase, the solute mass detected by TDR could be different
locally across the entire cross-sectional area. Evidence
from dye stains (Mallants et al., 1993) and field observations of macropores indicated that macropores in our
experiments existed and functioned mainly near the soil
surface, while the subsurface was found to be morehomogeneous. This finding would suggest a somewhat
more uniform transport process in the subsurface oncethe solute front had passed the surface layers. If thisassumption is correct, convolution of the TDR-measured
pulse response should result in C& for a given detection
point in the deeper soil layers as long as the measurement753

time is long relative to the nonequilibrium time scalefor detection points in the upper part of the soil column.
As shown in Fig. 5, the observed impedance returnedto the background impedance, Zi, within 400 h, even at
the deeper depths. Hence, we conclude that for thosedepths were the soil cannot be easily equilibrated with
the inlet solution, Method 2 provides a possible alternative for estimating ZO provided the final Z is close to
Zi. An advantage of method 2 is the fact that field-scaleleaching experiments with solute-free water (or locallyavailable water with a relatively low background concentration) are generally easier to execute than experiments
requiring large amounts of a tracer solution of constant CO.
Calibration Method 3 is based on an independently
determined EC,-EC, relationship for different water contents, 8. The reference impedance, ZO, at known concentration, CO, was obtained by first computing EC, for agiven EC, and 8, using Eq. [7] with calibration constantspreviously determined. Next, the value of EC, was transformed to Z0 according to Eq. [3]. Since the EC,EC,-8 relationship was determined only for soil takenfrom the upper Ap horizon (O-O.25 m), we computed
Z,J at CO only for the first observation depth, 0.05 m.
Similar to Fig. 9a, estimates of ZO from the calibration
were compared with measured values of ZO obtainedusing the continuous application approach (Fig. 9b).
Although nine out of 18 values were close to the measured
ZO, the overall agreement was poor, yielding an r2 of
0.417. Since the EC,-EC,-8 relationship was determinedon a repacked soil, soil structure differences (including
the destruction of macropores) are a likely cause for thedeviation. The effect of soil structure on current flow
through the void space of the soil matrix is describedby the transmission coefficient T (see Eq. [7]). Rhoades
et al. (1989) interpreted T as the fraction of the totalsoil water that is mobile and resides in the large pores.
It is thus reasonable to assume that T will be different
between undisturbed and repacked soil. Moreover, theEC,-EC-8 relationships may have been different forother soil layers due to different physico-chemical properties. Especially the higher clay content in the deeper
layers, i.e., 23% clay in the 0.55 to 1.00-m layer vs.
13% clay in the surface Ap horizon, may have affected
the electrical conductivity of the solid phase (EC, in Eq.
[8]), as Rhoades et al. (1989) demonstrated that EC,
could be linearly related to clay content. Hence, it may
be necessary to determine the EC,-EC,-8 relationships
using undisturbed soil taken from a location close to themeasurement point.

CONCLUSIONS
Impedance data measured with TDR in l-m-long undisturbed soil columns were evaluated using three different calibration procedures. In order to relate Z withthe concentration, C, it was necessary to determine thereference impedance, Z0, associated with the reference
concentration, CO. Although the continuous application
Method 1 is simple in concept, widely used, and shouldbe generally applicable, results in this study indicate that

