SCIENTIFIC BRIEFING
HYDROLOGICAL PROCESSES
Hydrol. Process. 16, 141–153 (2002)
DOI: 10.1002/hyp.513
Time domain reflectometry measurement principles and
applications
Scott B. Jones,1 * Jon
M. Wraith2 and Dani Or1
1
Department of Plants, Soils and
Biometeorology, Utah State
University, Logan, UT 84322-4820,
USA
2
Department of Land Resources
and Environmental Sciences,
Montana State University,
Bozeman, MT 59717-3120, USA
*Correspondence to:
S. B. Jones, Department of Plants,
Soils and Biometeorology, Utah
State University, Logan, UT
84322-4820, USA.
E-mail: sjones@mendel.usu.edu
Abstract
Time domain reflectometry (TDR) is a highly accurate and automatable
method for determination of porous media water content and electrical conductivity. Water content is inferred from the dielectric permittivity of the
medium, whereas electrical conductivity is inferred from TDR signal attenuation. Empirical and dielectric mixing models are used to relate water content
to measured dielectric permittivity. Clay and organic matter bind substantial amounts of water, such that measured bulk dielectric constant is reduced
and the relationship with total water content requires individual calibration.
A variety of TDR probe configurations provide users with site- and mediaspecific options. Advances in TDR technology and in other dielectric methods
offer the promise not only for less expensive and more accurate tools for electrical determination of water and solute contents, but also a host of other
properties such as specific surface area, and retention properties of porous
media. Copyright 2002 John Wiley & Sons, Ltd.
Key Words
TDR; dielectric; permittivity; soil moisture; soil electrical
conductivity
Introduction
Time domain reflectometry (TDR) is a relatively new method for
measurement of soil water content and electrical conductivity. Each of
these attributes has substantial utility in studying a variety of hydrologic
processes. The first application of TDR to soil water measurements
was reported by Topp et al. (1980). The main advantages of TDR
over other soil water content measurement methods are: (i) superior
accuracy to within 1 or 2% volumetric water content; (ii) calibration
requirements are minimal— in many cases soil-specific calibration is
not needed; (iii) lack of radiation hazard associated with neutron probe
or gamma-attenuation techniques; (iv) TDR has excellent spatial and
temporal resolution; and (v) measurements are simple to obtain, and
the method is capable of providing continuous measurements through
automation and multiplexing. A variety of TDR systems are available
for water content determination in soil and other porous media (e.g.
Figure 1). Many, but not all commercially available systems may also
be used to measure soil electrical conductivity. Thus potential users
should consider present and future measurement requirements before
purchasing.
Copyright 2002 John Wiley & Sons, Ltd.
141
Received 10 June 2001
Accepted 30 July 2001
S. B. JONES, J. M. WRAITH AND D. OR
Figure 1. Different TDR devices shown are: (a) 1502C (Tektronix Inc., Beaverton, OR); (b) TRIME-FM (IMKO, Ettlingen, Germany);
(c) TRASE System I (Soil Moisture Equipment Corp., Goleta, CA); (d) TDR100 (Campbell Scientific Inc., Logan, UT)
Basic principles
In the telecommunications industry TDR is used to
identify locations of discontinuities in cables, hence
the term ‘cable tester’ is a common name for generalpurpose TDR instruments. The signal propagation
velocity Vp (a function of the cable dielectric constant), along with a typical reflection at a point of
discontinuity in a cable, allows the operator to determine locations of line breaks or other damage to
cables using travel time analysis. Using similar principles, a waveguide or probe of known length L may be
embedded in soil (Figure 2) and the travel time for a
TDR-generated electromagnetic ramp to traverse the
probe length may be determined. From the travel time
analysis the soil’s bulk dielectric constant is computed
(the terms dielectric constant and dielectric permittivity are synonymous), from which the volumetric
water content is inferred. The bulk dielectric constant
εb of soil surrounding the probe is a function of the
propagation velocity (v D 2L/t) according to
εb D
c 2
D
ct
2L
2
⊲1⊳
where c is the speed of light (velocity of electromagnetic waves) in vacuum (3 ð 108 m s1 ), and t is
the travel time for the pulse to traverse the length of
the embedded waveguide (down and back: 2L). The
travel time is evaluated based on the ‘apparent’ or
electromagnetic length of the probe, which is characterized on the TDR output screen by diagnostic
Copyright 2002 John Wiley & Sons, Ltd.
