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Vadose Zone J. Accepted Paper, posted 02/23/2017. doi:10.2136/vzj2016.11.0112
A TDR Array Probe for Monitoring Near-surface Soil Moisture Distribution
1 2 3
Wenyi Sheng*, Rong Zhou, Morteza Sadeghi, David A. Robinson, Markus Tuller, and
4
Scott B. Jones
5 6
Wenyi Sheng, Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei,
7
Anhui 230031, China; Wenyi Sheng, Rong Zhou, Morteza Sadeghi, and Scott B. Jones,
8
Dep. of Soils, Plants and Climate, Utah State University, Logan, UT 84322-4820, USA;
9
David A. Robinson, Centre for Ecology and Hydrology, Environment Centre Wales,
10
Deiniol Road, Bangor, UK; Markus Tuller, Dep. of Soil, Water and Environmental
11
Science, The University of Arizona, Tucson, AZ, USA.
12
*Corresponding author (
[email protected])
13 14
Core Ideas:
15
A TDR array has been developed for soil moisture profiling.
16
The sensor provides eight incremental measurements at cm-depth resolution.
17
Permittivity, evaporation rate, and soil moisture profile were determined.
Vadose Zone J. Accepted Paper, posted 02/23/2017. doi:10.2136/vzj2016.11.0112
18
Abstract:
19
Near-surface soil conditions (i.e., moisture, temperature) moderate mass and energy
20
exchange at the soil-atmosphere interface. While remote sensing (RS) offers an effective
21
means for mapping near-surface moisture content over large areas, in-situ measurements,
22
targeting those specific remotely-sensed soil depths, are poorly understood and high
23
resolution near-surface measurement capabilities are lacking. Time domain reflectometry
24
(TDR) is a well-established accurate measurement method for soil dielectric permittivity
25
and moisture content. A TDR array was designed to provide cm-resolution measurements
26
of near-surface soil moisture. The array consists of nine stainless steel TDR rods spaced 1
27
cm apart, acting as waveguide pairs to form eight two-rod TDR probes in series. A critical
28
aspect of the design was matching the spacing of the coaxial cable-TDR rod transition to
29
avoid unwanted reflections in the waveforms. The accuracy of the TDR array permittivity
30
measurement (±1 permittivity unit) was similar to that of conventional TDR as verified in
31
dielectric liquids. Electric field numerical simulations showed minimal influence of
32
adjacent rods during a given rod-pair measurement. Evaporation rate determined by the
33
TDR array compared well with mass balance data in a laboratory test. Near-surface soil
34
moisture profile dynamics were monitored at cm-depth resolution using the TDR array in
35
a field experiment where volumetric moisture content estimates (0‒8 cm) were within 2%
36
of conventional three-rod TDR probes averaging over 0‒8 cm and from 1‒3 cm depths.
37 38
Abbreviations: TDR, time domain reflectometry; EM, electromagnetic; HFSS, high
39
frequency structure simulator.
40
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INTRODUCTION
42
Near-surface soil moisture is a highly dynamic environmental state variable of
43
fundamental importance for numerous
44
biogeochemical processes (Robinson et al., 2008; Vereecken et al., 2008; Seneviratne et
45
al., 2010). Therefore, it is often essential to accurately quantify and monitor its spatial
46
and temporal variations (Wang and Qu, 2009). Technological advances in satellite remote
47
sensing have offered a variety of techniques for continuously estimating soil moisture
48
across wide areas over time. A number of studies have shown that near surface soil
49
moisture content can be estimated with remote sensing techniques, within a number of
50
domains of the electromagnetic (EM) spectrum, e.g., shortwave infrared (Sadeghi et al.,
51
2015; Zeng et al., 2016) and microwave (Njoku and Entekhabi, 1996; Tabatabaeenejad et
52
al., 2015). Since the penetration depth of light in the solar domain is commonly less than
53
a few millimeters depending on soil optical properties, a very thin layer of the soil surface
54
will contribute to soil reflectance detected by optical remote sensors. Even for most
55
active microwave remote sensors operated within the X-, C- or L-band, penetration
56
depths are often on the order of only a few cm, depending on frequency, soil moisture
57
content, and soil type (Ulaby et al., 2014; Sadeghi et al., 2017). In addition, factors such
58
as surface roughness complicate remote sensing signal interpretation. Therefore, a
59
significant need and challenge is to accurately measure near-surface soil moisture with
60
millimeter or centimeter depth resolution within the thin and variable surface layer. The
61
need for these measurements is growing, not only for calibration of other measurement
climatic, hydrological, biological, and
Vadose Zone J. Accepted Paper, posted 02/23/2017. doi:10.2136/vzj2016.11.0112
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techniques such as remote sensing platforms and the Cosmic-ray Soil Moisture
63
Observing System (COSMOS) (Robinson et al., 2008), but also because important
64
environmental processes occur very close to the soil surface. Of particular interest are
65
processes linked to global climate change, e.g. methane and nitrous oxide emissions
66
(Saunois et al., 2016; Drury et al., 2006) and the dynamics of biocrusts and CO2
67
exchange in dryland climates (Bowling et al., 2011).
