Campbell Scientific TDR100 Time Domain Reflectometry Systems - Manual (Page 33)

TDR100
The relationship between dielectric constant and volumetric water content has
been described by, among others, Topp et al. (1980) and Ledieu et al. (1986) in
an empirical fashion using both polynomial and linear forms. These
expressions are presented here since it has been shown in numerous research
efforts that these equations are appropriate for nearly all applications. With
θ
v
the volumetric water content, the equation presented by Topp et al. (1980) is
[3] θ
v a a
K K = − ∗ + ∗ − ∗ + ∗ − − − −
5 3 10 2 92 10 55 10 4 3 10 2 2 4 2 . . . .
a
K 6 3
and that presented by Ledieu et al. (1986) is
θ
v a
K = − 01138 01758 . .
[4]
The TDR100 generates a very fast rise time pulse that is sent to the connecting
cable and probe. Reflections over a specified length of transmission line are
sampled and digitized. Discontinuities in cable impedance will cause changes
in the amplitude of the reflected signal. The travel time of the reflected signal
is used with a velocity value to give distance information. A probe consisting
of metal rods can be used as an extension of a coaxial cable. When the probe
is inserted in the soil, the travel time of the applied pulse along the probe
length will depend on the soil water content. In general, as the water content
increases, the travel time of the applied pulse increases. The reflected
waveform of the probe can be used to identify the impedance transitions
caused by the probe beginning and end. This information is then analyzed to
determine soil water content.
While the velocity of the applied pulse along a waveguide is dependent on the
dielectric constant of the material surrounding the waveguide, the amplitude of
the reflected voltage is dependent on electrical conduction of the applied signal
between probe rods. The presence of free ions in the soil solution will result in
attenuation of the applied signal. Theory presented by Giese and Tiemann
(1975) has been applied to the measurement of soil bulk electrical
conductivity. A commonly used expression is
σ
ρ
ρ
=
−
+ K
Z
p
c
1
1
[5]
where σ is the bulk electrical conductivity, K
p
is a probe constant, Z
c
is the
cable impedance (50 ohm), and ρ is the reflection coefficient. The reflection
coefficient is the ratio of the reflected voltage to the applied voltage and ranges
between plus and minus one.
The components of the Campbell Scientific TDR system are designed to apply
time domain reflectometry for the determination of soil volumetric water
content and bulk electrical conductivity as both hardware for the collection of
data and software for communications and analysis of the data.
27