Int. Agrophys., 2019, 33, 113-119
doi: 10.31545/intagr/104413

Estimation of electrical conductivity of a soil solution from the monitored TDR data
and an extracted soil solution
Katsutoshi Seki1*, Teruhiko Miyamoto2, and Yukiyoshi Iwata2
12

Natural Science Laboratory, Toyo University, 5-28-20 Hakusan, Tokyo 112-8606, Japan
Agricultural Environment Engineering Research Division, Institute for Rural Engineering, NARO, 2-1-6 Kannondai,
Tsukuba, Ibaraki 305-8609, Japan
Received April 24, 2018; accepted November 4, 2018

A b s t r a c t. In order to establish sustainable agricultural practices and to avoid excess fertiliser application, it appears importantto understand the process of water and solute transport. With a view
to analysing transport through the soil, based on the data obtainedby means of time domain reflectometry, the relationship between
the volumetric water content, the apparent electrical conductivity, and the soil solution electrical conductivity should be known.
This paper proposes a new method for estimating the three parameters relationship by optimising the parameters obtained throughRhoades model with the Levenberg-Marquardt method. The proposed method systematically determines the initial parameter set
required to conduct nonlinear optimisation. The method was used
to estimate the continuous apparent electrical conductivity data
based on the time domain reflectometry dataset, obtained fromthe field and occasional measurement of soil solution electrical conductivity data of the soil water, which was extracted bymeans of a suction sampler installed in the field. Compared withthe conventional method where the parameters of Rhoades model
are calibrated with a 2-step linear regression by means of laboratory experiment, the soil solution electrical conductivity estimatedwith the proposed method was closer to the field data, yielding
smaller root mean square error values. Supplementary use of thedataset obtained through a laboratory experiment under dry andwet conditions improved the accuracy of parameter estimation.
K e y w o r d s: time domain reflectometry, Rhodes model, parameter estimation
INTRODUCTION

In order to establish sustainable agricultural practices
and to avoid excess fertiliser application, it is importantto understand the process of water and solute transport.
Measuring the volumetric water content (θ) and the apparent soil electrical conductivity (ECa) under field conditions
is generally required for this purpose. Time domain reflec*Corresponding author e-mail: seki_k@toyo.jp

tometry (TDR) is widely used for determining θ and ECa
simultaneously (Noborio, 2001). Moreover, multi-sensor
probes have also been developed recently to assess θ andECa, with continuous and non-destructive measurements(Scudiero et al., 2012; Vaz et al., 2013). By using thesemeasurement techniques, we can easily obtain the θ and
ECa data in fields.
It does not appear practical to assess solute transport
in soil using ECa under transient conditions because of thestrong dependence of ECa on θ. Therefore, ECa must be
related to the soil solution electrical conductivity (ECw) so
as to estimate the solution concentration under transientconditions with varying water content. The physico-empirical and / or theoretical models describing the dependence of
ECa on ECw and θ (e.g. Rhoades et al., 1976; Rhoades et al.,
1989; Mualem and Friedman, 1991; Malicki and Walczak,
1999; Hilhorst, 2000) are used to estimate ECw for a given
combination of the measured ECa and θ in a particular soil
(Mallants et al., 1996; Risler et al., 1996; Das et al., 1999;
Muñoz-Carpena et al., 2005; Miyamoto et al., 2015).
Laboratory calibration experiments are conducted using
repacked soil columns to obtain model parameters for the
ECw − ECa − θ relationship (Heimovaara, 1995; De Neve etal., 2000; Muñoz-Carpena et al., 2005; Wilczek et al., 2012;
Miyamoto et al., 2015). However, this calibration method
is not suitable for field measurements because soils in thefield are often structured and more naturally heterogeneousthan the uniformly repacked soil columns. Moreover, thecalibration procedure of a 2-step linear regression requiresthat multiple datasets of precisely the same water content
or the same electrical conductivity are obtained, whichis hardly available from the field data. Das et al. (1999)© 2019 Institute of Agrophysics, Polish Academy of Sciences

