Reconstruction of Monthly and Yearly Group Sunspot Numbers From Sparse Daily Observations

Abstract

Some periods before 1820 are poorly covered by sunspot observations. In addition to apparent, long observational gaps, there are also periods when there are only few sparse daily sunspot observations during a long time. It is important to estimate the reliability of the monthly and yearly mean sunspot values obtained from such sparse daily data. Here we suggest a new method to estimate the reliability of individual monthly means. The method is based on comparing the actual sparse data (sample population) to the well-measured sunspot data in 1850–1996 (reference population), and assumes that the statistical properties of sunspot activity remain similar throughout the entire period. For each sample population we first found those months in the reference population that contain the same data set, and constructed the statistical distribution of the corresponding monthly means. The mean and standard error of this distribution represent the mean and uncertainty of a monthly mean sunspot number reconstructed from sparse daily observations. The simple arithmetic mean of daily values can be adequately applied for months which contain more than 4–5 evenly distributed daily observations. However, the reliability of monthly means for less covered months has to be estimated more carefully. Using the estimated, new monthly values, we have also calculated the weighted annual sunspot numbers.