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

► 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 ef...

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Bibliographic Details
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
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Summary:► 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.
ISSN:0309-1708
1872-9657
DOI:10.1016/j.advwatres.2012.03.026