K. SEKI et al.

proposed a field calibration procedure, which is an in situ
mass balance approach with a TDR probe installed vertically on the soil surface. This calibration procedure, however,can be only applied to the top soil layer.
Sensor pairing is a field measurement method of the soil
water characteristic (Baumgartner et al., 1994). The paired
sensors, such as neutron moisture meter access tubes or
TDR probes, and tensiometers are often used to simultaneously determine θ and the matric potential (ψ). As a result, the θ − ψ values are obtained. In an similar way, thesimultaneous measurements of ECw−ECa−θ values, using
soil solution samplers and TDR probes, will also be a useful method for an in situ determination of the ECw − ECa− θrelationship.
The objective of this study is to develop a method to
identify the parameters of Rhodes model (Rhoades et al.,1976) for the ECw − ECa − θ relationship based on a datasetof the ECw, ECa and θ values which are measured in thefield. To this end, we have designed a calculation procedureby adopting the Levenberg-Marquardt optimisation method(Marquardt, 1963), which has become a standard in nonlinear least-square fitting among both soil scientists andhydrologists (Šimůnek and Hopmans, 2002; Seki, 2007).
We have compared the ECw estimated from the proposed
method with the one obtained from the conventional method of a 2-step linear regression, as shown by Miyamoto
et al. (2015). In addition, we have discussed a supplemental use of the dataset of ECw, ECa and θ obtained througha laboratory experiment to improve the accuracy of the proposed method.
MATERIALS AND METHODS

The field data published in Miyamoto et al. (2015) wereused in this study. The field experiment was carried out inthe experimental field at the National Agriculture and Food
Research Organization in Tsukuba, Japan. The soil at thatsite was an Andosol (IUSS Working Group, 2014). The soil
profile was divided into two layers; the boundary between
the surface and subsurface layers (topsoil and subsoil) was
at 0.5 m depth. The bulk densities of topsoil and subsoil
were 710 and 630 kg m-3, respectively. Saturated hydraulic conductivities of these soils were 35.0 and 30.0 mm s-1,
respectively. The soil water retention curves of topsoil andsubsoil are shown in Fig. 1. The field was fertilised with
20.0 g m-2 of N, 8.7 g m-2 of P and 16.6 g m-2 of K, used as
chemical fertilisers, on 25 December 2007. The ground surface was maintained in an unplanted condition throughout
the field experiment until 31 August 2008.
Dielectric permittivity of the soil (εa) and ECa were measured with TDR probes installed horizontally into pit faces
at three locations and at three depths (0.2, 0.4, and 0.6 m,
respectively) during the experimental period, in orderto detect the TDR waveforms reflected from the probes.
A cable tester (Tektronix, 1502B) was used to detect the

0.8
Volumetric water content, q

114

topsoilsubsoil

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0.1

10
Matric suction (kPa)

1000

Fig. 1. Soil water retention curves of topsoil and subsoil in theexperimental field.

time domain of the electromagnetic wave, along with the
probes.
The observed data were recorded using a portablecomputer every hour. A copper-constantan thermocouple
was installed in the central pit at each of the three depths
to measure temperature in a continuous manner, which wasrecorded by means of a datalogger (Campbell ScientificInc., CR10X) every hour. The relationship between εa andθ was calibrated through a laboratory experiment, and thevalues of εa were converted into the respective values ofθ under field conditions, using the calibration equation.
The measured ECa values were calibrated to the value at
25°C with the temperature correction factor taken from
Heimovaara et al. (1995).
The porous ceramic soil solution samplers were alsoburied at three depths. Two samplers were buried at each
depth. The soil solution was sampled once to three times
a month by applying a suction of 50-70 kPa during the field
experiment. ECw was measured for each extracted soil solution using a portable EC meter (HORIBA ltd., Twin Cond).
The average of 2 measured values obtained for each soil
depth was used in the analysis. As a result, during 8 monthsof the measured period, 17 data points of ECw in the field
were obtained.
Figure 2A shows the process of estimating ECw bymeans of the conventional method. Rhoades et al. (1976)
derived the following equation:
ECa = ECw θT + ECs,

(1)

where: T is the transmission coefficient which accounts forthe tortuous nature of the current lines and any decreases
in the mobility of the ions near the solid-liquid and liquidgas interfaces, and ECs is the surface conductivity via
exchangeable cations. They assumed that T is linear to θ,
based on the empirical relationship by Gupta and Hanks(1972), which is as follows:(2)
T = aθ + b,
where: a and b are constants. Using the Eq. (2), the following equation was derived:

