Empirical Optimization of the Source-surface Height in the Potential Field Source Surface Extrapolation

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Abstract
The potential field source surface (PFSS) method is a widely used magnetic field extrapolation technique in the space weather community. The only free parameter in the PFSS method is the source-surface height ( R SS ), beyond which all field lines are open. Although R SS is known to vary with solar activity, there is no consensus on how to determine it for a given surface magnetic field distribution. In this study, we investigate the nature of R SS using a long-period (2006–2023) dataset, covering two solar minima and one maximum. We adopt ADAPT-GONG magnetograms and determine R SS by matching the open flux estimated from observations at 1 au with that calculated using the PFSS method. Our analysis reveals that R SS increases slightly after the solar minima and around the solar maximum, and that it can be characterized by both the mean unsigned photospheric magnetic field strength and the dipolarity parameter f dip , defined as f dip = B dip 2 / ( B dip 2 + B quad 2 + B oct 2 ) , with B dip , B quad , and B oct denoting the magnitudes of dipolar, quadrupolar, and octupolar components of photospheric radial magnetic field, respectively. Our results suggest that R SS does not exhibit a simple monotonic dependence on the solar activity and must be determined by properly considering both surface magnetic field strength and global field structure.
Funding Information
  • MEXT ∣ Japan Society for the Promotion of Science (JP24K00688)
  • MEXT ∣ Japan Society for the Promotion of Science (JP25K00976)
  • MEXT ∣ Japan Society for the Promotion of Science (JP25K01052)
  • MEXT ∣ National Institutes of Natural Sciences (OML032402)

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