On the Relationships Between Sunspot Number and Solar Radio Flux at 10.7 Centimeters

Regression analysis and neural network training procedures are used to study the relationship between sunspot number (SSN) and solar flux at 10.7 cm (F10.7). Measurements of SSN and F10.7 for the periods from December 1963 to January 2019 (including the periods from Solar Cycles 20 to 24) were used. The value of correlation coefficient between SSN and F10.7 for the entire data used in the study is 0.95, showing that the parameters are well correlated. Results from the study reveal that there are remarkable differences on the relationship between SSN and F10.7 during the four solar cycle phases of low (-activity), high (-activity), ascending, and descending. The relationships are identical for the ascending and descending phases when the SSNs are lower than about 150, but the regression curves diverge as the SSNs increase beyond that limit. A conspicuously changed relationship between SSN and F10.7 is also observed for years 2014 and 2015 in which the annual SSN-versus-F10.7 plots for those years are visibly above those of the prior years. The results indicate that F10.7 values can be predicted from SSNs using neural networks, with root-mean-square errors of about 13.68 solar flux units. Results from the neural network procedure also indicate that a newly introduced solar cycle phase index (defined to indicate the phase of the solar cycle in which given observations belong) was effective in improving the neural network predictions.