The Robustness of Vector-Vector Correlations between the Solar Wind and the Earth

Correlations are performed between a multivariable time-dependent solar-wind state vector and a multivariable time-dependent magnetospheric state vector using canonical correlation analysis (CCA). One result is two “projection formulas” that convert the solar-wind vector into a single time-dependent composite solar-wind scalar and the magnetospheric vector into a single time-dependent composite magnetospheric scalar. The correlation coefficient between the time-dependent solar-wind scalar and magnetospheric scalar can be quite high. This CCA methodology is found to be robust in two ways. (1) Very little data is needed to derive the correct projection formulas, and adding more data in the correlation process does not change those formulas. (2) Pathological subsets of the data will also yield approximately the same projection formulas. For example, using only low geomagnetic-activity data yields the same formula as does using only high-activity data, and using only slow solar wind yields the same results as using only fast solar wind. This second robustness points to a universality in the driving of the Earth by the solar wind. One consequence of this robustness is that with the projection formulas obtained from the data we have today, the methodology may be able to predict the reaction of the Earth to as-yet-unseen levels of extreme solar wind.