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

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">dip</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">dip</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>/</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">dip</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>+</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">quad</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>+</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">oct</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">)</mml:mo> </mml:math> , 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.