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

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.

► 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.