ῐ
J. Jpn. Soc. Soil Phys.
῏῍ῌῐῑ῎
No. 32, p. ,+ῌ-* ῍,**.῎

Practical Aspects of TDR for Simultaneous Measurementsof Water and Solute in a Dune Sand Field
Hossein DEHGHANISANIJ*, Tahei YAMAMOTO** and Mitsuhiro INOUE*** Agricultural Engineering Research Institute, Karaj, Iran, P.O.Box : -+/2/ῌ2./** Tottori University, Arid Land Research Center, +-3* Hamasaka,
Tottori 02*ῌ***+, Japan
Abstract
Simultaneous measurement of volumetric soil water content (qw) and soil solution electricalconductivity (ECw) was made for dune sand soil using Time Domain Reﬂectometry (TDR). The
best relationship between TDR dielectric constant (Ka) and qw, and that for bulk soil electricalconductivity (ECb) and ECw were deﬁned for dune sand soil and assessed in a dune sand ﬁeld. The
salinity of soil solution showed no e#ect on Ka and consequent qw. The commonly used linear
relation between TDR transmission coe$cient (T) and qw was inaccurate for dune sand soil when
qw was in the range of soil water holding capacity. A polynomial equation was suggested forexpressing the relation between T and qw, with less variation than a power relation. Based onﬁeld assessment, there was a better agreement between qw recorded by TDR and that from soil
sampling than a similar relation for ECw. The relative error (RE) between TDR measured and soil
sampling was ..31ῌ and +*.01ῌ for qw and ECw, respectively.
Key words : TDR, Dune sand soil, Soil water content, Soil solution electrical conductivity+.

Introduction

Simultaneously and non-destructively measuring soil water content (qw) and soil solution
electrical conductivity (ECw) can be a usefulapproach at critical stages of crop growth inﬁelds under irrigation with saline water. The
conventional method for measuring soil salinity is by taking soil samples and determining
the electrical conductivity of the extract of asaturated soil paste (Rhoades, +32,). These
measurements can be converted into the soil
solution salt concentration by correcting forthe soil water content at the time of sampling.
The soil solution can be sampled directly byporous suction cups. This method, however, islimited to a narrow range of soil moisture between (approximately) ﬁeld capacity and saturation and the small sample volume tends tomake the measurement variable (Broadbent,+32+). Soil water content can be measured bydestructive sampling and gravimetric determination or by the in situ neutron scattering
method (Graecen, +32+). The two main limitations of the neutron method are its relatively
large sampling and the radiation hazard involved. The fact that qw and ECw are usuallyobtained from separate samples with di#erent
geometry would introduce an additional error
in soil salinity assessment due to changes
associated with spatial and temporal variations in qw and ECw of soil samples (Dasberg
and Dalton, +32/) ; besides continues measurement is not possible.
The development of Time Domain Reﬂectometry (TDR) as a method for automated insitu measurement of bulk soil electrical conductivity (ECb) o#ers the promise of improved
temporal resolution in tackling solute movement. During the last two decades, TDR
method has become an established method tomeasure both qw (Topp et al. +32,) and ECb as a

