Geoscience Reference
In-Depth Information
of capillary potential (e.g. Gupta and Larson, 1979). In the second, equations are developed
to estimate the parameters of functional forms of the soil moisture characteristics, such as
the Brooks-Corey or van Genuchten curves of Box 5.4, or parameters of application-specific
functions, such as the infiltration equations of Box 5.2 (e.g Rawls and Brakensiek, 1982; Cosby
et al.
, 1984; van Genuchten
et al.
, 1989; Vereeken
et al.
, 1989, 1990; Schaap and Leij, 1998).
Rawls and Brakensiek (1982) provided regression equations for the Brooks-Corey functions
as a function of soil properties based on several thousand sets of measurements collected by
the US Department of Agriculture (USDA). A summary of this regression approach is given by
Rawls and Brakensiek (1989)
.
A typical equation for
K
s
in terms of the variables
C
(clay; 5%
<C<
60%),
S
(sand; 5%
<S<
70%), and porosity,
s
is:
0
.
00018107
S
2
K
s
=
exp[19
.
52348
s
−
8
.
96847
−
0
.
028212
C
+
0
.
0094125
C
2
8
.
395215
s
+
0
.
00298
S
2
s
−
−
0
.
077718
S
s
−
−
0
.
019492
C
2
s
+
0
.
0000173
S
2
C
+
0
.
02733
C
2
s
0
.
001434
S
2
s
−
0
.
0000035
C
2
S
]
+
where
K
s
is in cmh
−1
and the porosity
s
can be estimated from measured dry bulk density
d
as
d
s
s
=
1
−
(B5.5.1)
where
s
is the density of the soil mineral material (
2650 kgm
−3
) or, from another equa-
tion, to estimate
s
in terms of
C
,
S
, % organic matter, and cation exchange capacity of the
soil. These are all variables that are often available in soil databases. Rawls and Brakensiek
also provide equations for adjusting porosity to allow for entrapped air, to correct for frozen
ground and for surface crusting, to account for the effects of management practices, and for
the parameters of various infiltration equations including the Green-Ampt and Philip equa-
tions of Box 5.2. Some special pedotransfer functions have also been developed, such as those
of Brakensiek and Rawls (1994) to take account of the effects of soil stoniness on infiltration
parameters.
It is necessary to use all these equations with some care. Equations such as that for
K
s
above
have been developed from data generally collected on small samples (the USDA standard
sample for the measurement of hydraulic conductivity was a “fist-sized fragment” (Holtan
et al.
, 1968) that would exclude any effects of macroporosity). There is also considerable
variability within each textural class. The apparent precision of the coefficients in this equation
is, therefore, to some extent misleading. Each coefficient will be associated with a significant
standard error, leading to a high uncertainty for each estimate of
K
s
.
In the original paper
of Rawls and Brakensiek (1982), the order of magnitude of these standard errors is given. In
some later papers, this is no longer the case. The estimates provided by these equations are
then apparently without uncertainty. This gives plenty of potential for being wrong, especially
when in the application of a catchment scale model it is the effective values of parameters at the
model grid element scale that are needed. Some evaluations of the predictions of pedotransfer
functions relative to field measured soil characteristics have been provided by Espino
et al.
(1995), Tietje and Tapkenhinrichs (1993), Romano and Santini (1997) and Wagner
et al.
(1998).
An alternative approach to deriving pedotransfer functions has been to use neural network
methods (e.g. those by Schaap and Bouten, 1996; and Schaap
et al.
, 1998). Uncertainty in
the resulting functions cannot, then, be predicted by standard regression confidence estimates
but can be estimated using a bootstrap method (Shaap and Leij, 1998). Figure B5.5.1 gives
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