changes in the waveform: x1 marks the entry of the
signal to the probe, and x2 marks the reflection at the
end of the probe (Figure 3). As shown in Figure 3,
the apparent probe length (x2 x1 ) increases as the
water content (and dielectric constant) increases, a
consequence of reduced propagation velocity. The
relationship between locations of the two reflection
points x1 and x2 , and the bulk dielectric constant is:
x2 x1 2
⊲2⊳
εb D
Vp L
where Vp is a user-selected relative propagation
velocity, often set at Vp D 0Ð99.
For most practical applications it suffices to consider the definition of the dielectric constant in
Equation (1), which simply states that the dielectric
constant of a porous medium is the ratio squared of
the propagation velocity in vacuum relative to that in
the medium. The soil’s bulk dielectric constant εb is
dominated by the dielectric constant of liquid water
εw D 81 (20 ° C), as the dielectric constants of other
soil constituents are much smaller; e.g. soil minerals
εs D 3 to 5, frozen water (ice) εi D 4, and air εa D 1.
This large disparity of dielectric constants makes the
method relatively insensitive to soil composition and
texture, and thus a good method for ‘liquid’ water
measurement in soils. Note that, because the dielectric
constant of ice is much lower than for liquid water, the
method may be used in combination with a neutron
probe or other techniques that sense total soil water
content to determine separately the volumetric liquid
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Hydrol. Process. 16, 141–153 (2002)
SCIENTIFIC BRIEFING
TDR Cable Tester
(Tektronix 1502B)
BNC
Connector
Waveform
3-Rod
Probe
Figure 2. TDR cable tester with three-rod probe embedded vertically in surface soil layer
and frozen water contents in frozen or partially frozen
soils (Baker and Allmaras, 1990). Several factors
influence dielectric constant measurements, including soil porosity and bulk density, measurement frequency, temperature, water status (bound or free) and
dipole moments induced by mineral, water, and air
shapes. The need to relate water content to εb and to
account for the factors just mentioned has resulted in
a variety of empirical and ‘dielectric mixing’ models.
Empirical and dielectric mixing models
Two basic approaches have been used to establish the
relationships between εb and volumetric soil water
content . The empirical approach simply fits mathematical expressions to measured data, unique to the
physical characteristics of the soil or porous medium.
Such an approach was employed by Topp et al.
(1980), who fitted a third-order polynomial to the
observed relationships between εb and for multiple soils. The empirical relationship for mineral soils
Copyright 2002 John Wiley & Sons, Ltd.
proposed by Topp et al. (1980) of
v D 5Ð3 ð 102 C 2Ð92 ð 102 εb
5Ð5 ð 104 ε2b C 4Ð3 ð 106 ε3b
⊲3⊳
provides an adequate description for the water content
range <0Ð5, which covers the entire range of interest
in most mineral soils, with a estimation error of
about 0Ð013. However, Equation (3) fails to describe
the εb relationship adequately for water contents
exceeding 0Ð5, and for organic soils or mineral soils
high in organic matter or clay content.
In its simplest form the dielectric mixing approach
uses dielectric constants and volume fractions for
each of the soil constituents (e.g. solid, water, air) to
derive a relationship describing the composite (bulk)
dielectric constant. Such a physically based approach
was adopted by Birchak et al. (1974), Dobson et al.
(1985), Roth et al. (1990), and Friedman (1998).