῏22  32

nondestructive technique (Dalton et al., +32. ;Nadler et al., +33+ ; Dalton, +33,). The TDR
principle is based on launching a spectrum ofelectromagnetic waves into a waveguide (TDR
probe) embedded in the soil under investigation and measuring the reﬂected signal as afunction of time.
The travel time of the waves in the waveguide is proportional to the qw and the attenuation can be related to ECb. Topp et al. (+32*)
showed a unique equation between the apparent dielectric constant (Ka) and qw of measured
soil for a large range of soil structures fromclay to sandy loam, which is applied globally to
calculate qw from Ka (Drungil et al., +323 ;Grantz et al., +33* ; Pepin et al., +33,). However,there are some potential sources of error thathave received attention : (i) low density soil
(Dirksen and Dasberg, +33- ; Weitz et al., +331),(ii) clay and organic soils which caused a
sharper-than-average curvature of Ka-qw relations (Brisco et al., +33, ; Dasberg and Hopmans,+33, ; Roth et al., +33, ; Weitz et al., +331 ;Nadler et al., +333), and (iii) temperature whose
e#ect on TDR-measured Ka is related to thesoil texture and water content. According toPepin et al. (+33/), the temperature e#ect on
TDR-measured Ka is large in a wetter and ﬁner
textural soil. They speculated that a larger temperature e#ect on wetter and ﬁner-textured
soils dominated by free water might be attributed to bound water, which had a smaller
temperature dependency for Ka than freewater.
The temperature e#ect on TDRmeasured Ka for di#erent textural soils wasinvestigated experimentally and theoreticallyby Or and Wraith (+333). They concluded thatthe amount of bound water restricted, depending on clay minerals, on soil particles was
attributed to the temperature e#ect.
On the basis of TDR measurement in soils
wetted with solutions of a given salt concentration there are conﬂicting reports on the e#ect
of salinity on the Ka and on qw. Some studies
suggest that elevated salinity of the soil solution can cause over-estimation of Ka, resulting,**.

in an over-estimation of qw (Dalton, +33, ;Noborio et al., +33. ; Wyseure et al., +331), whileothers show no e#ect (Mallants et al., +330 ;Dalton and van Genuchten, +320 ; Timlin andPachesky, +330) and some show both underand over-estimation (Borner et al., +330 ; Bridge
et al., +330 ; Gregory et al., +33/).
Salinitya#ects TDR functionality in measuring qw byincreasing the attenuation of the TDR signal,
reducing its accuracy and eventually leading
to its disappearance (Nadler et al., +333). Fromthese results, there is need to explore how tomeasure qw and ECw simultaneously. Moreover, in some exceptional conditions TDR
method is constrained by uncertainty about its
accuracy and their applicability (Kachanoski etal., +33,). Dune sand soil, where the soil waterholding capacity is *.*-ῌ*.*2 cm- cm- and evena small error (*.*+ cm- cm- errorῌ,*῍ of soil
water holding capacity) is very critical forcrops life could be such exception.
Some probes can measure qw and ECw fromsoil samples with di#erent geometry. Inoueand Shiozawa (+33.) calibrated a four-electrodeprobe and tensiometer in dune sand soil formeasuring qw and ECw simultaneously. They
found a relative error (RE) of ,..῍ and /.0῍ for
qw and ECw respectively. However, they used
two di#erent probes for measuring qw and
ECw simultaneously, which were not set up in
the same sampling area. As a result, handmade TDR probes were developed to measureqw, ECb and temperature simultaneously froma soil sample for a given interval of time.
The objectives of this study were (i) to determine Ka-qw relationships and the best modelfor the estimation of ECw from ECb in dunesand soil and (ii) to assess some aspects of TDR
method for the estimation ECw and qw in adune sand ﬁeld.
,.

Theory,. + Relation between Ka and qw
The travel time for a pulsed electromagnetic
signal along a TDR probe is dependent on thevelocity of the signal and the length of theΐῒ : Practical Aspects of TDR for Simultaneous Measurements of Water and Solute in a Dune Sand Field 23

