Exploring the cross correlations and autocorrelations of the ULF indices and incorporating the ULF indices into the systems science of the solar wind-driven magnetosphere

Abstract

The ULF magnetospheric indices Sgr, Sgeo, T gr, and Tgeo are examined and correlated with solar wind variables, geomagnetic indices, and the multispacecraft-averaged relativistic-electron flux F in the magnetosphere. The ULF indices are detrended by subtracting off sine waves with 24 h periods to form Sgrd, S geod, Tgrd, and Tgeod. The detrending improves correlations. Autocorrelation-function analysis indicates that there are still strong 24 h period nonsinusoidal signals in the indices which should be removed in future. Indications are that the ground-based indices Sgrd and Tgrd are more predictable than the geosynchronous indices S geod and Tgeod. In the analysis, a difference index ΠSmag-≈-Sgrd - 0.693 Sgeod is derived: the time integral of ΠSmag has the highest ULF index correlation with the relativistic-electron flux F. In systems-science fashion, canonical correlation analysis (CCA) is used to correlate the relativistic-electron flux simultaneously with the time integrals of (a) the solar wind velocity, (b) the solar wind number density, (c) the level of geomagnetic activity, (d) the ULF indices, and (e) the type of solar wind plasma (coronal hole versus streamer belt): The time integrals of the solar wind density and the type of plasma have the highest correlations with F. To create a solar wind-Earth system of variables, the two indices Sgrd and Sgeod are combined with seven geomagnetic indices; from this, CCA produces a canonical Earth variable that is matched with a canonical solar wind variable. Very high correlations (rcorr-=-0.926) between the two canonical variables are obtained. ©2014. American Geophysical Union. All Rights Reserved.