68
Time domain reflectometry (TDR), the standard in soil moisture sensing for more than 35
69
years, provides potential solutions for near-surface measurements by considering novel
70
waveguide configurations to restrict the measurement volume (Selker, 1993; Ferré et al.,
71
1998; Jones et al., 2002; Robinson et al., 2003a; Ito et al., 2010; Vaz et al., 2013).
72
We present here a novel TDR array design for monitoring near-surface soil moisture
73
dynamics. The primary objectives were: (1) to layout the specific design details of the
74
TDR array; (2) to determine the sampling volume of the individual measurements on the
75
array; (3) to verify the accuracy of dielectric permittivity measurements; and (4) to
76
explore the capability of monitoring near-surface soil moisture content dynamics under
77
both laboratory and field conditions.
78 79
MATERIALS AND METHODS
80
TDR Array Design
81
Figure 1 depicts a schematic of the eight coupled two-rod TDR probes comprising the
82
array that includes: the TDR array with nine stainless-steel rods and eight coaxial cables,
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a Campbell Scientific (Logan, UT) eight-channnel SDMX50 multiplexer and a Tektronix
84
(Beaverton, OR) 1502B TDR cable tester. The TDR was connected to the coaxial input
85
line of the multiplexer, which provides channel switching of the eight individual TDR
86
probes. Note that each of the array’s internal rods were connected to a pair of adjacent
87
coaxial conductors. This dual connection facilitates continuous soil moisture profile
88
monitoring where the EM energy concentrates largely between the active rod pair during
89
a measurement. The two-rod TDR was shown to measure permittivity as well as balanced
90
three-rod probes for moisture content determination (Robinson et al., 2003a). It should
91
also to be pointed out that if the multiplexer has a common ground for all channels, this
92
should not impact travel time measurements but could lead to significant errors in
93
determining bulk soil electrical conductivity (Castiglione et al., 2006). To overcome this
94
problem an improved differential multiplexer design by Weihermueller et al. (2013) can
95
be used.
96
Waveform analysis and soil moisture content determination were conducted with
97
WinTDR (Or et al., 2004). The TDR array was installed vertically (i.e. TDR rod axes are
98
parallel to the surface) with the top rod coinciding with the soil surface plane, which
99
provides a measurement resolution of 1 cm from the surface to the 8-cm depth (Fig. 1).
100
Figure 2(a) illustrates the TDR array head design details, where nine 3.2-mm-diameter,
101
150-mm long stainless-steel rods aligned in series at 1-cm spacing were employed to
102
form eight two-rod waveguides. The first prototype was constructed following the
103
approach described in Robinson et al. (2003a), who cast a cuboid epoxy head around the
Vadose Zone J. Accepted Paper, posted 02/23/2017. doi:10.2136/vzj2016.11.0112
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soldered connections between the coaxial cables and the rods. However, signal
105
attenuation and multiple reflections created waveform analysis challenges, which we
106
discovered were created by inconsistent rod or cable conductor spacing combined with
107
our connecting pairs of coaxial cable conductors (either center conductor or shield). We
108
were able to minimize these noise sources using a printed circuit board (PCB) facilitating
109
cable-rod connections of uniform spacing. The PCB provided connections from 2
110
different coaxial cables to one TDR rod as shown in Fig. 2(b). Eight sections of 50-Ω
111
RG-174/U coaxial cables with BNC connecters at one end were cut to a length of 2
112
meters to connect the probes to the multiplexer. Insulation at the other end of each cable
113
was stripped back about 10 mm to access the signal and shield wires. On the top side of
114
the PCB shown in Fig. 2, the cable shield was soldered to the circular trace for
115
connection to a ground rod(s) (−) and the inner conductor and insulation was passed
116
through the PCB and the conductor was soldered to a circular trace on the PCB bottom
117
side making the connection to a pair of signal rods (+).
