On the Possible Use of Fractal Theory in Rainfall Applications

The rainfall data used in hydrological calculations are seldom sufficient to correctly represent the extreme variability of rainfall in time and space. Regarding for example traditional sewer design, the errors may be negligible, but the successively more complex hydrological models used today are much more sensitive to inadequate input data. The problem can be solved either by extensive data collection or by developing methods for extracting more information from limited data. An approach based on fractal theory has been shown to provide a suitable framework for this purpose. In this paper we apply two fractal-related analyzing methods to a two-year series of one-minute rainfall observations. The results indicate that the series exhibit statistical properties that are independent of scale, i.e., scale invariant. A possibility emerging from these findings is to make a shift from the scale defined by the available data to the scale needed for the hydrological problem in question, a prospect of tremendous practical importance.