wave-guide. The velocity is dependent on Kaof the material surrounding the wave-guide.
This relation can be expressed by the following
equation (Topp et al., +32*) :La cῑt῎ ῌ῍ ῎῎ῌL,Lwhere La (m) is apparent probe length, L (m) is
the wave-guide length, and c (m s῍+) is thevelocity of the electromagnetic signals in freespace. The dielectric constant of water relative
to other soil constituents is high. Consequently, changes in soil water content (qw) are directly related to the change in the Ka of bulk soilmaterial, qw῎f (Ka) (Topp et al., +32*).
,. , Relation between ECw and ECb
While the velocity of the applied pulse alonga waveguide is dependent on the dielectric constant of the material surrounding the
waveguide, the amplitude of the reﬂected voltage is dependent on electrical conduction of
the applied signal between probe rods. The
presence of free ions in the soil solution will
result in attenuation of the applied signal. The
TDR+** (Campbell Scientiﬁc) was used in thisstudy for measuring both Ka and ECb. The
theory of Giese and Tiemann (+31/) has been
applied to the measurement of soil bulk electrical conductivity in TDR+**. A commonly used
expression is :Kp +῍rECb῎῍
Zc +ῌrwhere Kp is a probe constant, Zc is the cable
impedance, and r is the reﬂection coe$cient.
The reﬂection coe$cient is the ratio of thereﬂected voltage to the applied voltage andranges between plus and minus one.
A two-pathway model (Rhoades et al., +310)
was used in this study to ﬁnd the relation
between ECw and ECb. In a two-pathway
model, electrical conduction is assumed to takeplace along two parallel conducting paths. The
predominant path is through the soil solution,
ECw, also known as pore water electrical conductivity. The contribution of the solid fraction, ECs, takes place along the continuous
ﬁlms of exchangeable cations residing on thesurface of the solid particles. According to thismodel, ECb at constant qw is linearly related toECw :ECb῎ECsῌTqwECw
῎
where T is a transmission coe$cient. The T
can be expressed as a function of qw by a linear(Rhoades et al., +310) or power (Amente et al.,,***) curve and the empirical constant of linear(a qwῌb) or power (aqwb) can be estimated byﬁtting ECb against qw measured under constant ECw. This technique of keeping ECw constant is used in the determination of the twoconstants, a and b. Under ﬁeld conditions, however, ECw is rarely constant because ofchanges in qw due to evaporation, drainage or
inﬁltration. Although originally Rhoades et al.
(+310) reported that ECs was essentially independent of water content, their later model
showed a dependency of the ECs on the qw(Rhoades et al., +323). As a result, the relation
between ECb and ECw is function of qw, for adeﬁned T and ECs as a function of qw.
-.

Materials and Methods

The experiments were conducted at the Arid
Land Research Center (ALRC), Tottori University, Japan (-/῏-,ῌN, +-.῏+-ῌE). The relations
between qw and Ka, and between ECw and ECbin dune sand soil collected from ALRC ﬁeld
was evaluated and quantiﬁed in a controlledtemperature environment (,/ῐ) using TDR
probes. Soil water characteristics curve for thedune sand soil is shown in Fig. + and the physical properties are given in Table +.
The -0 TDR probes (Fig. ,) used as a waveguide, were each connected to the Campbell Co.
TDR+** and SDMX/* multiplexers by ++-meterFujikura RG-/2A cable. The handmade TDR
probes used in this study were designed withsimilar structure as the ThetaProbe (Gaskin
and Miller, +330). It included . rods, - of which
performed as shield rods and one (central rode)as signal rod (Fig. ,). The calibration processes
were examined on dune sand soil columns,
with 2 levels of qw (*.*-+, *.*0-, *.*3., *.+,-, *.+.3,*.,-,, *.,3+, and *.-0- cm- cm῍-) and 2 levels of

24

32

,**.

Table +The physical properties of dune sand soil
Factors

ValuesSand (ῌ)
304+
Silt (ῌ)*4.
Clay (ῌ)-4/
Speciﬁc gravity (ῌ),400Apparent speciﬁc gravity (ῌ)+4/0
Field capacity, FC (cm- cm-)*4*1.
Initial wilting point, IWP (cm- cm-)*4*,/
Permanent wilting point, PWP (cm- cm-)*4*,,
Saturated soil moisture content (cm- cm-) *4.+Fig. +Relationship between matric-potential(Y) and soil water content (qw) in dune
soil.

Fig. ,

Structure diagram of handmade soil-TDR probe.

