Quelques réflexions sur l'utilisation des modèles en hydrologie. [Tribune libre] On the use of models in hydrology. [free opinion]

Résumé

Cette réflexion sur la modélisation en hydrologie, bien que se référant souvent à ce domaine précis de l'hydrologie, se veut d'ordre plus général et propose une classification très réductrice des modèles en deux genres: ceux établis à partir de données d'observation des processus étudiés, et ceux pour lesquels il n'existe aucune observation du phénomène à modéliser, à l'échelle étudiée.

A partir de cette classification et des règles bien connues de la tragédie classique (unité de lieu, de temps, d'action), une pratique de la modélisation est proposée et des pistes de recherche sont dégagées.

On conclut en rappelant qu'il doit exister aussi, dans la communauté scientifique, en sus de recherches en modélisation à caractère « utilitaire », d'autres travaux portant sur des modèles qui ne servent à rien.

Ces quelques réflexions, à caractère quelques peu polémique, ont pour objet d'initier si possible une discussion; d'où la rubrique « tribune libre » où elles paraissent.

Mots-clés:

• Modèles,
• boîtes noires,
• validation,
• prédiction,
• incertitudes

Abstract

This discussion article addresses the issue of the nature of models used in hydrolory. Although its emphasis is on contaminant transport in groundwater, I believe it is relevant to most areas of hydrologic modelling. It proposes a minimalist classification of models into two categories: models built on data from observations of the processes involved and those for which there are no observation data on any of these processes, at the scale of interest.

The argument is that the former should (or rather, ought to, since the question seems to attract little interest) obey serious working constraints, well-known from classical tragedy:

- unity of place,

- unity of time,

- unity of action.

The meaning of these rules, in terms of model calibration, validation and extrapolation, is analysed. They impose very strong limitations on the applicability of such models.

As to the models in the latter category which, in my opinion, are the more interesting and useful ones, several suggestions are made for their development and application.

1. MODELLING OBSERVABLE OR OBSERVED PHENOMENA

Observable phenomena such as nitrate or pesticide pollution are there to be measured and obserrved, although this might in practice involve considerable effort. Modelling is then used to forecast future behaviour of these pollutants.

The archetypal model for observable phenomena is that of the « black box ». If one can provide the box with one or several inputs and outputs and place something numerical inside, it will produce results. The modeller's task is to introduce a serviceable « engine » into the box, if possible. However, the least demanding of approaches is protrably the neural network method. Here, an engine is not even necessary: the series of observed inputs and outputs is given to the network which itself carries out a « weighting » of the input data resulting in the given output. The « engine » in the black box is created by the data, whereas in more familiar black boxes, the modeller decides on a form of relationship between the input and the output (e.g. a convolution equation, a groundwater model equation), and only tries to fit a limited set of parameters describing the black box. This phase of the fitting is called, in neural network terms, the « learning process » - it is modelling reduced to its bare essentials. Almost no physical understanding of the system is needed and the range of decisions left to the modeller is almost zero (e.g. number of neurons, of neural layers, forward or backward learning, etc.). This type of model looks simple but it must be remembered that most other models currently used in hydrology on series of observed data are actually quite similar. They may be called deterministic or even stochastic, conceptual or distributed but the basic principle of all these « fitted » models is the same: the « engine » in the box is created by the data set and its exact nature is irrelevant.

Validation of models fitted by the learning process

This important questions is at present being debated by modellers. For a blackbox model (as defined above), valdiation consists in testing it with a set of parameters that has not been used during the learning process trut for which the output is knovn and then, comparing the real and calculated outputs. A number of criteria has been proposed for this comparison and many conflicting opinions aired as to the possibility of validating a theory, and the model which is its expression, from observations. A counter- argument holds that a model is not an expression of a theory but of universally accepted principles, e.g. mass conservation, and of experimental laws, e.g. Darcy's law. Moreover, although a model may be invalidated at some point, it represents the « least unsatisfactory » way of trying to forecast the future, and each successful validation attempt increases the confidence in the model. Therefore, it would seem a good idea to separate the learning data into two groups: one for fitting and the other for validating.