118
The initial prototype TDR array yielded an undetectable first reflection at the impedance
119
disparity between the 50-Ω cable and the PCB due to signal attenuation from the
120
reflected signal passing into the adjacent cables connected to the same rods. Without
121
detectable reflection, standard waveform analysis could not be applied to determine the
122
travel time of the TDR pulse. Although the location of the first reflection will only
123
change slightly (e.g., due to temperature change) once the structure of the TDR array is
124
fixed, it is more efficient and reliable to employ standard travel time analysis of the
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waveform, especially when the first reflection cannot be set in the software or TDR
126
device. Therefore, we added a 3-cm air gap beneath the PCB and around the TDR rods to
127
amplify the first reflection using a 3D-printed mold made of Acrylonitrile Butadiene
128
Styrene (ABS) plastic. A similar solution was also applied to generate a reference
129
reflection in the FP/mts TDR probe (E-Test Ltd., Lublin, Poland) as described by
130
Skierucha et al. (2008). The air gap with relative dielectric permittivity (hereafter,
131
permittivity) ε = 1, produced a more detectable first reflection when compared to the
132
probe head embedded in epoxy resin with ε ≈ 3.54. With the PCB in position, the gap
133
above the PCB in the mold was filled with marine epoxy resin (epoxy resin and hardener,
134
System Three Resins, Inc., Seattle, WA) to secure the soldered connections and make the
135
array impervious to water. A thin layer (ca. 2 mm) of epoxy was also added to the inside
136
bottom of the mold where the rods exited for stability and waterproofing.
137
Probe Calibration and Permittivity Measurement
138
Accurate determination of travel time for permittivity estimation requires length
139
calibration for the TDR rods (Robinson et al., 2003b). The length of each rod from three
140
different TDR array prototypes was calibrated individually in deionized water with
141
WinTDR. The calibration calculates the rod-pair length required to accurately match the
142
permittivity of deionized water at a known temperature (Or et al., 2004). Deionized water
143
and 2-Isopropoxyethanol (99%, Aldrich Chemical, St. Louis, MO) mixtures were used
144
for verifying the permittivity measurement accuracy of the TDR array rod pairs. The
145
solutions were made by mixing different fractions of deionized water with
Vadose Zone J. Accepted Paper, posted 02/23/2017. doi:10.2136/vzj2016.11.0112
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2-Isopropoxyethanol, yielding a ε range from approximately 10 to 80. The advantage of
147
using 2-Isopropoxyethanol with deionized water, is that both have relaxation frequencies
148
(where relaxation losses peak) outside the TDR operating frequency (Heimovaara, 1994;
149
Blonquist et al., 2005a; Jones et al., 2005). The TDR arrays were placed into a
150
rectangular glass container (7" × 2.35" × 7.87") filled with the sample solutions, keeping
151
the rods at least 3 cm away from the wall of the container in every direction. An
152
HP8752C network analyzer and HP85070B dielectric probe were used as the reference
153
for dielectric measurements.
154
Modeling Sampling Volume
155
Because the TDR array couples multiple rods via switching from one pair to the next, we
156
examined the sensing volume of each rod-pair to check if or how a measurement from
157
one rod-pair is influenced by the adjacent rods, especially for the rods installed near the
158
soil-air interface. Electrostatic analyses have commonly been used to simulate the
159
sampling area for TDR probes (Knight, 1992; Ferré et al., 1998; Robinson et al., 2003a).