NaCL (ECw) concentration (*.*, *.0,, +.,,, +.33,,./0, -.+*, -.2- and /.0. dS m+), in a total of 0.
soil column samples. Each column with ,* cm
,/ cm (diameterheight) dimension was
packed with oven-dried soil mixed with theabove NaCl solutions.
The TDR probes were installed in verticaldirection, individually, in each soil column (0.
soil column samples. The gravimetric watercontent was determined by oven drying - soil
samples taken from each column and qw was
calculated using the known bulk density of thesoil (+./0 Mg m-). The ECw of the soil samples
was determined based on the conductivity of +: / extracts (Richards, +3/.) of oven-dried soil :distilled water. Each soil column sample wasshaken and repacked with known bulk density
after measuring qw and ECw by 0 of TDR
probes to minimize the error due to movementof solution during the measurement. The soilcolumn sample was always covered and only
opened shortly during the measurement to prevent evaporation.
The relation between qw and Ka was deﬁned
and statistically compared with Topp et al.
model (+32*) using the root mean square error(RMSE) and regression analyses. The following equation was used for the computation of
the RMSE :ῐ῍ῒ ῏ῑῌ῎῏ῌΐῐwhere ; di is the di#erence between ith predicted by model and ith measured values and n
is number of the data pairs.
The models deﬁned for the relationship between ECw and ECb were compared using therelative errors of measuring soil solution electrical conductivity (ECw*/ECw). Where ECw*
RMSE῔ΐ : Practical Aspects of TDR for Simultaneous Measurements of Water and Solute in a Dune Sand Field 25

shown. The regression equation for the relationship between Ka and qw obtained from ourdata (Fig. -) showed less RMSE than thatreported by Topp et al. (+32*) (Table ,). Obviously, Topp’s model predicted soil water contentῌ*.*, cm- cm῎- less for dune sand soil in
the area between ﬁeld capacity (FC) and nearsaturation condition (Fig. -). However, between ﬁeld capacity (FC) and initial wilting
point (IWP) when qwῑ*.*-῍*.*2 cm- cm῎-, theresults of Topp et al. (+32*) model are very
similar to that from gravimetric determination(Fig. -). Fig. - shows the scattering of datawhen qw῍*.+* cm- cm῎-, which can be attributed to solution movement in the soil column
samples during the experiments. Statisticallythe di#erence between results of calibration
equation and Topp model was not signiﬁcant(Pῒ*.*/). This result is in agreement with theresults of Dalton and van Genuchten (+320) andMallants et al. (+330) for a sandy loam soil withqw in the range of *.+,῍*..* cm- cm῎-, andis soil solution electrical conductivity with ameasurement error of dῑ῏*.*+ cm- cm῎- (qw*
ῑqw῏d) and ECw is the actual soil solution
electrical conductivity.
Finally, the relationship between qw and Ka,
and between ECw and ECb in dune sand soil
was assessed using ﬁeld data. The soil samples
for the ﬁeld data were collected at the end of aﬁeld study on water and solute movement
under drip irrigation system using TDR, where
all the -0 TDR probes were buried in the ﬁeld of
ALRC for - months (DehghaniSanij et al., ,**-).
The Ka and ECb were recorded for each TDR
probe (qTDR and ECTDR). At about the same timesoil samples were collected from the each TDR
probe geometry to determine qw and ECw in
the laboratory (qref and ECref).
Relative error statistical analyses were used
to compare qw and ECw measured by TDR
method (qTDR and ECTDR) with the results of soil
sampling qref and ECref determined by conventional methods as follows :ῐREῑΐ ῕ ῍ ῏ῑ῎῏῕῔ῐ

῏ῒῌ

῍

ῐ+**

ῌ

where ; RE is relative error (῎), i is numberof samples (iῑ+,ῌ, n), n is total number ofsamples, X is qref or ECref, Y is qTDR or ECTDR and
X is average of qref or ECref.
..

Results and Discussion.. + Water content measurement
The relationship between Ka measured with
TDR and the qw obtained by gravimetricmethod for all soil column samples was foundby making a polynomial plot between Ka andqw (Fig. -). The relationship as given by Topp
et al. (+32*) for di#erent soil materials is also

Table ,

Fig. -

Relation between dielectric constant(Ka) and soil water content (qw) in dune
soil.

