Deterministic chaos versus stochasticity in analysis and modelling of rainfall structure

In recent years, new methods for time series analysis, devised for description and characterization of chaotic behavior, yielded some fascinating results. Among them, the fact that deterministic processes may sometimes be statistically indistinguishable from random noise. Currently, discussion is going on about how to characterize a process and how to recognize whether it is stochastic or deterministic. A popular method for revealing the underlying dynamics from a time series, is the phase-space reconstruction via time delay embedding. This method is used here as a means to detect possible low-dimensional determinism in a historical rainfall time series and to compare the historical series synthetic series generated by a stochastic model. Specifically, the synthetic series has been produced using the scaling model of storm hyetograph combined with a stochastic process describing storm arrivals, durations and total depths. The comparison aims at revealing potential essential differences in the structure of the historical and synthetic data sets.