Uncertainty Quantification in Sunspot Counts

Abstract

Abstract Observing and counting sunspots constitutes one of the longest-running scientific experiments, with first observations dating back to Galileo (around 1610). Today the sunspot number (SN) time series acts as a benchmark of solar activity in a large range of physical models. An appropriate statistical modeling, adapted to the time series’ complex nature, is, however, still lacking. In this work, we provide the first comprehensive uncertainty quantification analysis of sunspot counts. We study three components: the number of sunspots (N s ), the number of sunspot groups (N g ), and the composite N c , defined as . Those are reported by a network of observatories around the world and are corrupted by errors of various types. We use a multiplicative framework to provide, for these three components, an estimation of their error distribution in various regimes (short-term, long-term, minima of solar activity). We also propose a robust estimator for the underlying solar signal and fit density distributions that take into account intrinsic characteristics such as overdispersion, excess of zeros, and multiple modes. The estimation of the solar signal underlying the composite N c may be seen as a robust version of the International Sunspot Number (ISN), widely used as a proxy of solar activity. Therefore, our results on N c may help characterize the uncertainty on ISN as well. Our results pave the way for a future monitoring of the observatories in quasi-real time, with the aim of alerting the observers when they start deviating from the network and preventing large drifts from occurring.