Description of the Daily Number of Rain-Free Hours Series from a Location in Southern Spain by Using the Multifractal Turbulence Formalism

Abstract

Rainfall occurrence is of a great variability in Mediterranean climate zones. This process has been studied here by applying the multifractal turbulence formalism to the daily number of rain-free hours series recorded during 23 years in Córdoba (southern Spain). A scaling break at 16 days was found from the analysis of the moments, this presumably being a manifestation of the “synoptic maximum.” A study of the empirical moments scaling exponent function for scales from 1 day to 8.5 months revealed the presence of a multifractal phase transition associated with one critical moment. The parameters of the universal multifractal model had been estimated using the double trace moment method and the simulated theoretical moments scaling exponent function showed an acceptable agreement with the corresponding empirical function. The average of the daily number of dry hours has been found to be equal at different scales meaning that the process studied was conserved or statistically stationary. The multifractal analysis overcomes the limitations of many existing deterministic and stochastic models to describe the temporal nonlinear variability of the rainfall occurrence.