Discriminant analysis, an efficient means for the validation of geohydrological hypothesis
The study of the hydrochemical data tables obtained during synchronous sampling (weekly, daily or hourly) is generally carried out by resuming the information by statistical methods. These methods, that disregard part of the initial information, allow to explain the structure of the data table in terms of hydrokinematics (BAKALOWICZ, 1979, 1982; MUDRY et BLAVOUX, 1986; ROLET et SEGUIN, 1986 a et b). These descriptive methods, based on the analysis of a single (bi or multivariate) statistical population, imply deductive reasoning. Their application, as well as the study of the untreated data table (or of its scattergrams), can show the presence of sub-groups based on hydrogeological criteria. The existence of such sub-groups can be tested by statistical methods based on variance analysis. Several methods use the variance ratio and compare it to Snedecor's distribution (single or double path variance analysis), others compare multidimensional intragroup variances to intergroup variance. This is the case with discriminant analysis. This paper describes the method from a point of view of statistics and presents two examples of application to karst springs. The first study deals with the chemical relationship of a low-water period with the preceding period of small floods and not to a hydrokinematical water drying up. The discriminant analysis allows to say Chat a recharge less visible on the hydrograph of the spring induces a non reversible chemical evolution of the reserve water. This is the case of the Fontaine de Vaucluse karst spring (Southeastern France) during a daily low water sampling. The second study allows to relate a karst spring to another one, thanks to its weekly physico-chemical behaviour, and not to a third one : this is the case of the La Rochefoucauld karst system (Charente, Western France) with the Bouillant, Font de Lussac and Lèche springs. The Bouillant and Font de Lussac springs behave in the same way hydrochemically, whereas the Lèche works independently. It is, hydrokinematically, a separate karst system, even if there is a certain relationship between all of them.