Analysis and synthesis of rainfall time series using disdrometer data

Hydrometeorological and radio propagation applications can benefit from the capability to model the time evolution of raindrop size distribution (RSD). A new stochastic vector autoregressive semi-Markov model is proposed to randomly synthesize (generate) the temporal series of the three driving parameters of a normalized Gamma RSD. Rainfall intermittence is reproduced through a discrete semi-Markov process, modeled from disdrometer measurements using two-state analytical statistics of rain and dry period duration. The overall model is set up by means of a large set of disdrometer measurements, collected from 2003 to 2005 at Chilbolton, U.K. The driving parameters of the retrieved RSD are estimated using three approaches: the Gamma moment method and the 1-D and 3-D maximum-likelihood methods. Interestingly, these methodologies lead to quite different results, particularly when one is interested in evaluating RSD higher order moments such as the rain rate. The accuracy of the proposed RSD time-series generation technique is evaluated against available disdrometer measurements, providing excellent statistical scores.