Fig. 3. Tests of robustness and usefulness of the power law displayed in Fig. 2.
a Effects of arbitrarily rescaling the axial dipole term at every realisation using four models shown in Fig. 1 (see Supplementary Note 2 for details and Supplementary Fig. 3 for individual Model G fits). Original model outputs (large symbols) are diverse; rescaled models (small symbols) can have entirely different values of AD/NADmedian to the original but the corresponding Model G fit adjusts simultaneously such that each point remains within the 95% prediction bounds derived from Fig. 2. b Results of a sliding window analysis using time series from the same four models as in Fig. 1. In each case, the sliding window of length given by the x-axis was moved from the start of the time series through to the end in window steps of 1−20 kyr (adjusted for the total time series length) drawing 15 random timesteps from each of 19 random locations on the surface of the Earth. Estimates of AD/NADmedian made using the power law in Fig. 2 were defined as accurate if they were within calculated uncertainties of the actual value of AD/NADmedian for that specific time window. See Supplementary Fig. 5 for individual plots of the AD/NADmedian time series and estimates from windows sliding along it. c Effects of down-sampling (15 timesteps at each of 19 locations) on 61 dynamo models and 12 observational models on their adherence to the power law shown in Fig. 2. Model G a parameters were calculated from the downsampled dataset whereas AD/NADmedian values were calculated directly from the models using every timestep. The overlaps of the majority of calculated uncertainties on Model G a parameters with the prediction bounds ascertained from Fig. 2 indicates that this method of estimating AD/NADmedian values from the Model G fit is reliable for palaeomagnetically feasible datasets.