ῐ
J. Jpn. Soc. Soil Phys.
ῑ῏῎ῒΐῐ
No. 3/, p. 0-ῌ1- ῍,**-῎

Estimation of Dry Bulk Density of Soils Using Amplitude
Domain Reﬂectometry Probe
Krissandi WIJAYA, Taku NISHIMURA and Makoto KATO
School of Agriculture, Tokyo University of Agriculture and Technology, -ῌ/ῌ2 Saiwai-cho,
Fuchu-shi, Tokyo +2-ῌ2/*3 Japan
Abstract
It is worthy to know the distribution of soil physical properties in the ﬁeld to gain better
understanding of soil behavior. However, taking undisturbed core samples in situ is usually
laborious and time consuming. In this study, estimation of dry bulk density of soil by using
Amplitude Domain Reﬂectometry (ADR) data was conducted.

The dry bulk density can becalculated by combining volumetric water content measured by using the ADR probe (qADR) witheither wet bulk density or mass wetness. Andisol (TUAT soil) and Alluvial soil (Fukaya soil,
Saitama) was used in this study. Soils were sieved through - mm mesh screen, and packed into aplastic acrylic cylinder of 02 mm in inner diameter and 03 mm long. Mass wetness ranged from .*ῌ
1*ῌ and +/ῌ-*ῌ, and packing dry bulk density ranged from *.-3ῌ*.30 g cmῌ- and *.12ῌ+.-* g cmῌ-,for the TUAT and the Fukaya soil, respectively. Three replicated ADR readings of output voltage
were measured by using a digital multimeter. The qADR was calculated by using a calibrated
polynomial equation, as a function of the averaged output voltage. The results showed that theoutput voltage was not a#ected by neither packing dry bulk density nor mass wetness. The
estimation of dry bulk density with wet bulk density (R, value῍*.323ῌ*.33., RMSE value῍*.*+*ῌ*.*+. g cmῌ-) was better than that with mass wetness (R, value῍*.3+-ῌ*.30+, RMSE value῍*.*,1ῌ
*.*-2 g cmῌ-). The accuracy of the qADR was a critical factor in estimating dry bulk density.
Key words : dry bulk density, ADR, dielectric constant, Andisol, volumetric water content+.

Introduction

Soil behavior generally changes with timeand be di#erent from place to place depending
on physical condition of soil. Many of soil
processes such as physical, chemical, and biological processes are strongly a#ected by theheterogeneity of soil physical properties.
Therefore, understanding of how the soil physical properties distribute in the ﬁeld is very
important for solving soil problems such as
irrigation scheduling, drainage, soil and water
conservation, nutrient transport, and soil andgroundwater contamination.
Dry bulk density of the soil, which can be
expressed as the ratio of the mass of dry solids
to the bulk volume of the soil (Foth, +33* ;Hillel, +332) is one of the most useful soil parameter and a widely used value for predicting
other soil physical properties (Culley, +33-).
According to Campbell (+32/), Miyazaki (+330),
and Zhuang et al. (,***), dry bulk density canbe used to estimate soil permeability, since itstrongly a#ects pore structure, which may
dominate soil hydraulic conductivity. The
gravimetrical method, which involves weighing and drying a sample of known volume
taken from the ﬁeld, has been commonly used
for determination of soil dry bulk density.
However, the method is laborious and timeconsuming. Therefore, the use of the alternative technique, which is simple and fast formeasuring soil dry bulk density, is needed.
Dielectric constant techniques for estimating῏  3/

