ROMA (Rank-Ordered Multifractal Analysis) for intermittent fluctuations with global crossover behavior

Abstract

Rank-Ordered Multifractal Analysis (ROMA), a recently developed technique that combines the ideas of parametric rank ordering and one parameter scaling of monofractals, has the capabilities of deciphering the multifractal characteristics of intermittent fluctuations. The method allows one to understand the multifractal properties through rank-ordered scaling or non-scaling parametric variables. The idea of the ROMA technique is applied to analyze the multifractal characteristics of the auroral zone electric field fluctuations observed by SIERRA. The observed fluctuations span across contiguous multiple regimes of scales with different multifractal characteristics. We extend the ROMA technique such that it can take into account the crossover behavior -- with the possibility of collapsing probability distributions functions (PDFs) -- over these contiguous regimes.