According to Roth et al. (1990), the bulk dielectric
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Hydrol. Process. 16, 141–153 (2002)
S. B. JONES, J. M. WRAITH AND D. OR
1.25
Reflection coefficient
1.00
εb =
(x 2 − x 1)
2
L . νp
θv = 0
0.75
0.1
0.50
0.2
0.25
X2
0.00
0.3
−0.25
X1
−0.50
2.50
2.75
3.00
3.25
3.50
Apparent distance [m]
Figure 3. Sample TDR waveforms measured in Millville silt loam soil using the Tektronix 1502B TDR cable tester and three-rod probes
(length L D 0.15 m). The calculation of the bulk dielectric constant is based on εb D [⊲x2 x1 ⊳/⊲LVp ⊳]2 , where Vp is the relative velocity
of propagation (usually set at 0.99)
constant of a three-phase system may be expressed as
1/ˇ
εb D εˇw C ⊲1 n⊳εˇs C ⊲n ⊳εˇa
⊲4⊳
where n is the soil’s porosity, 1 < ˇ < 1 summarizes the geometry of the medium in relation to
the axial direction of the wave guide (ˇ D 1 for an
electric field parallel to soil layering, ˇ D 1 for
a perpendicular electrical field, and ˇ D 0Ð5 for an
isotropic two-phase mixed medium); 1 n, and
n are the volume fractions and εs , εw and εa
are the dielectric constants of the solid, water and air
phases respectively. Note that the summed volumetric
contribution of each phase relative to the total volume
is unity. Rearranging Equation (4) and solving for
yields
ˇ
ε ⊲1 n⊳εˇs nεˇa
⊲5⊳
D b
ˇ
ˇ
εw εa
which determines the relationship between and
εb measured by TDR. Many have used ˇ D 0Ð5,
which was shown by Roth et al. (1990) to produce
a calibration curve very similar to the third-order
Copyright 2002 John Wiley & Sons, Ltd.
polynomial proposed by Topp et al. (1980) for the
water content range 0 < < 0Ð5. If we introduce
into Equation (5) common values for the various
constituents, such as ˇ D 0Ð5, εw D 81, εs D 4, and
εa D 1, we obtain an approximate simplified form:
D
p
εb ⊲2 n⊳
8
⊲6⊳
Note that the soil’s porosity must be known or estimated when using the mixing model approach. A
comparison between the Topp et al. (1980) expression [Equation (3)] and a calibration curve based on
Equation (5) with n D 0Ð5 and ˇ D 0Ð5 is depicted in
Figure 4.
Soils having high clay or organic matter content
often require soil-specific calibration. The presence
of high porosity combined with large amounts of
‘bound’ water fraction produces substantial differences between the dielectric signature of typical mineral versus organic soils. This is illustrated (Figure 4)
by comparing an empirical expression of Schaap et al.
(1996) fitted to 505 TDR measurements in organic
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Hydrol. Process. 16, 141–153 (2002)
SCIENTIFIC BRIEFING
80
70
Bulk dielectric constant
Topp et al.
60
Practical range of
water content
measurement in
mineral soils
50
40
30
Mixing
model
20
Forest soil
organic horizons
10
0
0.0
0.1
0.2
0.3
0.4
0.5
Volumetric water content
0.6
[cm3
0.7
0.8
0.9
cm−3]
Figure 4. Relationships between bulk soil dielectric constant and expressed using the Topp et al. (1980) empirical equation for mineral
soils and for the Birchak et al. (1974) mixing model using a porosity of 0Ð5. Higher porosities and bound water in forest soil organic horizons
exhibit a reduced dielectric signature by comparison (Schaap et al., 1996)
horizons of eight forest floor soils given as
p
D ⊲0Ð133 εb 0Ð146⊳0Ð885
⊲7⊳
Media with large porosities, such as horticultural
planting media (n ³ 0Ð95) and clays, are susceptible to large variations in bulk density and porosity.
Independent measurements of bulk density should
improve calibration, but the bound water influences,
which are generally correlated to surface area, may
be more difficult to account for.
Bound water and temperature effects
Water molecules within the vicinity of solid surfaces are subjected to interfacial forces that constrain
their movement, rendering them rotationally hindered.
