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

TL;DR

This study examines how sunspot group sizes vary with solar activity levels and introduces a nonlinear correction method based on observational acuity to improve the calibration of solar observers.

Contribution

It proposes a nonlinear $c$-factor correction based on observational acuity thresholds, replacing traditional linear $k$-factors for better calibration of solar observations.

Findings

Small sunspot groups decrease with higher solar activity

Traditional linear corrections overestimate activity during solar maxima

Nonlinear correction improves observer calibration accuracy

Abstract

The distribution of the sunspot group size (area) and its dependence on the level of solar activity is studied. It is shown that the fraction of small groups is not constant but decreases with the level of solar activity so that high solar activity is largely defined by big groups. We study 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 non-linear and cannot be approximated by the traditionally used linear scaling ($k-$factors). The observational acuity threshold [$A_{\rm th}$] is considered to quantify the quality of each observer, instead of the traditional relative $k-$factor. A nonlinear $c-$factor based on $A_{\rm th}$ 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 and Wolfer, and it is shown that the traditional linear correction, with the constant $k-$factor of 1.66 to scale Wolf to Wolfer, leads to an overestimate of solar activity around solar maxima.