ῐ
J. Jpn. Soc. Soil Phys.
ῒῐ῏ΐ῔ῑ
No. 3*, p. ++ῌ+3 ῍,**,῎The e#ect of heterogeneous soil-water distribution on
the TDR measurement of soil-water content
M. A. MOJID, Nobuo TORIDE and Hiroyuki CHO
Department of Agricultural Sciences, Saga University, Saga 2.*ῌ2/*,, Japan
Abstract
This study investigated the shape of the TDR waveforms and compatibility of TDR support
softwares to analyze the waveforms for dielectric constant, e, to estimate volumetric watercontent, q, in sands with heterogeneous distribution of water. When a dry layer was at thebottom, the waveform shifted upward due to reﬂection of the TDR pulse at the wet-dry interface
before the ﬁnal reﬂection of the pulse at the end of the sensor. The program algorithm incorrectly
located the point of ﬁnal reﬂection at the beginning of the dry sand layer when the water content
of the dry layer, qdry , was less than *.+/ m- mῌ- . Selection of inﬂection points at the wet-dry
interface resulted in underestimation of e and q. For qdry ῎*.,, m- mῌ- , the magnitude of the
upward shift was not signiﬁcant. The program then correctly determined the reﬂection point at
the end of the sensor. Thickness of the bottom dry sand layer, Ldry , had no e#ect on the wave
analysis. When the bottom layer was quite dry (qdry ῎*.*/ m- mῌ- ), the inﬂection point was always
selected just after the pulse reﬂected back at the wet-dry sand interface regardless of Ldry values,
resulting in underestimation of e and q. On the other hand, TDR always underestimated e and q
when water contents were di#erent between two rods of the sensor. The degree of underestimation was higher when the core wire of the sensor was in dry sand.
Key words : Time-domain reﬂectometry, soil-water distribution, longitudinal heterogeneity,transverse heterogeneity, wave form analysis+.

Introduction

Time-domain reﬂectometry (TDR) has becomea widely used technique for measuring soilwater content, q, since its introduction to measure the dielectric constant, e, of soil (Davis andChudobiak, +31/), and the development of acalibration equation between the dielectric
constant and soil-water content (Topp et al.,+32*). The technique is considered robust since
it is almost una#ected by temperature, salinity
and soil texture, and reliable over a wide rangeof soil-water condition within an accuracy of
῍*.*+ m- mῌ- of water content (Topp et al,+32*).
Topp et al. (+32,) showed both theoreticallyand experimentally that TDR measures the average dielectric constant of the sampled

volume using layered soil. However, Nadler etal. (+33+) showed that a heterogeneous soil
proﬁle with wet soil overlaid dry soil reduced
the accuracy of determining e by TDR.
Dasberg and Hopmans (+33,) also evaluated thee#ects of layered proﬁle on the TDR-measured
e for sandy loam and clay loam soils using ,*cm long ,-wire and --wire sensors. They obtained signiﬁcantly lower e when wet soil overlaid dry soil. A distinct reﬂection of TDR pulse
from the wet-dry soil interface caused di$culty to identify the ﬁnal point of reﬂection of thepulse from the end of the sensor.
Hokett et al. (+33,) studied water content heterogeneity in the transverse direction to the
TDR sensor by inserting one wire of a two-wiresensor in a dry sand and the other wire in a wet
sand ; the dry and wet sands were separated by῏

12

either an artiﬁcially made air- or water-ﬁlled
crack. They reported that TDR measurement
was signiﬁcantly inﬂuenced by the dry sandand e was underestimated. Air-ﬁlled crack
caused underestimation in e only slightly indry sand but signiﬁcantly in wet sand. The
e#ect of water-ﬁlled cracks was small in both
dry and wet sands.
The main current of the TDR pulse transmits
through the wire of the sensor connected to thecore of the coaxial cable. Intensity of electricalpotential is also higher around this wire thanthe other wire connected to the shield. As aresult, the transverse heterogeneous water distribution in a soil would a#ect TDR-measured edepending on the type of the sensor wire in dry
and wet soils. Hokett et al. (+33,) did not consider this factor in their study.
A heterogeneous soil-water distribution isoften encountered in practice, such as in theroot zone of layered soils, and during inﬁltration and evaporation processes in unsaturated
soils. We decided to further investigate theshape of the TDR-waveforms for various di#erent combinations of water content and thickness of dry and wet soil layers, and compatibility of TDR-support softwares to analyze thesewaveforms. The objectives of this study were :ῌ to investigate the e#ects of a dry soil layer
with di#erent water content and thickness at
the end of a sensor on the TDR waveform, ῍ toevaluate the comparative performance of thesoftware algorithms to identify two reﬂection
points on the waveform, and ῎ to evaluate theresponse of the core and shield wires of a ,-wiresensor for transverse heterogeneous soil-water
distributions and its e#ect on TDR-measured
dielectric constant.
,.