Consequently, both their ability to follow the alternating electric field, and their dielectric constant are
reduced. High surface-area porous media (e.g. clays,
peats, some forest soils) bind a substantial fraction
of the water phase, resulting in reduced bulk dielectric constant measurements relative to low surfacearea materials (e.g. sandy soils) when compared at
Copyright 2002 John Wiley & Sons, Ltd.
similar water contents. The amount of bound water
is related to the specific surface area and the thickness of the affected (bound) layer. Estimates of the
dielectric constant values for the first, second and
third monolayers of water are available (Thorp, 1959;
Bockris et al., 1963). Or and Wraith (1999) developed
a model for the temperature-dependent thickness of
the bound water phase. For media with large surface areas it was found that TDR-measured water
content increased with increasing temperature due to
reduction of the bound water layer thickness, without
any changes in the total mass of water (an example is depicted in Figure 5). This phenomenon has
important implications for interpretation of near-soilsurface measurements using TDR (e.g. infiltration or
evaporation studies), where the measurement artefact
must be filtered out. Interestingly, measurements of
the dielectric response of wetted porous media under
changing temperature may be useful in estimating the
specific surface area (m2 kg1 ), because of the fundamental relationship between bound water and solid
surface area (Wraith and Or, 1998). Expressions have
been derived for describing the combined bound- plus
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Hydrol. Process. 16, 141–153 (2002)
S. B. JONES, J. M. WRAITH AND D. OR
0.200
Water content [m3 m−3]
Water content
Electrical conductivity
0.175
0.4
0.150
0.3
0.125
0.2
0.100
55
45
35
25
15
5
Electrical conductivity [dS m−1]
0.5
0.1
Soil temperature °C
Figure 5. Measured volume water content and bulk soil electrical conductivity within sealed soil containers under imposed temperature
changes. Soil temperatures are indicated; actual water content did not change. Modified from Wraith and Or (1999), copyright 1999 by the
American Geophysical Union
free-water dielectric constant based on surface area
and bulk density (Friedman, 1998) and including the
temperature dependence (Jones and Or, 2001).
TDR probe configurations
Modelled after a coaxial design, Campbell (1990) and
Heimovaara (1994) used seven-wire probes to measure the dielectric constant of soils and liquids. A
number of different geometrical configurations have
been proposed, which have a single central conductor
and from one to six outer conducting rods (Figure 6).
The two-wire probe has the advantage of minimal
soil disturbance, but produces an unbalanced signal,
leading to unwanted noise and signal loss (White
and Zegelin, 1995). This problem may be minimized
using a balun (balancing transformer) embedded in
the probe head to reduce signal and information loss
(Spaans and Baker, 1993). The three- or more-rod
probes provide a balanced signal, avoiding the balun
requirement at the expense of some additional soil
disturbance [see Zegelin et al. (1989) for a comparison]. Though not commonly used in soils, the
parallel plate probe was shown by Robinson and
Friedman (2000) to provide a highly uniform electrical field between plates. The highly concentrated
electrical field converging on the central conductor
Copyright 2002 John Wiley & Sons, Ltd.
of the multi-wire probes (see Figure 6), more heavily
weights the dielectric constant of constituents within
this region. Ferre et al. (1998) found that two-rod
probes have a larger sample area compared with threerod probes, and that thin rod coatings (for reducing
conductive losses) for any probes will reduce the sampling area of the probe. Measurement error increases,
for example, as air gaps develop when probes are
repeatedly inserted and removed, or in shrink–swell
soils.
For all conventional probe designs, water content
is often assumed to be uniformly integrated along the
probe’s longitudinal axis. A recent study by Chan and
Knight (1999) cautions against the accepted notion
that, if water is evenly distributed along the rods or
concentrated in one or more ‘pockets’, the same measured mean dielectric constant results. Their analysis
is based on the wavelength to layer (heterogeneity) thickness t ratio /t. For /t > 10 the dielectric
constant of the soil is computed as an arithmetic average (effective medium theory) of the layers, whereas
for /t < 1 the geometric average (Ray theory) of
the soil layers is used to compute the soil dielectric constant. Scattering effects that occur within the
transition zone, 1 < /t < 10, may cause measurement difficulties, and the propagation direction of the
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Hydrol. Process. 16, 141–153 (2002)
SCIENTIFIC BRIEFING
Figure 6. Various TDR soil moisture probe designs have been proposed, such as the multi-wire and parallel plate configurations shown
here. Electrical field lines generated for different probe configurations are also shown, where closer line spacing is associated with a more
concentrated field (i.e. greater influence on permittivity)
electromagnetic wave relative to the layering is also
an important factor.
