Maximum Sunspot Numbers and Active Days

Abstract

Parameters associated with solar minimum have been studied to relate them to solar activity at solar maximum so that one could possibly predict behaviors of an upcoming solar cycle. The number of active days has been known as a reliable indicator of solar activity around solar minimum. Active days are days with sunspots reported on the solar disk. In this work, we have explored the relationship between the sunspot numbers at solar maximum and the characteristics of the monthly number of active days. Specifically, we have statistically examined how the maximum monthly sunspot number of a given solar cycle is correlated with the slope of the linear relationship between monthly sunspot numbers and the monthly number of active days for the corresponding solar cycle. We have calculated the linear correlation coefficient r and the Spearman rank-order correlation coefficient r s for data sets prepared under various conditions. Even though marginal correlations are found, they turn out to be insufficiently significant (r ~ 0.3). Nonetheless, we have confirmed that the slope of the linear relationship between monthly sunspot numbers and the monthly number of active days is less steep when solar cycles belonging to the "Modern Maximum" are considered compared with rests of solar cycles. We conclude, therefore, that the slope of the linear relationship between monthly sunspot numbers and the monthly number of active days is indeed dependent on the solar activity at its maxima, but that this simple relationship should be insufficient as a valid method to predict the following solar activity amplitude.

Do Inner Planets Modulate the Solar Wind Velocity at 1 AU from the Sun?

“…As far as we understand this is very difficult to take place since there must be instabilities on the boundary of the wake causing smoothing-out long before such a great distance. Second, it may also suggest that one should take into account a phase of inner planets when the space weather prediction is attempted (Chang 2013). It is because a forecast of the solar wind velocity is a crucial factor in the space weather prediction and the solar wind velocity concerns not only the solar activity but also a relative position of inner planets with respect to the Earth.…”

Active Days around Solar Minimum and Solar Cycle Parameter

“…When a relatively quiet solar minimum period prevails, on the contrary, such a slope during an active phase for a weak solar cycle is expected to be less steep. Based on the result of Chang (2013), however, even though the slope of the linear relationship is found to be less steep when solar cycles belonging to the Modern Maximum covered by solar cycles 17-23 in comparison with rests of solar cycles, weak anticorrelations are only found for individual cycles so that the simple relationship turns out to be insufficient as a robust method to predict the solar activity amplitude.…”

“…It has been proposed to use the number of active days with sunspots detected on the visible disk of the Sun, or otherwise equivalently spotless days, at the solar minimum as an indicator of the level of activity of the upcoming solar maximum (Harvey & White 1999;Usoskin et al 2000Usoskin et al , 2001Hamid & Galal 2006;Pesnell 2012;Váquero et al 2012). Having been motivated by a linear relationship between sunspot numbers and the monthly number of active days in percentage around the solar minimum (e.g., Hoyt & Schatten 1998;Váquero et al 2012), Chang (2013) statistically examined an idea how the monthly observed sunspot number at the solar maximum is correlated with the slope of the linear relationship between the monthly sunspot numbers and the monthly number of active days in percentage for the corresponding solar cycle. The following is how one may expect a correlation between the level of solar activity and the slope of the linear relationship between the monthly sunspot numbers and the monthly number of active days in percentage.…”

“…In this paper, the relationship between solar cycle parameters and the linear slope of the monthly sunspot numbers as a function of the monthly number of active days is statistically explored. In addition to the monthly observed sunspot number at the solar maximum (Chang 2013), we have further examined the duration of the solar cycle and the duration of the ascending phase. Unlike the previous analysis, we have used a new version of carefully calibrated sunspot numbers which are publicly available since 2015.…”

A note on the relationship between sunspot numbers and active days

“…Recently, Vaquero et al (2012) have used the relationship between annual sunspot numbers and AD to detect inconsistencies in low annual GSN. Moreover, Chang (2013) has found that the slope of the linear relationship between monthly ISN and the monthly number of AD is dependent on the solar activity at its maxima.…”