160
The quasi-static approximation is only valid for low frequency measurements (i.e., f
3 m in air) is much larger than
162
the probe dimensions (Feynman, 1979; Bolvin et al., 2004), whereas this does not hold
163
true for time-domain measurements operated at high frequency. Thus, the relative EM
164
field distribution of the TDR array (Fig. 3) was investigated by means of a commercial
165
finite element method (FEM) solver for EM structures — Ansys HFSS (Ansys Inc.,
166
Canonsburg, PA) as applied in several previous studies (Wagner et al., 2007; Wagner et
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al., 2014; Bore et al., 2016). For simplification, the rod length in the model was set to 12
168
cm without considering the air gap. The rod diameter and spacing were kept the same as
169
the actual TDR array design. A short 3 mm coaxial feeding line with inner and shield
170
conductors and dielectric insulator diameters identical to the RG174/U coaxial cable was
171
used. The inner and outer conductors of the feeding line were connected to two rods of
172
the TDR probe, as illustrated in a close-up view in Fig. 3. The materials in the numerical
173
simulation were assigned as copper for the rods and the coaxial conductors and as Teflon
174
for the dielectric insulator. Driven modal solution type and wave port excitation were
175
chosen for the simulation. The excitation was assigned on the outer surface of dielectric
176
insulator with an integration line pointing axially outward. The outer surfaces of the soil-
177
and air-domains were set as the radiation boundary. One-third wavelength-based adaptive
178
mesh refinement was operated automatically at a solution frequency of 1 GHz. The
179
permittivity backgrounds of air was set to 1 and soil was set to 20 (i.e., soil near field
180
capacity). Both backgrounds were treated as homogenous, nonrelaxing, and
181
nonconducting.
182
Laboratory Validation
183
The overall performance of the TDR array was tested in the laboratory by means of a
184
mass balance approach in a sand evaporation experiment. A 10-cm high bottom-sealed
185
cylindrical column was packed uniformly to a density of 1.6 g cm-3 with Wedron fine
186
silica sand and saturated. The TDR array was inserted into the wet sand through
187
pre-drilled holes in the column wall. The top and bottom rods were located at respective
Vadose Zone J. Accepted Paper, posted 02/23/2017. doi:10.2136/vzj2016.11.0112
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depths of 0.5 and 8.5 cm and a small fan passed air across the top of the column to
189
expedite evaporation. The selection of having the top rod at 0.5 cm was a compromise
190
between locating at the surface (the first probe will see the air/soil interface leading to
191
underestimation of θv) and at 1 cm (little influence from soil surface moisture).
192
Volumetric moisture content data from the TDR array were collected every 15 minutes
193
during the drying process while the column mass was tracked with a digital balance
194
recorded every 15 min. Evaporation rates were computed using the TDR array
195
measurements comparing instantaneous soil moisture profiles at two consecutive time
196
steps, which were then compared with the actual mass balance-based evaporation rate.
197
Note that the surface (0‒0.5 cm) and bottom layers (8.5‒10 cm) were assumed to have
198
the same moisture content as their adjacent measured layers.
199
Field Validation Test
200
In a second test of the TDR array, a field evaporation experiment from an
201
initially-saturated profile was conducted to monitor near-surface soil moisture for a
202
duration of 26 days in September, 2015 (monthly mean air temperature: 22.3 °C). Three
203
prototypes of the TDR array, shown in Fig. 4, were installed in a 2 × 5 m2 plot with bare
204
Millville Silt Loam Soil at the Greenville Research Farm (North Logan, UT). For ease
205
and convenience of installation, the top rods of the TDR array were set at the surface
206
rather than 0.5 cm depth as in the laboratory test. In addition, an 8-cm long three-rod
207
TDR probe (constructed per Robinson et al., 2003a) was inserted vertically to cover the
208
full measuring depth of the TDR array. Also, a 15-cm three-rod TDR-315 probe (Acclima
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Inc., Meridian, ID), which is a self-contained TDR system with all electronics required
210
for waveform acquisition embedded in the probe head (Schwartz et al., 2016), was
211
installed with all 3 rods in a common horizontal plane at a depth of 2 cm below the soil
212
surface for comparison. The sensing volume of three-rod TDR probes was determined to
213
be within a distance of 1.5 cm above and below the probe plane by Schwartz et al. (2013).
214
The TDR arrays were connected to a Tektronix TDR cable tester using two levels of
215
Campbell Scientific 8-channel SDMX50 multiplexers. Eight probes on each TDR array
216
were cycled through each level-2 multiplexer. The level-2 multiplexers in addition to the
217
8-cm three-rod TDR were then cycled through the level-1 multiplexer. The plot was
218
prepared prior to probe installation by tilling, leveling and flooding to deeply wet the soil
219
profile at the onset of the experiment. Data were collected along a continuous drying
220
process, where re-wetting by rainfall was prevented during the experiment with a plastic
221
cover installed 0.5 m above the ground. This covering may have influenced the
222
evaporation rate but all sensors were equally treated under the cover.
