ῐ
J. Jpn. Soc. Soil Phys.
ῑ῏῎ῒΐῐ
No. 31, p. -ῌ+, ῍,**.῎Field Estimation of Soil Dry Bulk Density Using Amplitude
Domain Reﬂectometry Data
Krissandi WIJAYA*, Taku NISHIMURA*, Makoto KATO* and Masanobu NAKAGAWA*** Tokyo University of Agriculture and Technology, -ῌ/ῌ2 Saiwai-cho, Fuchu, Tokyo+2-ῌ2/*3, Japan** Ryokusei Kenkyusho Inc., ,ῌ.*ῌ+* Kojima, Chofu, Tokyo +2,ῌ**,0, Japan
Abstract
Since permeability of ﬁeld soils is strongly a#ected by dry bulk density, knowledge of spatial
distribution of dry bulk density is beneﬁcial to predict water and chemical transport throughsoils.

In this study, ﬁeld soil dry bulk density was estimated by using Amplitude Domain

Reﬂectometry (ADR) data. The experiment was sited at the Sakae-cho experimental ﬁeld ofTokyo University of Agriculture and Technology (TUAT) covered by Andisol soil. The ﬁeld of .
ῌ. m in large was divided into 2+ small plots of *./ῌ*./ m each. The ADR probe was operated inevery small plot, and the ADR output voltage was measured by using digital voltmeter. Soilsamples were taken by using the steel ring of +** cm- in volume. The results showed that theestimated dry bulk density agreed well with the measured dry bulk density. The regression
coe$cient (R,) ranged from *.. to *.1. Dry bulk density estimated by using the ADR data and wet
bulk density (R,῍*./ῌ*.1) had greater accuracy than that by using the ADR data and mass wetness(R,῍*..ῌ*.0). Furthermore, spatial variability, which was expressed by semivariogram, of themeasured and the estimated dry bulk density by using the ADR data and wet bulk density agreed
well. However, spatial variability of the dry bulk density estimated by using the ADR data andmass wetness showed di#erent trend to others.

This indicated that the estimated dry bulk

density with wet bulk density had better performance to predict dry bulk density than that withmass wetness.
Key words : Dry bulk density, ADR, Andisol, Spatial variability, Semivariogram+.

Introduction

Field soil physical properties are quite variable, both in vertical and horizontal directions.
Beside, these properties also vary with time.
Since soil physical properties play a central
role in transport and reaction of water, solutes,
and gases in soils, knowledge of spatial variability of soil physical properties is very important for understanding transport phenomena
in soils, hence, for soil conservation and planning appropriate agricultural practices. Morespeciﬁcally, knowing ﬁeld soil dry bulk density
would help in scaling other important soil
physical properties, i.e., predicting soil permea-

bility as a function of dry bulk density byusing non-similar media concept (NSMC)
method (Miyazaki, +330). The soil permeability
data can be used to determine the better K
factor of Universal Soil Loss Equation (USLE)(Wischmeier and Smith, +312). However, measurement of the ﬁeld-spatially-distributed soil
parameters tends to be di$cult and complicated, such as time consuming, laborious and expensive (Zorita et al., ,**+). Therefore, the useof a proper method to measure ﬁeld soil physical properties with low cost, simple and quick
method is required.
Amplitude Domain Reﬂectometry (ADR)
probe is one of the methods for measuring῏

4

Table +
Soil parameters
Texture (kg kg+) : sand
silt
clay

31

,**.

Soil physical properties
First ﬁeld experiment(Sakae-cho soil)*4,3 ῌ
*4-1 ῍ Light Clay (LiC)*4-. ῎Mass wetness, w (ῌ)
Dry bulk density, rb (g cm-)Volumetric water content, q (cm- cm-)volumetric soil water content based on measurement of dielectric constant of the soil
(Gaskin and Miller, +330 ; Robinson et al., +333 ;Inoue, +332a, +332b ; Nakashima et al., +332).
The ADR probe has a similar performance toother permittivity methods, such as Capacitance Insertion Probe (CIP) and Time Domain
Reﬂectometry (TDR) probe (Miller and Gaskin,+330 ; Nakashima et al., +332). However, theADR probe has advantages over the latterprobes, and it is relatively cheaper and simpler
automatic measuring system compared to the
CIP and the TDR (Nakashima et al., +332). In
other word, since the ADR output is direct
current voltage, it can be simply connected tothe commercial multi-channel logger to monitor changes in soil water content. Practically,
the ADR probe was successfully applied to a
project, which tries to investigate the impact ofland use changes on catchments behavior, speciﬁcally hydrology and hydrochemistry (Miller
and Gaskin, +330).
In recent decades, special attention has been
focused on ﬁeld spatial variability of soil physical properties. Geostatistics, which involves
the theory of regionalized variable, is being
extensively used to characterize the structureof these variabilities (Tominaga et al., ,**,).
The regionalized variable is a property such as
soil moisture content, dry bulk density, hy
draulic conductivity, etc., which can be sampled. Accordingly, the properties (or samples)taken at close spacing will be similar or
spatially correlated, while the properties fromlarge sample spacing will be dissimilar or0*῏3*4.3῏*400*4-/῏*4/,

