A Cumulant-Based Approach To Understanding Magnetospheric Dynamics And Predicting Geomagnetic Indices

Because the magnetospheric response to the solar wind is highly nonlinear, correlation studies have limited utility for understanding magnetospheric dynamics. Information-theoretic quantities provide an elegant alternative that captures the essential features of the correlation function---and more. We employ a nonparametric, cumulant-based, statistical approach to nonlinear dynamics underlying the evolution of the Kp and Dst geomagnetic indices, given solar wind magnetic field and plasma input. We examine the underlying dynamics of the system, the temporal statistical dependencies, the degree of nonlinearity, and the rate of information loss. We find a significant difference in the nature of the nonlinear magnetospheric response between solar minimum and solar maximum. This approach also has the advantage that it is reliable even in the case of small data sets and therefore it is possible to avoid the assumption of stationarity, which allows for a measure of predictability even when the underlying system dynamics may change character. Evaluations of several leading Kp prediction models indicate that their performances are sub-optimal during active times. Possible improvements of these models using our results are discussed.