The particular spatial sensitivities of different probe
configurations can be used to one’s advantage in specific research applications. For example, a two- or
three-rod probe placed horizontally serves as an effective point (plane) measurement for water or solute
fronts moving vertically through soil profiles. Sevenrod or parallel plate designs, on the other hand, sample a larger effective volume of soil, which may be
desired for routine measurements. Other TDR probe
applications have been developed that provide soil
matric potential measurements (e.g. Wraith and Or,
2001). These may be used separately, or may be
paired with conventional probe designs to obtain
simultaneous in situ measurements of and matric
potential h from which the soil water characteristic
relationship ⊲h⊳ may be elucidated.
Copyright 2002 John Wiley & Sons, Ltd.
TDR measurements are easily automated using a
computer or datalogger, and analysis of waveforms
is commonly completed during measurement, or may
be analysed later if waveforms are saved. Automated
measurement of requires only a few seconds for
each probe. As many as 8 or even 16 probes may be
attached to a single multiplexer, and several multiplexers may be connected in series to provide a large
array of spatially distributed measurements. However,
owing to signal deterioration with cable length, practical distances from the probe to TDR unit are typically limited to 20 to 30 m. Longer cable lengths
may provide reliable readings where soil salinity and
clay content are low. The ability to obtain highresolution time series measurements at multiple locations (e.g. depths) using automated and multiplexed
TDR is a particularly useful research and management
tool.
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Hydrol. Process. 16, 141–153 (2002)
S. B. JONES, J. M. WRAITH AND D. OR
Measurement of salinity and ionic solutes
Dalton et al. (1984) also first demonstrated the utility
of TDR to measure the apparent bulk soil electrical
conductivity. This unique ability to measure both soil
water content and apparent soil electrical conductivity ECa using the same instrumentation and probes,
and in the same soil volumes, provided new opportunities to investigate salinity and the behaviour of
ionic solutes in soils. The most critical frequencies
for measurement of dielectric constant based on TDR
travel-time are near 1 GHz, whereas TDR ECa measurement relies on the lowest frequencies available
(low kilohertz range), as close to direct current (DC)
as feasible. Measurement of electrical conductivity
using TDR is based on attenuation of the applied signal voltage as it traverses the medium of interest. As
the transverse electromagnetic waves propagate along
TDR probes buried in soil, the signal energy is attenuated in proportion to the electrical conductivity along
the travel path. This proportional reduction in signal
voltage is accurately related to the bulk soil electrical conductivity. Comparisons between the electrical
conductivity measured in solutions using both TDR
and standard methods have repeatedly demonstrated
the potential accuracy and precision of TDR measurements (e.g. Spaans and Baker, 1993; Heimovaara
et al., 1995; Mallants et al., 1996; Reece, 1998). TDR
electrical conductivity measurements may also be easily automated and multiplexed in the same manner as
for . However, some commercially available TDR
equipment does not include provision to measure
electrical conductivity.
Originally proposed by Giese and Tiemann (1975),
the thin-section approach has been shown to be a
particularly effective means of quantifying ECa using
TDR. The Giese and Tiemann equation may be written as:
ε0 c Z0 2V0
1
⊲8⊳
EC⊲S m1 ⊳ D
L Zc
Vf
where ε0 is the dielectric permittivity of free space
(8Ð9 ð 1012 F m1 ), c is the speed of light in vacuum (3 ð 108 m s1 ), L (m) is probe length, Z0 ()
is the characteristic probe impedance, Zc is the TDR
cable tester output impedance (typically 50 ), V0
is the incident pulse voltage and Vf is the return
pulse voltage after multiple reflections have died out
0.4
ECW = 0 dS/m
Reflection coefficient
0.2
0.0
−0.2
3 dS/m
−0.4
6 dS/m
−0.6
V0
−0.8
12 dS/m
V1
Vf
−1.0
0
10
20
30
40
50
Travel time [ns]
Figure 7. Attenuation of the TDR signal due to increasing soil solution electrical conductivity results in a reduced reflection coefficient at
large distances (i.e. low frequency). The end-of-probe reflection is indistinguishable above about 6 dS m1 , where time domain analysis for
soil water content determination fails
Copyright 2002 John Wiley & Sons, Ltd.
