. Analysis of fit residuals for the annual Ap reconstructions shown in Figure 4a. In each panel, histograms of the fractional error are shown − i.e., the deviation predicted value, X_p, from the observed value, X_o, as a ratio of X_p. Any years giving X_p = 0 or with data availability f < 0.5 for either X_o or X_p are omitted. (a) X_o is the annual mean of the observed factor sin⁴(θ/2) for 1996–2016 (evaluated from 5-minute data and then averaged) and X_p is the constant value of [sin⁴(θ/2)]_all = 0.355 that must be used in the reconstructions. The grey histogram gives the probability distribution function (pdf) in bins 0.2 wide and the red line the best fit normal distribution to the histogram. The vertical red dot-dash lines mark the upper and lower 1−σ points. The histogram and fitted Gaussian (the green line) in (b) is for X_o = Ap and X_p is the Ap predicted using Pα measured by interplanetary craft (over 1964–2016 but only including years with Pα availability f > 0.5) and the linear regression given in Figure 3a. The red line distribution from part (a) is also reproduced in this panel for comparison purposes. The vertical green dot-dash lines mark the upper and lower 1−σ points of the fitted distribution. The histogram and fitted Gaussian (the blue line) in (c) is also for X_o = Ap and X_p is the Ap predicted using the modelled Pα again using the linear regression given in Figure 3a. The red and green distributions from the upper panels are both included for comparison. The blue dot-dash lines are at the upper and lower 1−σ points of the fitted distribution.