Geoscience Reference
In-Depth Information
quite adequate as a first approximation. This is especially true when the soil profile is deep,
without a shallow water table, or when, as is often the case in the field, there is some surface
connected macroporosity (not accounted for by the soil moisture characteristic) as a result
of shrinkage cracks, worm holes or root channels. Parlange and Hill (1979) have studied the
air effect by comparing solutions in which the air movement is considered with that resulting
from Richards's equation. For the case where the soil column is sealed at the bottom, the
difference was found to be quite large; however, their results showed a difference of only
2% in water intake for the case where the air can move ahead of the wetting front without
an appreciable pressure buildup. In experiments dealing with natural soils, a difference of
2% is very difficult to detect.
Soil variability
The spatial variability of soil properties has been studied with measurements in the field
(see Nielsen
et al.
, 1973; Rogowski, 1972; Warrick
et al.
, 1977); more recently attempts
have been made with remotely sensed data (Cosh and Brutsaert, 1999). However, it is still
very difficult to use this type of information to determine infiltration over a larger area.
The effects of stratification or layering of soil properties and of crusts at the surface have
received considerable attention (Miller and Gardner, 1962; Philip, 1967; Bouwer, 1969;
Hillel and Gardner, 1970; Ahuja and Swartzendruber, 1973; Bruce
et al.
, 1976). The details
of instabilities at the wetting front during infiltration into stratified soils have also been
investigated (White
et al.
, 1977; Selker
et al.
, 1992; Liu
et al.
, 1994a;b).
9.3.5
Some other expressions for potential infiltration
For most practical applications Equations (9.68) and (9.69) should be adequate as a
parameterization of infiltration capacity. However, over the years, several other equations
have been proposed and used in applied hydrology.
Truncated series expansion
A number of well-known equations can be considered truncated versions of Philip's
time expansion series (9.66). Probably the oldest formulation was developed by Kozeny
(1927), and can be written as
at
b
f
c
=
(9.74)
where
a
and
b
are constants. Kozeny (1927) arrived at this form with
b
2, by
making use of the analogy with flow into vertical capillary tubes, and by showing that this
agrees with Wollny's (1884) experimental data. Equation (9.74) was later also proposed
by Kostiakov (1932) and others (see, for example, Lewis, 1937) on empirical grounds.
Theoretically, if (9.74) is considered as the first term of (9.66) the constants should be
a
=−
1
/
2, but with these values it would only be valid for short times.
On the other hand, if (9.74) is to be used for large values of time, the constants should
be
a
=
A
0
/
2 and
b
=−
1
/
0, in accordance with Equation (9.4). Equation (9.74) can be useful
for certain purposes, but only over relatively limited time ranges, with values of
a
and
b
intermediate between these extremes and dependent on the range of interest.
=
k
0
and
b
=