Materials and Method

We conducted ﬁve di#erent experiments
using Tottori dune sand, Japan. The ﬁrst four
experiments were designed to evaluate thee#ect of longitudinal heterogeneity on TDR
measurements : water contents were heterogeneous along the sensor. Fifth experiment was

3*

,**,

for transverse heterogeneity : water contents
were di#erent between two rods of the sensor.
Summaries of these experiments are given in
Tables + and ,. We used TDR sensors of Easy
Test, Ltd., Poland consisting of , wires of *.+ m
in length ; the diameter and spacing between
the wires were + mm and / mm, respectively.
There was an 2 cm epoxy transition between
the wires of the sensor and the coaxial cable tohold the cable and sensor wires ﬁrmly. One
wire of the sensor was connected to the core of
the coaxial cable, and the other wire was connected to the shield of the coaxial cable. TDR
sensors were connected with a Tektronix +/*,
C cable tester of Tektronix Ltd. using a SDMX/* ohm coaxial multiplexer. The TDR waveforms were analyzed with a CR+*X datalogger
with PC,*2W program of the Campbell Scientiﬁc Ltd., and WinTDR33 program of Or et al.
(+333) as well.
A +* cm high acrylic soil column with / cm
inner diameter having a ceramic plate at thebottom was used in the ﬁrst four experiments.
Fig.+ shows water content proﬁles for theseexperiments. The column consisted of several
rings depending on the water content proﬁle.
Expt.+ compared a wet and dry layered column
and a uniform column, both having same average water content (q*.+3/ m- m- ). For Expt.
+.+, the bottom / cm of the column was relatively dry (qdry *.+* m- m- ) and the top / cm was
relatively wet (qwet *.,3 m- m- ). Expt., wasconducted for three di#erent water contents atthe bottom / cm layer (qdry *.*/, *.+/, *.,/
m- m- ) having a same water content (qwet *.,3 m- m- ) at the top / cm layer. Expt.- wasfor di#erent thickness of the bottom dry layer(qdry *.*/ m- m- ) ranging * to / cm below the
wet layer (qwet *.,3 m- m- ). Expt.. was similar to Expt.- but the bottom layer is relatively
wet (qdry *.,, m- m- ). In all experiments, thesoil column was ﬁlled uniformly with an average bulk density of +.00 Mg m- . The wet anddry sands were separated using a thin laboratory ﬁlm to prevent vertical ﬂow. Equally spaced
four TDR sensors were inserted vertically in῎῍ : The e#ect of heterogeneous soil-water distribution on the TDR measurement of soil-water content

13

Table +

Experimental details for the longitudinal heterogeneous water distributions (Expt. +ῌExpt. .)with average gravimetric and TDR-measured dielectric constants (egrav and eTDR ) and soilwater contents (qgrav and qTDR )

Expt.
No.

Measurement
No.

+

Soil layer arrangement
egrav

eTDR

qgrav

qTDR

*4+*
ῌ

342342,

14//
3412

*4+3/
*4+3/

*4+-2
*4+2.

/
/
/

*4*/
*4+/
*4,/

24./
++4-+.401

143,
+*4+2
+.42-

*4+1*
*4,,*
*4,1*

*4+.*
*4+3,
*4,1-

*4,3
*4,3
*4,3
*4,3
*4,3
*4,3

ῌ
+
,
.
/

ῌ
*4*/
*4*/
*4*/
*4*/
*4*/

+04,+
+.4.0
+,41.
++4,*
341+
24.*

+/431
+,4/2
+*42*
34+1
24++
0413

*4,3+
*4,01
*4,.,
*4,+2
*4+3*4+03

*4,3+
*4,-0
*4,*.
*4+1,
*4+/*
*4+,+

*4,3
*4,3
*4,3
*4,3
*4,3
*4,3

ῌ
+
,
.
/

ῌ
*4,,
*4,,
*4,,
*4,,
*4,,

+/410
+/4,/
+.41/
+.4,/
+-410
+-4,2

+/412
+.413
+/4*,
+.4/*
+-4-0
+,432

*4,2/
*4,12
*4,1+
*4,0.
*4,/1
*4,/*

*4,22
*4,1,
*4,10
*4,02
*4,.3
*4,.-

Lwet (cm)

qwet

Ldry (cm)

qdry

+
,

/
+*

*4,3
*4+3/

/
ῌ

,

+
,
-

/
/
/

*4,3
*4,3
*4,3

-

+
,
.
/
0

+*
3
2
1
0
/

.