Regression coe$cients (R,) and root mean square error (RMSE) for the
relationship between dielectric constant (Ka) and soil water content (qw)using equation qwῑa Ka-῍b Ka,῍c Ka῍d and Topp model

Experiment
Topp et al. (+32*)
Experimental data

n

a

b
῎/

/0

*4.-ῐ+*
1ῐ+*῎/c῎*4***// *4*,3,῎*4**-+ *4*//2

d

R,

RMSE

῎*4*/-*
῎*4++02

*433,

*4*+0
*4**3



26

32

Timlin and Pachesky (+330) for loamy sand andsilty clay soils with qw in the range of *.*2ῌ*..cm- cm-. From the soil texture and range of
qw in our study (Fig. -) and the results of otherresearchers, salinity of soil solution showed noe#ect on Ka and consequent qw in a wide rangeof soil water content (*.*-ῌ*..- cm- cm-) andsoil texture (sand to silty clay).
.. , Soil solution electrical conductivity
measurements
To use the TDR method (Eq. /), the T and
ECs must be deﬁned for any individual soil.
Theoretically, the interception of curves of ECb
and qw give ECs (Eq. /). However, arbitrarily
selecting water content values and evaluating
ECb corresponding with di#erent ECw at thesame qw can make better estimation of both T
and ECs (Mallants et al., +330).
According to Eq. (/), the ratio of (ECbECs)/
ECw is equal to Tqw which is plotted vs. qw in

Fig. .

Relation between (bulk soil electricalconductivity (ECb)ῌ apparent electricalconductivity (ECs)/soil solution electrical conductivity (ECw)) vs. soil watercontent (qw), in dune soil.

Table -

Transmission coe$cient (T) of dunesoil expressed as linear, polynomial
and power function of soil watercontent, qw (cm- cm-)Expression

a

b

c

R,

Ta qwb+24,., +4/0.1*433+
Ta qw,b qw  c -14+/ +4-++0 *40*33 *4333
Ta qwb++4/3+,4*1*3*4320

,**.

Fig. /

Variation in ratio of soil electrical conductivity with measurement error of d῎῍*.*+ cm- cmῌ- (ECw*) and actual soil
electrical conductivity (ECw) with soilvolumetric water content (qw).

Fig. .. T can be related to qw using a linear(Rhoades et al., +310), polynomial and power
relation with relatively high correlation (Table-). The polynomial relation showed higher
correlation (R,*.333). The relative errors ofmeasuring soil solution electrical conductivity(ECw*/ECw) were determined for each correlation equation in Table - to reduce the variation
in measuring ECw. The variation in ECw*/ECw
with qw for a d*.*+ cm- cm- are illustrated in Fig. /. The ratio of ECw*/ECw is+.*when d*.*+ and vise versa. The commonlyused linear relation between T and qw, suggested by Rhoades et al. (+310), is inaccurate fordune sand soil when qw is in dune sand soil
water holding capacity and the polynomial relation showed less variation than the power
relationship (Fig. /). Consequently, we suggesta polynomial relation between T and qw fordune sand soil as used in this study.
.. - Soil water content and soil salinity
measurements
The relationship between gravimetric determinations of soil water content from the experimental ﬁeld (qref) compared to values measured
by TDR (qTDR) and those calculated with Topp
et al. (+32*) model (qTopp) is presented in Fig. 0.
The correlation between qrefqTDR and qref
qTopp was almost same (*.3/* and *.3./ respec-ῐ῏ : Practical Aspects of TDR for Simultaneous Measurements of Water and Solute in a Dune Sand Field 27

Fig. 0Relation between volumetric soil watercontent measured by TDR (qTDR) andthat calculated by Topp et al4 (+32*)
model (qTopp) vs. gravimetric determination (qref).