223
RESULTS AND DISCUSSION
224
Permittivity Calibration
225
The apparent length of each probe in all three arrays was calibrated to be within ±0.1 cm
226
of their physical lengths. Figure 5 shows the difference between TDR array estimated ε'
227
(8 replicate measurements from each rod-pair on a given TDR array) and the reference
228
network analyzer measured ε' at 1 GHz. This frequency is close to the average maximum
229
passable frequency (Robinson et al., 2005), i.e., the highest frequency content of the
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reflected TDR waveform of the Tektronix TDR determined by Blonquist et al. (2005b).
231
We compared the measurement performance of the TDR array using liquid dielectrics
232
following Jones et al. (2005), illustrated in Fig. 5, where Blonquist et al.’s (2005b)
233
three-rod TDR measured permittivity fell within the range of about ±1 permittivity unit
234
compared with the network analyzer measurements. Our TDR array exhibited similar
235
permittivity differences with the same network analyzer measured values. The standard
236
deviations in residual permittivity for the 8 rod-pairs on the TDR array ranged from 0.34
237
to 1.79. Compared with the multi-TDR probe designed by Ito et al. (2010), which used
238
traces on a PCB as waveguides, our TDR array has the advantage of providing direct
239
permittivity estimates based on travel time in the medium of interest, while the PCB-trace
240
TDR yielded about half of the expected permittivity values because the PCB substrate is
241
included in the field of measurement and impacts travel-time of the signal.
242
TDR Array Sampling Volume
243
The distribution of the electric field strength ( || , V m-1) shown as normalized
244
(||⁄|| ) in Figure 3 has implications on the energy density ( = || , where ε
245
refers to absolute permittivity) and then on the spatial weighting of the soil permittivity
246
controlling signal travel time in soil. The array is illustrated as being installed to provide
247
1-cm thick horizontal layer measurements with the first rod located at the air/soil
248
interface. Simulations of signal propagation along the first and fifth rod pairs are
249
simulated for demonstration purposes. In reality the multiplexer only connects the TDR
250
to one rod-pair at a time. As shown in Fig. 3, the electric field exhibits half-wavelength
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segments corresponding to a wavelength of approximately 6.7 cm in soil with ε’ = 20 and
252
a measurement frequency of 1 GHz. Most of the electric field is concentrated between the
253
two active rods for both depths with higher field strength distributed near the rods. The
254
contrast in soil-air interface permittivity at the surface will cause a substantial difference
255
in the EM energy distribution around the top rod where almost all of the energy will be
256
concentrated in the region with higher permittivity. In addition, the lower dielectric of the
257
air phase may increase the apparent travel time and thereby reduce the effective
258
permittivity of the surface rod pair measurement relative to deeper rod pairs, assuming
259
uniform permittivity in the profile. The exact location of the surface rod will control the
260
extent to which the air phase affects the measurement (Ferré et al., 1998). In addition,
261
stainless-steel rods adjacent to the active pair show very minor interference with the
262
distribution of the EM field. The simulated result indicates the sampling volume of each
263
probe on the array will mostly be contained within the active pair of rods, even for the
264
pair installed at the air/soil interface.
265
Laboratory Evaporation Rate Experiment
266
Results from the lab evaporation experiment are presented in Fig. 6 where evaporation
267
rates computed from the TDR array soil moisture profile data are in good agreement with
268
the mass balance approach. This result illustrates the reliability of the TDR array
269
measurements, although the data are averaged across the entire sand profile. We note the
270
TDR array measurement dynamics during the first 30 hours (stage-1) of evaporation
271
likely resulted from the poor tracking of water outside of the 8 cm sensing length within
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the 10 cm profile (i.e., moisture content changes below 8 cm were not registered by the
273
TDR array). A transition from the stage-1 evaporation with relatively high evaporation
274
rate to stage-2 with much lower and falling rate was observed using both approaches.
275
Near-surface Field Soil Moisture Profile Tracking Experiment
276
Figure 7 shows the near-surface soil moisture profile dynamics under field conditions
277
from 0 to 8 cm estimated with one of the TDR arrays (the other two arrays have similar
278
responses with minor variations). Initially the soil moisture profile distribution within the
279
top 8 cm reached near saturation at 0.38 cm3 cm-3 as the plot was deeply wetted. The bare
280
soil surface dried out quickly from evaporation to where θv decreased to about half the
281
original moisture content within 24 hours and eventually to completely air dry after 26
282
days. In general, the top 3 cm of soil dried much faster over the 3.5 weeks compared to
283
the deeper soil where θv decreased more uniformly with time. The drying front remained
284
within the top 4 cm of the profile throughout the experiment, leaving the bottom half of
285
the array sensing somewhat constant θv with depth, (e.g., θv = 0.20 cm3 cm-3 after 26
286
days).
