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www.VadoseZoneJournal.org
Evaluaon of Standard Calibraon
Funcons for Eight Electromagnec
Soil Moisture Sensors
An increasing number of electromagnec (EM) sensors are deployed to measure volumet-
ric soil water content (q) for agricultural, ecological, and geotechnical applicaons. While
impedance and capacitance sensors generally operate at frequencies between 20–30 0 MHz,
me domain-reectometry (TDR) and-transmissometry (TDT) funcon in the GHz range. In
general, lower frequency sensors are less expensive but more sensive to confounding
eects of salinity, temperature, and soil textural variaons. To simplify sensor applicaon,
factory-supplied calibraons are oen provided for dierent porous media types such as
mineral, organic, and saline soils, or soilless-substrates. The objecve of the presented
study was to evaluate the performance of eight commercially available EM moisture sens-
ing systems (TDR 100, CS616, Theta Probe, Hydra Probe, SM300, Wet2, 5TE, 10HS) in seven
well-characterized and texturally varying soils using a standardized approach. The validity
of factory supplied-calibraon relaonships was evaluated and the inuence of soil prop-
eres on the EM responses for q measurements was observed. Results indicate that the
factory-supplied calibraon relaonships for groups of mineral and organic soils in general
performed well, but some inconsistences were idened and suggesons for improvement
are discussed. Soil-specic calibraons from this study yielded accuracies of around 0.015
m3m−3 for 10HS, SM300, and Theta Probe, while lower accuracies of about 0.025 m3 m−3
were found for TDR100, CS616, Wet2, 5TE, and the Hydra Probe. These results are based
on mineral soils having a large variaon in texture, elec trical conducvies below 2 dS m−1,
organic maer below 10%, and specic surface areas of less than 50 m2 g−1 .
Abbreviaons: CV, coecients of variaon; ECb, bulk electrical conducvity; EM, electromagnec; MW,
Maxwell–Wagner; ORG, organic soil; RMSD, root mean squared deviaons; SCL, silty clay loam soil; TDR,
me domain-reectometry; TDT, me domain-transmissometry; TLO, transmission line oscillaon
To maintain funcon and producvity of soils as an important natural
resource and to address anthropogenic inuences, proactive planning and responses are
imperative. Measuring and monitoring soil water status is vital for state-of-the-art man-
agement practice due to the intimate link between water content and numerous processes
involved with crop production (e.g., irrigation scheduling , fertilizer application, cultivation
practices, etc.), soil conservation, road construction, and preferential transport of chemicals
and pollutants to ground water resources, to name a few.
Among the many options to determine volumetric soil water content (q) in eld settings
and in the laboratory, EM based techniques or sensors responding to soil dielectric per-
mittivity (e) are particularly advantageous because: (i) they do not use ionizing radiation
and can be employed close to the soil surface (in contrast to neutron scattering and g ray
attenuation techniques), (ii) they are considered noninvasive (in contrast to gravimetric
techniques), (iii) they allow continuous monitoring and recording of soil moisture (in
addition to other measurements) from practically dry to saturated conditions, and (iv)
they can be applied in most soil types and plant growth substrates. ese advantages have
resulted in the development and deployment of an increasing number of EM sensors to
measure or estimate e for q determination; in addition, in many cases soil-bulk electrical
conductivity (EC
b
) and temperature are also measured (Table 1). Most of the currently
available impedance and capacitance sensors operate at frequencies between 20–300 MHz,
while TDR and TDT operate in the GHz frequency range. In general, lower frequency
sensors are less expensive but more sensitive to confounding eects of salinity, temperature,
and soil textural variations (Kizito et al., 2008; Blonquist et al., 2005).
A number of factors inuence the permittivity measurement of EM sensors. Ionic conduc-
tivity has a direct eect on dielectric loss. When dissolved ions are free to move within the
Eight commercially available electro-
magnec water content sensors were
evaluated in seven well-characterized
soils ranging from sand to clay tex-
tures, including an organic soil. Factory
supplied calibraons were compared
and sensor response to soil properes
demonstrated. Soil-specic calibraons
yielded measurement accuracies from
0.015 to 0.025.
C.M.P. Vaz, Embrapa Agricultural Instrumen-
ta o n, P.O. Bo x 741, Sã o Car los, SP, 135 60 -97 0,
Brazil; S. Jones, Dep. of Plants, Soils and Cli-
mat e, Utah Sta te Univer sity, Logan , UT 843 22;
M. Meding and M. Tuller, Dep. of Soil, Water
and Environmental Science, The University of
Arizona, Tucson, AZ, 85721. *Corresponding
author (carlos.vaz@embrapa.br).
Vadose Zone J.
doi:10.2136/vzj2012.0160
Received 14 Jan. 2013.
Special Section: Soil Water
Sensors and Measurement
Technologies
Carlos M.P. Vaz*
Sco Jones
Mercer Meding
Markus Tuller
© Soil Science Society of America
5585 Guilford Rd., Madison, WI 53711 USA.
All rights r eserve d. N o part of this periodical may
be reprodu ced or transmied in any form or by any
means, electronic or mechanical, including pho-
tocopying, recording, or any informaon storage
and retrie val system, withou t permission in wri ng
from the pu blisher.
www.VadoseZoneJournal.org p. 2 of 16
liquid phase of a porous medium, charge migration occurs during
application of an electromagnetic eld (EM measurement). In
addition, the ion’s ability to migrate depends on the opportunity
time or frequency of the applied eld, which at low enough fre-
quency facilitates charge buildup along interfaces and an appar-
ent enhancement of the energy storage. is eect becomes more
pronounced with increasing ion concentration and as the number
of interfaces increases (e.g., higher surface area, smaller particles,
optimal spacing). Oen referred to as Maxwell–Wagner (MW)
relaxation (Hilhorst, 1998), the enhancement of permittivity is
especially pronounced below 100 MHz (Chen and Or, 2006a,
2006b). Chen and Or (2006a, 2006b) studied the eects of ions
at low frequencies where MW polarization appears to enhance
the apparent permittivity as a charge buildup along interfaces in
the presence of an EM eld occurs. Considering the frequency
spectra of typical EM measurements, MW eects on network ana-
lyzer measurements of permittivity were negligible near the GHz
measurement frequency (e.g., TDR), while at lower frequencies
(<100 MHz), common for many commercial EM sensors, MW
polarization signicantly enhanced the apparent permittivity. Sev-
eral researchers (Logsdon and Laird, 2004; Saarenketo, 1998) have
also demonstrated that clay minerals exhibit continued dispersion
above 100 MHz and into the GHz region. is has been shown to
have a considerable impact on determination of water content in
clayey soils (Kelleners et al., 2005a; Robinson et al., 2005).
To address the various soil property eects on EM-based measure-
ments of q, soil-specic calibration is oen recommended, but chal-
lenging for many users to perform. To simplify sensor application,
factory-determined calibration equations are oen provided for
dierent soil textural classes and plant growth media, which may
be classied as mineral-, organic-, saline-, soilless-substrates, or
others. Despite a vast array of literature describing specic EM
sensor applications in dierent soils (Table 1) (Chow et al., 2009;
Evett et al., 2009; Mazahrih et al., 2008; Evett et al., 2006; Blon-
quist et al., 2005; Walker et al., 2004; Hanson and Peters, 2000),
little eort has been invested to compare the performance of com-
monly applied EM sensors along with their factory-supplied cali-
bration equations for a variety of soil types. A signicant challenge
in this regard is to establish an experimental protocol using the
same set of samples and experimental conditions to test the dier-
ent sensors, many of which have dierent geometries, rod numbers,
lengths, and sampling volumes.
In the present work, the performance of six well-established EM
sensors (TDR 100, CS616, eta Probe, Hydra Probe, Wet, 5TE)
and two recently released EM sensors (SM300 and 10HS) were
evaluated in ve mineral soils, one organic, and one mineral saline
soil. e objective was to evaluate the performance of these eight
EM sensors in seven well-characterized soils to test the validity of
factory supplied-calibration relationships and to evaluate the inu-
ence of the soil properties on the EM sensor response. To that end,
an experimental protocol was developed to test the sensors with
dierent geometries and sampling volumes. e potential need for
improvement of manufacturer calibrations was addressed.
6Materials and Methods
All measurements were conducted in the laboratory at an ambient
temperature of 22.3°C (±0.9) throughout the duration of the experi-
ments. e EM sensors were connected to a CR1000 datalogger
(Campbell Scientic Inc., Logan, UT) for signal excitation and data
Table 1. Commercially available electromagnetic (EM) sensors with
various outputs related to volumetric water content (q) [i.e., dielectric
permittivity (e), voltage, period, and count (proportional to the sensor
circuit resonant frequency)]. Some of the listed sensors also measure
bulk electrical conductivity (ECb) and temperature (T).