tively). The good agreement between qrefῌqTDR
and qrefῌqTopp where qTDR and qTopp was calculated using di#erent calibration equation can becontributed to applicability of Topp model formeasuring qw in dune sand soil when *.*,῎qw
῎*.*+ cm- cmῌ-, same results was concluded
earlier. The result of relative error (RE) statistical analysis was ..31῍ between qref and qTDR.
These results show that the TDR method isreliable and can be used for measuring qw indune sand ﬁeld. Dasberg and Dalton (+32/), andNadler et al. (+33+) presented a relatively highcorrelation between TDR and gravimetric determination in sandy loam soil (R, ῍*.2.,) andsilty loam soil (R, ῍*.32,) respectively.
The data for soil solution electrical conductivity measured by soil sampling from the experimental ﬁeld (ECref) and that measured by
TDR (ECTDR), and calculated with substitutionof Topp et al. (+32*) model in Eq. / (ECTopp) arepresented in Fig. 1. The percentage of RE for
ECTDR was about +*.01῍, which was higher
than that for qTDR. The percentage of RE washigher than that reported by Inoue andShiozawa (+33.), possibly due to (i) the soil usedin their study was washed dune sand soil,
where the percentage of clay was almost zero,Fig. 1

Relation between soil solution electricalconductivity measured by TDR (ECTDR)
and that calculated by Topp et al4
model (ECTopp) vs. soil sampling determination (ECref).

(ii) they used di#erent type of probes for measuring qw and ECw in soil samples with di#erent geometry.
The correlation between ECrefῌECTDR was
higher than between ECrefῌECTopp (Fig. 1).
This can be ascribed to less estimation of qw by
Topp et al (+32*) model when qref ῌ*.*2 cmcmῌ-. Regardless of the high correlation between the ECTDR and ECref (Fig. 1), many points
are not close to the + : + line. There was a low
scattering for both TDR data and data estimated from Topp et al. (+32*) model when
ECref was low and vice versa, which can lead toless accuracy of TDR method under high salinity. Similar results were reported by Dasberg
and Dalton (+32/) for a sandy loam soil withless scattering of the data, and for a silty loam
soil (Nadler et al., +33+) with much less scattering.
Since the main e#ective factor on soil electrical conductivity is soil water content values,
variation of ECTDR and qTDR simultaneously
plotted in Fig. 2. There was a relatively highnegative agreement between changes in qTDR
and ECTDR (Fig. 2). However, the scattering of
the data was high when qTDR was low. Fromthese results we conclude that the accuracy of

28

32

,**.

dune sand soil when qw was in water holding
capacity range. From our ﬁeld assessment, theRE for measuring ECw using TDR was relatively higher than that for qw. The accuracy of
TDR was less when ECw was high or qw was
low (*.*- cm- cm-). Practically, the TDR canbe used in a dune sand ﬁeld for recording ECw
and qw, when qw ranges between FC and IWP.
References

Fig. 2

Simultaneous variation in soil solution
electrical conductivity (ECTDR) and volumetric soil water content (qTDR) for dunesand ﬁeld.

ECTDR values is low when qwῌ*.*- cm- cmand high when *.*/ῌqwῌ*.*2 cm- cm-. We
conﬁrm the reliability and accuracy of TDR ina dune sand ﬁeld when the irrigation intensity
is high or soil water content is near ﬁeld capacity.
/.

Conclusion

The TDR method was tested for measuring
qw and ECw simultaneously in a dune sandsoil. The preliminary conclusion reached by
Dalton et al. (+32.) that “TDR, in conjunction
with known relations between relative electrical conductivity and soil water conductivity,
provides a new and powerful tool in soil water
research in that a measurement can yield bothqw and ECw” has been conﬁrmed by the data
presented in this paper for dune sand soil. The
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cm- cm-) dune sand soil. This may be attributed to (i) the di$culty in interpreting the
TDR in dune sand soil where the water holding
capacity is low and not related to the basic
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῍ῌ : Practical Aspects of TDR for Simultaneous Measurements of Water and Solute in a Dune Sand Field 29

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