Multiscale and cross entropy analysis of auroral and polar cap indices during geomagnetic storms

In order to improve general monoscale information entropy methods like permutation and sample entropy in characterizing the irregularity of complex magnetospheric system, it is necessary to extend these entropy metrics to a multiscale paradigm. We propose novel multiscale and cross entropy method for the analysis of magnetospheric proxies such as auroral and polar cap indices during geomagnetic disturbance times. Such modified entropy metrics are certainly advantageous in classifying subsystems such as individual contributions of auroral electrojets and field aligned currents to high latitude magnetic perturbations during magnetic storm and polar substorm periods. We show that the multiscale entropy/cross entropy of geomagnetic indices vary with scale factor. These variations can be attributed to changes in multiscale dynamical complexity of non-equilibrium states present in the magnetospheric system. These types of features arise due to imbalance in injection and dissipation rates of energy with variations in magnetospheric response to solar wind. We also show that the multiscale entropy values of time series decrease during geomagnetic storm times which reveals an increase in temporal correlations as the system gradually shifts to a more orderly state. Such variations in entropy values can be interpreted as the signature of dynamical phase transitions which arise at the periods of geomagnetic storms and substorms that confirms several previously found results regarding emergence of cooperative dynamics, self-organization and non-Markovian nature of magnetosphere during disturbed periods.