Sensor Ty p e f
Sensor
outputs† Pap ers ‡
GHz
Currently available and t his study
TDR 100 Campbell TDR 1.450 e, ECb–
CS616 Campbell TLO 0 .175 period 17
eta Probe Del t a-T I0.100 voltage 39
SM300 D e lta-T I0.100 volt age, T 2
Wet 2 D e lta -T C0.020 e, ECb, T 13
5TE Decagon C0.070 e, ECb, T 9
10HS Decagon C0.070 voltage 4
Hydra Probe Stevens I0.050 e¢, e¢¢, ECb21
EC-5 Decagon C0.070 voltage 12
CS650/655 Campbell TLO 0.175 e, ECb, T –
PR1/6 ; PR2/6 Del t a-T C0.100 voltage 6
Tri me Mesa TDR 1.000 voltage 10
Diviner 2000 Sentek C0.25–0.29 count 9
EnviroSCAN Sentek C0.10–0.15 count 17
EasyAg Sentek C – – 2
Watermark Irrometer R – resistance 26
Aqua-Pro – C – voltage –
Digital TDT Acclima TDT 1.23 e, ECb, T10
Gro-Point ESI TDT –current 1
TDT Aquaex –TDT –voltage –
Virrib AMET – 5
Discontinued
EC-20 Decagon C0.005 voltage 11
EC -10 Decagon C0.005 voltage 4
CS 615 Campbell TLO 0.044 period 15
SM200 D e lta-T I0.100 voltage 3
LOM/RS E as y Tes t TDR – 2
† ECb, electrical conductivity; TDR , time domain reectometry; T LO,
transmi ssion line oscillation; TDT, time doma in transmission; e¢, real di-
electric permittivity; e¢¢, imaginary dielectric per mittivity; I, imped ance;
C, capacitance; R, resistance; and T, temperature.
‡ Number of papers published (Web of Knowledge).
www.VadoseZoneJournal.org p. 3 of 16
acquisition (Fig. 1), except for the TDR100, where data were acquired
with the PCTDR soware (Campbell Scientic Inc., Loga n, UT) on
a PC, and for the Wet2 sensor, where data were collected with a GP1
datalogger (Delta-T Devices Ltd, Cambridge, UK).
Because of varying sensor geometries (i.e., number of rods, rod
spacing, and lengths) and associated variations in sensing vol-
umes (Table 2), an experiment was conducted to determine the
container size required to contain the electromagnetic elds of
all sensors within the measured soil samples. e container diam-
eter was chosen based on the instrument with the largest sensible
diameter. Each EM sensor was rst positioned vertically at the
wall of a rectangular container (0.22 m × 0.22 m × 0.30 m) lled
with deionized water (i.e., the sensor head in air and rods fully
submersed). Each sensor was then sequentially moved toward the
container center with a linear micro-positioning stage in 1.27 mm
steps. e sensor output plotted against the sensor position (dis-
tance from wall) within the container depicts locations of signal
change that mark the eective sensing distance of the sensor rela-
tive to the wall. e resulting sensing diameters are compared in
Table 2 with manufacturer specied values described in user manu-
als or charts. To allow direct comparison of the various EM sensors,
their outputs (dielectric permittivities, voltage, period, etc.) were
normalized according to:
( ) ( )
nor air c air
/
i
Y YY YY=- -
[1]
where Yi is the sensor response at any position between container
wall and center, Y
air
is sensor response in air, and Y
c
is the response
at the center of the container, where the sensor electrode EM eld
is assumed to be fully conned within the water.
Six nonsaline soils varying from sandy to clayey textures and one
saline soil, all from Arizona, were evaluated together with an
organic plant potting mix. Table 3 lists physicochemical properties
of considered soils. Clay, silt, and sand contents were determined
with a laser diraction analyzer (Beckman Coulter LS 13 320),
particle density was determined using a water pycnometer, and spe-
cic surface areas (SSA, m2 g−1) were measured with a gas adsorp-
tion surface area analyzer (Beckman Coulter SA-3100). Loss on
ignition (LOI, %), cation exchange capacity (CEC mmolc/100 g),
electrical conductivity (EC, dS m−1) and pH in CaCl2 were deter-
mined according to Sparks (1996).
Soil samples were compacted into polycarbonate containers (12
cm inner diameter, 20.3 cm tall) at varying water contents, from
oven dry to relatively wet conditions (about 0.35 m3 m−3) in
0.05 m3 m−3 steps. Initially, reference bulk density values were
determined for each soil by packing oven-dried soil into the poly-
carbonate containers, dening the reference dry mass for each soil.
Water was then added incrementally to obtain target volumetric
water contents based on the container total volume. At each incre-
ment, water was thoroughly mixed with a similar mass of dry soil
and packed into the polycarbonate containers at similar densities.
Table 4 shows sample statistics for bulk densities and water con-
tents for the seven soils. Gravimetric water content was determined
by oven drying (105°C, 24 h) of the soils aer measurements with
all EM sensors were completed.
Table 2. Number (n) and length (L) of prongs and sampling volume a nd
equivalent diameter of the tested EM sensors.
Sensor
Prong
Sampli ng‡
volume
Sampli ng‡
diameter
Meas.
sampling§
diameternL
cm cm3——— c m ——————
TDR100† 315 ––4.4
CS616 230 374 0 12.6 12
e ta P. 4675 4 2
Hy dra P. 44.5 32 32.4
SM300 25.1 100 55.2
Wet 2 36.8 500 9.7 nd¶
5TE 3 5.2 300 8.6 4.4
10HS 210 110 0 11. 8 nd
† Custom-made probe.
‡ Obtained from user manuals.
§ Obtained experimentally (Fig . 3).
¶ nd: not determi ned.
Fig. 1. Evaluated electromagnetic (EM) sensors and experimental setup
(datalogger and a soil sample).
www.VadoseZoneJournal.org p. 4 of 16
Evaluated sensors included the TDR100 and CS616 (Campbell
Scientific Inc., Logan, UT), SM300, Wet2, and Theta Probe
(ML2x) (Delta-T Devices Ltd, Cambridge, UK), 5TE and 10HS
(Decagon Devices Inc., Pullman, WA), and Hydra Probe (Stevens
Water Monitoring System Inc., Portland, OR). e sensors were
inserted one at a time into each soil sample in the following order:
TDR100/CS616/10HS/SM300/eta Probe/5TE/Hydra Probe/
Wet2. e 20.3 cm tall polycarbonate container was made of two
10.15 cm tall cylinders taped together and packed with each soil. To
deal with possible soil variability in terms of bulk density and water
content along the 20.3 cm tall soil sample and due to the variable
sensor electrode lengths (Table 2), each soil sample was rst mea-
sured with the longer sensors (TDR100, CS616, and 10HS) in the
20.3 cm tall sample; the soil column was then split into two halves
and measured with the shorter sensors (SM300, eta Probe, 5TE,
Hydra Probe, and Wet2), as shown in Fig. 2. As a result, the shorter
EM sensors were inserted and measured at four ends (inserted from
top and bottom into both sample halves) and the longer sensors
were inserted and measured at two end positions (inserted from
top and bottom of the entire column). To avoid artifacts due to soil
disturbance, the EM sensors were carefully inserted into the soil
sample, avoiding locations of previously inserted sensors. Average
values of the dielectric permittivity, voltage, or period were plotted
against measured volumetric water content to evaluate the per-
formance of each sensor with factory-supplied calibration equa-
tions. Root mean squared deviations (RMSD) of q determination
with factory-supplied and soil-specic equations were computed
to assess quality-of-t and accuracy. Sensor reproducibility was
evaluated by the coecient of variation (CV, %) obtained from
replicate measurements.
Table 3. Physicochemical properties of investigated soils.
Soil Clay Silt Sand ρp† ρbfSSA LOI CEC EC pH (C aCl 2)
————— % —————————— —— g cm−3———— cm3 cm−3 m2 g−1 %mmolc/100g dS m−1
AZ2 3.0 4.3 92.7 2.63 1.55 0.42 1.8 0.6 1.8 1.21 7.3
AZ6 21.5 21.4 5 7.1 2 .59 1.40 0.55 17. 5 2.1 8.2 1.32 7.6
AZ9 20 .9 59.7 19.4 2.57 1.13 0. 61 8.8 10.0 30.7 1.40 6.3
AZ11 36.7 37.0 26.3 2.69 1.36 0.60 30.1 3.4 14 .1 0.94 7.9
AZ15 28.0 62 .9 9.1 2.46 1.30 0.58 21.6 5.5 21.3 8.39 7. 4
AZ18 6 8.9 17.7 13.4 2 . 61 1.30 0.63 50.8 6.0 16 .3 1.65 6.5
ORG 2.6 13.7 83.7 1.83 0.38 0.79 2.1 55.1 2 7.3 4.80 5.9
† ρp, soil par ticle density; ρb, soil bu lk density, f, soil tota l porosity (f = 1 − ρb/ρp); SSA, specic surface are a; LOI, loss on ignition for organic mat ter content; CEC,
cation exchange capacit y; CE, soil electrical conduct ivity in the saturation extract; pH in CaCl2.
