Tests of Sunspot Number Sequences: 4. Discontinuities Around 1946 in Various Sunspot Number and Sunspot-Group-Number Reconstructions

Abstract

We use five test data series to search for, and quantify, putative discontinuities around 1946 in five different annual-mean sunspot-number or sunspot-groupnumber data sequences. . These test data all vary in close association with sunspot numbers, in some cases non-linearly. The tests are carried out using both the before-and-after fitresidual comparison method and the correlation method of Lockwood, Owens, and Barnard, applied to annual mean data for intervals iterated to minimise errors and to eliminate uncertainties associated with the precise date of the putative discontinuity. It is not assumed that the correction required is by a constant factor, nor even linear in sunspot number. It is shown that a non-linear correction is required by R C , R BB , and R ISNv1 , but not by R ISNv2 or R UEA . The five test datasets give very similar results in all cases. By multiplying the probability distribution functions together, we obtain the optimum correction for each sunspot dataset that must be applied to pre-discontinuity data to make them consistent with the postdiscontinuity data. It is shown that, on average, values for 1932 -1943 and 5.2 %, respectively. The correction that was applied to generate R C from R ISNv1 reduces this average factor to 0.5 % but does not remove the non-linear variation with the test data, and other errors remain uncorrected. A valuable test of the procedures used is provided by R UEA , which is identical to the RGO N G values over the interval employed.

An Assessment of Sunspot Number Data Composites Over 1845–2014

“…This has the potential to have influenced group numbers derived using different classification schemes in different ways. Lockwood et al (2016d) have refined the fit residual comparison procedure yet further. They initially take all available data between 1920 and 1976 (thereby avoiding any effects of both the putative RGO calibration drift and the Locarno error) but omit all data between 1943 and 1949, a six-year interval centred on the optimum date for the discontinuity found by Clette and Lefèvre (2016).…”

“…To find the optimum interval, Lockwood et al (2016d) used a basket of test data series and varied the duration of the "before" and "after" intervals until the net uncertainty was minimised. They also used 2 nd -order polynomial fits so that assumptions of both proportionality and linearity were avoided.…”

“…The analysis was repeated with 3 nd -order polynomial fits but some of the fit-residual Q-Q plots began to show non-Gaussian distribution tails and so these fits were not used further. To reduce the number of variables in this parametric study, Lockwood et al (2016d) required the "before" interval and the "after" intervals be of the same duration. Minimum uncertainty (i.e.…”

“…optimum agreement between the results for the various test data) was obtained using "before" and "after" intervals that were 11 years in duration and hence the "before" data were from 19321943 and the "after" date from 19491960. In addition, Lockwood et al (2016d) did not assume that the correction needed is just a multiplicative factor or even linear but allowed for both a zerolevel offset  and non-linearity in R, as well as a sensitivity change (hence they evaluate the corrected series R = f R R n +  for "before" interval that is consistent with the "after" interval). For (R G /12.08) and R UEA , Lockwood et al (2016d) found the net correction required to the "before" interval is +0.005%  0.05%.…”

Tests of Sunspot Number Sequences: 1. Using Ionosonde Data

“…R = f R R). However, Article 3 in this series (Lockwood et al, 2016b) shows that this assumption can be very misleading, and Article 4 (Lockwood, Owens, and Barnard, 2016) carries out a number of tests assuming linearity but not proportionality by also allowing for a zero-level offset, δ (i.e. R = f R R + δ).…”