+
,
.
/
0

+*
3
2
1
0
/

the columns from the soil surface. The TDR
waveforms, ﬁrst derivatives of the waveforms,
e and q were measured for all experiments. An
average of ﬁve measurements was recorded foreach sensor. Note that ﬁve successive measurements of each sensor resulted in almost identical results and, furthermore, there was no remarkable di#erence between these sensors.
We therefore assumed overall averages of four
sensors could represent reliable e and q values.
For the transverse heterogeneity (Expt./), a+* cm long plastic column with +./ cm innerdiameter was partitioned longitudinally into
two approximately equal portions with a thinadhesive tape. The two portions of the column
were ﬁlled with sands of two di#erent watercontents. One TDR sensor was inserted in thiscolumn keeping the core and shield wires in its
two portions. The measurement of e and q was
repeated by interchanging the mutual positions of the two wires of the sensor in thesample. Di#erent sampling volumes of the dry

Fig. +

Soil water content proﬁles for thelongitudinal heterogeneous conditions(Expt. +ῌExpt. .).

and wet sands were also measured by changing the relative position of the sensor from thepartition (No. 3ῌ++ in Table ,). After the measurements, the average water contents in thetwo portions of the column were measured
gravimetrically. We note that we failed todetermine exact water contents of wet and dryΐῐ῎῔῕ῑ ῒ 3* ῏ ῌ,**,῍

14Table ,

Experimental details for the transverse heterogeneous water distributions (Expt. /) with average gravimetric and TDR-measured watercontents (qgrav and (qTDR), and corresponding dielectric constants (qgrav and(qTDR) based on the Topp equation
Arrangementof wires

No.

qgrav

egrav
Core
wire

Shield
wire

qTDR

eTDR

+

*4,1,

+/4.3

wet
dry

dry
wet

*4+2.
*4+-/

+*4*+
14..

,

*4-+1

+241-

wet
dry

dry
wet

*4,.1
*4,+*

+-413
++4.1

-

*4,,.

+,4-0

wet
dry

dry
wet

*4+11
*4+.,

340142,

.

*4+20

+*4+-

wet
dry

dry
wet

*4++/
*4+*1

04/.
04+3

/

*4,--

+,43,

wet
dry

dry
wet

*4+0/
*4+/+

2433
24,0

0

*4++/

04/,

wet
dry

dry
wet

*4+*,
*4*2-

/431
/4+2

1

*4+0*

241+

wet
dry

dry
wet

*4+.+
*4*31

141.
/410

2

*4-**

+14/*

wet
dry

dry
wet

*4,.+
*4,,.

+-4..
+,4-/

3

*4,-2

+-4,,

wet
dry

dry
wet

*4+.,
*4+,+

142*
042,

+*

*4,-2

+-4,,

wet
dry

dry
wet

*4+/+
*4+,2

24,0
14+.

++

*4,-2

+-4,,

wet
dry

dry
wet

*4,,/
*4+22

+,4-1
+*4,.

+,

*4-**

+14/*

wet
air

air
wet

*4+**
*4*03

/423
.40.

sands in Expt./. Total twelve measurements
were carried out for di#erent combinations ofwater contents and sampling volumes. In one
measurement, one of the wires was kept in air(No. +,).
-.

TDR Principle to Measure Soil-Water
Content

TDR cable tester sends a high frequency

Fig. ,A TDR waveform and its ﬁrst derivative in distilled water.

electromagnetic pulse through a coaxial cable
to a sensor. The launched pulse reﬂects backwhen it encounters a change in impedance on
its path of travel. The reﬂected pulses superimpose on the launched pulse and are displayed
as a waveform in time. The horizontal axis
represents the distance from the output pointof the TDR cable tester. The vertical axis
provided the impedance of the TDR pulse. The
shape of the waveform on the horizontal axis
up to the beginning of the sensor wire is thecharacteristic feature of a particular sensor.
The TDR waveform shifts up or down at any
point due to the lower or higher dielectric constant of the surrounding material than for theprevious point (Tektronix, +33*).
Figure , shows a TDR waveform and its ﬁrst
derivative in distilled water. Initial and ﬁnal
points of reﬂection of the launched TDR pulse
from the starting and end points of the sensor,
denoting C (or I) and D in Fig. ,, respectively,
are utilized for the interpretation of dielectric
constant. The dielectric constant of the soil
controls the distance between these points(Lorrain and Corson, +31*). Substantial e#orts
have been made to locate these two points(Baker and Allmaras, +33* ; Heimovaara andBouten, +33* ; Evett, +332 ; Or et al., +333) since
they are not clearly deﬁned on the waveformas can be seen in Fig. ,. Virtually, all TDRsupport softwares identify these points moreor less in a similar way by utilizing the ﬁrst

