The statistical relationship between sunspot area (SA) and sunspot number (SN) is investigated through analysis of their daily observation records from May 1874 to April 2015. For a total of 1607 days, representing \(3~\%\) of the total interval considered, either SA or SN had a value of zero while the other parameter did not. These occurrences most likely reflect the report of short-lived spots by a single observatory and subsequent averaging of zero values over multiple stations. The main results obtained are as follows: i) The number of spotless days around the minimum of a solar cycle is statistically negatively correlated with the maximum strength of solar activity of that cycle. ii) The probability distribution of SA generally decreases monotonically with SA, but the distribution of SN generally increases first, then it decreases as a whole. The different probability distribution of SA and SN should strengthen their non-linear relation, and the correction factor [\(k\)] in the definition of SN may be one of the factors that cause the non-linearity. iii) The non-linear relation of SA and SN indeed exists statistically, and it is clearer during the maximum epoch of a solar cycle.
Sunspots, statistics Solar cycle, observations
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We thank the anonymous referees for careful reading of the manuscript and constructive comments that improved the original version of the manuscript. The daily sunspot number is freely available from the World Data Center SILSO, Royal Observatory of Belgium, Brussels. The daily sunspot area is publicly downloaded from the web site of NASA’s Marshall Space Flight Center (MSFC). The authors would like to express their deep thanks to the staff of SILSO and MSFC. This work is supported by the 973 program 2012CB957801, the National Natural Science Foundation of China (11573065, 11633008 and 11273057), the Specialized Research Fund for State Key Laboratories, and the Chinese Academy of Sciences.
Disclosure of Potential Conflicts of Interest
The authors declare that they have no conflicts of interest.