Nonparametric monitoring of sunspot number observations: a case study

TL;DR

This paper introduces a comprehensive nonparametric statistical framework for monitoring and analyzing long-term sunspot number data, addressing challenges like non-stationarity, missing data, and measurement errors to improve solar activity records.

Contribution

It presents the first systematic approach combining smoothing, bootstrap-based control charts, and support vector classification for detecting anomalies in sunspot observations.

Findings

Effective detection of various anomalies including jumps and drifts.

Identification of causes behind major deviations, often related to observers or equipment.

Enhanced accuracy in reconstructing the International Sunspot Number.

Abstract

Solar activity is an important driver of long-term climate trends and must be accounted for in climate models. Unfortunately, direct measurements of this quantity over long periods do not exist. The only observation related to solar activity whose records reach back to the seventeenth century are sunspots. Surprisingly, determining the number of sunspots consistently over time has remained until today a challenging statistical problem. It arises from the need of consolidating data from multiple observing stations around the world in a context of low signal-to-noise ratios, non-stationarity, missing data, non-standard distributions and many kinds of errors. The data from some stations experience therefore severe and various deviations over time. In this paper, we propose the first systematic and thorough statistical approach for monitoring these complex and important series. It consists of three steps essential for successful treatment of the data: smoothing on multiple timescales, monitoring using block bootstrap calibrated CUSUM charts and classifying of out-of-control situations by support vector techniques. This approach allows us to detect a wide range of anomalies (such as sudden jumps or more progressive drifts), unseen in previous analyses. It helps us to identify the causes of major deviations, which are often observer or equipment related. Their detection and identification will contribute to improve future observations. Their elimination or correction in past data will lead to a more precise reconstruction of the world reference index for solar activity: the International Sunspot Number.