Geoscience Reference
In-Depth Information
Thus, the soil moisture characteristics of similar soils can be scaled by representing their
variability in terms of the distribution of the characteristic length
˛
. Note that a consequence
of the geometric similarity is that the porosity of the soil
s
is a constant for all similar soils. This
type of scaling has been applied in many studies (e.g. Simmons
et al.
, 1979; Clausnitzer
et al.
,
1992); its relevance here is as a way of incorporating a simple description of soil variability
into predictions of infiltration and runoff generation (e.g. Luxmoore and Sharma, 1980; Clapp
et al.
, 1983; Warrick and Hussen, 1993).
Using the Brooks-Corey characteristics as an example, assuming that we have knowledge
of the parameters for one particular soil with
˛
=1, then for any other similar soil:
˛
o
−
r
r
=
(B5.4.7)
s
−
while saturated hydraulic conductivity is given by
˛
2
K
s
K
s
(
˛
)
=
(B5.4.8)
where
K
s
is the saturated hydraulic conductivity of the reference soil. The expression for relative
hydraulic conductivity, Equation (B5.4.2), stays the same.
The analysis can be extended to other parameters dependent on the soil moisture charac-
teristics of the soil. Thus, the Philip infiltration equation (see Box 5.2) can be scaled as:
0
.
5
˛
1
.
5
S
1
t
−0
.
5
˛
2
A
1
f
(
t
)
=
+
(B5.4.9)
where
S
1
and
A
1
are the sorptivity and final infiltration capacity parameters for a reference soil
with
˛
=1. An analysis of multiple infiltration curves is one way of calculating a distribution of
˛
values for a particular soil type (see for example, Shouse and Mohanty, 1998). An example
of the scaling of infiltration curves in this way is demonstrated in Figure B5.4.3.
The Miller and Miller
similar media
concept is just one possible scaling theory that could be
used to provide a simple representation of heterogeneity of soil properties. A number of other
possibilities have been reviewed by Tillotson and Nielsen (1984). Mohanty (1999) has pro-
posed a method for scaling the properties of soils with macropores, treating their soil moisture
characteristics as continuous curves spanning the matrix/macropore pore sizes. This assumes
that such a dual porosity medium responds as a continuum, which may not always be a good
assumption.
B5.4.5 Identification of the Soil Moisture Characteristics Function Parameters
Both the Brooks-Corey and the van Genuchten soil moisture characteristics functions require
the calibration of a number of parameter values before they can be used in a predictive model.
Both laboratory and field measurements may be used in calibration, as well as indirect tech-
niques based on
pedotransfer functions
(discussed in Box 5.5). The resulting parameter values
are not independent of the measurement techniques and parameter identification techniques
used.
In principle, the soil moisture characteristics and conductivity characteristics at different
capillary pressures can be measured directly in the laboratory. Different functions can then be
fitted directly to the measured curves using a nonlinear least squares regression procedure (see
for example Kool
et al.
, 1987). However, such measurements are only currently possible on
small samples which tend to show significant heterogeneity from sample to sample, especially
close to saturation.
