Quelques réflexions sur l'utilisation des modèles en hydrologie. [Tribune libre]

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.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 PHENOMENAObservable 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 processThis 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 actionThis 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 timeIf 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 PHENOMENAThere 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

Les sciences de l'eau : présent et futur

Les sciences de l'eau connaissent actuellement un développement accéléré. Plusieurs facteurs contribuent à cet élargissement de la base de connaissances explicatives et instrumentales sur l'eau. On note, par exemple,1. les investissements accrus dans la mise au point de systèmes de mesure permettant l'étude approfondie des propriétés de l'eau,2. l'expansion considérable des approches mathématique et systémique à l'interprétation des données, ou encore3. les progrès récents des outils informatiques qui ont favorisé le développement et l'usage des modèles de prédiction et ainsi, l'amélioration significative des connaissances sur la chimie, la biologie et la toxicologie.D'un autre côté, la croissance et la diversification des problèmes sociaux reliés à la raréfaction de l'eau viennent multiplier les domaines d'application des connaissances en vue de trouver des solutions durables aux problèmes. Dans cet article, on s'interroge, dans un tel contexte d'élargissement, sur l'évolution des sciences de l'eau au cours des prochaines années en mettant en évidence les problèmes socio-économiques dont la solution fait appel aux connaissances actuelles, à leur raffinement par les applications ou encore, à de nouvelles capacités techniques d'interprétation des phénomènes hydrologiques. On y distingue entre les activités qui seront entreprises pour résoudre des questions scientifiques fondamentales pouvant se justifier par des retombées possibles pour la société (la poussée scientifique) de celles qui seront engagées pour élaborer des solutions à des problèmes socio-économiques d'importance (les besoins socio-économiques de connaissances). On met ensuite en évidence les facteurs qui interviendront pour favoriser l'épanouissement des initiatives scientifiques, et on évalue l'effet de ces facteurs sur l'orientation de ces initiatives. On pose ainsi l'hypothèse que ce serait surtout la solution des problèmes socio-économiques, en conjugaison avec les aptitudes scientifiques actuelles, qui orienteront les développements des sciences de l'eau dans l'avenir. Enfin, on présente une approche émergente pouvant aider à comprendre l'évolution des sciences de l'eau. Ce modèle de représentation de la dynamique des initiatives scientifiques est caractérisé par deux pôles d'attraction relevant de la solution des problèmes sociaux reliés à la ressource : l'un en relation avec les besoins de connaissances pour la gestion de l'eau et l'autre lié aux besoins spécifiques de connaissances pour l'administration publique de l'eau.The water sciences are now entering a process of accelerated development. Numerous factors can explain this rapid evolution : a) the important investments in measuring systems that now allowed the characterization of water properties, b) the considerable expansion of mathematical and systemic approaches to the interpretation of data, c) the recent progress in interface tolls for computer modeling and the subsequent diversification of simulation models and the remarkable development in water chemistry, biology and toxicology that followed, have all largely contributed to the actual broadening of the theoretical and applied knowledge base on water. Furthermore, the scientific and technical efforts unfolded in order to explain social problems related to water shortages and to find sustainable solutions have also contributed to the diversification and deepening of this wide knowledge base. In this article, taking into consideration the deepening and diversification of the related knowledge base, we question ourselves on the evolution of water sciences in the future. We first underlined the socioeconomic problems that can be solved either by the application of actual knowledge, its refinement by learning from applications, or by the development of new technical ability for the interpretation of hydrological phenomena. We then distinguished between the activities undertake to solve scientific problems justified by long term social benefits (the science push) from those that aim to find solutions to important socioeconomic problems (the social needs for scientific knowledge). We then look at the different factors that help the achievement of research enterprises and explain the effect of those factors on the orientation of scientific projects. Doing this, we formulate the hypothesis that it is the search for solutions of socioeconomic problems that, on the basis of actual scientific ability, that will be the prime factor for the evolution of water sciences in the future, its dynamic and orientation. Finally, we propose a general approach that can help the understanding of the evolution of water sciences. This model represent the dynamic of scientific initiatives as affected by two attracting poles : the first pole is related to the needs for scientific knowledge for water management problems (i.e. the rational and engineering approach to water problems), and the second being the needs for the specific knowledge required for public administration of water (i.e. the policy and political approach to water problems).In general, we may conclude that the water sciences can be conceived as the scientific constructs generated by the application of particular scientific basic knowledge to water and its relations with natural and human systems. Those scientific constructs on water and its systemic interactions with terrestrial and human systems develop from this process are not as well structured as the sub-domains that emerge under traditional domains like biophysics, biochemistry, basic hydrology, political economy, or so. They are coherent sets of inter-disciplinary constructs elaborated to explain or predict complex natural processes or systems of relations between human and nature, mostly in response to real or perceived social needs. Is this to say that the scientific works on water will not succeed in the establishment of well-structured scientific subdomains like hydrology for example ? In spite of the evident progress, natural water and its relation with nature and human systems will remain for a long time applications domains of the fundamental knowledge that have been developed in the basic or applied sciences. Those applications will certainly produced new theories or original basic knowledge with high explicative or predictive values. In this manner, the object of the applications (water) and its context (natural and human systems) are the prime determinant of knowledge development, while in comparison, in basic sciences, it is the knowledge per se and its related instrumental capacities that mostly determine its own evolution. The development rhythm of technical and scientific knowledge on water is strongly influenced by the attention that society brings upon the resource. In the future, social preoccupations about water should increase considerably in light of its growing scarcity and the collective obligations to cope with higher probabilities of related extreme events. The type of knowledge that should developed will depend upon the specific approaches to social problem solving retained by political and administrative authorities, while in turn, those approaches will be influenced by research and development done in the field of management and public administration of water