Second ﬁeld experiment(Sakae-cho soil)*4,3 ῌ
*4-1 ῍ Light Clay (LiC)*4-. ῎
0*῏22*4.3῏*402*4-0῏*4/,

spatially uncorrelated (Isaaks and Srivastava,+323). The phenomena above can be clearlyclariﬁed by using semivariogram as one of themost common geostatistics tools, which canquantify the spatial dependence and spatial
structure based on distance of separation anddirection (Scot, ,***), and, in turn, it is essential
to design of optimal sampling grids and interpolation methods (Isaaks and Srivastava, +323).
Objective of this presenting study was toestimate the ﬁeld soil dry bulk density byusing the ADR data.
,.

Materials and Methods,. + Soil Materials
The ﬁeld experiment was located at the
Sakae-cho experimental ﬁeld of Tokyo University of Agriculture and Technology (TUAT),
Japan. The Andisol ﬁeld of .. m in large wasdivided into 2+ small plots (3 rows and 3 columns) with *./*./ m each. The physical properties of the soil are shown in Table +.
,. , Experimental Procedures
The ﬁeld experiment was conducted twotimes, such as in July ,*** (ﬁrst ﬁeld experiment) and December ,*** (second ﬁeld experiment). In each experiment, core samples andthe ADR data were collected from every small
plot. Soil core samples were taken by using thesteel ring of +** cm- in volume. The ADR data
were collected by embedding the ADR probe of
0* mm in length into the ﬁeld soil and the ADR
output voltage was measured by using digital
voltmeter. The embedding of the ADR probe
was replicated three times surrounding the soilῒῑ : Field Estimation of Soil Dry Bulk Density Using Amplitude Domain Reﬂectometry Data

core sample location and averaged. To stabilize the ADR output signals, the embedding the
ADR probe was kept for ,* to -* seconds. Since
the ﬁeld contains 2+ small plots, the amounts ofsamples were totally 2+ soil core samples and2+ the ADR data for each experiment. All soilcore samples were brought to the laboratory
and several soil parameters such as mass wetness, wet bulk density, dry bulk density, andvolumetric water content were measured byusing gravimetric method.
In addition, the ﬁrst ﬁeld experiment was
conducted on ﬁeld soil having dry layer at thesurface. However, it was expected that thepresence of surface dry layer might enhanceheterogeneity in soil moisture distribution
within the ﬁeld proﬁle, which a#ects the ADR
performance (Wijaya et al., ,**,). To improve
the ADR performance, therefore, in the secondﬁeld experiment, the surface dry layer of a cm
in thickness by observation was removed prior
to the ADR measurement and the soil coresampling. Such treatment resulted in relatively less heterogeneity in moisture content distribution within the ﬁeld proﬁle.
,. - Calculation of Dry Bulk Density withADR Data
Dry bulk density can be calculated as function of volumetric water content measured byusing the ADR probe (qADR) combined witheither wet bulk density (Eq. (+)) or mass wetness (Eq. (,)),
rbest +ῐrt῏ῌqADRῌrw῍
qADR῏
rbest ,ῐ῍+**
ῌrw
῎
w ῐ

ῌ
῍

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῏-), w is the mass wetness (ῑ). Eq. (,) is multiplied with +** to convert the mass wetness by percentage to that bydecimal form.