115

ESTIMATION OF ELECTRICAL CONDUCTIVITY OF A SOIL SOLUTION FROM TDR

mised with Eq. (3) simultaneously by the non-linear leastsquare optimisation algorithm of Levenberg-Marquardt
method (Marquardt, 1963).
Let the independent variable vector x in Eq. (3) bedefined by x = (x1, x2) = (θ, ECw), and the parameter vector p be defined by p = (p1, p2, p3) = (a, b, ECs). The model
Eq. (3) is rewritten as:(5)f(x, p) = (p1 x1+p2)x1 x2 + p3.
Let the data points be denoted by:(Yi, Xi) = (Yi, X1i, X2i), i = 1, 2, …, m,(6)

where: X1i, X2i, and Yi are the i-th data point of θ, ECw, andECa, respectively. The objective function of the least squareanalysis O(p) is:,Fig. 2. Estimation of electrical conductivity of the soil solution(ECw). (A) The conventional method (Miyamoto et al., 2015) (B)The method proposed in this study.

ECa = (aθ+b) θECw + ECs.

(3)

The conventional method is a 2-step linear regression. In
the first linear regression, for different sets of water content(e.g., θ = 0.35, 0.40, 0.50, 0.60 for the experiment conducted by Miyamoto et al., 2015) the relationships between
ECw and ECa were written, and the fitted lines with slope
S = (aθ + b)θ and intersect ECs were obtained. In the second
linear regression, S/θ was plotted against θ, and the linear
fit yielded a and b. Finally, the Rhoades parameter set, a, b
and ECs was used to estimate ECw based on the measured
θ and ECa from Eq. (3). The conventional method requiresthat multiple datasets of precisely the same water content
are plotted in the first regression to obtain parameters forthe second regression.
In the proposed method, the field-obtained values of θ,
ECa and ECw were basically used to determine a, b and ECs
of Rhoades model (Fig. 2B), with a successive optimisation
technique as follows. In the present study, we used 17 ECw
data obtained from soil solution samplers. By coupling thedata with the θ and ECa values measured with TDR probes
in the field, both at the same depth and on the same day,we obtained 17 sets of measured data (θ, ECa, ECw), whichwere then used to estimate the parameter set (a, b, ECs).
Eq. (3) can be transformed as follows:.

(4)

Equation (4) shows the linear relationship between θand (ECa – ECs)/ECwθ. At first, ECs was assumed to be 0.25
dS m-1, one of the values obtained in Rhoades et al. (1976),
and the parameters a and b were obtained with the linear
regression of equation (4). Then, a, b and ECs were opti-(7)

where: the weights wi are normally set to 1 (unity). The
Levenberg-Marquardt algorithm efficiently solves parameter vector p so that O(p) is minimised. The LevenbergMarquardt method requires an initial estimate of parameter
vector p. It then updates the estimate iteratively to find thefinal estimate of p. In the iterative procedure, vector p may
not converge to a proper value when the initial estimateof the parameter is not close enough to the final solution.
Therefore, selecting a reasonably good set of the initial
parameter is a very important step for this algorithm. In the
proposed method, the initial estimate of parameter vector p
can be obtained systematically by the regression of Eq. (4)as described above.
The difference in the two methods shown in Fig. 2 concerns the methods of obtaining the Rhoades parameters(parameter vector p). The advantage of using the proposed method is that it does not require separate laboratory
experiments that are both time-consuming and tedious.
The conventional method requires calibration curves of theECw−ECa relationship for the same θ values. Such data are
not usually available in the field, and thus the conventional
method can only be used with laboratory data. The proposed method does not require that the θ values be exactly
controlled, and thus the field data can be directly used for
obtaining Rhoades parameters. Moreover, as the conventional method simultaneously optimises all the parameters,
it may require a smaller dataset for estimation. To verify
whether the proposed method requires a smaller amountof data, we also performed calculation with smaller datasets. From each month between January and August, one
measuring dataset of (θ, ECa, ECw) was selected so that theinterval between the data points was around 30 days, and 8
data were used in the analysis.
The algorithm was implemented in the mathematicsoriented programming language of GNU Octave. The
programme first fits the given dataset of θ, ECw and ECa
to Eq. (4) to get the initial estimate of the parameter set,

K. SEKI et al.

116

and then the initial parameter set is successively optimised
with the iterative procedure of the Levenberg-Marquardt
method to get the final parameter set of a, b and ECs. In the
programme, the parameters were constrained with a > 0 and
0 < ECs< min (ECa).
RESULTS AND DISCUSSION