754

S oil SCI. SOC. AM. J., VOL. 60, MAY-JUNE 1996

this method may be problematic, especially for undisturbed or structured soils exhibiting nonequilibrium solute transport. This is because the method may require
an inordinate amount of tracer solution to ensure proper
equilibration of the soil solution with the input concentration. For example, some of our columns required solute
applications for more than 660 h in order to reach equilibrium. Proper equilibration with the input solution is
critical since, as demonstrated in this study, the tail ofa TDR-measured BTC can change significantly if thereference impedance, 20, is incorrectly determined.
The convolution Method 2 is based on the assumptionthat all the mass of solute applied to the soil surface
during a relatively short pulse time (to) will pass by andbe monitored by the TDR probes. This method agreed
well with the continuous application method at 0.05 m
where the soil was completely saturated with the applied
solution. Since the subsurface layers of the soil columns
used in this study were more homogeneous than the soil
layers near the surface, we assumed that the TDR probes
at the deeper depths eventually could detect all of thesolute passing through the surface layers, provided
enough time is allowed for the TDR measurements.
Moreover, it may generally by much easier to measure
for a long period of time than to keep applying a tracer
solution for a long period of time to ensure reaching the
input concentration, CO. Hence, we believe that for thosedepths where the soil cannot be easily and quickly equilibrated with the input solution, the convolution method
will provide an attractive alternative for estimating ZO.
We also compared the calibration method using an
independently determined EC,-EC,-8 relationship withthe continuous application method at 0.05 m. The
agreement was relatively poor, in part because of theuse of repacked soil for the independent calibration.
Accurate calibration probably will require that the EC,EC,-8 relationship be determined using undisturbed soil
taken from a location close to the measurement point.
ACKNOWLEDGMENTS
We sincerely appreciate the help of Armando Espino andCarlos Gonzalez in collecting the tracer data. We also thankFrancois Serneels, Wim Smets, and Pol Janssens for theirtechnical assistance in setting up the experiment.
REFERENCES
Heimovaara, T.J., A.G. Focke, W. Bouten, and J.M. Verstraten.
1995. Assessing temporal variations in soil water composition withtime domain reflectometry. Soil Sci. Soc. Am. J. 59:689-698.
Kachanoski, R.G., E. Pringle, and A. Ward. 1992. Field measurementof solute travel times using time domain reflectometry. Soil Sci.
Soc. Am. J. 56:47-52.
Kreft, A., and A. Zuber. 1978. On the physical meaning of thedispersion equation and its solutions for different initial and boundary conditions. Chem. Eng. Sci. 33:1471-1480.
Mallants, D., J. Feyen, N. Toride, and M.Th. van Genuchten. 1993.
Using dyes for quantifying preferential flow in a sandy loam soil.
EOS Trans. 74(3):240.
Mallants, D., M. Vanclooster, M. Meddahi, and J. Feyen. 1994.
Estimating solute transport parameters on undisturbed soil columns
using time domain reflectometry. J. Contam. Hydrol. 17:91-109.
Nadler, A., S. Dasberg, and I. Lapid. 1991. Time domain reflectometry measurements of water content and electrical conductivity oflayered soil columns. Soil Sci. Soc. Am. J. 55:938-943.
Rhoades, J.D. 1981. Predicting bulk soil electrical conductivity vs.
saturation paste extract electrical conductivity calibrations fromsoil properties. Soil Sci. Soc. Am. J. 45:42-44.
Rhoades, J.D., N.A. Manteghi, P.J. Shouse, and W.J. Alves. 1989.
Soil electrical conductivity and soil salinity: New formulations andcalibrations. Soil Sci. Soc. Am. J. 53:433-439.
Rhoades, J.D., P.A.C. Raats, and R.J. Prather. 1976. Effects ofliquid-phase electrical conductivity, water content, and surface
conductivity on bulk electrical conductivity. Soil Sci. Soc. Am.
J. 40:651-655.
Topp, G.C., M. Yanuka, W.D. Zebchuk, and S. Zegelin. 1988.
Determination of electrical conductivity using time domain reflectometry. Soil and water experiments in coaxial lines. Water Resour.
Res. 24:945-952.
Vanclooster, M., D. Mallants, J. Diels, and J. Feyen. 1993. Determining local scale solute transport parameters using time domainreflectometry (TDR). J. Hydrol. (Amsterdam) 148:93-107.
Vanclooster, M., D. Mallants, J. Vanderborght, J. Diels, J. Van
Orshoven, and J. Feyen. 1995. Monitoring solute transport in a
multi-layered sandy lysimeter using time domain reflectometry.
Soil Sci. Soc. Am. J. 59:337-344.
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.
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.