Geoscience Reference
In-Depth Information
Pathways of Electrical Conductance
Soil Cross Section
1
2
3
Solid
Liquid
Air
fIGURe 2.5
The three conductance pathways for the ECa measurement. (Modified from Rhoades, J.D.,
Manteghi, N.A., Shouse, P.J., and Alves, W.J.,
Soil Sci. Soc. Am. J.
, 53, 433-439, 1989. With permission.
flow are illustrated in Figure 2.5. Rhoades et al. (1989) formulated an electrical conductance model
that describes the three conductance pathways of EC
a
:
2
(
)
⋅ ⋅
⋅ +⋅
θθ
θ
+
EC
EC
ss
ws
ws
ss
(
)
+⋅
(
)
EC
=
+⋅
θ
EC
θ
EC
(2.16)
a
sc
sc
wc
wc
EC
θ
EC
ss
ws
ws
s
where θ
ws
and θ
wc
are the volumetric soil water contents in the soil-water pathway (cm
3
cm
−3
) and
in the continuous liquid pathway (cm
3
cm
−3
), respectively; θ
ss
and θ
sc
are the volumetric contents
of the surface-conductance (cm
3
cm
−3
) and indurated solid phases of the soil (cm
3
cm
−3
), respec-
tively; EC
ws
and EC
wc
are the specific electrical conductivities of the soil-water pathway (dS m
−1
)
and continuous-liquid pathway (dS m
−1
); and EC
ss
and EC
sc
are the electrical conductivities of the
surface-conductance (dS m
−1
) and indurated solid phases (dS m
−1
), respectively. Equation (2.16) was
reformulated by Rhoades et al. (1989) into Equation (2.17):
2
(
)
⋅ ⋅
θθ
θ
+
EC
EC
ss
ws
ws
ss
(
)
⋅
EC
=
+−
θ
w
EC
(2.17)
a
s
wc
(
)
+⋅
(
))
⋅
EC
θ
EC
ss
ws
ws
s
where θ
w
= θ
ws
+ θ
wc
= total volumetric water content (cm
3
cm
−3
), and θ
sc
· EC
sc
was assumed to be
negligible. The following simplifying approximations are also known:
(
)
PW
100
⋅
ρ
b
θ
=
(2.18)
w
(2.19)
θ
ws
=
0 639
.
θ
+
0 011
.
w
ρ
θ
=
b
2.65
(2.20)
ss
(2.21)
EC
ss
=
0 019
.
(
SP
)
−
0 434
.
EC
⋅ ⋅
⋅
ρ
SP
(2.22)
EC
=
e
b
w
100
θ
w
