Gustav Sp\"orer Was Not a Perfect Observer: Failure of the Active Day Fraction Reconstruction of Sunspot Group Numbers

TL;DR

This paper demonstrates that the Active-Day-Fraction calibration method fails for Gustav Spörer’s sunspot observations, revealing that it overestimates the accuracy of historical sunspot group counts and is not universally applicable.

Contribution

The study critically tests the ADF calibration method on Spörer’s data, showing its limitations and invalidating its assumption of perfect observer calibration.

Findings

RGO reported 45% more groups than Spörer

ADF method overestimates observer accuracy

Calibration method fails for historical data

Abstract

We show that the Active-Day-Fraction calibration method (Willamo et al. [2017]) fails for Gustav Sp\"orer's sunspot group observations. Sp\"orer was labeled a 'perfect observer' on account of his 'observational threshold SS area' being determined to be equal to zero, based on the assumption that the observer can see and report all the groups with the area larger than SS, while missing all smaller groups. So, Sp\"orer could apparently, according to the ADF calibration method, see and report all groups, regardless of size and should never miss any. This suggests a very direct test: compute the yearly average group count for both Sp\"orer and the 'perfect observer' exemplar, the Royal Greenwich Observatory (RGO), and compare them. They should be identical within a reasonable (very small) error margin. We find that they are not and that RGO generally reported 45% more groups than Sp\"orer, and that therefore, the ADF-method is not generally applicable