Influence of the zero-rainfall on the assessment of the multifractal parameters

• Published in: Advances in water resources 2012-09, Vol.45, p.13-25
• Main Authors: Gires, A., Tchiguirinskaia, I., Schertzer, D., Lovejoy, S.
• Format: Article
• Language: English
• Subjects: Applied geophysics; Earth sciences; Earth, ocean, space; Environmental Sciences; Exact sciences and technology; Hydrology; Hydrology. Hydrogeology; Internal geophysics; Multifractal phase transition; Multifractals; Scale invariance; Truncated fields; Zero rainfall
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/j.advwatres.2012.03.026

► Truncated multifractal fields exhibit a 2nd order phase transition for low moments. ► Universal multifractal exponents’ estimates are affected by truncation of the field. ► The main features of rainfall data are retrieved on truncated simulated fields. ► A new technique to thwart this threshold effect provides encouraging results. Rainfall data contains numerous zero values, either real or spurious, especially at high resolution. This paper investigates how a truncation of a multifractal field affects the scaling analysis. Synthetic multifractal fields are used. The main result, which is theoretically expected and empirically observed, is that the truncated fields exhibit a multifractal phase transition for small moments. This implies an under-estimation of the multifractality index, and consequently of the extremes. This framework enables one to retrieve most of the features observed on radar data corresponding to a heavy rainfall event that occurred in September 2005 in the South of France. Finally a new technique is proposed to improve the estimation of characteristic multifractal parameters. It yields imperfect but encouraging results.