Easy identification of chemical signatures characteristic of water systems has become a major issue in the field of environmental protection and management. We propose an exploratory method, exclusively based on the statistical analysis of river water composition, capable of characterizing river waters in a given watershed through their chemical composition, as well as of detecting modifications, even when not related to pollution sources. Although the method is based on well-known statistic techniques (Principal Component Analysis and Linear Discriminant Analysis), and therefore is very simple and straightforward to apply, it goes far beyond the common data reduction use of these techniques. Its capabilities are illustrated through its application to rivers in Canton Geneva, Switzerland, a hydrographical network consisting of 310 km of waterways with 250 streams and rivers. The procedure results in a very satisfactory classification of watersheds, in our case by using only two geochemical indicators: U and Ba concentrations. The method also makes it possible to follow the seasonal evolution of river regimes or the effect of wetlands on river water composition.