ῒῑ : The e#ect of heterogeneous soil-water distribution on the TDR measurement of soil-water content

derivative of the waveform. In PC,*2W, anapproximate location of the initial reﬂection isdeﬁned by the electrical length of the cablebetween the cable tester and the sensor, and acorrection factor of the sensor. The point ofinitial reﬂection C is located at the intersectionof a horizontal line passing through the global
maximum of the waveform and a line tangent
drawn to the inﬂection point of the waveform(point E) determined by its lowest ﬁrst derivative (point A). In WinTDR33, the point of initial
reﬂection is deﬁned by the intersection of two
tangent lines, which are drawn at the two inﬂection points on the waveform (points H and E).
H is located at the highest positive peak of theﬁrst derivative (point G) before the ﬁrst peak of
the waveform. The point of initial reﬂection
deﬁned in WinTDR33 (point I) does not di#er
signiﬁcantly from C ; both C and I provide
comparable dielectric constants. The ﬁnal
point of reﬂection D is located in both programs at the intersection of a horizontal line
passing through the global minimum of the
waveform or a regression line through a rangeof points around this minimum and a line tangent drawn at the inﬂection point of the waveform after the minimum (point F). The inﬂection point F is located at the point of thehighest ﬁrst derivative of the waveform after
the global minimum (point B).
The distance between the initial and ﬁnal
points of reﬂections is the apparent length oftravel of the pulse through the sensor La (m).
The average dielectric constant, e, of the surrounding medium is calculated from the electrodynamic relationship as
La ῎,
eῐῌ
ῌ
῍Ls np῏
where Ls is the length of the sensor (*.+ m inthis study), and np is a ratio of the velocity of
the TDR pulse in a medium to that in freespace, which is obtained from TDR setting.
The volumetric soil-water content, q, is related
to e each other by the equations of Topp et al.
(+32*) :15qῐ῍/.-῏+*῍, ῌ,.3,῏+*῍, e῍/./῏+*῍. e,
ῌ..-῏+*῍0 e῍eῐ-.*-ῌ3.-qῌ+.0.*q, ῍10.1q ῎
The gravimetrically measured qgrav agreed
well with the TDR-estimated qTDR based on the
TDR-measured eTDR using Eq.(,) for the Tottoridune sand with an accuracy of ῎*.*, m- m῍- ofsoil-water content. We therefore assumed thatthe dielectric constant based on qgrav using Eq.
(-), denoting egrav , represented a true dielectric
constant for the comparison with the TDRmeasured eTDR .
..

Results and Discussion

Longitudinal Heterogeneity along the
SensorFig. - shows two waveforms for a wet-dry
sand combination (Expt.+.+) and a uniformly
wet sand (Expt.+.,), both having same averagewater content of qῐ*.+3/ m- m῍- . The ﬁrst derivatives of these waveforms are also displayedin this ﬁgure to distinguish the ﬁnal points ofinﬂection on the waveforms. For the uniform
sand, as similar to Fig. ,, the TDR pulse
reﬂected back at the end of the sensor (point A
in Fig.-) resulting in the inﬂection point at B.
In case of the wet-dry sand combination, themajor portion of the TDR pulse reﬂected backand moved up considerably after traveling in.. +Fig. -

TDR waveforms and their ﬁrst derivatives for a wet-dry sand combination
and a uniformly wet sand both having
same average water content of (qῐ*.+3/m- m῍- (Expt. +).

16

Fig. .