Table 1 shows the parameters used in Eq. (3) that were
estimated on the basis of the ECw values of the extracted soil
solution, and θ and ECa were measured with TDR probes
using the developed method (Fig. 2B). Figure 3 shows therelationship between the measured and estimated ECa withparameters in Table 1 of the 3 TDR probes at each depth.
The agreement between the measured and estimated ECa
is not very good, compared to the laboratory calibration
experiment outlined by Miyamoto et al. (2015), because
the field experiment could not be controlled to the same
extent as the laboratory experiment. However, many plots
were found to be close to the identity line.
Figure 4 shows the change in the estimated ECw thatwas calculated from the θ and ECa values measured with
TDR probes, and parameters in Table 1, compared with the
ECw directly measured from the soil solution. The estimation at topsoil (0.2 m depth) was not successful because theTa b l e 1. Estimated parameters with field extracted soil solution and field measured TDR data
Depth

0.2 m

Probe ID

0.4 m

0.6 m

2A

2B

2C

4A

4B

4C

6A

6B

6C

a

3.73334.25085.14570.40190.32920.36890.00110.00000.0001b-1.5934-2.0348-2.3268

0.52280.17620.1433

1.06831.04081.0429ECs

0.04630.01820.00000.00000.00000.00000.00460.00000.0000

0.6

0.2 m

0.5
0.4

2.0

0.3
0.2

1.0

0.1
0

0.0

0.2

0.4

0.0

0.6

2.5

0.4 m

0.5
0.4

ECw (dS m-1)

Estimated ECa (dS m-1)

0.6

0.3
0.2
0.1
0
0.6

0.0

0.2

0.4

0.6

2.0
1.5
0.5
0.0
2.5

0.4

1.5

0.3

1.0

0.2

0.5

0.1

0.0
0.0

0.2

0.4

0.6

Measured ECa (dS m-1)
Fig. 3. Measured
and estimated apparent electrical conductivity
(ECa) of each TDR probe for each depth, the closed circle, theopen triangle and the cross representing TDR probes.

Dec Jan Feb Mar AprMay Jun Jul Aug

0.4 m

1.0

2.0

0.6 m

0.5

0

0.2 m

Dec Jan Feb Mar AprMay Jun Jul Aug

0.6 m

Dec Jan Feb Mar AprMay Jun Jul Aug
Time (day)Fig. 4.Figure
Estimated
4 ECw (solid line, dashed line and chain line, each representing a TDR probe) and the measured ECw of the extracted
soil solutions (the closed and open circles representing suction cups).

117

ESTIMATION OF ELECTRICAL CONDUCTIVITY OF A SOIL SOLUTION FROM TDR

0.60
0.55
0.50
0.45

0.2 m

Volumetric water content, q

0.40

Dec Jan Feb Mar AprMay Jun Jul Aug

0.60
0.55
0.50
0.45

0.4 m

0.40

Dec Jan Feb Mar AprMay Jun Jul Aug

0.60
0.55
0.50
0.45
0.40

0.6 m
Dec Jan Feb Mar AprMay Jun Jul Aug
Time (day)Fig. 5.Figure
Volumetricwater content measured at depths of 0.2, 0.4
5
and 0.6 m in three TDR locations (the solid line, the dashed line
and the chain line representing TDR probes). The shadow areashows the range of the volumetric water content (the corresponding TDR value) of the extracted soil solution.
Ta b l e 2. Estimated parameters with field extracted soil solution
and field measured TDR data, with supplementary laboratory dataat dry and wet conditions
Depth

0.2 m

Probe ID

2A

2B

2C

a

2.04211.8905

2.1467b-0.7269-0.6339-0.7814ECs

0.03040.00000.00002.5

ECw (dS m-1)