Fig. 2. Sketch illustrating the experimental procedure used to obtain a
representative measurement for various electromagnetic (EM) sensors
with dierent rod lengths.
Table 4. Statistics for volumetric water contents (q) and bulk densities
(ρb) of all soil samples prepared for this study.
Soil
θ ρb
Min. Max. Min. Max. Avg. CV
—— m 3 m−3——— ——— g c m −3———————— %
AZ2 0.003 0.342 1.497 1.602 1.553 2.3
AZ6 0.012 0.345 1.341 1.464 1.404 3.0
AZ9 0.011 0 .351 1.088 1.169 1.130 2 .5
AZ11 0.003 0.355 1.309 1.478 1.363 4.1
AZ15 0. 010 0.358 1.239 1.383 1.299 4.0
AZ18 0 .013 0.352 1.070 1.204 1.134 3 .5
ORG 0.010 0.340 0. 353 0.400 0.378 4.2
www.VadoseZoneJournal.org p. 5 of 16
Characteristics of EM sensors and evaluated calibration equations
are presented in the following.
TDR100
e TDR technique determines soil water content by measuring
the travel time of a GHz frequency electromagnetic pulse through
a metallic waveguide (probe) inserted into the soil. As the soil water
content increases, the soil dielectric permittivity and travel time
increases, and q can be determined by means of an empirical or
physically-based ca libration function. In general, the TDR dielectric
permittivity determinations for mineral soils are well described by
the Topp et al. (1980) equation (Eq. [2a]) and Schaap et al. (1997),
for example, works well for organic forest soils (Eq. [2b]).
23
0.053 0.0292 0.00055 0.0000043q =- + e- e + e [2a]
0.885
(0.133 0.146)q = e- [2b]
Wet2
e Wet2 sensor measures the capacitance of the material between
the inner and outer metallic rods of the sensor and infers the
dielectric properties from a sensor calibration le, which contains
standard capacitance readings obtained with the sensor inserted
in various reference liquids with known dielectric permittivity
(Hamed et al., 2006; de Paz et al., 2011). e manufacturer rec-
ommended calibration equations are (Delta-T Devices, 2007):
( )
0.099 0.178 for mineral soilsq= e- [3a]
( )
0.091 0.182 for clay soilsq = e- [3b]
( )
q = e- 0.119 0.167 for organic and sandy soils [3c]
5TE
e 5TE is the new version of the ECH
2
O-TE sensor (Decagon
Devices, Inc., 2010) that measures the water content by means
of a capacitance technique. e sensor is precalibrated for four
standards, namely: air, glass beads, glass beads saturated with
ethylene glycol, and pure ethylene glycol. e individual sensor
calibration corrects sensor-to-sensor variability and establishes a
linear relationship between the sensor output and the real part
of the dielectric permittivity (Rosenbaum et al., 2010). e user
manual suggests to apply the Topp et al. (1980) equation (Deca-
gon Devices, Inc., 2010) for inferring soil water content with an
accuracy of about 3% in mineral soils with a solution EC below 10
dS m−1 and the use of soil-specic calibrations, if higher accuracy
(1–2%) is desired. A unique aspect of the 5TE (and 10HS) relative
to the other tested EM sensors is the coating on the electrodes. e
electrodes are embedded within a circuit board, thus the epoxy
of the circuit board aects the sensor output in a similar way to
coated probes (Nemali et al., 2007, Blonquist et al., 2005). is can
be a benet as it isolates the electrodes from lossy or conductive
soil, allowing measurements at higher EC; however, it also makes
direct soil permittivity measurements hard to interpret.
is sensor has been well-characterized for the inuences of tem-
perature (Kizito et al., 2008; Saito et al., 2009; Assouline et al.,
2010; Rosenbaum et al., 2011) and solution electrical conductivity
(Kizito et al., 2008; Rosenbaum et al., 2011) on dielectric permit-
tivity measurements. Sensor-to-sensor variability (Rosenbaum et
al., 2010) as well as calibrations for some soils and standard liq-
uids have also been reported (Ganjegunte et al., 2012; Sakaki et al.,
2011; Rosenbaum et al., 2011; Rosenbaum et al., 2010; Saito et al.,
2009). However, there is a lack of information about the inuence
of soil properties on the dielectric permittivity response as pointed
out by Rosenbaum et al. (2010).
10HS
e operation principle of the 10HS sensor is similar to the 5TE,
which charges and discharges the two prongs of the electrode
(capacitor) while measuring the charge time and relating it to the
material dielectric permittivity (Decagon Devices, Inc., 2009). e
user manual claims an accuracy of 0.03 m
3
m
−3
q when the calibra-
tion for mineral soils (Eq. [4a]) is applied for solution EC < 10 dS
m
−1
, and also presents a calibration function obtained in reference
media (Eq. [4b]) to determine the real dielectric permittivity.
93 62
3
2.97 10 mV 7.37 10 mV
6.69 10 mV 1.92
--
-
q= ´ - ´
+´ - [4a]
10 4 7 3
42 2
2.589 10 mV 5.01 10 mV
3.523 10 mV 9.135 10 mV 7.457
--
--
e= ´ - ´
+´ -´ +
[4b]
SM300
e relatively new SM300 sensor replaces the previous SM200 and
operates at 100 MHz with a dierential voltage output measured
with a datalogger. e SM300 reading in volts (V) is converted
to water content values by combining soil calibrations along with
sensor calibration steps as presented in the following (Delta-T
Devices, 2010).
543
2
1.157 V 4.319 V 6.098 V
3.995 V 1.77 V 0.071
q= - +
- +- (mineral) [5a]
543
2
1.262 V 4.712 V 6.652 V
4.358 V 1.931 V 0.039
q= - +
- +-
(organic) [5b]
www.VadoseZoneJournal.org p. 6 of 16
2
3 45
1 14.868 V 33.56 V
51.223 V –36.283 V 9.715 V
e= + -
++
[5c]
Theta Probe
e eta Probe is an impedance sensor with a xed working fre-
quency of 100 MHz. e voltage output is proportional to the soil
dielectric permittivity as dened in Eq. [6a]. e voltage output
can also be expressed in terms of soil water content using similar
polynomial calibration curves for mineral (Eq. [6b]) and organic
(Eq. [6c]) soils (Delta-T Devices, 1999).
23
1.07 6.4 V 6.4 V 4.7 Ve= + - + [6a]
32
0.56 V 0.762 V 0.762 V 0.063q= - + - (mineral) [6b]
32
0.61 V 0.831 V 0.831 V 0.030q= - + - (organic) [6c]
e eta Probe has been widely used (Table 1) for monitoring
water content under both laboratory and eld conditions (Schmutz
and Namikas, 2011; Baggaley et al., 2009; Lopez-Vicente et al.,
2009; Verhoef et al., 2006) and calibration functions have been
developed for a variety of media such as soilless substrates (Nemali
et al., 20 07; Kang et al., 2010; Kargas and Kerkides, 2008) and for
soils with dierent physicochemical properties (Fares et al., 2011;
Kargas and Kerkides, 2008; Foley and Harris, 2007; Lukanu and
Savage, 2006; Kaleita et al., 2005; Tsegaye et al., 2004; Huang et
al., 2004; Robinson et al., 1999).
Hydra Probe
e Hydra Probe is an electrical impedance probe that operates
at 50 MHz and measures real (e¢) and imaginary (e²) dielectric
permittivities. e raw signal outputs are four analog dc voltages
which are used to calculate e¢, e², bulk electrical conductivity, and
temperature (Seyfried and Grant, 2007). is unique characteristic
of providing both components of the complex permittivity may
contribute to the heightened interest in research and the broad
application of the Hydra Probe by many agencies (Table 1).
e performance of the Hydra Probe has been evaluated for frozen
soils (Kelleners and Norton, 2012; Pringle et al., 2009; Yoshikawa
and Overduin, 2005), dead and live moss (Yoshikawa et al., 2004),
solid waste (Loiskandl et al., 2010), and for soils with dierent
physicochemical characteristics (Logsdon et al., 2010; Leao et al.,
2010; Kelleners et al., 2009; Seyfried et al., 2005; Seyfried and
Murdock, 2004; Bosch, 2004) for both water content and bulk
electrical conductivity measurements.