64

volumetric water content of soil such as Capacitance Insertion Probe (CIP), Time Domain
Reﬂectometry (TDR) probe, and Amplitude
Domain Reﬂectometry (ADR) probe are becoming popular (Topp et al., +32* ; Gaskin andMiller, +330 ; Inoue, +332 a, +332 b ; Robinson etal., +333). These techniques depend on the factthat the dielectric constant of water (2*) is
signiﬁcantly greater than that of most soil
matrix materials (.) and of air (+). Although the CIP, TDR and ADR probe have asimilar performance (Nakashima et al., +332),
the ADR and the TDR probe are easier to install and facilitate the accumulation of data
than the CIP, which requires the permanent
installation access tubes and operator intervention to position of the sensing head withinthese tubes (Gaskin and Miller, +330). Some
problems in the data interpretation and theﬁeld calibration may be obscured by inhomogeneities around probe wire such as
voids and stones, and confused by conductivity e#ect (Whalley, +33-). Furthermore, theTDR probe and the CIP have some disadvantages of high cost and their complex automatic
measuring system (Nakashima et al. +332). On
the other hand, the ADR probe is relatively
cheap and the output is direct current voltage,
which can be measured by commercial multichannel logger to monitor change in water content (Gaskin and Miller, +330). The ADR probe
has been developed to solve the problems of
the CIP and TDR probe (Nakashima et al., +332).
The objective of this study was to apply the
ADR technique for estimation of the dry bulk
density of disturbed soils.

Fig. +,**-,.

Materials and Methods,. + ADR Probe Components
According to Miller and Gaskin (+330), there
are three major components of the ADR probe
including an input and output cable, probe
body, and a sensing head (Fig. +). The cableprovides connection for a suitable power
supply (/ῌ+/ volt) and for an analogue signal
output. The probe body contains an oscillator,
a specially designed internal transmissions line
and measuring circuitry within a waterproof
housing. The sensing head has an array of fourelectrodes of 0* mm in length and - mm in diameter with a radial spacing of +/ mm, theouter three of which connected to instrument
ground from an electrical shield around thecentral (signal) electrode.
Principally, the ADR probe applies a +** MHz
sinusoidal signal via a specially designed internal transmission line to a sensing array of fourelectrodes whose impedance depends on dielectric constant of water content of the soil into
which it is embedded. If this impedance di#ers
from that of the internal transmission line,
then a proportion of the signal is reﬂected backfrom the junction (J), which lies between thesensing array and the transmission line. This
reﬂected component interferes with the incident signal causing a voltage standing wave to
be set up on the transmission line, i.e. a variation of voltage amplitude along the length ofthe line. Once the amplitude is measured, therelative impedance of the probe and then the
dielectric constant will be known. Hence, thevolumetric water content of the soil matrix canbe obtained.

A schematic diagram of the ADR probe.

ΐῒ : Estimation of Dry Bulk Density of Soils Using Amplitude Domain Reﬂectometry Probe,. , Soil Materials
Two soils such as Andisol (TUAT soil) andAlluvial soil (Fukaya soil) were used in thisstudy. The soils were sieved through a - mmmesh screen. A half of the soils were kept inplastic bag to keep mass wetness of //ῌ and,1ῌ, and the remaining soils were air-dried
until mass wetness of .*ῌ and +0ῌ, for the
TUAT and the Fukaya soil, respectively. Physical properties of the soils including texture,mass wetness (ῌ), dry bulk density (g cm῎-),volumetric water content (cm- cm῎-) and clay
mineral (X ray di#raction) are summarized inTable +.
,. - Experimental Methods
To cover the range of soil mass wetness between .*῎1*ῌ for the TUAT soil and +/῎-*ῌ
for the Fukaya soil, the air-dried sieved soils
were moistened with spraying distilled waterfor four to six times. Each moistened sample
was packed into a plastic acrylic cylinder of 02
mm in inner diameter and 03 mm long as uniformly as possible by manually increasing theincrements of a few centimeter thickness of thesoil to the cylinder up to the full volume. The
sample was then weighted by using an electricbalance to obtain wet bulk density.
The ADR probe was vertically inserted into
the sample (Fig. ,). The ADR reading of output
voltage was then measured by using a digital
multimeter. Three replicated ADR readings
were taken by re-installing the ADR probe vertically into an undisturbed part of the cylinder
and then averaged. After the ADR operation, aTable +
Soil parameters

