Natural catastrophes and point-like processes Data handling and prevision

A frequent approach when attempting to manage a natural catastrophe is in terms of a numerical model, by which we try to forecast its occurrence in space and time. But, sometimes this is difficult or even unrealistic. On more pragmatic grounds we can appeal to a formal analysis of the historical time series of every catastrophe of concern. Only approximately, however, can such series be likened to a point-like process, because the "detector-mankind" experienced substantial changes versus time. Nevertheless, such algorithms can be approximately applied by means of a few suitable assumptions. In the ultimate analysis, four basic viewpoints can be considered: i) either by assuming that phenomena are periodic; ii) or by assuming that an event occurs only whenever some energy threshold is attained (calorimetric criterion); iii) or by assuming that it occurs only whenever the system experiences some abrupt change in its boundary conditions; or iv), whenever no such algorithm is viable due to scanty observational information, just by applying fractal analysis, in terms of the box counting method, or some other more or less related and/or equivalent algorithms. The mutual relations, advantages, and drawbacks of any such approach are briefly discussed, with a few applications. They already lead to an apparently successful long-range forecast of a large flood in Northern Italy which occurred in 1994, and to the prevision of the next explosive eruption of Vesuvius. But the success of every application is closely determined by the quality of the historical database, or by the physical information that is fed into the analysis, rather than by mathematics that per se have only to be concerned with avoiding some arbitrary input being added, based only on the human need for simplicity. The present paper gives a synthesis of several algorithms that were previously independently applied on a simple intuitive basis to different case studies, although with no comparisons or discussion of their similarities and/or differences.