Several q vs. e¢ relationships (a total of 23 equations) are factory-sup-
plied for dierently textured soils including both corrected (e¢TC)
and uncorrected (e¢) temperature eects on real dielectric permit-
tivity (Stevens Water Monitoring System, Inc., 2007). Default
calibrations are presented for sand, silt, clay, and loam. Previous
studies of Seyfried et al. (2005), Seyfried and Murdock (2004), and
Bosch (2004) show the performance of the default sand, silt, and
clay equations. ey concluded that application of the clay equation
leads to overestimation of q. e calibration function attains an
unrealistic shape at high q values and was not adequate for all tested
soils. is is in part due to the limited dielectric range of the Hydra
Probe and other EM sensors, which are oen targeted for dielectric
permittivities of dr y through saturated mineral soils (i.e., 3 < e < 40,
Blonquist et al., 2005). None of the four above mentioned calibra-
tion equations eectively described measured data over a wide range
of q. Seyfried and Murdock (2004) concluded that the calibration
for sand is probably the best choice for q up to 0.33 m3 m−3 and the
silt calibration is best for higher q values. For our data, best ts were
obtained with the default equation for loam soils (Eq. [7]), which is
provided with no correction for temperature eects on e¢ (Stevens
Water Monitoring System, Inc., 2007).
( )
0.109 0.179 mineral, loam
¢
q= e- [7]
CS616
e Campbell Scientic soil water reectometer, CS616, is the
replacement for the CS610 and CS615 sensors and has a higher
frequency oscillator (175 MHz input signal) than the previous
versions. It sends electromagnetic pulses along its two metal rods
and measures the period, P, which is the inverse of the number
of reected pulses per second. e measured signal travel time or
period increases as the water content and the dielectric permittiv-
ity of the soil increases. is probe may be considered a pseudo-
TDR probe but operates at an order of magnitude lower frequency.
e probe has two 30 cm stainless steel rods and the typical peri-
ods measured in air and in water are 14.7 and 42 μs, respectively
(Campbell Scientic Inc., 2011).
To allow better comparison with other investigated sensors, which
have prong lengths between 4.5 cm (Hydra Probe) and 15 cm
(TDR 100), and to test the CS616 within the same soil volume
(12-cm internal diameter, 20.3 cm tall), the prongs were cut to
15 cm length. While shortening of the prongs facilitates better
comparison and application of the same experimental setup, it
also induces complexity as factory-supplied calibration equations
cannot be directly applied to the resulting data. For reduced prong
lengths, the sensor period outputs in air and water were measured
as 14.2 and 29.3 μs, respectively.
Applying an equation that relates the measured period (P) to probe
length (L) and e (Eq. [8a]), as presented in Campbell and Ander-
son (1998), allows conversion of the period measured with the
15-cm probe to an equivalent 30 cm probe length and evaluation
www.VadoseZoneJournal.org p. 7 of 16
of the factory-supplied calibration equations. Equation [8a] has
been used by Kelleners et al. (2005b) and Hansson and Lundin
(2006) to convert the measured period (P) to e values, thus facili-
tating comparison of the experimental data with other q versus e
calibration curves such as the Topp et al. (1980) equation.
( )
2
1
d
f
24
P
c tL
S
-
ìü
éù
æö
ïï
ïï
÷
ç
êú
÷
e= -
ç
íý
÷
êú
ç÷
ïç ï
èø
êú
ïï
ëû
îþ
[8a]
where Sf is a scaling factor, equal to 1024 for the CS616 sensor, c
is the speed of light in vacuum (2.9979 × 108 m s−1), and td is the
circuit delay time(s).
Although the physical length L for the CS616 probe is known, Kel-
leners et al. (2005b) suggested optimizing L for each probe because
the apparent dielectric length may vary. is can be accomplished
considering period values measured in air and water, according to:
( )
( )
w air
0.5 0.5
f w air
4
cP P
LS
-
=e -e
[8b]
where eair and ew are the dielectric permittivities of air and water,
respectively.
6Results and Discussion
Sensing Distance/Volume
Figure 3 shows the normalized sensor output as a function of
sensor position (i.e., between zero at the container wall and 11
cm in the center of the container). Table 2 presents diameters of
inuence (i.e., twice the lateral sensing distance indicated by the
EM eld being completely conned within the sample), which in
general show good agreement with values provided in the sensor
user manuals. Only for one sensor, the 5TE (Decagon Devices
Inc., Pullman, WA), there was a signicant deviation between our
measurements and the factory-supplied inuence diameter, where
the factory value was signicantly larger than our determination.
Based on these measurements and the information provided by the
sensor manufactures, the internal container diameter for sensor
evaluation in soils was chosen as 12 cm. It should be noted that the
measurement volume of the EM sensors typically decreases with
decreasing permittivity of the surrounding media.
Evaluaon of EM Sensor Output with Varying θ
Figures 4 and 5 show responses of the dielectric permittivity,
period, or voltage for EM sensors as a function of the volumet-
ric water content (q) for the seven reference soils from Arizona
listed in Table 3. Lines represent factory-supplied calibrations or
commonly applied functions from literature for dierent textural
groups and mineral, organic, and high EC
b
soils. e EM sensor
outputs as a function of q vary between devices, exhibiting linear
(e.g., CS616), concave upward (Wet2), and concave downward
(eta Probe) shapes. ese dierences can be attributed to dier-
ences in the measurement frequency and operation mode [capaci-
tance, impedance, TDR, or transmission line oscillation (TLO)]
of each sensor. ere are also eects from the specic electronic
measurement circuitry as well as from hardware and soware inter-
nal calibrations and corrections. Sakaki et al. (2011), who tested
four EM sensors in sand and applied the two-point a-mixing
model (Sakaki and Rajaram, 2006), also found similar variations
Fig. 3. Normalized sensor output (Eq. [1]) obtained in a container
lled with deionized water by moving the sensor from the container
wall toward the center.
Fig. 4. TDR100, Wet2, 5TE, and 10HS sensor outputs as a function
of volumetric water content for all investigated soils.
www.VadoseZoneJournal.org p. 8 of 16
between sensors with the shape factor a varying from 0.46 to 4.6.
ey attributed these variations to specic sensor characteristics
including prong geometry, printed circuit board design, and sensor
head sensitivity.
In general, the sensors exhibit signicant output dierences for
the organic soil (ORG) and for the high EC soil (AZ15) when
compared to mineral soils (AZ2, AZ6, AZ9, AZ11, and AZ18),
although the extent of these dierences varies among sensors. For
the ORG, the sensor outputs are in general lower than for min-
eral soils. is is expected due to the low bulk density and high
porosity of organic material (Topp et al., 1980; Roth et al., 1992).
However, for the Wet2 and Hydra Probe, the ORG responses to q
are similar to the sandy soil AZ2, and for the CS616, practical ly no
dierence was found between the organic and mineral soils. e
largest deviations between responses to mineral soil AZ2 (higher
sand content and lower EC value) and the ORG were observed
with the TDR100, 10HS, eta Probe, SM300, and 5TE sensors.
ese variations are probably due to the dielectric dispersion or
relaxation eect on sensor output, which increases with decreas-
ing sensor frequency oscillation and increases with increasing q.
Coecients of variation (CV) of the sensor’s repeated measure-
ments were 0.4% for TDR, 1.3% for CS616, 4.2% for eta probe,
4.6% for 10HS, 5.9% for 5TE, 6.6% for Wet2, 8.4% for SM300,
and 8.6% for Hydra Probe. ese values were obtained by com-
puting average, standard deviation and CV values for each sample
and then computing an average CV for all soil samples across the
range of measured q. e variation in CV values shown here are
likely associated with sensor specic electronics and oscillation
frequency, probe geometry, and their sensitivity to soil heteroge-
neities and air gaps. e low average CV values for the TDR100
(0.4%) and the CS616 (1.3%) seem to correlate to their high mea-
surement frequencies, while the high-CV SM300 (8.4%) and
Hydra Probe (8.6%) sensors are at the midrange of measurement
frequencies as shown in Table 1.
Sensor Response, Performance and
Calibraon Funcon Evaluaon
Evaluated sensor output responses to q and their dierences among
considered soils are discussed in detail below as well as the perfor-
mance of manufacturer-provided calibration functions and other
functions from the literature (i.e., those presented in the Material
and Methods section).
TDR100
For the evaluated mineral soils (Fig. 4a) the Topp et al. (1980)
equation provided RMSDs from 0.009 (AZ1) to 0.042 m3 m−3
(AZ18) and an average value of 0.023 m3 m−3 for all mineral soils,
including the high EC soil (AZ15). However, for the AZ15 soil,
the acquired waveforms were increasingly aected by the EC
b
as
water content increased (i.e., due to attenuation of the electro-
magnetic signal) and the second reection of the waveform at the
end of the rod could not be determined for water contents higher
than about 0.25 m
3
m
−3
. erefore the dielectric permittivity was
determined only up to this limit. In general, an increase in R MSD
was observed (Table 5) with increasing clay content or specic sur-
face area of the mineral soils (Table 3). is result is anticipated
due to eects of clay mineralogy, particle shape, and high surface
area (i.e., eects of bound water) altering the dielectric permittiv-
ity of the soil relative to the Topp et al. (1980) function response
(Hoekstra and Doyle, 1971; Dirksen and Dasberg, 1993; Or and
Wraith, 1999; Yu et al., 1999; Jones and Or, 2005; Blonquist et al.,
2006). For the ORG, the response was well described by Eq. [2b]
with RMSD = 0.013 m3 m−3. is signicant deviation of the
ORG from the mineral soils is due to the very low density and high
porosity of the solid phase (Topp et al., 1980; Roth et al., 1992).
