With the aim of suggesting some practical rules for the use of hydrological models, G. De MARSILY in his "free opinion" (Rev. Sci. Eau 1994, 7(3): 219-234) proposes a classification of hydrologic models into two categories:
He claims that for the former group of observable phenomena, models developed through a learning process as well as those based on the underlying physical laws are of the black box type. For the latter group of unobservable phenomena, he suggests that physically-based hydrologic models be developed.
Physically-based hydrologic models should introduce to the phenomenological laws the correct empirical coefficients, which correspond to the proper time and space scales (GANOULIS, 1986). Well-known examples are Darcy's permeability coefficient on the macroscopic scale as derived from the Navier-Stokes equations on the local scale and the macroscopic dispersion coefficients in comparison with the local Fickian diffusion coefficients. Misuse of these models by confusing the proper time and space scales and determining the coefficients by calibration is not a sufficient reason to consider them as belonging to the black box type. Black box type hydrologic models, although very useful when data are available, remain formally empirical. They fail to give correct answers when serious constraints of unity in place, time and action are not fulfilled.
Concerning the second class of models, we may notice that purely unobservable phenomena without any available data do not really exist in hydrology. In the case of very rare events and complex systems, such as radioactivity impacts and forecasting of changes on a large scale, physically-based models with adequate parameters may be used to integrate scarce information from experiments and expert opinions in a Bayesian probabilistic framework (APOSTOLAKIS, 1990).
The most important feature of hydrologic models capable of describing real hydrologic phenomena, is the possibility of handling imprecision and natural variabilities. Uncertainties may be seen in two categories: aleatory or noncognitive, and epistemic or cognitive. Probabilistic hydrologic models are more suitable for dealing with aleatory uncertainties. Fuzzy logic-based models may quantify epistemic uncertainties (GANOULIS et al., 1996). The stochastic and fuzzy modeling approaches are briefly explained in this free opinion as compared to the deterministic physically-based hydrologic modeling.
Hydrologic models, black box, physically-based, uncertainties, deterministic, stochastic, fuzzy logic.
J Garnoulis, Department of Civil Engineering, Aristotle University of Thessaloniki, 54006 Thessaloniki, GREECE