fluctuation of the estimated ECw was very large (note thatthe data gap from mid-July to mid-August at the top panelin Fig. 4 was caused by unreasonable calculation resultsof the ECw), and RMSE was 0.34, 0.57, 0.68 dS m-1 foreach probe. This was because the range of θ, when the soil
solution was sampled, was too narrow as compared to therange of θ measured by TDR probes. As shown in Fig. 5,
θ ranged from 0.40 to 0.57 in the field, while the extracted
soil solution was in the θ range of 0.46 to 0.55 (the corresponding TDR measurement values). The soil solution
was not extracted in the period of mid-July to mid-August,when the soil was relatively dry (0.40 < θ < 0.46). When thefield data of θ exceeded the fitted range, the estimated ECw
took unrealistic values. In some cases, the estimated ECw
had negative values (from mid-July to mid-August). In the
topsoil layer of 0.4 m, and the subsoil layer of 0.6 m, thediscrepancy in the range of θ was not severe as comparedto that at 0.2 m, and the estimation of ECw at 0.4 and 0.6 m
depth was more stable than the data obtained at a depth of
0.2 m; RMSE was 0.27, 0.22 and 0.42 dS m-1 for probes at
a depth of 0.4 m, and 0.12, 0.12 and 0.18 dS m-1 for probes
at a depth of 0.6 m. Compared with the estimation made byMiyamoto et al. (2015), which yielded RMSE of 0.42, 0.29
and 0.42 dS m-1 for probes at a depth of 0.4 m, and 0.38,
0.33 and 0.21 dS m-1 for probes at a depth of 0.6 m, theestimation with the proposed method was more close to thefield-obtained data, especially at a depth of 0.6 m.
Figure 4 shows that the proposed method worked
fine with the subsoil layer but did not work at a depth of
0.2 m as well as expected. The main reason for failure
was that we could not extract the soil solution from drysoil. Especially at the driest period of mid-July to midAugust, the water content reached θ = 0.40 at topsoil andθ = 0.46 at subsoil, corresponding to 100 kPa matric suction(Fig. 1). Extracting the soil solution of such high matricsuction through porous cups proved difficult.
We tried to overcome this difficulty (i.e. the unavailability of the dry soil solution) by adding a small amount ofexperimental data for our analysis. Note that in the laboratory experiment the soil solution was centrifuged and data
were available for lower water contents when compared to
the field data. As our method aims at reducing the workload required for a laboratory experiment to be performed,
we only introduced 2 data sets, i.e. (1) dry soil with small
EC and (2) wet soil with high EC. Based on the laboratory
data provided by Miyamoto et al. (2015), we used these 2
data points; (1) θ = 0.35, ECa = 0.030 dS m-1, ECw = 0.49
dS m-1 (2) θ = 0.60, ECa= 1.20 dS m-1, ECw = 3.94 dS m-1.
In addition to 17 data points from the field, 2 data points
from the laboratory experiment were used for estimating
the Rhoades parameter sets. For compensating the numbersof data points in the laboratory, as compared to the field
data, weights (wi in Eq. (7)) were set as 3 for the laboratory
data and 1 for the field data.

2.0
1.5
1.0
0.5
0.0

Dec Jan Feb Mar AprMay Jun Jul Aug
Time (day)Fig. 6. estimated ECw (the solid line, the dashed line and the
Figure 6
chain line representing TDR probes) and the measured ECw of theextracted soil solutions (the closed and open circles representing
suction cups) at a depth of 0.2 m, estimated with the field extracted soil solution and laboratory data under dry and wet conditions.

K. SEKI et al.

118

0.2 m

2.0
1.0
0.0

ECw (dS m-1)

2.5

Dec Jan Feb Mar AprMay Jun Jul Aug

2.0

0.4 m

1.5
1.0
0.5
0.0
2.5
2.0

Dec Jan Feb Mar AprMay Jun Jul Aug

0.6 m

1.5
1.0
0.5
0.0

Dec Jan Feb Mar AprMay Jun Jul Aug
Time (day)Fig. 7. Estimated ECw (the solid line, the dashed line and thechain line Figure
representing
TDR probes) and the measured ECw of
7
the extracted soil solutions (the closed and open circles representing suction cups), estimated from a reduced set of field data. At
a depth of 0.2 m, laboratory data under dry and wet condition was
also used.