Wet2
Figure 4b shows the sensor output (dielectric permittivity) as a
function of q and the factory-supplied calibration equations for
mineral (Eq. [3a]), clay (Eq. [3b]), and organic and sand (Eq. [3c])
soils (Delta-T Devices, 2007) with the Topp et al. (1980) equation
as reference. In general, all measured points are above the Topp et
al. (1980) equation, suggesting that the Wet2 sensor overestimates
e when compared to TDR100, similarly to the data presented by
Inoue et al. (2008) and Bouksila et al. (2008) for sandy soils and
Regalado et al. (2007) for three volcanic soils (clay, sandy clay, and
sandy loam textures). As the Wet2 has the lowest oscillation fre-
quency (20 MHz) among all tested EM sensors, its higher permit-
tivity output can in part be due to the frequency dependency of
the real permittivity component, which tends to increase as mea-
surement frequency decreases (Regalado et al., 2007; Jones et al.,
Fig. 5. Sensor output of (a) SM300, (b) eta Probe, (c) Hydra
Probe, and (d) CS616 as a function of the volumetric water content
for all investigated soils.
www.VadoseZoneJournal.org p. 9 of 16
2005). However, the mechanisms behind this behavior are not well
understood and should be further investigated.
e factory-supplied calibration for mineral soils (Eq. [3a]) worked
well for all soils, including the organic soil, but not for the AZ15
(high EC) soil. e average RMSD for all soils, excluding AZ15,
was 0.034 m3 m−3 (Table 5). Kargas et al. (2011) obtained simi-
lar RMSD for seven inorganic soils (0.040 m3 m−3). e mea-
sured data for the ORG soil for water content values higher than
0.2 m3 m−3 deviates from the factory supplied calibration function
for organic and sand soils (Eq. [3c]). is result may indicate a
stronger inuence of dielectric dispersion or relaxation eects due
to the relatively high EC of the ORG soil. For the soil with the
highest sand content (AZ2), measurements were also poorly cor-
related with the organic and sand calibration equation (Eq. [3c]).
Hamed et al. (2006) tested the Wet2 sensor in ve soils (two sandy
loam soils, a medium sand, a loamy sand, and a heavy clay) and
also obtained calibration coecients close to the factory-supplied
values (Eq. [3a]) for mineral soils. For the heavy clay soil (65.2%
clay with predominantly smectite clay minerals), the tted equa-
tion deviated considerably from the factory-supplied equation.
Dierences between the ORG and the mineral soils (AZ2, AZ6,
AZ9, AZ11, and AZ18) were less pronounced for the Wet2 sensor
when compared to TDR100. e response for the more saline
AZ15 soil was somewhat unexpected since it increases rapidly and
then remains almost stable for water contents higher than 0.2 m3
m
−3
. While the same nonlinear behavior (approximately a second
degree polynomial) was observed for data presented by Inoue et al.
(2008) for a sandy soil spiked with NaCl solution to reach a soil
solution EC higher than 10 dS m
−1
, the reasons for this convex
downward behavior are not clear. Because of the obvious high sen-
sitivity to soil salinity Inoue et al. (2008) suggested to calibrate the
Wet2 sensor for dierent salinity levels (low: < 4 dS m
−1
, medium:
4–10 dS m−1, and high: > 10 dS m−1).
In summary, the factory-supplied calibration equation for mineral
soils seems to be the best choice for estimating q with the Wet2
sensor if no soil-specic calibration is available. Soil-specic cali-
brations are necessary for saline soils, soilless media, and horticul-
tural substrates (as the materials evaluated by Kargas et al., 2011,
Incrocci et al., 2009, Hansen et al. (2006), and Scoggins and van
Iersel, 2006). e factory-supplied calibration for organic and sand
soils can be only used for organic soils with low EC; the calibration
did not work well for the very sandy soil (AZ2) and the ORG soil
with an EC = 4.8 dS m−1.
5TE
Figure 4c shows the dielectric permittivity response of the 5TE
sensor for all considered soils, along with the Topp et al. (1980)
(Eq. [2a]) and other calibration equations presented in Rosenbaum
et al. (2011), Varble and Chavez (2011), and Sakaki et al. (2011)
for mineral soils, and the Schaap et al. (1997) equation for organic
soils (Eq. [2b]). e measurements obtained for the mineral soils
(AZ2, AZ6, AZ9, AZ11, and AZ18) closely follow the Topp et
al. (1980), Rosenbaum et al. (2011) and Varble and Chavez (2011)
equations for water content values up to about 0.15 m
3
m
−3
, but
deviate signicantly for higher q values. is deviation from the
Topp et al. (1980) equation is unexpected. Good agreement of
dielectric permittivities measured with the 5TE sensor using the
Table 5. Root mean square deviation (RMSD) for measured and estimated q. When two equations are cited, the rst refers to factory-supplied
relationships and the second to selected relationships from literature (e.g., Eq. [8e]). For the eta Probe, Eq. [6a] converts row counts to e and then the
Topp et al. (1980) equation is applied for all soils.
Sensor Eq. AZ2 AZ6 AZ9 AZ11 A Z15 A Z18 ORG AV 1† AV 2‡
———————————————————— m 3 m−3 ———————————————————————————————————————————
TDR100 [2 a], [2b] 0.009 0.016 0.034 0.026 0.024 0.042 0.013 0.023 0.023
Wet 2 [3a] 0.023 0.018 0. 019 0.046 0.078 0.051 0.046 0.040 0.034
5TE [2a], [2 b] 0.050 0.036 0.040 0.033 0.083 0.039 0.041 0.046 0.040
10HS [4a] 0.077 0.064 0.084 0.063 0.086 0.078 –0.075 0.073
[2a] , [2b] 0.041 0.041 0.058 0.033 0.049 0.059 0.025 0.044 0.043
SM300 [5 a], [5 b] 0. 019 0.036 0.039 0.049 0.136 0.047 0.035 0.052 0.037
[2a] 0.016 0.035 0.034 0.048 0.120 0.042 0.059 0.051 0.039
e ta P. [6b], [6c] 0.020 0.029 0.020 0.042 0. 091 0.026 0.014 0.035 0.025
[6a], [2a] 0.024 0.033 0.022 0.045 0.093 0.027 0.036 0.040 0.031
Hy dra P. [7] 0.018 0.042 0.039 0.068 0.272 0.056 0.046 0.077 0.045
[2a] 0.024 0.067 0.055 0.092 0.522 0.072 0.038 0.124 0.058
CS616 [8d] 0.058 0.156 0.049 0 .15 7 0.962 0.169 0.179 0.247 0.128
[8e] 0.016 0.043 0.034 0.043 0.344 0.050 0.060 0.084 0.041
† AV1: average of all soil s.
‡ AV2: average of all soils but AZ15.
www.VadoseZoneJournal.org p. 10 of 16
Topp et al. (1980) equation have been reported by Rosenbaum
et al. (2011), Varble and Chavez (2011), and Kizito et al. (2008).
However, Saito et al. (2009) also found the same kind of devia-
tion for water contents higher than 0.20 m3 m−3, for a Loess soil
from China. is problem may result from diering experimental
procedures used for each study. Here and in Saito et al. (2009),
the sensors were inserted vertically, leaving the probe head out of
the soil sample and always surrounded by air. e 5TE has a thin
probe head covered with a so black plastic material that obviously
aects the measured permittivity; therefore, measurement resu lts
are inuenced by the dielectric surrounding the probe head (air in
this case). Since the 5TE sensor was factory-calibrated with prongs
and head completely submerged in liquids and solid–liquid mix-
tures (Decagon Devices, Inc., 2010), the manufacturer calibration
is most accurate when the sensor head is also surrounded by soil,
liquid, or other media.
For the mineral soils AZ2, AZ6, AZ9, AZ11 and AZ18, little
inuence of soil texture on the dielectric permittivity response
was observed. e inuence was similar to the TDR100, but much
lower than the variation found for the Wet2 sensor. is might
be attributed to a combination of coated electrodes (reduced sen-
sitivity) and a higher frequency oscillation of the 5TE (70 MHz)
compared to the 20 MHz of the Wet2 sensor. Kizito et al. (2008)
evaluated the ECH
2
O-TE (the old version of the 5TE) and also
found little dierence in the sensor response for six soils with vary-
ing textures and relatively low EC (0–0.5 dS m
−1
), concluding that
a single calibration curve could be used for all tested mineral soils.
