A simple model of rain in time: An alternating renewal process of wet and dry states with a fractional (non-Gaussian) rain intensity

A simple model of rainfall in time is proposed coupling the theory of renewal processes with a scale invariant representation of rain intensity. In particular, a strictly alternating renewal process mimes the sequence of wet and dry synoptic weather states, while a Fractional Noise represents the rain variability within each wet state. The rain model is adapted to Osservatorio Ximeniano (Florence) and Osservatorio di Brera (Milan) datatasets. Some rain characteristics are considered to check the agreement between model and data, namely, the annual volume of rainfall, the wet fraction of the year, the extreme values through the classic DepthDurationFrequency curves, and the maximum annual volume of the rainfall event.