287
We also compared three-rod TDR measurements with specific domains of the TDR array,
288
for example to observe the moisture content variations at specific depths as a function of
289
time, presented in Fig. 8. Here, the TDR array data are plotted along with data from a
290
vertically-installed three-rod TDR and from a horizontally-installed Acclima TDR located
291
adjacent to the TDR arrays (see Fig. 4). In Fig. 8(a), data of the vertically-installed 8-cm
292
long three-rod TDR are compared with the TDR array data averaged from all 8 probes
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(0‒8 cm). In Fig. 8(b), moisture content measurements with the Acclima TDR installed
294
horizontally at 2 cm are compared with the TDR array data averaged from the second (1‒
295
2 cm) and third (2‒3 cm) rod-pairs. The diurnal variations in soil moisture content with
296
rapid decrease during daytime and minor changes during nighttime were observed by the
297
TDR array, in addition to both TDR probes. During the 6-day drying process illustrated in
298
Fig. 8, moisture content determined with the TDR array was generally in good agreement
299
(R2 = 0.97) with the two three-rod probes in both 0‒8 cm and 1‒3 cm soil profiles. The
300
TDR array data were generally lower than both three-rod TDR measurements of
301
volumetric moisture content by about 0.01‒0.02 cm3 cm-3, especially during nighttime.
302
These discrepancies could be caused by the difference in evaporation rate or water
303
movement due to the local soil heterogeneity. For the caparison with the Acclima
304
TDR-315, sampling volume (1‒3 cm) differences may have played a role as well,
305
volumes that vary as the soil moisture content changes. For the caparison with the 8-cm
306
three-rod TDR, the sensor head covering the soil where the probe measures may slightly
307
reduce the evaporation as well.
308 309
CONCLUSIONS
310
A novel TDR array designed for near-surface soil moisture profiling was introduced. The
311
array provides eight continuous 1-cm depth measurements of soil moisture content using
312
a TDR device and an eight-channel multiplexer. The performance of the TDR array for
313
determining permittivity was demonstrated to be comparable to individual three-rod TDR
Vadose Zone J. Accepted Paper, posted 02/23/2017. doi:10.2136/vzj2016.11.0112
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probes. High-frequency simulation of the EM field distribution indicates that the sensing
315
volume of each rod-pair is concentrated around the two active rods, with minor
316
interference from neighboring rods or contrasting dielectric interfaces (e.g. soil surface).
317
The laboratory experiment verified the overall ability of the TDR array to track
318
near-surface water loss by means of a mass balance comparison during soil drying. The
319
field test and comparisons with other single TDR probes indicated that the near-surface
320
soil moisture dynamics over the range of soil moisture from saturation to air dry can be
321
successfully monitored.
322
Experiments to increase the first reflection, such as including baluns (impedance
323
matching transformer) on the PCB are being made by the authors to improve the TDR
324
array head design and waveform analysis quality. There is also potential to obtain reliable
325
monitoring of near-surface moisture content on the order of mm-depth with alternative
326
waveguide spacing and installation angle (e.g., 45 degree installation versus vertical
327
installation).
328 329
ACKNOWLEDGEMENTS
330
This project was funded by the National Science Foundation (NSF) grant no. 1521469
331
awarded to Utah State University and the University of Arizona. Additional support was
332
provided by the National Natural Science Foundation of China (NSFC) grant no.
333
31401295 and by the Utah Agricultural Experiment Station, Utah State University, Logan,
334
Utah 84322-4810, approved as UAES journal paper no. 8940. The China Scholarship
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Council (Grant No. 201404910296) provided financial support for Wenyi Sheng as a
336
postdoctoral fellow at Utah State University. The authors would like to acknowledge Dr.
337
Norman Wagner at the Institute of Material Research and Testing (MFPA) for his
338
assistance with the HFSS simulation.
339 340
REFERENCES
341
Blonquist, J.M., S.B. Jones, and D.A. Robinson. 2005a. Standardizing characterization of
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electromagnetic
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10.2136/sssaj2016.06.0188.
