The Effect of Sunspot Weighting

TL;DR

This paper investigates the inflation of sunspot counts caused by Waldmeier's weighting method, quantifies the over-counting, and proposes a correction to align historical data with the Wolfer method.

Contribution

It provides an empirical model to estimate and correct the over-counting in sunspot numbers due to weighting introduced in 1947.

Findings

Sunspot counts are overestimated by 44% on average due to weighting.

A simple empirical equation accurately models the weight factor over time.

The correction allows for consistent sunspot data from 1893 onwards.

Abstract

Waldmeier in 1947 introduced a weighting (on a scale from 1 to 5) of the sunspot count made at Zurich and its auxiliary station Locarno, whereby larger spots were counted more than once. This counting method inflates the relative sunspot number over that which corresponds to the scale set by Wolfer and Brunner. Svalgaard re-counted some 60,000 sunspots on drawings from the reference station Locarno and determined that the number of sunspots reported were 'over counted' by 44% on average, leading to an inflation (measured by a weight factor) in excess of 1.2 for high solar activity. In a double-blind parallel counting by the Locarno observer Cagnotti, we determined that Svalgaard's count closely matches that of Cagnotti's, allowing us to determine the daily weight factor since 2003 (and sporadically before). We find that a simple empirical equation fits the observed weight factors well, and use that fit to estimate the weight factor for each month back to the introduction of weighting in 1947 and thus to be able to correct for the over-count and to reduce sunspot counting without weighting to the Wolfer method in use from 1893 onwards.