sub-sample was taken and oven-dried to determine mass wetness. Measured volumetricwater content and dry bulk density were calculated from the mass wetness and the wet bulk
density.
The whole procedure was repeated for packing dry bulk density ranged from *.-3῎*.30 g
cm῎- and *.12῎+.-* g cm῎- for the TUAT and the
Fukaya soil, respectively. The ADR measurement was also applied on the oven-driedsamples whose volumetric water content wasconsidered to be zero. To prevent the excess
evaporation from the samples during the procedure, the experiment was done inside a smallchamber covered with a plastic ﬁlm.
,. . Estimation of Dry Bulk Density by
Using ADR Probe Data
For the estimation purpose, dry bulk density
can be calculated as function of volumetricwater content measured by using the ADR
probe (qADR) combined with either wet bulk
density (Eq. (+)) or mass wetness (Eq. (,)).
rbest+ῐrt῎ῌqADR῏rw῍ῌrbest,ῐῌ+**῏qADRῌw῍῏rw
῍
where, rbest+ is the estimated dry bulk densitywith wet bulk density (g cm῎-), rbest, is theestimated dry bulk density with mass wetness(g cm῎-), rt is the wet bulk density (g cm῎-), rw is
the density of water (ῐ+ g cm῎-), qADR is thevolumetric water content measured by using
the ADR probe (cm- cm῎-), and w is the mass
wetness (ῌ). Especially, Eq. (,) was multipliedwith +** to convert the mass wetness by percentage to that by decimal form.

Soil physical properties
Andisol soil (TUAT soil)

Alluvial soil (Fukaya soil)

sand : silt : clayῐ*4-,* :*4-,. : *4-/0 (LiC)sand : silt : clayῐ*4.0* :*4-,* : *4,,* (CL)

.*῎1*

+/῎-*

*4-3῎*430*412῎+4-*

Volumetric water content, q (cm cm )*4,,῎*40.

*4+0῎*4-/

Clay mineral (by X ray di#raction)

amorphousKrῑVrῑMi, Sm

῎+

Texture (kg kg )Mass wetness, w (ῌ)῎-

Dry bulk density, rb (g cm )
-

῎-

65

  3/

66

The use of either Eq. (+) or (,) in estimating
dry bulk density from the volumetric watercontent measured by using the ADR probe(qADR) gives some advantages especially when it
is applied to the ﬁeld measurement. For example, to obtain the estimated dry bulk density byusing Eq. (+) needs only the information of thewet mass (weight) of the soil occupying the
known volume of the core sample, and it is notnecessary to spend a day for oven drying thesample. It helps us to perform easy and fastestimation of ﬁeld dry bulk density, especiallywhen the large numbers of data are required.

,**-

Furthermore, although obtaining the mass
wetness data spends more time than the wetbulk density because of the need to ovendrying the sub-sample, incorporating the mass
wetness to Eq. (,) is still reasonable. For example, when the estimation of the dry bulk density is applied on taking larger numbers of ﬁeld
data, the mass wetness can be obtained byoven drying the only a small fraction of disturbed sample, so that it is capable to performnumber of estimation with less labor.
-.

Results and Discussions

Relationship between Volumetric Water
Content and Output Voltage
The calibration curve of the volumetricwater content and the output voltage for the
TUAT soil shows increase in output voltage
with increasing in volumetric water content(Fig. -). The output voltage ranged from *.+0ῌ
*.33 volt corresponded to volumetric soil watercontent of *.,,ῌ*.0. cm- cm-. The relationshipbetween output voltage and volumetric watercontent can be expressed in Eq. (-) with regression coe$cient (R,) value of *.32.,-. +Fig. ,

Schematic diagram of the experiment.

Fig. - (a)Relationship between volumetricwater content and ADR output
voltage for the TUAT soil, in caseof packing dry bulk density.

