Radiation belt electrons respond to multiple solar wind inputs

The multivariate statistical basis that underlies both single- and multi-input linear prediction filter analyses is reviewed, providing context necessary to understand the full capabilities and limitations of such models. A brief reanalysis of single-input filters is conducted primarily as a contrast to subsequent analysis of multi-input linear filters, which (1) guarantee similar or better prediction capabilities than single-input linear filters and (2) reduce bias in estimated filter coefficients that is inherent to underspecified linear models when ordinary least squares algorithms are employed. The former is clearly valuable from a practical standpoint, but the latter helps build confidence in any physical interpretations of both the filter coefficients, which often emulate stable low-order dynamical response functions quite well, as well as prediction error statistics that can be used to provide a lower bound on the fractional or percent variance of radiation belt electron flux that can be attributed to each different solar wind input. We find that the solar wind bulk speed tends to be the primary driver of electron flux enhancements at magnetic L shells larger than 4, with little or no relation to flux decreases. Changes in the solar wind's magnetic field strength tend to temporarily reduce electron fluxes between L = 4 and L = 8, while enhancing it between L = 3 and L = 4. In contrast to predictions generated by single-input linear filters, multi-input filters show that solar wind plasma density only contributes weakly to electron flux variability, although it does so consistently across nearly all L shells. Finally, we studied two distinct 4-year intervals within the most recent solar cycle and found that smaller, more time-stationary prediction errors are generated by multi-input linear filters. We therefore conclude that multi-input filters more accurately reflect real dynamic relationships than any single-input linear filter alone.