Double rank-ordering technique of ROMA (Rank-Ordered Multifractal Analysis) for multifractal fluctuations featuring multiple regimes of scales

Abstract. Rank-Ordered Multifractal Analysis (ROMA), a technique capable of deciphering the multifractal characteristics of intermittent fluctuations, was originally applied to the results of a magnetohydrodynamic (MHD) simulation. Application of ROMA to measured fluctuations in the auroral zone, due to the dominant physical effects changing from kinetic to MHD as the scale increases, requires an additional level of rank-ordering in order to divide the domain of scales into regimes. An algorithm for the additional step in this double rank-ordering technique is discussed, and is demonstrated in the application to the electric field fluctuations in the auroral zone as an example. As a result of the double rank-ordering, ROMA is able to take into account the nonlinear crossover behavior characterized by the multiple regimes of time scales by providing a scaling variable and a scaling function that are global to all the time scales.