Fig. - (b)Relationship between volumetricwater content and ADR output
voltage for the TUAT soil, in caseof mass wetness.

ῐ῏ : Estimation of Dry Bulk Density of Soils Using Amplitude Domain Reﬂectometry ProbeqADR῎*.**+++ῌ+./-+v῍,.-.,v,ῌ+...2vῌ
where, v is the output voltage of the ADR
probe. Mathematical expression shown in Eq.
(-), (.), (0) and (1) are the third polynomial equations which were accomplished by applying
least square method.
Increasing the output voltage with the increasing in volumetric water content was also
found in the Fukaya soil (Fig. .). The soil withvolumetric water content ranged from *.+0῎*.-/
cm- cm῍- corresponded to the output voltage of*.,,῎*.20 volt, and the relationship between
output voltage and volumetric water content
can be expressed in Eq. (.) with R, value of*.32+.
qADR῎*.**--/ῌ*.30.v῍+./-*v,ῌ+.*-2v῍The q-v curve shown in Fig. - and . contains
two cases such as either packing dry bulk density or mass wetness as a parameter. Each caseis divided into three data intervals. For the
TUAT soil, the packing dry bulk density
ranged from *.-3῎*./2, *./2῎*.11, and *.11῎*.30 g
cm῍- and the mass wetness ranged from .*῎/*,

Fig. . (a)Relationship between volumetricwater content and ADR output
voltage for the Fukaya soil, incase of packing dry bulk density.

67/*῎0*, and 0*῎1*ῌ, respectively. For Fukayasoil, the packing dry bulk density ranged from*.12῎*.3/, *.3/῎+.+-, and +.+-῎+.-* g cm῍- and themass wetness ranged from +/῎,*, ,*῎,/, and ,/῎-*ῌ, respectively. Although dry bulk densityof the TUAT soil was smaller than that of the
Fukaya soil, the TUAT soil had greater mass
wetness. It was due to micro structure of the
TUAT soil (Light Clay) was more complicatedthan the Fukaya soil (Clay Loam). As a consequence, the TUAT soil was capable to retain
more water per unit weight of the soil than the
Fukaya soil.
The division of the packing dry bulk density
and the mass wetness into three data intervals
was aimed to clarify the dependence of theoutput voltage against the two parameters. As
shown in Fig. - and ., the plotted data overlapped through the regression line withinthose three data intervals. It suggested thatthe output voltage was not a#ected by neither
packing dry bulk density nor mass wetness.
The root mean square error (RMSE) value between the measured q and the qADR of whole
data with di#erent packing dry bulk density

Fig. . (b)Relationship between volumetricwater content and ADR output
voltage for the Fukaya soil, incase of mass wetness.

68



and mass wetness was *.*+. cm- cm- and *.**2
cm- cm- for the TUAT and the Fukaya soil,
respectively.
It revealed that the qADR
signiﬁcantly depended on the type of soil. The
independence of the qADR on either packing dry
bulk density or mass wetness was also clariﬁedby the RMSE value of each interval of theparameters. In case of the TUAT soil, theRMSE value for packing dry bulk density
ranged from *.-3῎*./2, *./2῎*.11, and *.11῎*.30 g
cm- was *.*+., *.*+-, and *.*+0 cm- cm-, whilethat for mass wetness ranged from .*῎/*, /*῎0*,
and 0*῎1*῍ was *.*+/, *.*+,, and *.*+1 cm- cm-,respectively.
Furthermore, in case of the
Fukaya soil, the RMSE value was *.**1, *.**2,
and *.*+* cm- cm- for packing dry bulk density ranged from *.12῎*.3/, *.3/῎+.+-, and +.+-῎+.-*g cm-, and *.*+,, *.**0, and *.**3 cm- cm- formass wetness ranged from +/῎,*, ,*῎,/, and ,/῎-*῍, respectively.
-. , Relationship between Volumetric Water
Content and Dielectric ConstantMiller and Gaskin (+330) found that in therange of output voltage of *῎+ volt, the relationship between the ADR reading of output voltage and the square root dielectric constant canbe precisely described by the third polynomial
equation, as shown in Eq. (/). In this study, theequation was employed for the TUAT and the
Fukaya soil.
ῌe+.*10..*v0..*v,..1*vῌ
where, ῌe is the square root dielectric constant.
Since the volumetric soil water content was
the primary factor a#ecting the apparent dielectric constant, increasing volumetric watercontent resulted in the increase of the dielectric
constant (e), as shown in Fig. / and 0. For the
TUAT soil (Fig. /), in the range of the dielectric
constant of .῎-,, which corresponded to thevolumetric water content of *.,,῎*.0. cm- cm-,the relationship can be expressed in Eq. (0).
qADR*.+3/*.*,0/e*.***32.e,*.****+2-e*.,1/e+*.**0,/e,῍The dielectric constant of the Fukaya soil
ranged from /῎,. corresponded to the volumet-