Unity of spaceThis means that the model only applies to the domain on which it has been fitted through the learning process. There are three examples of how this rule is infringed: (i) Extrapolation in space. The set of parameters derived at site A, said to be « representative » of the medium, are used at site B. To my knowledge, no evidence exists at present of the merits of this method nor has it been reliably validated by experience. Quite the opposite, except in rare cases ofvery uniform media. (ii) Transposing in space through a formal link between the parameters obtained through the learning process for site A and the corresponding geometrical and geological data for site B. A new set of parameters is derived characterizing the latter. This could prove a fruitful line ofresearch but it has not as yet, received much attention . (iii) Method of « relay element », which applies specifically to transport in porous media. As movement of strongly retarded solutes cannot be observed, a laboratory experiment is done with the solute in question and another weakly retarded « relay element ». The relay element is then used alone in the field, at the transport distance of interest The difference in their retardation, measured at the laboratory scale, is then extrapolated to the real medium in order to make the prediction. This approach is certainly preferatrle to a simple extrapolation from the laboratory to reality of a retardation coefficient related to a perfect tracer, since it uses information of the retardation over the entire transport distance of interest. However, it is totally dependent on the similarity of retardation mechanisms affecting the two elements and on the « representativeness » of the tested sample.

Unity of action

This rule is simple and no exceptions should be tolerated. If the modelled action were to change, the model fitted by the learning process is dead. The learning process is based on a given medium, driven by given mechanisms. It does not identify any general intrinsic characteristics.

Unity of time

If the system is modified by time, the model is no longer relevant. The changes may be seasonal, long-term or due to inherent nonstationary conditions. For example, nitrate transport depends on the type of winter soil cover, ploughing techniques, etc., and the representative parameter sets will change in consequence.

These constraints severely limit the use of black-box models.

2. MODELLING OF UNOBSERVABLE PHENOMENA

There are several reasons why certain phenomena cannot be observed. Consider nuclear waste disposal in deep repositories: if this becomes a source of pollution, it will happen untold years hence - the pollution phenomenon is therefore unobservable today, predictive impact studies generally make use of this type of modelling.

Here, the important question is: what parameters to introduce ? The decision must be based on the ability to describe the system and its behaviour without the benefit of observation. At present the general tendency seems to be:

(i) to identify the real geometry of the system,

(ii) to thoroughly analyse and represent the physics of the underlying driving mechanisms,

(iii) to analyse scenarios.

(i) Identifrication of the real geometry. Since it is impossible to blindly fit global coefficients by the learning process, the medium must be observed and described, starting with the geometry. This is an entirely new discipline in groundwater hydraulics. Several methods are being developed, genetic models (e.g. alluvium sedimentation in streams, diagenetic processes in pores), stochastic facies models (e.g. Boolean techniques, Indicator simulation techniques, Truncated Gaussian techniques) which produce a very detailed description of the geometry and properties of the medium. In general, an infinite number of possible « realizations » of the real medium is generated and the variatlility between them indicates the urrcertainties on the medium under consideration. These realizations can be conditioned by available measurements of medium properties, e.g. at boreholes. These models usually function with a very small discretization (on the order of decimeters to meters) and produce descriptions which are coherent with what can be observed in the field at the sample scale. Then, a change of scale, as exact as possible, has to be made in order to provide a description of the medium that can be handled by the model. This is a difficult process on which much more work needs to be done.

(ii) Anatysis and representation of the underlying physical processes. In the black-box models ihere is a tendency to globalize the processes. Here, the tendency is reversed: the individual, elementary mechanisms must be examined and their strength and kinetics studied and measured. This involves lengthy and expensive investigations but it is the only way to obtain physically significant parameters. However, this method results in extremely complicated models and although it seems to be the only rigorous one, it is, as yet impossible to judge its success.

(iii) Scenario analysis. When the model is ready, it is used in forecastng. This is done through the development of scenarios which take into account all possible factors of change and evolution, natural and man-made. This by itself is a very demanding task, which requires considerable effort both from the technical and the sociological viewpoint, considering all inter - and retroactions between the physical and the decision-making worlds.

The concluding passage suggests that somewhere in the scientific community, over and above the modelling work guided by « useful » aims, work must also continue on models that serve no particular purpose. consider the lattice gas models, which are fascinating tools, although it is impossible, at this stage, to know if they will ever play a significant role in any facet of hydrology.

Keywords:

• Models,
• black box,
• validation,
• prediction,
• uncertainty