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Hydrol. Process. 16, 141–153 (2002)
SCIENTIFIC BRIEFING
(Figure 7). The quantity ε0 c/L in Equation (8) may
be simplified to 1/(120L), and the values of V0 and
Vf are easily acquired from the TDR output signal.
A separate calibration procedure is required to determine the probe characteristic impedance Z0 . This may
be determined by immersion of the probe in deionized water with known (e.g. Weast, 1986) dielectric
constant ε according to:
p
V1
Z0 D Zc ε
⊲9⊳
2V0 V1
where the required signal voltages V0 and V1 are
illustrated in Figure 7. For specific probe geometries
(e.g. true coaxial, two-rod balanced design), Z0 may
be calculated with formulae found in electronics textbooks, but because of inconsistencies in probe manufacture we prefer to use the simple deionized water
calibration procedure. Finally, ε0 cZ0 /L D Z0 /120L
may also be lumped into a geometric probe constant K, and EC may thereby be estimated using
Equation (8) as
K 2V0
EC D
⊲10⊳
1
Zc Vf
with K either calculated using Equation (8) and the
relevant physical quantities (ε0 , c, L), or empirically
determined by immersing the probe in one or (preferably) more solutions of known EC, and using
K D ECref
ZL
fT
⊲11⊳
with ECref the known electrical conductivity of the
reference solution, ZL as the measured resistive load
impedance across the probe [ZL D Zc /⊲2V0 /Vf 1⊳]
and fT a temperature correction coefficient to relate
the measured reference solution to a desired standard
temperature. Heimovaara et al. (1995) found that the
relationship fT D 1/[1 C 0.019⊲T 25⊳] was appropriate for a variety of saline solutions, using 25 ° C as
the standard temperature.
The unique ability of TDR to measure both
and EC provides many opportunities for research.
For example, it has been used to measure transport
properties for ionic solutes under steady and nonsteady flow conditions in soils, to monitor water and
nitrogen status in the root zone, and to characterize the distribution of water and fertilizers around
drippers. Figure 8 illustrates bromide concentrations
Copyright 2002 John Wiley & Sons, Ltd.
and electrical conductivity measurements in effluent
fractions from a soil column compared with ECa measurements using TDR a few centimeters above the
column base. The results in Figure 8 are plotted as
relative ‘concentrations’ consistent with conventional
breakthrough curve format. The excellent correlation
of ECa and soil solution ECw shown for this saturated system degenerates under partially saturated
conditions, where enhanced tortuosity, variable liquid
configuration, and hysteresis complicate the measurement. Calibration models are, therefore, needed to
relate measured ECa to the EC or ionic concentration of soil solution because of the dependence of EC
on water content as well as on ionic strength and soil
geometry. Examples of such models and their application may be found in various papers, including those
by Risler et al. (1996), Mallants et al. (1996), Das
et al. (1999) and others.
Alternative frequency domain analyses
Although TDR offers simultaneous and accurate water
content and electrical conductivity determination in
soils and other porous media, waveform reflections
necessary for dielectric constant measurements can be
totally attenuated in lossy materials. Factors such as
soil texture, salinity, cable length, probe geometry and
water content all influence signal attenuation. Attenuated waveforms of varying degree, resulting from a
range of solution electrical conductivities, are illustrated in Figure 7. Nadler et al. (1999) found that
at field capacity water content in sandy and loamy
soils, TDR could be safely used for measurements
up to ECa of approximately 2 dS m1 . TDR applications are, therefore, limited to soils with moderate
to low salinity, unless measures are taken to preserve the waveform reflection occurring at the end
of the waveguide. Rod coatings have been used successfully to reduce signal attenuation and preserve
information needed to evaluate the dielectric constant
in highly saline soils. Since these coatings significantly influence the resulting permittivity εb , specific
εb calibration is required for measurements using
coated rods, making this a less appealing method
(Mojid et al., 1998). Coated rods also make measurement of EC extremely difficult (i.e. requiring
extensive calibration over a range of conditions) or
ineffective.