3/

,**-

ric water content of *.+0῎*.-/ cm- cm-, asshown in Fig. 0. The following Eq. (1) expressed the relationship between volumetricwater content and dielectric constant for the
Fukaya soil.

Fig. /

Relationship between volumetric watercontent and dielectric constant of the
TUAT soil.

Fig. 0Relationship between volumetric watercontent and dielectric constant of the
Fukaya soil.

ῐ῏ : Estimation of Dry Bulk Density of Soils Using Amplitude Domain Reﬂectometry ProbeqADR῎*.*31.ῌ*.*+,3e῍*.****3+0e,ῌ*.*1..e῍+
῍*.,0/e῍,ῌTopp et al. (+32*) presented the “universal
calibration formula” for measuring volumetricwater content based on dielectric constant ofmany (common) soils in all over the world, as
shown in Eq (2).
q῎῍*.*/-ῌ*.*,3,e῍*.***//e,ῌ*.*****.-e῍Comparison between the Topp’s universal
equation and the equations derived from theq-v calibration of the two Japanese soils in thisstudy showed that the dielectric constant of
the TUAT soil was signiﬁcantly greater thanthat of the Topp’s soils, while for the Fukayasoil, it was rather similar to the data presented
by Topp et al. (+32*) and was higher only whenvolumetric water content was *῎*., cm- cm῍-.
It suggested that the universal equation was
not always applicable for measuring volumetric water content of the soils such as the TUAT
soil. For the Fukaya soil, Topp’s equation was
rather acceptable especially for volumetricwater content ranged from *.,/῎*.-- cm- cm῍-.
These trends were similar to the results presented by Miyamoto and Chikushi (,***). Also,
Fig. / and 0 revealed that dielectric constant
was strongly a#ected by the type of soil.
-. - Comparison between Estimated andMeasured Dry Bulk Density
Since the estimated dry bulk density (rbest)
was calculated by substituting the qADR dataobtained from Eq. (-) and (.) into Eq. (+) and (,),
the accuracy of the rbest was strongly a#ectedby the accuracy of the qADR data. In case of the
TUAT soil, the accuracy of the rbest can be
determined from the comparison between therbest and the measured dry bulk density (rbmsr)
shown in Fig. 1. The ﬁgure describes that the
rbest agreed well with the rbmsr. The cloud of thedata points was laid and concentrated aroundthe + : + regression line. The R, value for thedata estimated by using Eq. (+) and (,) were*.323 and *.30+, respectively. It revealed thatthe estimation of dry bulk density with wet
bulk density had greater accuracy than that69

