From Sunspot Area to Solar Variability: A Linear Transformation

The relationship between sunspot area and other observable solar parameters, such as spectral solar irradiance or total magnetic flux, is frequently sought by examining scatterplots of daily data, which generally show a non-linear distribution of points. We show that the scatterplots are consistent with our published result that these observable solar parameters are related to sunspot area by a transformation that is both linear and time invariant, namely by convolution with a finite impulse response function. Most solar parameters are affected by extended active regions, not just by sunspots. The fact that a complex active region evolves much more slowly than its associated sunspots provides a simple physical explanation of the observed non-linearities in scatterplots.