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Abdelgader A., Achour F. and J. Mudry (1996) Validation of Underground Flows by Discriminant Analysis. Rev. Sci. Eau 9 (2) : 219-230. [article in French]

Original Title: Validation des écoulements par l'analyse discriminante.

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The plateau of Besançon (Eastern France) spreads between the large valley of the Ognon to the north and the enclosed valley of the Doubs to the south. Stratigraphically, the principal formations belong to the middle Jurassic era and the region is marked by a brittle tectonic characterized by NE-SW faults. Bajocian and Bathonian limestones constitute a karstic aquifer (200 m in thickness), which is free for much of its extent but becomes confined under Oxfordian marls towards the Doubs valley. The hydrogeological and structural boundaries of the drainage basin are complex, as are its hydrodynamic functioning and the hydrochemical responses observed at the outlets. The reservoir is drained principally by the Mouillère, Trébignon and Roche-lez-Beaupré springs, these outlets being situated mainly in the Doubs valley. The region is largely covered by dense vegetation, essentially forests, which constitute a groundwater recharge zone, and by the conglomeration of Besançon. One of the most karstified regions in France, the site includes two groups of wells that supply the town of Besançon with drinking water: the first group is situated on the unconfined zone of the aquifer (Chailluz), and the second is located on the confined part of the karstic aquifer (Thise). The wells are equipped with piezometers to monitor water levels continuously.

The rainfall distribution in this karstic region is homogeneous. During the 1991- 1992 hydrological year, the observed precipitation was 1144 mm at Besançon, with an evapotranspiration constituting about 50 % of the measured precipitation. On the Besançon plateau, the water mineralization of the different karstic springs is related to the nature of the underlying geological media (lithology, importance of karstification, etc.), to the water residence time and to seasonal variables (characteristics of the rainfall episode, hydroclimatic events, etc.). The water chemistry is relatively stable during dry intervals, but exhibits high fluctuations during flood periods. Outlets were sampled every 7 to 10 days from January 1991 to August 1992, in order to follow variations in water physico-chemistry. The sampling frequencies covered diverse water-level situations in the aquifer (low-water period, high-water period, drying-up period, etc.), and allowed the application of some multidimensional statistical tools.

The piezometric profile and lithologic correlations between the boreholes of Chailluz and Thise show that the highest hydraulic gradient is calculated between the Chailluz boreholes and the Trébignon spring. The hydraulic gradient is low in the confined part of the aquifer (between the Thise boreholes and the spring of Roche-lez- Beaupré). Two zones can be identified:

  1. a free zone distinguished by flow and drainage relationships between the Chailluz boreholes and the Trébignon spring;
  2. a confined zone linking the Thise boreholes and the Roche-lez-Beaupré spring, which corresponds to a common water circulation.

To confirm the results obtained from the piezometric study, we have used multidimensional statistical techniques to process the hydrochemical data from the karstic springs.

Factorial discriminant analysis is a multivariate method that allows the testing of hypotheses. It belongs to the field of decisional statistics, and is based on the comparison of multidimensional intragroup variances to intergroup variance. These methods can show the presence of certain relationships between a qualitative explained criterion and a group of quantitative explanatory characters, and they allow one to describe these latter relationships. Cross discriminant analysis can be used to evaluate the pertinence of a given hypothesis and to identify the dominant factor(s). The introduction of a qualitative variable within a population allows the division of this population into different groups, with each individual assigned to one group. Discrimination of the groups consists of maximizing the variance between their centres of gravity (a principal components analysis is performed on the matrix of the centres of gravity of the defined groups a priori); one can then clarify the properties that distinguish the different groups. If the individual is close to the centre of gravity of its group, it is "well classified". In the case where the distance to the centre of gravity of its group is superior to that to the centre of gravity of another group, the individual is "poorly classified" and it will be reassigned to this other group.

Another advantage of these methods is the use of supplementary individuals, which are not involved in the definition of the groups. Supplementary individuals are reassigned to the groups to which they are statistically linked. In karstic hydrogeology, cross factorial discriminant analysis of a population enables one to validate the classification criteria based on the analysis of flows and concentrations. These units of classification deal with the hydrokinematic phases (seasonal variable) or with the intrinsic systems (geographic variable). Therefore, in our case we have crossed two qualitative factors, "system" (Trébignon, Roche-lez-Beaupré) and "season" (spring, summer, autumn, winter) by undertaking two different analyses on the same series of data.

The application of these techniques to the limestone aquifer of the Bathonian- Bajocian shows that intrinsic factors predominate in determining the mineralization of the outlet water. On the other hand, this method enables one to associate borehole chemistry to tested springs: the association of a group of boreholes with particular springs is explained by the rapid circulation and drainage in the unconfined zone of the karstic media. This is the case of the association of the Chailluz boreholes (situated in the unconfined zone of the aquifer) with the Trébignon spring, which behave hydrochemically in the same manner. Other boreholes are grouped with the confined aquifer; this case corresponds to the assignment of the Thise boreholes (located in the confined zone of the aquifer) to the Roche-lez-Beaupré spring. These results corroborate those obtained from the piezometric study.

Factorial discriminant analysis allowed the verification of the appropriation of the predefined groups to the discriminant factors: hydrogeologic character (lithology, structure of the drainage, gradients, etc.) and hydroclimatic phenomena (season, hydrometeorological episodes, etc.). The choice of the property groups based on the geographic and geologic criteria proved pertinent.


Piezometry, discriminant analysis, hydrogeochemistry, flow, karst, plateau of Besançon (France).

Corresponding author

A. Abdelgader, Laboratoire de Mécanique des fluides et Génie Civil, quai Frissard B.P. 265, 76055 Le Havre Cedex, FRANCE

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