with mass wetness. The greater the accuracyof the rbest, the lower the error of the rbest. In thisstudy, the error is expressed in the RMSE value
between the rbmsr and the rbest. For whole data,
the RMSE value of the rbest by using Eq. (+) was
generally a half of that by using Eq. (,) such as*.*+. g cm῍- and *.*,1 g cm῍-, respectively. The
RMSE value within the given ranges of packing dry bulk density and mass wetness were
ﬂuctuated. In the range of packing dry bulk
density of *.-3῎*./2, *./2῎*.11, and *.11῎*.30 g
cm῍-, the RMSE value of the rbest by using Eq.
(+) was *.*+., *.*+-, and *.*+0 g cm῍-, and that byusing Eq. (,) was *.*,., *.*,1, and *.*,3 g cm῍-,
respectively. In the range of mass wetness of.*῎/*, /*῎0*, and 0*῎1*ῌ, the RMSE value ofthe rbest by using Eq. (+) was *.*+/, *.*+,, and*.*+1 g cm῍-, and that by using Eq. (,) was *.*-.,*.*,,, and *.*,/ g cm῍-, respectively. As can beseen from Fig. 3, the ﬂuctuation of the RMSE
value of the rbest by using Eq. (+) was
signiﬁcantly smaller and not di#erent enoughfrom the value of whole data compared to thatof the rbest by using Eq. (,). The RMSE of therbest by using Eq. (,) was more sensitive to thechange of mass wetness from the lower to theFig. 1Comparison between estimated andmeasured dry bulk density of the
TUAT soil.

  3/70

higher mass wetness than that by using Eq. (+).
Therefore, the use of Eq. (,) in the estimation ofdry bulk density became less reliable than thatof Eq. (+) although the RMSE value of the rbest
by using that equation was still acceptable.
Fig. 2 shows the comparison between the rbest
and the rbmsr, for the Fukaya soil. The rbest of the
Fukaya soil also agreed well with the rbmsr. The
data of rbest by using Eq. (+) and rbest by using
Eq. (,), which were plotted around the + : +regression line showed the R, value of *.33. and*.3+-, respectively. It suggested that similar to
the TUAT soil the estimation of dry bulk density with wet bulk density was better than thatwith mass wetness. For whole data, the RMSE
value of the rbest by using Eq. (+) was lower thanthat by using Eq. (,), such as *.*+* g cm- and*.*-2 g cm-, respectively. The RMSE value
within the ranges of packing dry bulk densityof *.12ῌ*.3/, *.3/ῌ+.+-, and +.+-ῌ+.-* g cm- was
ﬂuctuated such as *.*+,, *.**3, and *.*+* g cmfor the rbest by using Eq. (+), and *.*-*, *.*-/, and*.*.2 g cm- for the rbest by using Eq. (,), respectively. The RMSE value within the ranges ofmass wetness of +/ῌ,*, ,*ῌ,/, and ,*ῌ-*ῌ wasFig. 3,**-also ﬂuctuated such as *.*+,, *.**1 and *.*++ gcm- for the rbest by using Eq. (+), and *.*01,*.*,/, and *.*-- g cm- for the rbest by using Eq.
(,), respectively. As can be seen from Fig. +*,Fig. 2Comparison between estimated andmeasured dry bulk density of the
Fukaya soil.

Error of the estimated dry bulk density by either Eq. (+) or (,), for the TUAT soil.

῍ῌ : Estimation of Dry Bulk Density of Soils Using Amplitude Domain Reﬂectometry Probe

Fig. +*

71

Error of the estimated dry bulk density by either Eq. (+) or (,), for the Fukaya soil.

ﬂuctuation of the RMSE value occurred in therbest by using Eq. (,), and it was slightly in therbest by using Eq. (+). The change of mass wetness from the lower to the higher mass wetness
caused the greater RMSE value of the rbest byusing Eq. (,) and had small e#ect on the RMSE
value of the rbest by using Eq. (+). Therefore, Eq.
(+) seems to give better estimation of the dry
bulk density than Eq. (,) although the RMSE
value resulted from the rbest by Eq. (,) was
considered reasonable. Furthermore, small
ﬂuctuation of the RMSE value of the rbest ofeither the TUAT or the Fukaya soil suggested
that the dry bulk density estimated by using
the ADR data and either wet bulk density or
mass wetness was independent on mass wetness of the soil. The di#erence in the RMSE
value of the rbest between the TUAT and the
Fukaya soil revealed that the type of soil had
also signiﬁcant e#ect on the accuracy of therbest.
Incorporating the wet bulk density into theestimation of dry bulk density was more reasonable than incorporating the mass wetness.
Di#erence in mathematical formula between

