I processi di interpolazione spaziale nella ricostruzione della superficie piezometrica. Un'applicazione all'acquifero alluvionale dell'Alta Valtiberina

The data collected during three piezometric surveys (1975, 1991 and 2001), carried out downstream of Montedoglio Dam, in Upper Tiberian Valley (province of Arezzo, Tuscany, central Italy) were analysed in order to evaluate the effects of the dam, built at the end of 80's. In order to carry out such study, the static levels of the existing wells were interpolated. With the term of spatial interpolation or prediction all methods (both deterministic and stochastic) allowing to know the value of a spatial variable, even where it was not measured, are classified. Obtaining a distributed information starting from a given punctual data is obviously a complex operation and it is strongly related to the interpolative algorithm. Within the two main groups of deterministic and stochastic interpolators, the authors considered 4 algorithms: 1. IDW, i.e. Inverse Distance Weighting (deterministic) 2. RST, i.e. Regularized Spline with Tension (deterministic) 3. UK, i.e. Universal Kriging (stochastic) 4. CK, i.e. Co-Kriging (stochastic) These were applied to the data obtained during the three piezometric surveys. The comparison among the algorithms was carried out by means of the Leave-one-out Cross Validation. The Kriging and the Co-Kriging give the best expected results, even if by means of more complex analysis, when the data have a well defined trend and when the sample sizes are small. From the hydrogeological point of view, even if important variations of the piezometric level were not put in evidence, a different behaviour between the northern sector and the central and southern sectors of the Upper Tiberian Valley emerges. This is probably due to the discharge variation of the River Tiber, consequently to the activation of Montedoglio Dam.