As expected, the ORG and the more saline mineral soil (AZ15)
deviated from the responses for the other mineral soils, suggesting
that soil-specic calibrations are necessary for these media. e
5TE user manual (Decagon Devices, Inc., 2010) claims that no
decrease in accuracy occurs for soil solutions with EC < 10 dS
m
−1
, but does not provide a reference standard EC threshold value
of saturated paste or other soil–water extraction method. While
Saito et al. (2009) showed no accuracy decrease in q determination
for a Loess soil with EC = 3 dS m−1 (measured in a 1:5 soil–water
mixture), our study indicates a signicant deviation from the aver-
age mineral soil behavior for the AZ15 soil with an EC = 8 dS m
−1
measured on a saturation paste extract, according to the procedure
described in Sparks (1996). Ganjegunte et al. (2012) also reported
overestimation of q with the 5TE sensor in laboratory and eld
tests using the Topp et al. (1980) equation in a clay loam soil with
EC (saturation extract) of 3.2 dS m−1.
10HS
Figure 4d depicts the 10HS sensor raw output (volts) as function
of the water content for the studied soils and the factory-supplied
calibration equation for mineral soils (Eq. [4a]). No calibration
is provided for organic or soilless substrates. e suggested cali-
bration equation ts measured data well for the mineral soils
AZ2, AZ6, AZ9, AZ11, and AZ18 for water contents between
0.15 and 0.3 m3 m−3. Outside this range, the water content is
underestimated when suggested calibration (Eq. [4a]) is applied,
as manifested in relatively high RMSDs (average RMSD = 0.073
m
3
m
−3
, shown in Table 5). Mittelbach et al. (2012) found similar
results for clay loam soil from Switzerland, stating that the 10HS
fails to measure water content beyond 0.4 m
3
m
−3
. Because the
10HS is relatively new, there is little scientically-based perfor-
mance information available in literature (Table 1).
e calibration provided for the dielectric permittivity (Eq. [4b])
allows conversion of the 10HS sensor voltage output to e (Fig. 6a).
As illustrated in Table 5, the application of the Topp et al. (1980)
Eq. [2a] and Schaap et al. (1997) Eq. [2b] improved water content
estimations for the mineral and organic soils (average RMSD =
0.044 m
3
m
−3
), despite the fact that as shown in Fig. 6a the e data
for all mineral soils (excluding AZ15) fell below the Topp et al.
(1980) equation, resulting in underestimation of q when the Topp
et al. (1980) equation was applied. erefore, improvement of
factory-supplied calibration seems necessary for the 10HS sensor.
SM300
In Fig. 5a, the SM300 sensor raw count response is presented as a
function of q together with the factory-supplied equations for min-
eral (Eq. [5a]) and organic (Eq. [5b]) soils. e equation for min-
eral soils ts the sandy soil data (AZ2) considerably well (RMSD
= 0.019 m3 m−3), but deviates for all other mineral soils (AZ6,
AZ6, AZ11, and AZ18) for q higher than about 0.25 m3 m−3 and
Fig. 6. Dielectric permittivities determined from raw counts and
plotted as a function of q for sensors 10HS (a) with the calibration
presented in Eq. [4b], for the SM300 (b) with Eq. [5c], for the eta
Probe (c) with Eq. [6a] [# equations from Kargas and Kerkides (2008)
for sand1, silty clay loam (SCL), and compost], and for CS616 with
Eq. [8a] (d).
www.VadoseZoneJournal.org p. 11 of 16
completely fails for the more saline AZ15 soil. e equation for
organic soils (Eq. [5b]) worked well for the investigated ORG soil.
Average RMSD for al l soils (mineral and organic), excluding AZ15,
was 0.037 m3 m−3.
Sensor raw counts (volts) were converted to dielectric permittivities
with Eq. [5c] (Fig. 6b). As shown, estimation of q obtained with
Topp et al. (1980) (Fig. 6b) and Eq. [5a] (Fig. 5a) are very similar
for mineral soils (Table 5).
Theta Probe
e factory-supplied calibration equations (Eq. [6b] and [6c]) are
well correlated with the sensor response to q (Fig. 5b) for the sandy
soil (AZ2) and the ORG soil with RMSDs of 0.020 and 0.014 m
3
m
−3
, respectively (Table 5). Excluding the more saline AZ15 soil,
the accuracy of measured water contents was 0.025 m
3
m
−3
for all
other mineral and the organic soils, which is also specied in the
user manual. In general, the experimental data for all mineral soils
(AZ2, AZ6, AZ9, AZ11, AZ15, and AZ18) lie above the calibra-
tion curve, indicating overestimation of q by about 3% (relative
error of 0.031 m3 m−3, considering the six mineral soils). Kargas
and Kerkides (2008) obtained similar results with the lowest
RMSD for sandy soils and higher RMSD and overestimation of
q for the more clayey and loamy soils. is overestimation for the
mineral soils is also observed when converting the sensor output
to dielectric permittivity with Eq. [6a], compared to the Topp et
al. (1980) equation (Fig. 6c). According to Robinson et al. (1999)
the reasons for eta Probe overestimation of q (approximately
4% in their work) is unclear, but could be associated with the sen-
sor’s rod conguration, which connes the EM eld closer to the
inner rod than other tested sensors (see Table 2). is makes the
eta Probe more sensitive to compaction due to soil displacement
caused by probe insertion.
Kargas and Kerkides (2008) studied 21 soils and organic porous
media. Some of their tted calibration curves are presented in
Fig. 6c for a sandy soil (sand1), a silty clay loam soil (SCL, 0–5
cm) and an olive waste compost material (compost). As expected,
their sandy soil calibration (sand1) ts the data obtained for AZ2
very well and closely follows the Topp et al. (1980) equation. e
calibration for the SCL soil is in accordance with data obtained
for all other mineral soils (AZ6, AZ9, AZ11, and AZ18). Cosh
et al. (2005) also proposed calibration equations for distinct soil
textural classes (clay, loam, and sand) and attributed the dierences
between soils to dierences in soil salinity, density, and soil compo-
sition eects. Working with 180 eld sites, these authors found an
average RMSD of 0.053 m
3
m
−3
using the factory-supplied calibra-
tion equations and 0.037 m
3
m
−3
when eld specic calibration
equations were applied.
As expected, the sensor response to the more saline soil (AZ15)
deviated signicantly from all other mineral soils, and exhibited
the same concave downward behavior that was observed for the
Wet2 and 10HS sensors.
Hydra Probe
e factory-supplied loam calibration (Eq. [7]) worked very well (Fig.
5c) for the AZ2 soil (RMSD = 0.018 m
3
m
−3
), but consistently over-
estimated the water content for all other mineral soils (AZ6, AZ11,
AZ15, and AZ18). Since no calibration is supplied for ORG soils,
we evaluated the ORG soil with Eq. [7] and the Topp et al. (1980)
equation and found a better t when the Topp equation was applied.
Response for the ORG soil was close to the sandy soil (AZ2), possibly
indicating inuence of EC and dielectric relaxation on the soil real
dielectric permittivity. e average RMSD for all soils, excluding
the more saline soil (AZ15), was 0.045 m3 m−3. e systematically
higher real dielectric permittivity response for soil AZ15 increased
dramatically for q higher than 0.25 m
3
m
−3
, reaching e¢ values as
high as 100 (higher than water) for q around 0.35 m3 m−3. Seyfried
and Murdock (2004) also observed higher values of e¢ for the Hydra
Probe when compared to TDR for some soils and attributed this to
the low frequency of the Hydra Probe (50 MHz), compared to the
GHz range of TDR instruments and to the inuence of soil proper-
ties such as clay content and clay mineralogy. Seyfried et al. (2005)
evaluated 20 soils with dierent textures and mineralogies. ey
found correlation between the deviation from a baseline equation
(Dq) and the tangent loss (tgd = e¢¢/e¢), and Logsdon et al. (2010)
found a correlation between the amount of sorbed water and the
slope of the calibration curves for a group of 18 soils.
CS616
To calibrate the CS616 sensor for the trimmed 15-cm rods, we
measured periods in water (P
w
) and air (P
air
) and calculated an
apparent dielectric probe length of L = 13.9 cm using Eq. [8b].
e circuit delay time t
d
was then determined with Eq. [8a] (t
d
=
6 ´ 10−9 s). Kelleners et al. (2005b) obtained optimized values
of L = 26.3 cm and td = 4.9 ´ 10−9 s for the original 30-cm long
CS616 probe. Figure 7a shows the optimized relations between
period and dielectric permittivities for the original 30-cm probe
Fig. 7. (a) Optimized relationships between e and CS616 raw count
(period) according to Eq. [8a] and [8b] for 30 cm and 15 cm long
probes and (b) converted raw count from 15 cm to 30 cm rod length
as a function of q.
www.VadoseZoneJournal.org p. 12 of 16
(data from Kelleners et al., 2005b) and the shortened 15-cm probe.