Eq. (+) and (,), into which the wet bulk density
or the mass wetness was substituted, may be areason of the result above. In this calculation,
since the rbmsr, rt and w value, which employ the
wet and the dry soil mass of a given core
volume, was carefully obtained throughgravimetrically measurement, their errors was
assumed to be very small and could be
neglected. It was also assumed that the signiﬁcant error resulted from the qADR measurement.
As Eq. (,) was mathematically formulated in adivision formula, so that when the qADR including the errors were substituted into the equation, the errors of rbest may increase since themass wetness (w) in the Eq. (+*) was always lessthan unity. Thus, this error may enhance withdecreasing in mass wetness. On the other
hand, when the qADR data was substituted into
the Eq. (+), which was known as a subtracting
formula, the error of rbest shown in Eq. (3) was
lower compared to when it was substituted
into Eq. (,).
Derivation of Eq. (+)

72rbest+ῌrbmsrrbest+ῌ
ῌrbmsrrtqADRrwῌ
ῌrbmsrrtqmsrqADRrwῌ
ῌrbmsrrtqmsrrwqADRrwῌ
ῌrbmsrrbmsrqADRrwῌ
ῌrbmsrrbmsrqADRrwῌ
ῌqADRrwῌ
qADRrw
ῌ
Derivation of Eq. (,)
rbest,ῌrbmsrrbest,ῌ
ῌrbmsr+**qADRῌwrwῌ
ῌr bmsr +**q msr qADR ῌ wrwῌ
ῌr bmsr +**q msr ῌ wrw +**qADRῌwrwῌ
ῌr bmsr rbmsr +**q ADR ῌ w
rwῌ
ῌrbmsrrbmsr+**qADRῌwrwῌῌ+**qADRῌwrwῌ
+**qADRῌwrw
῎
῍
where, rbmsr is the dry bulk density measured
gravimetrically ; qmsr is the volumetric watercontent measured gravimetrically ; rbest+ isthe error of rbest+ ; rbest, is the error of rbest, ; qADR is the error of the qADR to the true q.
In this study, since the qADR data originallycontained some extents of errors calculating
the qADR involved combination of the qmsr andthe qADR (qADRqmsrqADR). This error wasconsidered as a primarily factors a#ecting theaccuracy of rbest, especially rbest,. For example, if
the qADR for a given soil with w ranged from.*῏1*῍ (TUAT soil) is *.+ cm- cm-, thereforethe rbest+ is *.+rw, and rbest, is ranged from*.+. (+***.+/1*) rw*.,/(+***.+/.*)rw.
The phenomena indicated that the error of estimated dry bulk density with mass wetness
was higher than that with wet bulk density,
especially for the lower mass wetness (Fig. 3
and +*).
..

Conclusions

The output voltage using the ADR probe
was not a#ected by neither packing dry bulk
density nor mass wetness. In other word, the q
ADR was independent upon these two parame- 3/  ,**-