Models of the water retention curve for soils with a fractal pore size distribution

The relationship between water content and water potential for a soil is termed its water retention curve. This basic hydraulic property is closely related to the soil pore size distribution, for which it serves as a conventional method of measurement. In this paper a general model of the water retention curve is derived for soil whose pore size distribution is fractal in the sense of the Mandelbrot number-size distribution. This model, which contains two adjustable parameters (the fractal dimension and the upper limiting value of the fractal porosity) is shown to include other fractal approaches to the water retention curve as special cases. Application of the general model to a number of published data sets covering a broad range of soil texture indicated that unique, independent values of the two adjustable parameters may be difficult to obtain by statistical analysis of water retention data for a given soil. Discrimination among different fractal approaches thus will require water retention data of high density and precision. (Résumé d'auteur

Essais de quantification du débit des résurgences sous-marines autour du Piton de la Fournaise (la Réunion, Océan Indien)

On étudie, par des mesures en plongée sous-marine, les émergences en mer des écoulements souterrains dans le Piton de la Fournaise (île de la Réunion) dans le cadre de recherches sur les relations entre circulations souterraines, flux de chaleur et phénomènes magmatiques. On établit:- que l'ensemble des émergences se situe au niveau du rivage, et non en profondeur- que grâce à des mesures approchées des phénomènes de mélange des eaux, on peut estimer le débit moyen des résurgences en mer à 0,4 m3s-1 par kilomètre de côte sur la façade sud de l'île. Ce chiffre est cohérent avec des estimations indirectes obtenues à partir du bilan hydrique.The « Piton de la Fournaise » on the island of la Réunion receives as much as 6 to 10 m y-l of rainfall, which almost immediately infiltrates due to the highly pervious nature of the basalt (microfissures, scoria). Very few springs or rivers drain the systeml however, numerous marine outlets have been observed by infrared thermographic surveys. Some of these outlets can also be observed on SPOT images, although no infrared charmel is available on SPOT.In an attempt to study the role of underground flow in the thermal balance of the volcano and its relation with magmatic phenomena, we have tried to observe the nature of these outlets by underwater exploration and to evaluate their flow rate by salinity and temperature mesurements.Longitudinal and transverse salinity profiles were measured by divers using a salinity-conductivity meter with automatic correction of temperature, transported in a waterproof container, on those plumes that had been observed on airborne images or by helicopter surveys.All the observed plumes are indeed mixing zones of seawater and freshwater, with salinity ranging from 29.9 to 35.1 %o (ocean salinity is35.2%o at la Réunion). Their temperature is in general lower than that of the sea, which explains why they are visible on infrared irnages.It was found, however, that all outlets are systematically situated very close to the shore line, with an elevation between + 1 and - 2 m of sea level. In none of the observations were outlets found that could originate deeper down in the sea. Most observable oulets are located at the base of basalt flows, in natural « tunnels » under such lava flows. This is consistent with the existence of an abrupt interface between seawater and freshwater on the