5

Application of the ADR method, which involves the use of either Eq. (+) or (,), in estimating dry bulk density from volumetric watercontent measured by using the ADR probe(qADR) o#ers more beneﬁts compared to traditional oven drying method such as simple, lesslabor and less time consuming. Wijaya et al.
(,**-) reported that to obtain dry bulk density
by using Eq. (+) needs only the information ofsoil wet mass (weight) occupying the known
volume of core sample and it is not necessary
to spend a day to oven dry the sample. Also,
only a small fraction of the disturbed soil
sample, less than +* grams, which is used tomeasure mass wetness, is required to estimate
the dry bulk density by using Eq. (,). Therefore, the ADR method helps us to perform easy,
quick, and less labor determination of ﬁeld soil
dry bulk density, especially when large numbers of data are required.
The qADR data, which is substituted into Eq.
(+) and (,) was obtained from the third orderpolynomial equation (Eq. (-)) as a result of
calibration between the ADR output voltage
and volumetric water content of the Andisol
soil (Wijaya et al., ,**-). The dry bulk density
was ranged from *.-3 to *.30 g cm῏- during thecalibration, which was performed on the soil
with mass wetness ranged from .* to 1* ῑ.
qADRῐ*.**+++῎+./-+v῏,.-.,v,῎+...2v῎
where, v is the ADR output voltage (volt).
,. . Semivariogram
Generally, classical measures of locationsuch as arithmetical mean (M), and spread ofdata such as standard deviation (Std. Dev.) andcoe$cient of variation (CV) are used to evaluate statistical characteristics of the sample population, which can be described as the frequency distribution. However, the frequency distribution is somewhat limited in its ability todescribe variability of a sampled population
because it does not provide any information
about spatial correlation between samples at agiven location.

6

 31  ,**.

To solve the problem above, semivariogram,which can express the degree of spatial dependence between two samples at a given separation distance and direction, has been used tocharacterize spatial variability of hydraulicconductivity (Mohanty, et al., +33. ; Ciolarro
and Romano, +33/), soil water content and dry
bulk density (Tominaga et al., ,**,), soil watercontent and solute concentration (Netto et al.,+333), soil organic matter, NO--N, pH and electric conductivity (Imade, et al., ,**+). It can bedeﬁned as a graph (and/or formula) describing
the expected di#erence in value between pairsof samples with a given relative distance anddirection (Clark, +313). The vertical axis issemivariance, g (h) and the horizontal axes isdistance between two data points, h. For onedimensional data, the g (h) value at given position can be computed by the following equation,

Fig. +

Comparison between the estimated dry
bulk density by using Eq. (+) andmeasured dry bulk density.

Fig. ,

Comparison between the estimated dry
bulk density by using Eq. (,) andmeasured dry bulk density.

῍ῑ῎ῒ

gh

+
ΐ
zxizxih,,Nh ῔ῌ῏ῐῌ

where, N (h) is the number of data pairs
separated by the lag interval h, z (xi) is themeasured sample value at point xi, and z (xih)is the measured sample value at a distance hfrom xi.
-.

Results and Discussions

Comparison between Estimated andMeasured Dry Bulk Density
Figure + shows comparison between the estimated dry bulk density by using Eq. (+) andthe measured dry bulk density, including dataobtained from the ﬁrst and the second ﬁeld
experiment. As can be seen from the ﬁgure, theestimated and the measured data points werelaid on and concentrated around + : + regression line. It indicated that the rbest ﬁtted wellwith the rbmsr. The estimated dry bulk density
obtained from the second ﬁeld experimenttended to be more reliable than that from theﬁrst ﬁeld experiment. The regression coe$cient (R,) was *.01. and *..00, for the second andthe ﬁrst ﬁeld experiment, respectively. Cor-. +respondingly, the root mean square error(RMSE) value between the rbmsr and the rbest byusing Eq. (+) was *.*-, and *.*/3 g cm-, for thesecond and the ﬁrst ﬁeld experiment, respectively.
Figure , shows comparison between the estimated dry bulk density by using Eq. (,) and῎῍ : Field Estimation of Soil Dry Bulk Density Using Amplitude Domain Reﬂectometry Datathe measured dry bulk density, including datafrom the ﬁrst and the second ﬁeld experiment.
Unlike the results shown in Fig +, the estimated and the measured data points shownin Fig , were slightly deviated from andscattered around + : + regression line. It indicated that the rbest tended to be underestimatedand less agreed with the rbmsr. The estimateddry bulk density from the second ﬁeld experiment was better than that from the ﬁrst ﬁeld
experiment, however, it still showed lower accuracy compared to the results of Eq. (+) as
shown in Fig +. In Fig ,, the R, was *./3- and*..--, for the second and the ﬁrst ﬁeld experiment, respectively. The RMSE value between
the rbmsr and the rbest by using Eq. (,) was *.*-3
and *.*1. g cmῌ-, for the second and the ﬁrst
ﬁeld experiment, respectively.
Di#erence in accuracy between the estimated dry bulk density obtained from theﬁrst and the second ﬁeld experiment was due
to di#erence in the surface treatment among
them. The presence of the surface dry layer ofa cm thickness in the ﬁrst ﬁeld experiment,
which enhanced greater heterogeneity in soil
moisture distribution within the ﬁeld proﬁle,could reduce the ADR performance. The surface dry layer might be produced mainly
through evaporation process especially in thebare ﬁeld soil. Greater the thickness of the drylayer in the soil, greater the vertical heterogeneity in soil moisture distribution within its
proﬁle, which, in turn, enhances the error of the
ADR output (Wijaya, et al., ,**,). The ﬁeld soil
with removal of surface dry layer in which the
ADR probe and the core sample was embedded
had more uniform in soil moisture distribution
than that with a surface dry layer (ﬁrst ﬁeld
experiment). Therefore, the errors of the ADR
output could be reduced when the ADR probe
was applied on such soil.
Comparison between the results shown in
the Fig + and , showed that the estimated dry
bulk density with the wet bulk density had
greater accuracy than that with the mass wetness. Di#erence in calculation process between