ters. Therefore, the ADR data can be used for
estimation of dry bulk density.
The estimation of dry bulk density with wet
bulk density was better than that with mass
wetness. The lower accuracy of the rbest withmass wetness was a#ected by the division formula of calculation process.
Since the rbest was determined from the qADR,
therefore the accuracy of the qADR was a criticalfactor in estimating dry bulk density.
Acknowledgement
Part of this study was supported by Grantsin-Aid for Scientiﬁc Research by Japan Societyof the Promotion of Science : No. ,**+῏+-10*+03.
References
Campbell, G.S. (+32/) : Soil physics with basic :Transport models for soil-plant system, pp. .3῏/3, Elsevier, Amsterdam, Netherland.
Culley, J.L.B. (+33-) : Density and compressibility
in Soil sampling and method of analysis (Carter,
M.R., Ed.), pp. /,3῏0-*, Lewis Publisher, New
York, USA.
Foth, H.D. (+33*) : Fundamentals of soil science (2thedition), pp. +,῏-., John Wiley & Sons, Inc.,
Boca Raton, USA.
Gaskin, G.J., and Miller J.D. (+330) : Measurementof soil water content using simpliﬁed impedance measuring technique, J. Agric. Eng. Res.,
0- : +/-῏+0*.
Hillel, D. (+332) : Environmental soil physics, pp. -῏+1, Academic Press, San Diego, USA.
Inoue, M. (+332 a) : Evaluation of measuring precision of ﬁeld-type dielectric soil moistureprobes using salty sand, J. Japan Soc. Hydrol.
& Water Resour., ++ : ///῏/0..
Inoue, M. (+332 b) : Monitoring system for ﬂow andsolute transport, Sand Dune Research, ./ (+) :+/῏,/.
Miller, J.D. and Gaskin G.J. (+330) : Theta probe ML,x : Principle of operation and applications (,nd edition), Macaulay Land Use Research Institute (MLURI), Aberdeen, UK.
Miyamoto, T. and Chikushi, J. (,***) : Relations between soil water content and apparent dielectric constant evaluated by dielectric mixing
models, Trans. of Japan Society of Irrigation,
Drainage and Reclamation Engineering, ,*0 :0-῏1+.
Miyazaki, T. (+330) : Bulk density dependence of air

|} : Estimation of Dry Bulk Density of Soils Using Amplitude Domain Reﬂectometry Probe

entry suctions and saturated hydraulic conductivities of soils, Soil Science, +0+ : .2.ῌ.3*.
Nakashima, M., Inoue, M., Sawada, K. and Nicholl,
C. (+332) : Measurement of soil water content
by Amplitude Domain Reﬂectometry Method
and its calibrations, J. of Groundwater Hydrology, .* : /*3ῌ/+3.
Robinson, D.A., Gardner, C.M.K. and Cooper, J.D.
(+333) : Measurement of relative permitivity insandy soils using TDR, Capacitance and Theta
Probe : Comparison, including the e#ects ofbulk soil electrical conductivity, J. of Hydrology, ,,- : +32ῌ,++.

Topp, G.C., Davis, J.L. and Annan, A.P. (+32*) : Electromagnetic determination of soil water content : Measurement in coaxial transmission
lines, Water Resour. Res., +0 : /1.ῌ/2,.
Whalley, W.R. (+33-) : Considerations on the use oftime-domain reﬂectometry (TDR) for measuring soil water content, J. of Soil Science, .. : +ῌ3.
Zhuang, J., Yu, G.R., Miyazaki, T. and Nakayama,
K. (,***) : Modeling e#ect of compaction on
soil hydraulic properties : A NSMC scaling
method for saturated hydraulic conductivity,
Adv. in GeoEcology, -, : +..ῌ+/-.





 

ῌ 

ῌ




73



ADR  !"#$%&"'()*+,%-./0()*123+,/45"6 78
9volt:6 ;<=>?3@=ABCD$'E FGHA+,I Topp 9+32*: AJK>LM%N;<=ῌOPQ"'E R-/6 ADR STU"'?3@=>V/WX6 YZ/TU[\%]^_`6 @a5Fbcd_`AeUfg'E FGHA+,/hFbI6 eU"'cd_`L6 ijk
STU"'l/m"b6 nBCo R,p*.3+-q*.33. SrFnBQ"'E cd_`AeUlL6 ADR /sN?3@=>]^_`5F'>t/surFJKQ"'E
 : cd_`6 ;<=6 ADR6 ()*+,6 ?3@=vwxyz : ,**- x + y ,+ zv{xyz : ,**- x 3 y +3 z