52
⚫
Technical Reference
the solution, and is can be applied automatically by the WET150
Sensor
The complex permittivity of the pore water,
p
, is equal to that of
pure water. The real part of the complex permittivity of the pore
water
p
= 80.3 at 20°C, with a temperature coefficient of about -
0.37 per °C (Kaatze and Uhlendorf, 1981).
By analogy with Eq. [4] we can write the following approximation
for
p
:
0
p
p
p
j
−
[6.]
The permittivity and conductivity of the bulk soil will be denoted
by the subscript
b
. The complex permittivity of the bulk soil,
b
,
is proportional to both
p
and a function of
,
g
(
)
. For dry soil
there is no water to facilitate ionic conduction, so the
conductivity of the bulk soil
b
0.
Dry soil material is still polarisable,
so
0
=
b
0 and
0
=
b
appear as an offset to
b
.
By assuming that
g
(
)
takes into account the proportionality
constant, it is reasonable to postulate the following form for the
complex permittivity of the bulk soil:
( )
g
p
b
b
+
=
=
0
[7.]
Note that
0
=
b
is a complex value and includes dielectric and
ionic loss. However since
b
= 0, we may approximate
0
=
b
by
its real part
0
=
b
. With this and Eq. [6] substituted in Eq. [7],
b
can be written as:
( )
( )
g
j
g
p
p
b
b
0
0
−
+
=
=
[8.]
An electrical model for a dielectric material such as soil between
two electrodes is a lossy capacitor. We can calculate the
admittance,
Y
, of this soil-filled capacitor. The admittance is the
inverse of impedance,
Z
, and is a complex quantity which is
proportional to the permittivity
b
of the bulk soil, and can be
defined by:
b
j
Y
0
=
[9.]
