New reconstruction of the sunspot group numbers since 1739 using direct calibration and "backbone" methods

Context. The group sunspot number (GSN) series constitute the longest instrumental astronomical database providing information on solar activity. This database is a compilation of observations by many individual observers, and their inter-calibration has usually been performed using linear rescaling. There are multiple published series that show different long-term trends for solar activity. Aims. We aim at producing a GSN series, with a non-linear non-parametric calibration. The only underlying assumptions are that the differences between the various series are due to different acuity thresholds of the observers, and that the threshold of each observer remains constant throughout the observing period. Methods. We used a daisy chain process with backbone (BB) observers and calibrated all overlapping observers to them. We performed the calibration of each individual observer with a probability distribution function (PDF) matrix constructed considering all daily values for the overlapping period with the BB. The calibration of the BBs was carried out in a similar manner. The final series was constructed by merging different BB series. We modelled the propagation of errors straightforwardly with Monte Carlo simulations. A potential bias due to the selection of BBs was investigated and the effect was shown to lie within the 1 sigma interval of the produced series. The exact selection of the reference period was shown to have a rather small effect on our calibration as well. Results. The final series extends back to 1739 and includes data from 314 observers. This series suggests moderate activity during the 18th and 19th century, which is significantly lower than the high level of solar activity predicted by other recent reconstructions applying linear regressions. Conclusions. The new series provides a robust reconstruction, based on modern and non-parametric methods, of sunspot group numbers since 1739, and it confirms the existence of the modern grand maximum of solar activity in the second half of the 20th century.