TDR waveforms and their ﬁrst derivatives for three di#erent water contents of the bottom dry sand layer, (qdry(Expt. ,).

the wet sand while the remaining portion traveled in the dry sand until it reﬂected back at
the end of the sensor. The approximate reﬂection point at the wet-dry interface is point C in
Fig.-. The ﬁrst inﬂection point of the waveform after the interface was identiﬁed by adistinct positive peak on the ﬁrst derivative at
D. The second reﬂection corresponding to theend of the sensor should be at A since theaverage water content was identical to the uniformly wet sand. Since the reﬂection of thepulse at the end of the sensor was very small,there was no any distinct peak on the ﬁrst
derivative for the inﬂection point. From close
observation of Fig.-, a small upward shift of
the ﬁrst derivative at E might correspond to
the inﬂection point after the reﬂection of theend of the sensor.
The programs drew a tangent line at D for
the wet-dry layers to determine the ﬁnal reﬂection point while point B was used for theuniformly wet sand. This interpretation of the
ﬁnal reﬂection point C in the wet-dry combination underestimated the travel path of thepulse La of Eq.(+), resulting in underestimationof e and q according to Eqs.(+) and (,), respectively. As shown in Table +, qgrav and qTDR for
the wet-dry combination were *.+3/ m- m- and*.+-2 m- m- , respectively. For the uniformly
wet sand, eTDR and qTDR agreed well with egrav

3*

,**,

Fig. /

TDR waveforms for four di#erent
thickness of the dry sand layer, Ldry,with (qdry*.*/ m- m- (Expt. -).

and qgrav , respectively, showing the applicability of Eq.(,) for the Tottori dune sand.
The water content of the bottom dry sandlayer, qdry , was an important factor thatgoverned the performance of the programs.
Fig. . displays waveforms and their ﬁrst derivatives for three di#erent qdry values in Expt.,.
The reﬂected pulse moved up considerably
after major reﬂection at the wet-dry sand interface (A and B) and resulted in waveforms without the reﬂected pulse from the end of thesensor (around C and D) for qdry *.*/ and *.+/
m- m- . Accordingly, the major peak of theﬁrst derivative was found after the reﬂection of
the pulse at the wet-dry sand interface (E and
F). The points G and H showing small upward
shift on the ﬁrst derivative might be the actual
points of inﬂection after ﬁnal reﬂection of thepulse at the end of the sensor. Selection of theinﬂection points at E and F reduced La in Eq.(+),
consequently resulting in underestimation of eand q as similar to Expt.+.+ in Fig. -. Although
the waveform was generated from a part of thesensor within the wet sand, the entire length of
the sensor (*.+ m) was used in calculating e
according to Eq.(+). There still remains scope
to improve the programs for analyzing thistype of irregular-shaped waveforms. One suchpossibility is to use a short-circuited sensor at
the end, which could result in a sharp downward shift of the waveform at the end of thesensor. In case of qdry *.,/ m- m- (Expt.,.-),

῏῎ : The e#ect of heterogeneous soil-water distribution on the TDR measurement of soil-water content

Fig. 0

TDR waveforms for six di#erent
thickness of the dry sand layer, Ldry,with (qdry῍*.,, m- mῌ- (Expt. .).

whereas the waveform did not move up noticeably at the wet-dry sand, it moved up signiﬁcantly after the major reﬂection of the pulse
from the end of the sensor at point I in Fig...
The programs selected the appropriate inﬂection point at J and reasonably estimated e inthis case.
While the reﬂected pulse moved up considerably at the wet-dry sand interface dependingon qdry , thickness of the dry sand layer, Ldry ,had virtually no e#ect on the determination of
the reﬂection point at the end of sensor. For
qdry ῍*.*/ m- mῌ- in Expt.-, the reﬂected TDR
pulse always shifted up considerably at the
wet-dry sand interface before the ﬁnal reﬂection from the end of the sensor regardless of
Ldry values. Fig./ presents four waveforms in
Expt.- where A, B, and C show the approximate
locations of reﬂection of the TDR pulse at the
wet-dry sand interface. As can be viewed fromthe shape of the waveforms, the reﬂection of
the pulse from the end of the sensor could not
be identiﬁed since the major reﬂections
occurred at A, B, and C. As a result, the inﬂection of the waveform at the wet-dry sandinterface, as similar to Expt.,.+ and Expt.,.,, theprograms underestimated e and q.
Fig. 0 shows six waveforms for qdry ῍*.,,m- mῌ- in Expt... The inﬂection of the waveform always occurred after the ﬁnal reﬂection
at the end of the sensor regardless of Ldry
values as it occurred for qdry ῍*.,/ m- mῌ- in

