Calibration of the Sunspot and Group Numbers Using the Waldmeier Effect

TL;DR

This paper uses the Waldmeier Effect to calibrate sunspot and group numbers, confirming the constancy of scale factors over 250 years and showing no evidence of a modern Grand Maximum in solar activity.

Contribution

It extends the analysis of the Waldmeier Effect to new sunspot data, validating the stability of sunspot number scale factors over centuries.

Findings

Scale factors have remained stable over 250 years.

No evidence of a modern Grand Maximum in solar activity.

The Waldmeier Effect is observed across multiple solar activity proxies.

Abstract

The Waldmeier Effect is the observation that the rise time of a sunspot cycle varies inversely with the cycle amplitude: strong cycles rise to their maximum faster than weak cycles. The shape of the cycle and thus the rise time does not depend on the scale factor of the sunspot number and can thus be used to verify the constancy of the scale factor with time as already noted by Wolfer (1902) and Waldmeier (1978). We extend their analysis until the present using the new SILSO sunspot number (version 2) and group number and confirm that the scale factors have not varied significantly the past 250 years. The effect is also found in sunspot areas, in an EUV (and F10.7) proxy (the daily range of a geomagnetic variation), and in Cosmic Ray Modulation. The result is that solar activity reached similar high values in every one of the (17th?) 18th, 19th, and 20th centuries, supporting the finding that there has been no modern Grand Maximum.