Parametric identification of a karst aquifer

The parametric identification of non-homogeneous aquifers is a highly complex task because it requires the performance of a large number of infield trials, which often yield results that are difficult to interpret or have doubtful reliability. Moreover, the physically continuous nature of the hydrogeological parameters to be identified (typically conductivity) means that the experimental data need to be applied to the territory, a task which is often difficult in view of their great variability. An alternative approach that has been studied in recent years is parametric identification by means of the solution of the Inverse Problem (I.P.). This method requires a generic hydrogeological knowledge of the aquifer, and the availability of a sufficient number of piezometric survey points on the area where the identification is to be made. The method is potentially able to provide detailed information on the aquifer characteristics, at decidedly competitive costs in terms of money and time as compared with those for the application of the direct method. However, its use is largely limited to the scientific field at present, and few technical applications have been described for the management of territorial scale aquifers. This is because by its very nature, the inverse problem has the characteristic of an intrinsically ill-posed problem, in the sense that it frequently has no unique, stable solution. Many researchers have investigated the causes of this poor formulation of the problem, recognizing the fundamental role played by the type of boundary conditions, the accuracy of reconstruction of the piezometric surface and the type and structure of the parametric method adopted. In the present work, after making a preliminary overview of the theoretical reasons why the I.P. is ill-posed, the above aspects are analysed in the context of a real aquifer with an extension of approximately 100 km2. After describing the method used to reconstruct the piezometric surface and individuating the boundary conditions, we illustrate the effects on the solution of the I.P. of different types of parametrization of conductivity. Keywords: inverse solution, territorial scale aquifer, piezometric surface, mathematical model.