Can a simple stochastic model generate rich patterns of rainfall events?

Several of the existing rainfall models involve diverse assumptions, a variety of uncertain parameters, complicated mechanistic structures, use of different model schemes for different time scales, and possibly classifications of rainfall patterns into different types. However, the parsimony of a model is recognized as an important desideratum as it improves its comprehensiveness, its applicability and possibly its predictive capacity. To investigate the question if a single and simple stochastic model can generate a plethora of temporal rainfall patterns, as well as to detect the major characteristics of such a model (if it exists), a data set with very fine timescale rainfall is used. This is the well-known data set of the University of Iowa comprising measurements of seven storm events at a temporal resolution of 5-10 s. Even though only seven such events have been observed, their diversity can help investigate these issues. An evident characteristic resulting from the stochastic analysis of the events is the scaling behaviors both in state and in time. Utilizing these behaviors, a stochastic model is constructed which can represent all rainfall events and all rich patterns, thus suggesting a positive reply to the above question. In addition, it seems that the most important characteristics of such a model are a power-type distribution tail and an asymptotic power-type autocorrelation function. Both power-type distribution tails and autocorrelation functions can be viewed as properties enhancing randomness and uncertainty, or entropy.