Spatiotemporal and Multiscale Validation of Ideal and Anisotropic MHD Models within the Space Weather Modeling Framework using Distance Correlation Functions

The interaction of the solarwind with Earth's magnetosphere produces complex nonlinear phenomena at disparate length and time scales. These phenomena generate fluctuations in the magnetic and electric potential fields in the magnetosphere, which map to the surface to create non-stationary geomagnetic pulsations and currents with diverse spectral profiles. Using ground-based magnetometers to measure these fluctuations grants access to global magnetospheric and space weather activity at all scales, but attempts to validate magnetohydrodynamic models against these observations using traditional linear metrics fail to capture the full extent of model performance. Here we present the first such attempt to validate and compare ideal and anisotropic MHD models spatiotemporally within the SWMF framework using ground-based magnetometers by using the distance correlation coefficient, which can assess nonlinear dependence in order to measure nonlinear, multiscale phenomena. Distance correlations of discrete frequency domains within both magnetic and linearly and circularly polarized electric ground perturbations are compared across the MLT domain above and below the plasmapause, whose latitude is determined by observations. These frequency domains correspond to particular classes of plasma waves whose sources are various plasma instabilities, field-aligned currents, and changes in convection patterns generated by the viscous interaction of the solarwind with the magnetosphere. In this way, correlating against observations and calculating correlation lengths and periods can indirectly measure how well these MHD models replicate not only long-wavelength activity mediated by topological changes in the magnetosphere, but plasma instabilities, activity mediated by the propagation and dissipation of Alfven waves, and the time-varying plasma density distribution in the inner magnetosphere. Distance correlation functions of ground-based magnetometer data across the frequency domain offer a powerful method to validate MHD models spatiotemporally by scale of activity.