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Group sunspot number (GSN) series constitute the longest instrumentalastronomical database providing information on solar activity. It is acompilation of observations by many individual observers, and theirinter-calibration has usually been performed using linear rescaling. There aremultiple published series that show different long-term trends for solaractivity. We aim at producing a GSN series, with a non-linear non-parametriccalibration. The only underlying assumptions are that the differences betweenthe various series are due to different acuity thresholds of the observers, andthat the threshold of each observer remains constant throughout the observingperiod. We use a daisy chain process with backbone (BB) observers and calibrateall overlapping observers to them. The calibration of each individual observeris performed with a probability distribution function (PDF) matrix, constructedconsidering all daily values for the overlapping period with the BB. Thecalibration of the BBs is done in a similar manner. Propagation of errors ismodelled with Monte Carlo simulations. The final series extends back to 1739and includes data from 314 observers. It suggests moderate activity during the18th and 19th century, which is significantly lower than the high level ofsolar activity predicted by other recent reconstructions applying linearregressions. The new series provides a robust reconstruction, based on modernand non-parametric methods, of sunspot group numbers since 1739, and itconfirms the existence of the Modern grand maximum of solar activity in thesecond half of the 20th century.

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