Fig. -

7

Field distribution of soil dry bulk
density for the second ﬁeld experiment :(a) the rbmsr, (b) the rbest by using Eq. (+),
and (c) the rbest by using Eq. (,).

8  31

Eq. (+) and (,) could be a primary factor a#ecting the results. The Eq. (,) is a division formula, thus, when the qADR containing an error was
substituted into this equation, running the division process might increase the error in rbest
since denominator (w) was smaller than unity.
This error was relatively greater compared tothe case when the qADR data were substituted
into Eq. (+) (Wijaya et al., ,**-). Therefore, thegreater accuracy of qADR was very important toenhance the greater accuracy of rbest.
-. , Field Distribution of Dry Bulk Density
Field distribution of dry bulk density at thesecond ﬁeld experiment is shown in Fig -,which is consisted of (a) measured, (b) estimated by Eq. (+) and (c) estimated by Eq. (,).
As can be seen from the ﬁgures, the distribution of the cloud of data points for the rbest was
similar with that for the rbmsr. The greater
values of rb were dominantly contoured
around the northern part of the ﬁeld from west
to east, and the middle of the ﬁeld. The lower
values of rb spread out around southernwestern part, southern-eastern part and middleof the ﬁeld. The greater values of rb ranged
from *./2 to *.02 g cm-, while the lower valuesof rb ranged from *..2 to *./. g cm-.
Degree of similarity between the distributionof the rbest by using either Eq. (+) or (,) and thatof the rbmsr are shown in Fig . (a) and . (b),respectively. According to the ﬁgures, the similarity can be simply evaluated by the contourof the square di#erence in data points between
the rbest and rbmsr, which was expressed as theerrors of rbest. The errors of the rbest by using Eq.
(,) (Fig . (b)) were greater than that by using
Eq. (+) (Fig . (a)). The errors ranged from *.***/
to *.**// g cm- and from *.***/ to *.**.* g cm-,for the rbest by using Eq. (,) and (+), respectively.
These errors were mostly distributed aroundthe southern part of the ﬁeld from west to east,
due to the greater errors of qADR at the same
area (Fig /). Since accuracy of the ADR probe
is strongly a#ected by volumetric water content distribution along with sensing rods
(Wijaya et al., ,**,), it was suspected that some,**.

Fig. .

Square error distribution of the estimated dry bulk density : (a) square errorof the rbest by using Eq. (+), and (b) square error of the rbest by using Eq. (,).

vertical heterogeneity in moisture or dry bulk
density might be occurred at southern part ofthe ﬁeld. Error distribution of the qADR aroundthe northern part was very small, and only
small error distribution of the rbest was encountered at the same location. It indicatedthat the qADR accuracy was an important factor
in the estimation of dry bulk density.

῎῍ : Field Estimation of Soil Dry Bulk Density Using Amplitude Domain Reﬂectometry Data

Spatial Variability of Dry Bulk Density
Statistical values for the measured and theestimated soil physical properties, including
mass wetness, w, measured volumetric watercontent, qmsr, estimated volumetric water content, qADR, measured dry bulk density, rbmsr andestimated dry bulk density, rbest by using either
Eq. (+) or (,) are summarized in Table ,. Coe$cient of variation (CV) for all the measured andthe estimated soil physical properties obtained
from the ﬁrst and the second ﬁeld experiment-. -Fig. /

Square error distribution of the volumetric water content measured by using
the ADR data (qADR).