Period values measured with both probes are linearly correlated
(Eq. [8c]), which allows conversion of data presented in Fig. 5d to
equivalent 30-cm probe data (Fig. 7b). is allows comparison of
data obtained for this study with factory-supplied calibrations for
mineral soils (Eq. [8d]) and with an equation (Eq. [8e]) published
by Udawatta et al. (2011).
15cm 30cm
6.965 0.528PP=+
[8c]
2
0.0007 0.0063 0.0663
PP
q= - - (mineral) [8d]
2
0.0002 0.0182 0.283
PP
q= + - (Udawatta et al., 2011)[8e]
As seen in Fig. 7b, the factory supplied calibration only works well
for q values up to about 0.15 m3 m−3 and signicantly overestimates
q above this water content. As a result, a high RMSD is obtained
for all soils (average of 0.128 m3 m−3 even without the more saline
soil AZ15). Previous results of Mittelbach et al. (2012), Udawatta
et al. (2011), Varble and Chavez (2011), and Evett et al. (2011) also
indicated very high overestimation of q (higher than 0.1 m
3
m
−3
)
using the factory calibration (Eq. [8d]). On the other hand, the
calibration suggested by Udawatta et al. (2011) for a silt loam, silt
clay loam, and silt clay soils (Eq. [8e]) produced more reasonable
estimates for our data (RMSD = 0.041 m
3
m
−3
) as shown in Fig.
7b and Table 5. Rudiger et al. (2010), who tested the CS616 sensor
in 25 Australian soils with ECs rang ing from 0.1 to 3.8 dS m
−1
(5:1
soil–water proportion) found similar results. In their study, they
identied three groups of soils: (i) coarse sandy soils with responses
close to the factory-supplied calibration, (ii) clayey and high salinity
soils displaying a shi to higher period values, and (iii) high salinity
or electrical conductivity soils (3.8 dS m−1) with a signicant shi
to higher periods, reaching values higher than the period measured
in water (42 ms). Data obtained in this study (Fig. 7b) follow the
same trend as data obtained by Rudiger et al. (2010). e lowest
RMSD (0.058 and 0.049 m3 m−3), considering the factory calibra-
tion (Eq. [8d]), was obtained for soils AZ2 and AZ9, respectively
(Table 5), probably due to their lower clay content, specic surface
area and electrical conductivities (Table 3).
In general, organic soils exhibit lower values of raw count or equiva-
lent e than sandy soils for most of the evaluated EM sensors (see Fig.
4 and 5). However, for the ORG soil, the CS616 measured periods
were shied to the mineral soil region when the water content was
above 0.15 m
3
m
−3
. is was probably caused by the relatively high
EC value of this soil (4.8 dS m−1 in saturated paste extract).
Water content plotted against estimated e (from Eq. [8a] and [8c])
for all seven studied soils and the Topp et al. (1980) equation is
depicted in Fig. 6d. Again, q was estimated reasonably well for
water contents up to about 0.15 m
3
m
−3
, aer which signicant
overestimation of q was observed relative to the Topp et al. (1980)
equation. Unrealistic values of e, much higher than 80 (dielectric
permittivity of water), were obtained with the CS616 sensor and
with the Hydra Probe for very wet samples of the AZ15 soil.
Accuracy of Soil-Specic Calibraons
As with other studies, we also compared the performance of the
factory-supplied calibration equations with soil-specic calibra-
tions developed using soils from this study. is includes providing
alternative equations for specic soil textures. Taking a simplied
approach, relationships between q and the square root of sensor
output (e, voltage or period) were tted with a linear function for
the Wet2, 5TE, SM300, Hydra Probe, and CS616 sensors and a
third order polynomial was used for the 10HS, eta Probe, and
TDR100 (q vs. sensor output). For the soils investigated in this
study, all nonsaline mineral soils were grouped together for t-
ting (AZ2, AZ6, AZ9, AZ11, and AZ18), while the ORG and
the saline soils (AZ15) were tted separately, except for TDR100,
where AZ15 was included with the mineral soils. e tted coef-
cients, a, b, c, and d along with coecients of determination (r2)
are listed in Table 6. e sensor measurement accuracy reported by
manufacturers for standard factory-provided and soil-specic cali-
brations as well as q-RMSD values from this study are presented
in Table 7 for each sensor and tested mineral soil.
Soil water content measurement accuracies reported by manufac-
turers varied from 0.025 m
3
m
−3
for CS616 and SM300 to 0.05 m
3
m−3 for Wet2 and eta Probe, when factory-supplied calibrations
were applied for mineral soils (i.e., based on sensor user manuals).
ere is also evidence that soil-specic calibrations improve mea-
surement accuracy to values ranging from 0.020 to 0.030 m3 m−3.
For the investigated mineral soils, q-RMSD (used as a measure of
accuracy) obtained with factory-supplied calibrations showed a
much wider range of from 0.029 to 0.129 m3 m−3, and were, in
general, less accurate than what is claimed in sensor manuals (Table
7). is indicates a need for improving factory-supplied calibrations,
mainly for sensors CS616, 10HS, and the Hydra Probe. Exceptions
were the TDR100, Wet2, and eta Probe, where application of
factory-supplied calibration yielded even higher accuracies than
the values claimed in the user manuals. Use of the average soil-
specic calibrations obtained in this study for mineral soils AZ2,
AZ6, AZ9, AZ11, and AZ18 (Table 6) improved the accuracies
to levels ranging from 0.013 to 0.028 m3 m−3, which is a signi-
cant improvement and, in general, lies within the accuracy range
specied by the sensor manufacturers. Of course, these results are
limited to the soils considered in this study and comparisons should
be viewed with the understanding that ca librations presented here
are subject to the soil-specic features and conditions of this study
and by the sensors used as well as their manufacturer calibrations.
e soil-specic variability is one of the major motivations for using
dielectric standard uids rather than soils, for sensor calibrations,
and sensor-to-sensor comparisons, as performed by a number of
www.VadoseZoneJournal.org p. 13 of 16
researchers (Blonquist et al., 2005; Jones et al., 2005; Bogena et
al., 2007; Rosenbaum et al., 2010). However, it is dicult to nd
liquids that reproduce specic soil relaxing and conducting charac-
teristics, and soil-specic cal ibrations are oen necessary to improve
measurement accuracy on a site to site basis.
Assuming an accuracy threshold of 0.04 m
3
m
−3
for factory-sup-
plied calibrations of general mineral soils, the resulting measured
data in this study indicate that the TDR100, eta Probe, Wet2,
SM300, and 5TE calibrations met this accuracy threshold. e
CS616, 10HS, and Hydra Probe exhibited q-RMSD beyond this
limit. It is important to note that the 5TE sensor (and potentially
10HS) was used with the head outside of the soil sample, and there-
fore, its performance should be better with the probe completely
embedded within the soil.
Analyzing the q-RMSD obtained for the average mineral soil-
specic calibration (Table 7) we can categorize sensors in two
groups: one with q-RMSD of about 0.015 m3 m−3 (10H S ,
SM300, and eta Probe) and another with q-RMSD of about
0.025 m
3
m
−3
(TDR100, CS616, Wet2, 5TE, and Hydra Probe).
For the rst group of sensors, which are more accurate when
applied using average soil-specic calibrations for mineral soils
(lower q-RMSD), the data for the seven Arizona soils exhibit a
narrower distribution than data for the second group of sensors.
is suggests the second group of sensors (Hydra Probe, 5TE,
Wet2, CS616, and TDR100) may be more sensitive to variations
in soil-texture, clay content, and mineralogy, specic surface area
etc., than the rst group (10HS, SM300, and eta Probe). In
addition, while one might consider this dierence to be associ-
ated with the measurement frequency of the sensors, there is no
obvious correlation between these resu lts. Beyond a measurement
frequency eect, the sensitivity of the sensor to soil type seems
to also be dependent on the sensor type (capacitance, impedance,
or TLO), specic electronics and circuitry, and probe size and
design. With regard to measurement frequency, there is, however,
an interesting separation if we only look at the RMSD for the
AZ15 soil, the most challenging soil with 28% clay and EC of
8.4 dS m−1. For this case, the TDR had the lowest RMSD of all
sensors, and by comparison, the two coated sensors (5TE, 10HS)
and Wet2 sensor were 2–4 times larger in terms of the RMSD
while the remaining EM sensors had R MSDs 5–40 times greater
than the TDR100. Although the TDR100 was not able to mea-
sure e beyond a q value of about 0.25 m
3
m
−3
due to loss of the
second reection, it is clear from other studies that the higher
frequency measurements of TDR provide improved accuracy for
water content determination under challenging soil conditions
because interfacial polarization signicantly aects EM measure-
ments below about 200 MHz (Kelleners and Verma, 2010).
