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

TL;DR

ROMA is a novel multifractal analysis method that captures the complex scale-dependent behavior of intermittent fluctuations, including crossover phenomena, demonstrated on auroral zone electric field data.

Contribution

This paper extends ROMA to account for crossover behavior, enabling the collapsing of PDFs across multiple scale regimes in multifractal analysis.

Findings

ROMA effectively characterizes multifractal properties of electric field fluctuations.

The extended ROMA captures crossover behavior across different scale regimes.

The method allows collapsing PDFs over multiple regimes.

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.