Table ,

9

ranged from -.- to +*.3 ῌ. According to theseCV values, all the soil physical properties
above were conﬁrmed relatively low variability (Wilding, +32/ ; Scot, ,***). The greater CV
values occurred on mass wetness, w, rbest byusing Eq. (,) and qmsr, while the lower CV values occurred on the qADR, rbmsr, and rbest by using
Eq. (+). From Standard Deviation (Std. Dev.)
value, it was also clear that the rbmsr and rbest byusing Eq. (+), especially for the second ﬁeld
experiment, were not signiﬁcantly di#erent
and considered to be similar each other. However, the Std. Dev. value for the rbest by using
Eq. (,) was distinctly di#erent to the two previous parameters. It indicated that the rbest byusing Eq. (+) had similar variability with rbmsr,
while the rbest by using Eq. (,) did not.
Another aspect in performance of presenting
method was discussed by evaluation on spatial
variability of the dry bulk density, which was
carried out by semivariogram (Fig 0 (a), (b) and(c)). In these three ﬁgures, semivariance wereplotted within distance between two points
ranged from of *./ to , m. From the trend of
semivariance, the rbmsr (Fig 0 (a)) and the rbest byusing Eq. (+) (Fig 0 (b)) were similar. Although
the rbmsr tended to show smaller semivariance,
both the rbmsr and rbest by using Eq. (+) showedsteady semivariance with increasing distance
between two points. It indicated that the rbmsr
and the rbest by using Eq. (+) had similar struc-

Statistical values for the ﬁeld soil physical properties
First ﬁeld experiment

Variables

Second ﬁeld experiment

Mean

Std.
Dev.

CV
(ῌ)

Mean

Std.
Dev.

CV
(ῌ)

1-...,

1.33/

+*.23

1..-12

1..,.

3.32

Measured volumetric water content, qmsr (cm cm )

*..,*

*.*./

+*.0-

*..-,

*.*--

1.1,

ῌ-

*.-13

*.*-+

2.*1

*..+.

*.*+.

-.,1

Measured dry bulk density, rbmsr (g cm )

*./1-

*.*-0

0.-2

*./2-

*.*.,

1.,/

Estimated dry bulk density by using Eq. (+),
rbest + (g cmῌ-)

*.0+.

*.*0*

3.12

*.0**

*.*.-

1.+3

Estimated dry bulk density by using Eq. (,),
rbest , (g cmῌ-)

*./,*

*.*/0

+*.02

*./0,

*.*/3

+*.0.

Mass wetness, w (ῌ)ῌ--

Estimated volumetric water content, qADR (cm cm )
-

ῌ-

10

ΐῐ῎῔῕ῑ ῒ 31 ῏ ῌ,**.῍ture of spatial distribution over space. However, the semivariogram of rbest by using Eq. (,)(Fig 0 (c)) monotonously increased with increasing distance between two points and did
not reach a constant value. Results above
suggested that the characteristic of spatial distribution of the rbmsr agreed well with that of
the rbest by using Eq. (+) and did not agree withthat of rbest by using Eq. (,).
..

Fig. 0Semivariogram of the measured andestimated dry bulk density : (a) semivariogram of the rbmsr, (b) semivariogram of
the rbest by using Eq. (+), and (c) semivariogram of the rbest by using Eq. (,)(numbers in the ﬁgures are the numberof data pairs for a given lag interval h).

Conclusions

Application of the ADR data on estimation ofﬁeld dry bulk density showed good results.
The rbest by using Eq. (+), combined with wet
bulk density data, was better than that byusing Eq. (,) with mass wetness. Furthermore,since higher uniformity in soil moisture distribution can reduce the errors of the ADR probe
measurement, the second ﬁeld experiment involving removal of the surface dry layer yielded the greater accuracy of dry bulk density
estimation compared to the ﬁrst ﬁeld experiment, which was conducted with a surface drylayer.
According to the results of semivariogram, it
was found that characteristic of spatial distribution of the rbest by using Eq. (+) was similar tothat of the rbmsr. However, the rbest by using Eq.
(,) showed di#erent structure of spatial variability to that of the rbmsr and the rbest by using
Eq. (+). Therefore, Eq. (+) was expected to be
useful to estimate soil dry bulk density.
This method can serve reasonable quality ofdry bulk density data with saving either timeor amount of soil sample. Employing Eq. (+)
can estimate dry bulk density by taking andweighing sample in situ, while using Eq. (,)
requires taking less than +* grams of soil
sample for a dry bulk density data. For some
purpose, i.e. taking large number of dry bulk
density data for vast area, this method may
partly substitute traditional oven drying
method with undisturbed sample which requires labor and be time consuming.

῍ῌ : Field Estimation of Soil Dry Bulk Density Using Amplitude Domain Reﬂectometry Data

Acknowledgement
This study was supported by Grants-in-Aid
for Scientiﬁc Research by Japan Society of thePromotion of Science : No. ,**+ῌ+-10*+03. Also,in conducting ﬁeld experiments the authors
would like thank to the help o#ered by students of Laboratory of Land Use, Tokyo University of Agriculture and Technology.
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