Study of rainfall intensities for micro-scales in a semi-arid zone (Tunis) by FIF model
Résumé
This work focuses on studying the rainfall intensities of high frequencies (less than a few hours). Multifractal fractionally integrated model (FIF) which is a universal multifractal model modified, based on a multiplicative cascade and having three parameters is used. The intensity of rain derived from recorded rainfall data at a resolution 5 minutes, collected between 2007 and 2010 at three stations belonging to the Grand Tunis are the subject of this study. The spectral analysis and the study of the structure function, have allowed detecting the scaling regime corresponding to micro-scales which stops at time scales for around 2h30min. It has proved that the process of rain is not conservative. Multifractal fractionally integrated model (FIF) is then adjusted. However, a problem of bias due to the high rainfall intermittency appears when estimating its parameters. Analysis of the results reveals that the increase of intermittency leads to overestimate the model parameter the codimension C1, which measures the average heterogeneity of the process and to underestimate the model parameter α which measures the degree of multifractality. To solve this problem, we select continuous sequences, on which we have applied the FIF model, which results in parameters almost identical to those obtained in the literature for very different rainfall patterns.
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