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 5996-2016 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 Palpha and SME at $tau of 1 min. is 0.7046 plus/minus 0.0004.
|Number of pages||24|
|Early online date||30 Jan 2019|
|Publication status||Published - Jan 2019|