A New Calibrated Sunspot Group Series Since 1749: Statistics of Active Day Fractions

Although sunspot-number series have existed since the mid-nineteenth century, they are still the subject of intense debate, with the largest uncertainty being related to the calibration of the visual acuity of individual observers in the past. A daisy-chain regression method is usually applied to inter-calibrate the observers, which may lead to significant bias and error accumulation. Here we present a novel method for calibrating the visual acuity of the key observers to the reference data set of Royal Greenwich Observatory sunspot groups for the period 1900 - 1976, using the statistics of the active-day fraction. For each observer we independently evaluate their observational thresholds [SS] defined such that the observer is assumed to miss all of the groups with an area smaller than SS and report all the groups larger than SS. Next, using a Monte-Carlo method, we construct a correction matrix for each observer from the reference data set. The correction matrices are significantly nonlinear and cannot be approximated by a linear regression or proportionality. We emphasize that corrections based on a linear proportionality between annually averaged data lead to serious biases and distortions of the data. The correction matrices are applied to the original sunspot-group records reported by the observers for each day, and finally the composite corrected series is produced for the period since 1748. The corrected series is provided as supplementary material in electronic form and displays secular minima around 1800 (Dalton Minimum) and 1900 (Gleissberg Minimum), as well as the Modern Grand Maximum of activity in the second half of the twentieth century. The uniqueness of the grand maximum is confirmed for the last 250 years. We show that the adoption of a linear relationship between the data of Wolf and Wolfer results in grossly inflated group numbers in the eighteenth and nineteenth centuries in some reconstructions.