Spectral analysis of 49 years of rainfall rate and relation to fade dynamics

The nature of the rainfall rate R(t) as a transient random process is presented in the context of microwave attenuation and fade dynamics. Using 49 years of data recorded in Barcelona, the spectral densities of energy and power and the autocorrelation function are presented, together with their analytical model. Examples for specific rain events are also presented. Several regimes covering a wide range of intensities have been investigated, and it is found that the spectral densities all exhibit a similar form which is independent of the average regime of R considered. This leads to a mean frequency and a spectral width which appear to be universal constants and independent of the regime. Similar features are found for the autocorrelation function. The mathematical models and numerical values found are compared to the Maseng-Bakken model (1981) proposed in earlier work of fade dynamics, and the agreement is good. The method is proposed for modeling the denormalized autocorrelation, and hence the spectrum, using only the measured average rainfall rate during a period of interest. Finally, the average number of crossings per unit of time is modeled and compared to the experimental results, and the agreement is satisfactory