  We propose a new statistical protocol for the estimation of precipitation
using lightning data. We first identify rainy events using a scan statistics,
then we estimate Rainfall Lighting Ratio (RLR) to convert lightning number into
rain volume given the storm intensity. Then we build a hierarchical Bayesian
model aiming at the prediction of 15- and 30-minutes cumulated precipitation at
unobserved locations and time using information on lightning in the same area.
More specifically, we build a Bayesian hierarchical model in which
precipitation is modeled as function of lightning count and space time
variation is handled using specific structured (random) effects. The mean
component of the model relates precipitation and lightning assuming that the
number of lightning recorded on a regular grid depends on the number of
lightning occurring in neighboring cells. We analyze several model formulations
where storms propagation speed, spatial dependence and time variation
incorporates different descriptions of the phenomena at hand. The space-time
variation is assumed separable. The study area is located in Central Italy,
where two storms, that differ for duration and intensity, are presented.
