Geoscience Reference
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first principles of fluid mechanics, can be obtained only for grossly idealized conditions,
which are coarse approximations of any real situation.
The hydrologic “systems” (also “operational” or “empirical”) approach is presumably
based on a diametrically opposite philosophy. In this approach the physical structure
of the various components of the hydrologic cycle and their inner mechanisms are not
considered; instead, each component, however it may be defined, is thought of as a “black
box,” and the analysis focuses on discovering a mathematical relationship between the
external input (e.g. rainfall, air temperature, etc.) and the output (e.g. river flow, soil
moisture, evaporation, etc.). The structure of this mathematical relationship is mostly
quite remote from the physical structure of the prototype phenomena in nature. This lack
of correspondence between the inner physical mechanisms and the postulated functional
formalisms makes this approach quite general operationally, because it permits the use of
well-known algorithms and objective criteria in identification and prediction. However,
this also underlies the main limitations of this approach. First, in assigning cause and
effect the definition of input and output variables is mostly based on intuition guided by
past experience, and the danger exists that some important phenomena are overlooked.
Second, the best that can ever be expected with a black box approach is a satisfactory
reproduction of a previously obtained input-output record; even when such data are
available, it is difficult to accommodate fully the nonstationary effects in the system,
and it is impossible to anticipate subsequent hydrologic changes, such as those resulting
from urbanization, deforestation, reclamation, or climate change.
Because many hydrologic methods do not really fit in this physical-versus-empirical
classification, a third possible approach was taken to be an intermediate one. In this
view the performance of a hydrologic unit, say a catchment, is represented in terms of
some idealized components or “grey boxes,” which correspond to recognizable ele-
ments in the prototype, whose input-output response functions are structured after
solutions of some tractable or suitably simplified situations of the physical processes
perceived to be relevant. This third way was often called the “conceptual model”
approach.
At first sight, a classification based on three distinct approaches, namely physical,
empirical and conceptual, may appear reasonable. However, it is less than obvious how
this classification can be applied to specific cases. Indeed, one might ask what the dif-
ference is between physical and empirical. After all, the essence of physical science
is experimentation and conceptualization. Moreover, the physical approach of one dis-
cipline is usually the empiricism or the conceptual model of another. For example,
Newton's “law” of viscous shear constitutes the physical basis of a wide area of fluid
mechanics, whereas it represents a mere black box simplification in molecular physics.
Darcy's law is the physical basis of much of groundwater hydrology, but in fluid mechan-
ics it can be considered an operational approach, to avoid the complexity of flow analysis
in an irregular and ill-defined pore network. The same dilemma is inherent in most other
special concepts used in hydrology. This ambiguous difference between physical, empir-
ical and conceptual shows that the classification of the methodologies should be based
on other criteria.
