Dependence of the Sunspot-Group Size on the Level of Solar Activity and its Influence on the Calibration of Solar Observers

We study the distribution of the sunspot-group size (area) and its dependence on the level of solar activity. We show that the fraction of small groups is not constant but decreases with the level of solar activity so that high solar activity is mainly defined by large groups. We analyze the possible influence of solar activity on the ability of a realistic observer to see and report the daily number of sunspot groups. It is shown that the relation between the number of sunspot groups as seen by different observers with different observational acuity thresholds is strongly nonlinear and cannot be approximated by the traditionally used linear scaling (k-factors). The observational acuity threshold [Ath] is considered to quantify the quality of each observer, instead of the traditional relative k-factor. A nonlinear c-factor based on Ath is proposed, which can be used to correct each observer to the reference conditions. The method is tested on a pair of principal solar observers, Wolf andWolfer, and it is shown that the traditional linear correction, with the constant k-factor of 1.66 to scaleWolf toWolfer, leads to an overestimate of solar activity around solar maxima.