Table 7. Soil water content accuracies provided by sensor manufacturers
and root mean squa re deviations (RMS D) obtained i n this study for min-
eral soils with factor y-supplied and soil-specic ca librations (Table 6).
Sensor
θ accura cy, UM† θ-RMSD‡
Factory Soil specic Factory Soil specic§
————— m 3m−3 —————————————————
Wet 2 ±0.050 ±0.030 0.034 0.025
5TE ±0.03 0 < ±0.020 0.040 0.026
10HS ±0.030 ±0.020 0.073 0.013
SM300 ±0.025 _0.037 0.014
eta Probe ±0.050 < ±0.020 0.029 0. 015
Hydra Probe ±0.030 _0.048 0.028
CS616 ±0.025 _0.129 0.025
TDR100 ±0 .030 ±0.020 0.023 0.022
† UM: from user manual s.
‡ From this study for mineral soils AZ2, A Z6, AZ9, AZ11, and AZ18.
§ Average soil-spe cic calibrations obtained for t he mineral soils in this study
(Ta ble 6).
Table 6. Soil-specic calibrations for mineral soils AZ2, AZ6, AZ9,
AZ11, and AZ18 (Min.), and soils AZ15 [high electrical conductivity
(EC)] and ORG (organic, with moderate to high EC).
Sensor Group a b c d r2
Wet 2 Min .† −0.1323 0 .0833 0.95
AZ15 −0.2004 0.0906 0.99
ORG −0.0946 0.0861 0 .74
5TE Min. −0.2945 0.1625 0.97
AZ15 −0.1410 0.0849 0.98
ORG −0.2162 0.1619 0.98
10HS Min. −1 .3 054 5.8357 −8.3973 4.3775 0.98
AZ15 −2 .1243 9.8224 −14 .575 7. 2 6 4 4 0.98
ORG −1.4339 6.7254 −9.7848 5.1867 0.99
SM300 Min. −0.0795 0.5303 0.98
AZ15 −0.0931 0.4 465 0.97
ORG −0.0343 0.5749 0.99
eta
Probe
Min. −0.0444 0.5739 −0.4929 0.4182 0.98
AZ15 −0 .0357 0.5186 − 0.9741 0.9494 0.99
ORG −0.0053 0.5684 − 0. 2163 0 .1400 0.9 9
Hydra
Probe
Min. −0.1107 0.0826 0.95
AZ15 −0.0242 0.0399 0.99
ORG −0.0909 0.0948 0.93
CS616 Min. −0.5783 0 .15 27 0.95
AZ15 −0 .3352 0.0839 0.94
ORG −0.4422 0.1272 0.98
TDR100 Min. &
AZ15
−0.1070 0.0567 −0.0032 7.0 7´10−5 0.96
ORG −0.1229 0.1033 0.0089 2 .95´10−4 0.99
† Min., m ineral soils; a , b, c, and d are tting coe cients. For Wet2, 5TE, a nd
Hydra Probe: q = a + bÖe ¢; for SM300 : q = a + bÖV; for CS616: q = a +
bÖP; for 10HS, eta Probe: q = a + bV + cV2 + dV 3; and for TDR100:
q = a + be + ce2 + de3; r2 is the determi nation coecient.
www.VadoseZoneJournal.org p. 14 of 16
6Summary and Conclusions
e performance of factory-supplied calibration equations for
water content q were evaluated for eight EM sensors in seven well-
characterized soils using an experimental protocol that allowed
sequential insertion and measurement of investigated sensors into
the same soil samples with q varying from air dry to near satura-
tion. Insertion of the sensors into a large water-lled container and
step-wise movement of the sensors from the container wall toward
the container center allowed determination of the minimum soil
sample diameter (12 cm) required to fully contain the EM elds
emitted by all investigated sensors.
Most of the manufacturer-supplied calibration functions relating
q to voltage, raw count, or e were developed for dierently tex-
tured mineral soils. Application of dierent experimental calibra-
tion procedures to a varying number of dierently textured soil
samples render most supplied calibration equations inapplicable
for the entire range of textural classes as clearly shown in this study
(Fig. 4 and 5). For example, the factory-supplied calibration for
mineral soils for the Wet2 sensor represents an average response
for several mineral soils varying from very sandy to very clayey, but
the calibrations for the SM300, eta Probe, Hydra Probe, and
CS616 sensors are more adequate for sandy soils since they closely
followed the response of the soil with the highest sand content
considered in this study. It is suggested that manufacturers supply
calibration relationships for a general group of mineral soils (cover-
ing a wide range of textures), and specically for sandy and clayey
soils. Only the Wet2 (Delta-T Devices, 2007) and Hydra Probe
(Stevens Water Monitoring System, Inc., 2007) sensors come with
more specic factory calibrations. However, evaluation of these
calibration functions for clayey or sandy soils in this study and
in the literature reveals inaccuracies for organic substrates and
sandy soils for the Wet2 sensor (Eq. [3c]) and for several equa-
tions provided for the Hydra Probe. erefore, it would be useful if
manufacturers use a standardized procedure to develop calibration
equations. We believe the procedure presented here moves toward
the establishment of a standardized laboratory protocol for soil
water content- EM sensor calibrations.
Specic factory-supplied calibrations for organic soils are only
provided for the Wet2, SM300, and eta Probe sensors. ese
calibration equations were well correlated with experimental data
obtained with the eta Probe (RMSD = 0.014 m3 m−3), and
considerably well correlated with the SM300 sensor measurements
(RMSD = 0.035 m
3
m
−3
). e factory-supplied calibration for the
Wet2 sensor did not provide satisfactory results (RMSD = 0.046
m
3
m
−3
). e deviation of the Wet2 sensor calibration is in part
due to the eect of elevated EC (4.8 dS m
−1
) on sensor response,
which is especially pronounced in lower frequency sensors such
as the Wet2 (20 MHz compared to 100 MHz used in the eta
Probe and SM300 sensors). In future studies, organic soils with
lower EC values should be included, as well as soils with similar
characteristics but with varying amount of organic matter. In
particular, it came as a surprise that studies about the inuence of
organic matter on capacitance and impedance EM sensor response
are practically nonexistent in literature. Determination of water
content in a variety of organic soils with EM sensors is poorly
studied and not well understood in contrast to TDR (Nagare et
al., 2011; Kellner and Lundin, 2001; Roth et al., 1992; Schaap et
al., 199 7).
From evaluation of calibration equations relating e and raw count
(e.g., Eq. [4b], [5c], and [6a] for the 10HS, SM300, and eta
Probe), and expressions developed, but not explicitly presented
in user manuals for the Wet2, 5TE, and Hydra Probe sensors, it
is evident that they were developed for very specic conditions
for a variety of dielectric media (pure liquids, liquid mixtures, or
granular media). Jones et al. (2005) suggested that the application
of dielectric calibration standards requires in-depth knowledge
of their inuence on EM sensors, such as dielectric relaxation
and electrical conductance. ey recommended several standard
uids, classied as relaxing or nonrelaxing and conducting or
nonconducting , which covers the dielectric behavior of most soils
except for the worst case of relaxing and conducting, for which
a representative liquid analog has yet to be discovered. Because
each manufacturer may use a dierent set of dielectric calibration
standards (or dierent soils), dierent output responses (voltage,
e) may be observed relative to a calibration standard such as the
well-known Topp et al. (1980) relationship. erefore, it would be
benecial if common nonrelaxing and nonconducting dielectric
uids were applied by all EM sensor manufacturers to determine
output response as a function of e, i.e., for 10HS, SM300, eta
Probe, and CS616 (Hydra Probe provides direct measurement of
e and e¢¢). Such relationships can be included as an internal cali-
bration, as they are for Wet2 and 5TE sensors or presented in user
manuals. is approach favors sensor comparisons, performance
evaluations and better understanding of the inuences of soil type
and physicochemical characteristics on sensor response.
Results of this study suggest that the soil-specic calibrations
obtained for mineral soils (Table 6) can be applied with an accu-
racy of about 0.015 m3 m−3 for the 10HS, SM300, and eta
Probe sensors, and with 0.025 m3 m−3 accuracy for the TDR100,
CS616, Wet2, 5TE, and Hydra Probe sensors, for mineral soils
with large textural variations, for ECs lower than 2 dS m
−1
, organic
matter content lower than 10% and a specic surface area lower
than about 50 m2 g−1.
Acknowledgments
e authors gratefully acknowledge support from the Brazilian Agricultural Research
Corporation (EMBRAPA), the Brazilian National Council for Scientic and Tech-
nological Development (CNPq) under grant no. 301057/2009-5, and from the Ari-
zona Agricultural Experiment Station (AAES).
www.VadoseZoneJournal.org p. 15 of 16
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