17

Expt.,.-. The dry sand layer at the bottom
could not change the major inﬂection point
regardless of its thickness in this case. The
approximate locations of reﬂection at the wetdry interface occurred at A, B, C, D, and E in
Fig. 0. Since the reﬂected pulse at the wet-dry
interface did not move up considerably, theprograms properly interpreted the waveforms
and accurately estimated e and hence q in Expt.
. for all values of Ldry .
.. ,. Transverse Heterogeneity between Two
Rods of the Sensor
TDR underestimated e in all twelve measurements of Expt./ depending on : (i) the volumeof the dry sands within the sampled volume ofthe sensor, and (ii) whether the core wire or theshield wire of the sensor was in the dry sand.
Table , lists the results of twelve measurements in Expt./. TDR sensor sampled a cylindrical volume of soil with length equal to thelength of the sensor and diameter approximately +.. times the spacing of the wires(Zegellin et al., +323). The sampling volumes ofdry and wet sands were adjusted by changing
the relative position of the sensor from thepartition (Expt./.3ῌ/.++ in Table ,). Underestimation of e and q increased as the sampling dry
sand volume increased.
Because of the low e of dry sand the TDR
pulse traveled faster than in the wet sand(Lorrain and Corson, +31*). The pulse reﬂected
earlier from the wire inserted in the dry sandthan from the wire inserted in the wet sand.
Fig. 1 demonstrates the inﬂuence of two di#erent speeds of the pulse in the core and shieldwires on the waveforms of Expt./.+ (Table ,).
The ﬁnal points of inﬂection (C and D) andhence the ﬁnal points of reﬂection (A and B)
were di#erent for these two waveforms. The
path of travel of the pulse La in Eq.(+) was
shorter when the core wire was in dry sandthan in wet sand. The mutual interchange ofthe two wires of the sensor in the dry and wet
portions of the same sample resulted in two
di#erent e (Table ,). Since intensity of theelectrical potential was much higher around

18

Fig. 1

TDR waveforms and their ﬁrst derivatives for di#erent positions of the two
wires of the sensor in a transverse
heterogeneous water proﬁle (Expt. /.+).

the core wire than around the shield wire
(Zegelin et al., +323), TDR exerted greater
weight around the core wire than around theshield wire. This resulted in higher e when thecore wire was in wet sand than in dry sand.
/.

Conclusions

The TDR-support softwares located the initial and ﬁnal points of reﬂection of the TDR
pulse on the waveform using its ﬁrst derivative
to calculate the dielectric constant, e, based on
the distance between these points. When a dry
sand was at the bottom TDR, waveforms
shifted up to some extent at the wet-dry sandinterface depending on the water content of
the dry layer, qdry . In case of qdry *.*/ and *.+/
m- m- , the early upward shift of the waveform
was much higher. The maximum ﬁrst derivative occurred after the reﬂection of the pulse at
the wet-dry sand interface. The programs
analyzed only part of the waveform that
resulted in underestimation of e and q. For qdry
*.,, m- m- , the magnitude of this upward
shift was insigniﬁcant. The algorithms of the
programs correctly estimated the travel pathof the pulse La in Eq.(+). The major inﬂection
point on the waveform located at the maximum ﬁrst derivative occurred after the ﬁnal
reﬂection of the pulse at the end of the sensor.
Thickness of the bottom dry sand layer,

3*

,**,

Ldry , had no e#ect on the wave analysis. Whenthe bottom layer was relatively wet (qdry *.,,m- m- ), the program algorithms selected theﬁnal inﬂection of the waveform after the pulse
reﬂected back from the end of the sensor regardless of Ldry values providing the correct
measurement of e and q. On the other hand, theinﬂection point was selected just after thepulse reﬂected back at the wet-dry sand interface for all values of Ldry for quite low qdry
(*.*/ m- m- ), resulting in underestimation ine and q.
In case of soil-water heterogeneity in the
direction transverse along the sensor, the TDR
pulse traveled faster through the wire of thesensor inserted in the dry sand than throughthe wire inserted in the wet sand. The earlyreﬂection of the pulse in the dry sand shortened its path of travel and TDR always underestimated e and q regardless of the position of
the two wires of the sensor. The degree ofunderestimation was higher when the corewire of the sensor was in dry sand.
Acknowledgement
The principal author is an Associate Professor of the department of Irrigation and Water
Management of the Bangladesh Agricultural
University (BAU), Mymensinghῌ,,*,. This research was conducted at Saga University using
the funding of Japan Society for Promotion of
Science (JSPS). We sincerely acknowledge the
JSPS and the BAU authorities for their support.
References
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19

content and electrical conductivity of layeredsoil columns. Soil Sci. Soc. Am. J., // : 3-2ῌ3.-.
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