Hydrologic properties, such as rainfall, aquifer characteristics (porosity, hydraulic conductivity, transmissivity, storage coefficient, etc.), effective recharge and so on, are all functions of space (and time) and often display a high spatial variability, also called heterogeneity. This variability is not in general random. It is a general rule that these properties display a so called ``scale effect'', i.e., if we take measurements at two different points the difference in the measured values dicreases as the two points come closer to each other.
It is convenient in certain cases to consider these properties as random functions having a given spatial structure, or in other word having a given spatial correlation, which can be conveniently described using appropriate statistical quantities. These variables are called ``regionalized'' variables (5).
The study of regionalized variables starts from the ability to interpolate a given field starting from a limited number of observation, but preserving the theoretical spatial correlation. This is accomplished by means of a technique called ``kriging'' developed by (4,5) and largely applied in hydrology and other earth science disciplines (1,7,6,3) for the spatial interpolation of various physical quantities given a number of spatially distributed measurments.
Although theoreticallly kriging cannot be considered superior to other surfave fitting techniques (7) and the use of a few arbitrary parameters may lead absurd results, this method is capable of obtaining ``objective'' interpolations evaluating at the same time the quality of the results.
In the next sections we discuss first the statistical hypothesis that are needed to develop the theory of krigin and then we proceed at describing the method under different assumptions and finally report a few applications.
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