Estimation of copulas between solar wind parameters and a geomagnetic index during intense geomagnetic storms

Solar activity, through geomagnetic storms, has the ability to cause a number of negative effects on critical technologies such as power grids and various communication systems. Geomagnetic storms are intervals of disturbed geomagnetic field lasting ∼ 10 hours. The most intense storms are caused by energetic plasma from coronal mass ejections impacting the geomagnetic field after propagating the 1.5 × 10
⁸
km (= 1AU) via the solar wind to Earth. The relationship between the shocked solar wind and the geomagnetic field can be viewed as a highly non-linear, non-stationary transfer function. Fully understanding the coupling between the solar wind and the magnetosphere is an important task for space physicists striving to provide accurate predictions of geomagnetic storms. With this in mind we investigate the use of copulas as a way to quantify the coupling efficiency between the solar wind and magnetosphere for the three known phases of storms: onset, main and recovery. Seven intense storms are identified and the dynamic and static copulas between two solar wind parameters (B
Z
and V
sw
) and a geomagnetic disturbance index (SYM-H) are calculated. We find that copula functions can be used to reliably identify storm phase changes, and to quantify the changes in coupling efficiency for different storm phases.