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Scatter plots and best regressions used to reconstruct the Ap index. (a) Annual means of the Ap index as a function of annual means of the normalised power input into the magnetosphere, Pα/Po, for the best-fit coupling exponent α = 0.53 (see Lockwood et al., 2017a). These data are for 1964–2016 (inclusive) and points are only shown if the availability f of Pα/Po data points exceeds 0.5. The line is the best-fit linear regression. (b) is the same as (a) for the fraction of storm-like days f[Ap > Apo] (where Apo = 38 and is the 95-percentile threshold). (c) f[Ap > Apo] as a function of f[Ap > Apo]′, the fraction of Ap values in the top 5 percent, estimated from the Ap value using the best fit polynomial show by the mauve line in Figure 2d. In each case, the line is the best fit linear regression. The fit residuals all follow a Gaussian distributions (as revealed using a Q-Q plots against a normal distribution: not shown) and the scatter plots show the data are homoscedastic (the scatter does not increase with the fitted parameter).
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