island, which has been observed in a fewboreholes, and which forces the freshwater flow upwards towards the shore line, even if the nature of the flow is very discontinuous in the basalt.Based on the salinity profiles, we have attempted to estimate the flow rate. We focus here on a particular outlet at Vincendo. We liken the development and mixing of the plume to what occurs in an estuary with low flow. It has been observed that three mechanisms control the mixing in an estuary: wind which creates currents and pushes freshwater toward the edges; tidal effects and waves creating currents and turbulent mixing due to rugosity of the sides and bottom; density difrerences between seawater and freshwater, the latter floating on top of the former. Three cases are generally considered:a - Seas without tide: the interface is stratified;b - Seas with small tides: stratification and mixing occur sirnultaneously;c - Seas with large tides: no stratification and regular mixing in the vertical dimension.The observed salinity profiles at Vincendo clearly indicate that we are in the second case at la Réunion, where the tide amplitude is small (0.7 m).Two dimensionless numbers are used in estuaries: the Richardson and Froude numbers (see expression in text) (FISHER et al., 1979). It has been observed that the transition from case a to c corresponds to Richardson numbers in the range 0.08 to 0.8. Assuming that salinity profiles are consistent with case b, i.e. a Richadson number in the range 0.25 - 0.80, we find that the freshwater flowrate should be in the range 0.020 - 0.260 m3. s-1.A second independent estimation can be obtained by observing that the average concentration gradient in the 7,000 m2 of the obseved mixing zone (30 x 40 m) is on the order of 0.3 kg. m-3. m-1. Selecting (from FISCHER et al., 1979) a turbulent dispersion coefficient for coastal watcrs over the scale of several thousand m2 of 2 to 5 x 10-3 m2. s-1, we can estimate the vertical dispersive flux over the mixing zone and, by mass balance, we obtain another estimate of the flux in the range 0.150 - 0.400 m2. s-1.We conclude that the flowrate is on the order of 0.150 m3.s-1, with a plausible range of 0.100 - 0.300 m3.s-1.These results were extrapolated to the entire South and East shores ofthe island by assuming that the flow rate of an outlet was proportional to its area as observed on infrared surveys. We obtain an average flux of 0,4 m3.s-1 km-l for the southern flank of the volcano. This ligure is consistent with a global estimate (0,6 m3.s-1km-l) obtained by a surface hydrologic balance over this part of the volcano. The difference can represent diffuse outlets into the sea

Coastal karst springs in the Mediterranean basin : study of the mechanisms of saline pollution at the Almyros spring (Crete), observations and modelling

International audienceno abstrac

Continuous-time random-walk approach to normal and anomalous reaction-diffusion processes

We study the dynamics of a radioactive species flowing through a porous material, within the Continuous-Time Random Walk (CTRW) approach to the modelling of stochastic transport processes. Emphasis is given to the case where radioactive decay is coupled to anomalous diffusion in locally heterogeneous media, such as porous sediments or fractured rocks. In this framework, we derive the distribution of the number of jumps each particle can perform before a decay event. On the basis of the obtained results, we compute the moments of the cumulative particle distribution, which can be then used to quantify the overall displacement and spread of the contaminant species.Comment: 6 pages, 4 figure