The parameter set at the topsoil layer (0.2 m depth)
estimated in this modified method is shown in Table 2.
Figure 6 shows the change in the estimated ECw, calculated
from θ and ECa measured with TDR probes, and parameters in Table 2, when compared with to the ECw directly
measured from the soil solution. The estimated curve ismore stable than in Fig. 4, where no laboratory data wasused. RMSE was 0.37, 0.50 and 0.53 dS m-1 for each probe.
Figure 7 shows a similar result as in Fig. 4, but witha reduced set of field data; 8 data were included out of full
dataset comprising 17 entries. As for a depth of 0.2 m, thesame data from the laboratory experiment, as shown in Fig.
6, i.e., the two datasets of the dry and wet soils, were also
used in the analysis. Weights were set as 1 for both the field
and laboratory data. The estimated parameter in this figure
is summarised in Table 3. By comparing the curves ofFig. 4 (for depths of 0.4 m and 0.6 m) and Fig. 6 (for a depthof 0.2 m) with Fig. 7, the estimated curves represent themeasured data equally well. In other words, decreasing themeasured data from 17 to 8 did not significantly deteriorate
the estimation, as the reduced data included the driest datain mid-July and, therefore, the range of the water content
of the reduced dataset was similar to that of the whole data.
In Figs 7, 8 data out of the full set of 17 data wereused. The remaining 9 data were used for the validation
set. RMSE for the estimated ECw for the validation set was
0.41, 0.50 and 0.35 dS m-1 for probes at a depth of 0.2 m,
0.27, 0.25 and 0.23 dS m-1 for probes at a depth 0.4 m depth,
and 0.09, 0.12 and 0.09 dS m-1 for probes at a depth of
0.6 m. This result was not particularly higher than the
RMSE of the estimation from the whole set of data; in someof the probes, RMSE got smaller. Therefore, it was confirmed that the estimation of Fig. 7 did not deteriorate from
Figs 4 and 6 although the numbers of data were reduced
from 17 to 8.
As we have shown in the reduced set of field data,
increasing the numbers of data points (from 8 to17) does
not always improve the estimation. The estimation can be
improved by using as wide range of water content as possible, from dry soil to wet soil, to minimise the discrepancyof the fitted range of water content and the monitored rangeof water content, as shown in Fig. 5. When it is technicallydifficult to obtain a wide range of water content, laboratory
data under extreme water content conditions can be used toform an additional dataset, as shown in Fig. 6.
The estimation of ECw based on the parameter set determined under laboratory conditions (Fig. 3 in Miyamoto
et al., 2015) was improved with the proposed method,which uses the parameter set determined directly from thefield-obtained value. For example, in Miyamoto’s estimation, the NO3-N concentration at a depth of 0.6 m was twiceas large as the NO3-N concentration measured with theextracted soil solution because ECw rose twice as much as
the soil solution ECw. In the proposed method, the highest
value of the estimated ECw was similar to that of the measured ECw value. Therefore, a more realistic value of NO3-N
can be obtained by the proposed method.
This is because the parameters estimated in the proposed
method (Table 1) reflect the properties found under the sitespecific heterogeneous condition, and they are different
from the parameters shown in Miyamoto et al. (2015); they
are soil-specific parameters determined through a laboratory experiment. Therefore, the parameter set obtained at

Ta b l e 3. Estimated parameters with reduced numbers of field data
0.2 m*

Depth
Probe ID

0.4 m

0.6 m

2A

2B

2C

4A

4B

4C

6A

6B

6C

a

2.11322.14812.24850.81230.25860.23070.00000.08900.0003b-0.7660-0.7975-0.84300.24310.18510.17801.00881.3214

1.2144ECs

0.03040.00010.00000.00000.00000.00000.00020.00020.0000*Laboratory data at dry and wet condition was also used.

ESTIMATION OF ELECTRICAL CONDUCTIVITY OF A SOIL SOLUTION FROM TDR

one field site by using this method should not be used forother field sites even if the soil properties are similar. The
parameters determined are not soil-specific but site-specificvalues.
CONCLUSIONS

1. Compared to the conventional method of estimating Rhoades parameters through a laboratory experiment,
the method proposed in this study, where Rhoades parameters are estimated based on the field-monitored values of
the time domain reflectometry and the field-extracted soil
solution, can give better estimates of soil solution electrical conductivity. The method is reliable since it is basedon the actual soil solution electrical conductivity values
measured in the field. It was made possible because ourmethod determines the initial parameter set for nonlinear regression systematically and does not requirea 2-step linear regression process as the one performed in
the conventional method.
2. The key to success in this method is to obtain thesoil solution of a wide range of water content. When a sufficiently wide range of water content is not available in thefield, a small amount of supplementary data obtained underlaboratory conditions can be added to widen the calibration
range.
3. When researchers, engineers or farmers want to estimate the soil solution electrical conductivity accurately
without much effort, the method proposed here may be useful for them provided that they can access the field data of
the soil solution electrical conductivity easily.
Conflict of interest: The authors do not declare any
conflict of interest. There is a patent pending in Japan (application number: 2018-080205) for the method described inthis paper. There are no other patents.
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