Geoscience Reference
In-Depth Information
Morel-Seytoux and Khanji (1974) have shown that a parameter called the “capillary drive”,
with units of length and defined as
C
D
f
ı
˜
, is a relatively constant parameter for a range
of initial moisture conditions defined as
ı
˜
=
(
˜
i
) which is the change in moisture content
between the initial state of the soil,
i
, and field saturation,
˜
. The Green-Ampt equation is
then better applied in the form:
=
−
h
o
ı
˜
1
K
s
B
+
C
D
f
(
t
)
=
+
(B5.2.3)
z
f
ı
˜
where
B
is an additional parameter proposed by Morel-Seytoux and Khanji (1974) to allow for
air pressure effects, called the “viscous resistance correction factor” (1
<B<
1
.
7).
The original Green-Ampt infiltration equation assumes constant soil characteristics with
depth. An analysis of a wide variety of soil moisture characteristics data by Rawls
et al.
(1983;
see also Box 5.5) has led to a classification of the Green-Ampt parameters by soil texture (see
Figure B5.2.2). These type of relationship should be used with care, however, since they are
based on measurements of small samples brought back to the laboratory, not field measure-
ments at the plot scale. Beven (1984) has produced a solution with equivalent assumptions
for the case where hydraulic conductivity declines exponentially with depth, often a useful
approximation of real soil characteristics.
B5.2.3 The Philip Infiltration Equation
Philip (1957) obtained an analytical solution to the Richards equation by assuming a delta
function change in diffusivity for the soil across the wetting front. His widely used infiltration
equation has the form
0
.
5
St
−0
.
5
f
(
t
)
=
+
A
(B5.2.4)
where
S
is called the “sorptivity” of the soil and is calculated from knowledge of the soil
moisture characteristics of the soil and
A
is a final infiltration capacity equivalent to the
f
c
of the Horton equation or
K
s
of the Green-Ampt equation. The effects of the sorptivity term
gradually reduce with increasing time, eventually leaving the final infiltration capacity as a
function of the effective saturated hydraulic conductivity of the soil.
B5.2.4 The Smith-Parlange Infiltration Equation
Under assumptions of a diffusivity that changes exponentially with moisture content, Smith
and Parlange (1978) derived another widely used infiltration equation that takes the form:
exp
F
(
t
)
/C
D
exp
F
(
t
)
/C
D
−
K
s
f
(
t
)
=
(B5.2.5)
1
=
t
where
F
(
t
)
0
f
(
t
)
dt
, and
C
D
is the capillary drive, as above.
B5.2.5 An Infiltration Equation Based on Storage Capacity
Treating infiltration capacity as a function of infiltrated volume can also be used to treat the
case where overland flow is produced as a result of the topsoil layer becoming saturated as
a result of a limitation on vertical flow at some depth within the soil. This can occur either
where a thin soil overlies an impermeable bedrock or where there is some horizon of lower
permeability at some depth into the soil profile (e.g. Taha
et al.
, 1997). In this circumstances,
infiltration rates might be controlled more by a saturation excess than by a surface infiltration
