Geoscience Reference
In-Depth Information
To summarize, these observations indicate that, in deciding on a strategy to describe
a hydrologic phenomenon, the relevant question is probably not so much whether a
physical, a black box or a conceptual approach should be used. Rather, it is more useful
to determine what scales are appropriate for the available and measurable data, and for
the problem at hand. In other words, what is the appropriate level of parameterization?
Spatial variability and effective parameters
As mentioned above, a parameterization can be defined as a functional relationship
between the variables describing the phenomenon in question. This relationship invari-
ably contains one or more constant terms, reflecting material and fluid properties and
vegetational, geomorphic, geologic and other physiographic features; these are called
parameters and they are normally determined by experiment. Most hydrologic parame-
ters tend to be highly variable in space. It stands to reason, therefore, that the experimental
determination of any such space-dependent parameter must be carried out at the scale at
which it is to be applied to describe the flow.
A second important issue is that any given parameterization is usually valid only
over a certain finite range of spatial scales, and that the computational scale, that is the
integration domain or the discretization of the equations, must lie within that range.
Because the necessary data may be available only at a coarser resolution, in practical
application a parameterization may have to be applied at scales, for which it was not
intended originally and which are larger than permissible. This means in such a case that
the spatial variability of the parameters at the finer scales, which is normally present in
the natural environment, cannot be accounted for with the available data. This difficulty
is often resolved by assuming that the parameterization is still valid at the larger scale,
and that it can be implemented with averaged or effective values of the parameters.
This approach is not always satisfactory, and it is still the subject of intense research.
Some aspects of this issue related to land surface-atmosphere interactions are discussed
elsewhere (Brutsaert, 1998).
Requirements
To be useful, a parameterization must satisfy several requirements. First, a parameteriza-
tion must be valid , that is, it must be able to give a faithful description of the phenomenon
in question. The word comes from the Latin “validus,” which means healthy or strong,
and thus reliable. Validation is the term, which refers to the testing of a parameterization,
and it consists usually of the application of some goodness of fit measure to results of
calculations with the parameterization relative to observations. Beside being valid, a use-
ful parameterization must satisfy the dual requirements of parsimony and robustness. 1 A
1
The law of parsimony, also known as Ockham's razor, comes to mind here. Actually, the principle was already
promulgated by Aristotle, and the razor is essentially Ockham's (1989; pp. 17, 20, 128) paraphrase of it.
More than 2300 years ago Aristotle (1929) wrote, for instance, in Physics (I, 6, 189a,15) “inasmuch as it can
be done from the limited, the limited is better,” and in (VIII, 6, 259a,10) “for when the outcome is the same,
the limited is always to be preferred, and indeed in matters of nature, the limited, being the better, occurs more
when possible.”
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