Dynamics of Wetting Fronts in Porous Media

We propose a new phenomenological approach for describing the dynamics of wetting front propagation in porous media. Unlike traditional models, the proposed approach is based on dynamic nature of the relation between capillary pressure and medium saturation. We choose a modified phase-field model of solidification as a particular case of such dynamic relation. We show that in the traveling wave regime the results obtained from our approach reproduce those derived from the standard model of flow in porous media. In more general case, the proposed approach reveals the dependence of front dynamics upon the flow regime.Comment: 4 pages, 2 figures, revte

Modélisation 3D des transports de sel et de chaleur au cours des 248 Ma d’évolution du bassin de Paris : implications diagénétiques

Un modèle de bassin 3D a été développé sur le bassin de Paris, reconstituant ses 248 Ma d’histoire géologique depuis le Trias jusqu’à l’actuel. Cette modélisation s’appuie sur une base de données stratigraphique et lithologique détaillée constituée d’environ 1100 forages pétroliers. Ce modèle, d’échelle régionale, couvre un domaine de 700 000 km2, plus vaste que l’extension actuelle du bassin, afin de prendre en compte l’évolution paléogéographique de la plaque européenne. Cette histoire géologique est simulée à l’aide du modèle numérique NEWBAS de l’Ecole des Mines de Paris. Le modèle simule la sédimentation, l’érosion, la compaction, les écoulements de fluides et les processus de transport de solutés et de chaleur. L’objet du présent article est de montrer l’intérêt d’une telle modélisation pour l’estimation et la quantification de l’importance des circulations de fluides dans les processus géologiques. Les études sur les ciments diagénétiques des réservoirs Dogger et Keuper du bassin de Paris ont souvent conduit leurs auteurs à invoquer des circulations de fluides régionales. Ces études, qui fournissent des estimations de paléotempératures et de paléosalinités, apportent des contraintes à la modélisation, mais en retour la modélisation peut apporter un calage dans le temps de ces événements et une estimation des processus pertinents. La reconstitution des transports de chaleur et de sel proposée dans cet article permet ainsi de cerner l’influence de l’hydrodynamique sur ces processus. L’histoire thermique et saline du bassin est présentée à différentes étapes sur une coupe NW-SE représentative d’une ligne d’écoulement actuelle également valable au cours du Tertiaire. On montre l’importance de la paléotopographie pour expliquer les fortes salinités dans les réservoirs et le rôle de la faille de Bray pour l’évolution de la salinité dans le Dogger. Le basculement et l’érosion de la base tertiaire crée un écoulement gravitaire qui se substitue au régime d’écoulement en compaction, permettant ainsi la migration de saumures depuis la formation salifère à l’est du bassin vers les réservoirs du Keuper à l’ouest. La recharge des aquifères aux affleurements et la mise en charge des systèmes permet une migration ascendante des eaux salées depuis le Keuper vers le Dogger en considérant une perméabilité plus importante au niveau de la faille de Bray. Bien que dominé par la composante conductive, le transport de chaleur est également influencé par l’hydrodynamique avec un effet de refroidissement convectif possible lors de la mise en charge des aquifères à la fin de l’érosion tertiaire, pouvant expliquer une partie de l’excès de température déduit des inclusions fluides du Keuper entre l’état thermique à la fin du dépôt de la craie et l’actuel. D’après nos simulations, la base du Tertiaire est la période la plus compatible avec les observations diagénétiques, pour des raisons thermiques (maximum d’enfouissement et effet de refroidissement convectif) et chimique (topographie favorable aux migrations de saumures dans le Keuper et le Dogger)

Refinement indicators for estimating hydrogeologic parameters

We identify simultaneously the hydraulic transmissivity and the storage coefficient in a ground water flow governed by a linear parabolic equation. Both coefficients are assumed to be functions which are piecewise constant in space and constant in time. Therefore the unknowns are the coefficient values as well as the geometry of the zones where these parameters are constant. The identification problem is formulated as the minimization of a misfit least-square function. Using refinement indicators, we refine the parameterization locally and iteratively. We distinguish the cases where the two parameters have the same parameterization or different parameterizations