Vadose Zone J. Accepted Paper, posted 02/23/2017. doi:10.2136/vzj2016.11.0112
Fig. 1. Schematic diagram of the time domain reflectometry (TDR) array system showing end- and side-views of the linear rod array in addition to the paired configuration of the coaxial cable-rod connections attached to the Multiplexer (MUX).
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Fig. 2. (a) Schematic diagram and dimensions of the TDR array prototype. (b) Top and bottom view of the printed circuit board (PCB) vias used for 2-sided coaxial cable connections and for supporting TDR rod solder connections at uniform spacing.
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|E| / |E|max 1 0.75
Air ε' = 1
0.50
Coaxial feeding
0.25 0
Soil ε' = 20 Fig. 3. Numerical simulation of the normalized electric field strength distribution at 1 GHz surrounding paired rods (probes) spaced 1 cm apart. The rod pairs were at z = 0 and 1 cm, near the air-soil interface, and at 4 and 5 cm, deeper in the profile. The soil real permittivity, ε', was assumed to be 20, with ε' of air equal to 1. Simulations were carried out using HFSS software (Ansys Inc., Canonsburg, PA).
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Fig. 4. Field installation of the TDR arrays and two other referenced TDR probes (an 8-cm three-rod probe and an Acclima True TDR-315). We dig a trench before installation which allows us to insert the arrays and the True TDR-315 sideways. The TDR arrays were installed vertically with the top rods exposed in air to measure the moisture content in each centimeter within the depth of 0–8 cm while the three-rod TDR probe was inserted vertically into the soil also to measure the moisture content within the same depth range but just give one average value for the entire profile. The Acclima True TDR-315 was inserted horizontally at a depth of 2 cm below the soil surface. All these arrays/sensors were placed 10 cm apart from each other.
Vadose Zone J. Accepted Paper, posted 02/23/2017. doi:10.2136/vzj2016.11.0112
Residual Permittivity
4
2
0
-2
TDR Array Network Analyzer 3-rod TDR (Blonquist et al., 2005b)
-4 0
10 20 30 40 50 60 70 80 Permittivity Measured by Network Analyzer at 1 GHz
Fig. 5. Residual apparent real permittivity, εa', derived from the TDR array travel-time measurements and from the 1 GHz real permittivity, ε', measured by the network analyzer. Symbols and vertical bars represent mean and standard deviation, respectively, of εa' predictions from the eight two-rod probes in one TDR array. Diamond symbols represent residual εa' values between a single three-rod TDR and the same network analyzer (Blonquist et al., 2005b).
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Evaporation rate (cm/day)
1.2 TDR array mass balance
1.0 0.8 0.6 0.4 0.2 0.0 0
20
40
60
80
100
120
140
Time (h) Fig. 6. Evaporation rate determined using the TDR array soil moisture data compared with mass balance. Due to insignificant changes of soil moisture profile during the 15-min time intervals, a moving average of the data over a 2-hour period was applied to both the TDR array and the mass balance data.
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3 3 v estimated by TDR array (cm /cm )
0.0
0.1
0.2
0.3
0.4
0
-1
-2
Depth (cm)
-3
-4
-5
-6
-7
0 hrs 2 hrs 5 hrs 12 hrs 24 hrs 48 hrs 72 hrs 96 hrs 120 hrs 26 days
-8 Fig. 7. Temporal changes in soil volumetric moisture content (θv) profile determined by the TDR array at inter-rod locations, i.e., θv shown at 0.5 cm was from between TDR rods at 0 and 1 cm depth, etc.
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0.40
Estimated v (cm3 /cm3 )
(a) TDR array 3-rod TDR
0.35 0.30 0.25 0.20 0.15 0.10 0.40
Estimated v (cm3 /cm3 )
(b) TDR array Acclima TDR
0.35 0.30 0.25 0.20 0.15 0.10 252
253
254
255
256
257
258
DOY
Fig. 8. Soil volumetric moisture contents determined using the TDR array in different modes compared with traditional TDR probes (see Fig. 4). In (a) the TDR array output is averaged for comparison to an 8 cm long three-rod TDR probe inserted vertically near the TDR array. In (b) a three-rod Acclima TDR probe was inserted horizontally (three-rod alignment also horizontal) at a depth of 2 cm for comparison to the TDR array rods at 1 and 2 cm averaged with measurements from rods at 2 and 3 cm.
