The development of a space climatology: 2. the distribution of power input into the magnetosphere on a 3-hourly timescale

Paper 1 in this series [Lockwood et al., 2018b] showed that the power input into the magnetosphere Palpha is an ideal coupling function for predicting geomagnetic ?range? indices that are strongly dependent on the substorm current wedge and that the optimum coupling exponent alpha is 0.44 for all averaging timescales, $tau, between 1 minute and 1 year. The present paper explores the implications of these results. It is shown that the form of the distribution of Palpha at all averaging timescales $tau is set by the IMF orientation factor via the nature of solar wind-magnetosphere coupling (due to magnetic reconnection in the dayside magnetopause) and that at $tau = 3hrs (the timescale of geomagnetic range indices) the normalized Palpha (divided by its annual mean, i.e. $tau=3hr /$tau=1yr) follows a Weibull distribution with k of 1.0625 and $lambda of 1.0240. This applies to all years to a useful degree of accuracy. It is shown that exploiting the constancy of this distribution and using annual means to predict the full distribution gives the probability of space weather events in the largest 1002 respectively, at the one-sigma level.