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Hydrol. Process. 16, 141–153 (2002)
S. B. JONES, J. M. WRAITH AND D. OR
1.2
Observed
Temp-corrected
TDR EC
1.0
0.8
0.6
0.4
0.2
Relative concentration
0.0
1.2
EFFLUENT BR
1.0
0.8
0.6
0.4
0.2
0.0
1.2
1.0
EFFLUENT EC
0.8
0.6
0.4
0.2
0.0
0
2
4
6
8
10
Time (d)
12
14
16
Figure 8. Relative EC measured using TDR during steady flow compared with relative bromide concentration and EC in the column effluent
fractions. Source: Wraith et al. (1993). Reproduced by permission of Soil Science Society of America
The potential benefits of a combination of shorter
TDR probes combined with waveform transformations for improving dielectric constant determination
at higher levels of electrical conductivity are illustrated in Figure 9. Travel-time analysis provided reliable εb measurement for 10 and 15 cm probes up
to ECw ³ 6 dS m1 , whereas, for frequency domain
Copyright 2002 John Wiley & Sons, Ltd.
analysis, shorter 2 and 3 cm probes extended εb
determination by a factor of four to five, up to
24 dS m1 , as shown for a silt loam soil.
Conversion of the TDR waveform to the frequency
domain provides the frequency-dependent dielectric
constant, in addition, other information, such as electrical conductivity, relaxation frequency, and static
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Hydrol. Process. 16, 141–153 (2002)
SCIENTIFIC BRIEFING
34
32
30
28
2 cm
3 cm
6 cm
10 cm
15 cm
Bulk dielectric constant
26
24
Time domain analysis
22
34
32
Frequency domain analysis
30
28
26
24
22
0
10
20
30
40
50
Soil solution electrical conductivity [dS m−1]
Figure 9. Bulk permittivity determined using time domain analysis and frequency domain analysis as a function of probe length and soil
solution electrical conductivity. The shaded region indicates the ‘true’ bulk permittivity of the saturated Millville silt loam soil used
and high-frequency permittivities, may be extracted
using optimization procedures (Heimovaara, 1994;
Friel and Or, 1999). Despite the laborious nature of
this approach, including fast Fourier transformation of
the waveform and fitting of an appropriate model to
the transformed scatter function, the procedure has the
potential to be automated to make it more amenable
to real-time measurements.
Outlook
In such a short review there are many inevitable omissions of details and complexities of the theory behind
TDR. Nevertheless, we have attempted to provide
Copyright 2002 John Wiley & Sons, Ltd.
potential practitioners with essential elements and
an overview of the state-of-practice using TDR. A
particularly important advantage of TDR, relative to
other methods, is the ability to provide intensive time
series measurements, at multiple locations, which are
critical to resolution of many hydrologic processes.
Concurrent measurement of both and EC has also
provided new research and management opportunities. Since its introduction in the early 1980s, the
TDR method has stimulated increased interest in other
electromagnetic methods based on different principles
ranging from capacitance to frequency-shift sensors.
This trend will undoubtedly continue with advances
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Hydrol. Process. 16, 141–153 (2002)
S. B. JONES, J. M. WRAITH AND D. OR
in technology and with reduction in costs of electronic
components; there are already available several standalone and relatively inexpensive sensors for water
content measurement based on dielectric properties.
Many of these inexpensive sensors currently have
substantial measurement limitations relative to true
TDR, however. The TDR method is maturing, as evidenced by the introduction of devices (e.g. Figure 1)
specifically designed for hydrological applications.
Moreover, the application of alternative methods of
analysis, such as frequency domain techniques, provides a means to extend the useful range of utility
as well as a potential for extraction of supplementary
information concerning water and its interactions with
porous media. Some potentially useful applications
derived directly from the TDR method include measurement of specific surface area, and in situ determination of water retention properties of field soils.
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