Abstract/Summary

Different terrestrial space weather indicators (such as geomagnetic indices, transpolar voltage, and ring current particle content) depend on different “coupling functions” (combinations of near-Earth solar wind parameters) and previous studies also reported a dependence on the averaging timescale, {\tau}. We study the relationships of the am and SME geomagnetic indices to the power input into the magnetosphere P_{\alpha}, estimated using the optimum coupling exponent {\alpha} for a range of {\tau} between 1 min and 1 year. The effect of missing data is investigated by introducing synthetic gaps into near-continuous data and the best method for dealing with them when deriving the coupling function, is formally defined. Using P_{\alpha}, we show that gaps in data recorded before 1995 have introduced considerable errors into coupling functions. From the near-continuous solar wind data for 1996-2016, we find {\alpha} = 0.44 plus/minus 0.02 and no significant evidence that {\alpha} depends on {\tau}, yielding P_{\alpha} = B^0.88 Vsw^1.90 (mswNsw)^0.23 sin4({\theta}/2), where B is the Interplanetary Magnetic Field (IMF), Nsw the solar wind number density, msw its mean ion mass, Vsw its velocity and {\theta} is the IMF clock angle in the Geocentric Solar Magnetospheric reference frame. Values of P_{\alpha} that are accurate to within plus/minus 5% for 1996-2016 have an availability of 83.8% and the correlation between P_{\alpha} and am for these data is shown to be 0.990 (between 0.972 and 0.997 at the 2{\sigma} uncertainty level), 0.897 plus/minus 0.004, and 0.790 plus/minus 0.03, for {\tau} of 1 year, 1 day and 3 hours, respectively, and that between P_{alpha} and SME at {\tau} of 1 min. is 0.7046 plus/minus 0.0004.