Centennial variations in sunspot number, open solar flux, and streamer belt width: 1. Correction of the sunspot number record since 1874

We analyze the widely used international/Zürich sunspot number record, R , with a view to quantifying a suspected calibration discontinuity around 1945 (which has been termed the “Waldmeier discontinuity”). We compare R against the composite sunspot group data from the Royal Greenwich Observatory network and the Solar Optical Observing Network, using both the number of sunspot groups, N G , and the total area of the sunspots, A G . In addition, we compare R with the recently developed interdiurnal variability geomagnetic indices IDV and IDV (1d). In all four cases, linearity of the relationship with R is not assumed and care is taken to ensure that the relationship of each with R is the same before and after the putative calibration change. It is shown the probability that a correction is not needed is of order 10 −8 and that R is indeed too low before 1945. The optimum correction to R for values before 1945 is found to be 11.6%, 11.7%, 10.3%, and 7.9% using A G , N G , IDV , and IDV (1d), respectively. The optimum value obtained by combining the sunspot group data is 11.6% with an uncertainty range 8.1–14.8% at the 2 σ level. The geomagnetic indices provide an independent yet less stringent test but do give values that fall within the 2 σ uncertainty band with optimum values are slightly lower than from the sunspot group data. The probability of the correction needed being as large as 20%, as advocated by Svalgaard (2011), is shown to be 1.6 × 10 −5 .