Abstract/Summary

Using 65,133 hourly averages of transpolar voltage ({\Phi}_{PC}) from observations made over 25 years by the SuperDARN radars, with simultaneous SML and interpolated am geomagnetic indices, we study their optimum interplanetary coupling functions. We find mean lags of 18, 31 and 45 min. for {\Phi}_{PC}, am and SML respectively, and fit using a general coupling function with three free fit exponents. To converge to a fit, we need to average interplanetary parameters and then apply the exponent which is a widely-used approximation: we show how and why this is valid for all interplanetary parameters, except the factor quantifying the effect of the clock angle of the interplanetary magnetic field, sin^d({\theta}/2), which must be computed at high time resolution and then averaged. We demonstrate the effect of the exponent d on the distribution, and hence weighting, of samples and show d is best determined from the requirement that the coupling function is a linear predictor, yielding d of 2.50+/-0.10, 3.00+/-0.22 and 5.20+/-0.41 for {\Phi}_{PC}, am and SML. To check for overfitting, fits are made to half the available data and tested against the other half. Ensembles of 1000 fits are used to study the effect of the number of samples on the distribution of errors in individual fits and on systematic biases in the ensemble means. We find only a weak dependence of solar wind density for {\Phi}_{PC} and SML but a significant one for am. The optimum coupling functions are shown to be significantly different for {\Phi}_{PC}, am and SML.