Concurrent Empirical Magnetic Reconstruction of Storm and Substorm Spatial Scales: Overcoming the Disparate Data Density Curse

Abstract:

Data-mining has ushered in a new era of empirical magnetic reconstructions of the magnetosphere via application of the nearest-neighbors (NNs) method. In this approach, the state of the magnetosphere is represented by a multidimensional state vector, the components of which are macroscopic parameters, such as the Sym-H and AL indices, their time derivative, and the solar wind electric field vB_z. As the magnetosphere evolves in time, it traces curves within this state space. At any given moment there are at most only ~10 magnetospheric spacecraft with magnetometers, far too few to fit a sufficiently complex empirical magnetic field model. However, in state space, there are potential thousands of nearby data points (NNs) for that moment, presumably from other times when the magnetosphere was in a similar storm or substorm configuration. It also fulfills a postulate of machine learning, that more data usually allows for a more complex model, in our case by increasing the model’s spatial resolution. However, the inhomogeneity of data points in both the state space and physical space is problematic. In state space, weaker events are more numerous than strong ones, biasing the reconstructions toward them. We mitigate this by distance-weighting the NNs. In physical space, two distinct regions exist based on data density, with the inner region r ≤ 12 R_E having a much higher density of data than the mid-tail region 12 R_E ≤ r ≤ 22 R_E, resulting in two models of differing spatial resolution. The higher resolution model of the inner region reconstructs the storm time dynamics, including the formation of the westward and eastward ring current and the concomitant pressure distributions, while the lower resolution model of the mid-tail region captures substorm features, including the thinning and rapid dipolarization of the tail sheet during the growth and expansion phases respectively. However, the lower resolution is insufficient to reconstruct the eastward ring current while the higher resolution overfits the mid-tail region. We address this issue by sampling the lower resolution model in the data sparse mid-tail region and adding these samples when fitting the inner region. The result is merged resolution model that concurrently captures the spatial scales associated with both storms in the inner region and substorms in the mid-tail.