Geology Reference
In-Depth Information
Rainfall
Soil
Slope
Land cover
S-factor
R-factor
K-factor
L-factor
C-factor
P-factor
R
´
K
´
S
´
L
´
C
´
P
Fig. 2.2
The structure of the
Universal Soil Loss Equation:
an example of a grey-box model.
Soil loss
relationships, but these are usually more complex
than those used in black-box models and involve
multiple regression analysis or polynomial rela-
tionships. Good examples are the nomograph for
determining the value of the soil erodibility factor
(
K
) as a function of soil texture, structure and
permeability (Wischmeier
et al
., 1971), and the
Universal Soil Loss Equation (USLE), in which the
relationship between soil loss, rainfall and soil
type is adjusted by coefficients representing slope
steepness, slope length, crop management and
physical protection measures (Wischmeier &
Smith, 1978).
In white-box models an attempt is made to
describe as many of the processes of the erosion,
transport and deposition of sediment as possible.
Mathematical equations are used to do this, or
sometimes simple arithmetical calculations, but
more often, differential and difference equations.
Since these equations are generally based on satis-
fying the laws of conservation of mass and energy,
the models are often described as being physically-
based. The use of complex mathematics can be off-
putting for many model users who do not always
have the same mathematical background and
expertise as the model developers. In practice,
however, model users should not be frightened by
this but, instead, should adopt a questioning
approach. They should be more concerned about
the processes being described, as to whether they
are relevant to the problem and have the same
level of importance within the model as in the
field. The user should be sure that the equations
used are based on sound science and can be sup-
ported by underlying knowledge and measured
data. Often such questioning reveals that the sci-
entific understanding of many of the processes
described in the model is limited, and that many of
the equations used are actually empirical and simi-
lar to those used in grey-box models. In reality, no
truly white-box model of erosion exists, but there
are several which could be considered as pale
grey to cream in that they are certainly process-
based but only partially physically-based (Fig. 2.3).
Examples include WEPP (Nearing
et al
., 1989b),
EUROSEM (Morgan
et al
., 1998), GUEST (Rose
et al
., 1983), LISEM (De Roo
et al
., 1998) and SHE
(Wicks & Bathurst, 1996).
2.3 Conceptual Framework
Being able to determine the questions to ask of
modellers means that users need to have a good
understanding of their objectives in using a
model, an understanding which is enhanced if
their problem is conceptualized in terms of
relevant processes and outputs. Since defining
objectives and conceptualizing the problem rep-
resents the first two stages in model develop-
ment, there should be some common ground
between model developers and model users.
The pioneering work of Meyer and Wischmeier
(1969) represents a good example of setting objec-
tives and developing a conceptual framework for
erosion modelling (Fig. 2.4). Indeed, it has laid
