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Relationship Between F10.7 and SSN

As of 24 May 2021 this site has switched from using a decades-old quadratic relationship between the 10.7cm solar radio flux (F10.7) and the solar sunspot number (SSN). This relationship was based on data collected prior to 1972. We have been using it in order to retain some continuity over the many solar cycles despite a known deficiency around solar minimum (a single linear relationship starts to break down below a sunspot number of 25-35).

Over the past several years the international solar research community has rescaled the sunspot number counts, which results in this algorithm no longer being valid. There are several relationships between F10.7 and the new sunspot number series, but rather than use one of these I have decided to develop my own tailored to this relationship over the past two cycles. In the Tapping and Morgan (2017) paper listed below, evidence is presented that the relationship between these two indexes has been changing over the past two cycles. Also in that paper, they present a relationship derived from all cycles for which there are F10.7 observations available (from mid-Cycle 18 through Cycle 24) which includes a "knee" at around SSN=20 which they speculate as being due to a change of the energetics involved at low activity.

Based on this, I have derived a simple relationship using two linear fits to data from the past two cycles (23 and 24) with the two linear segments matched near SSN=20:
F10-v-SSN relationship
where SSNb is the SSN value where the two linear sections intercept (SSNb = 21.30 for the equations shown). The plot below shows this relationship (grey circles) along with the 13-month smoothed SSN and F10.7 for Cycles 23 and 24. Also included are relationships from the Tapping and Morgan paper (green circles) and a relationship from the Australian Space Weather Services (SWS) group (red circles). These two curves are derived from fits to Cycles 18 through 24 and illustrate the issue raised in Tapping and Morgan regarding changes in the relationship over the past two cycles.

F10-v-SSN relationship

Tapping, K., and C. Morgan (2017), Changing relationships between sunspot number, total sunspot area and F10.7 in Cycles 23 and 24, Solar Phys., 292, DOI 10.1007/s11207-017-111-6.

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