Photospheric and coronal magnetic fields in six magnetographs

II. Harmonic scaling of field intensities

ReSoLVE Centre of Excellence, Space Climate research unit, University of Oulu, PO Box 3000, 90014 Oulu, Finland
e-mail: ilpo.virtanen@oulu.fi; kalevi.mursula]@oulu.fi

Received: 24 March 2017
Accepted: 6 April 2017

Abstract

Context. Photospheric magnetic fields have been observed since the 1970s by several ground-based and satellite instruments. While the different instruments show a fairly similar large-scale structure and temporal evolution of the photospheric magnetic field, the magnetic field intensity varies significantly between the observations.

Aims. We introduce a new method for scaling the photospheric magnetic field in terms of the harmonic expansion. Contrary to earlier scaling methods, the harmonic scaling method can be straightforwardly used for data sets of different resolutions.

Methods. We use synoptic maps constructed from Wilcox Solar Observatory, Mount Wilson Observatory (MWO), Kitt Peak (KP), SOLIS, SOHO/MDI and SDO/HMI measurements of the photospheric field. We calculate the harmonic expansions of the magnetic field for all these data sets (for most, up to n = 180) and investigate the scaling of the harmonic coefficients between all possible pairs of data sets.

Results. The six data sets generally scale to one another relatively well, with the exception of even axial terms, especially the g₂⁰ quadrupole for a few pairs of data sets. Differences in polar field observations, pole-filling methods and possible zero-level mainly affect the scaling of even axial terms. Scaling factors typically slightly increase with harmonic order. The mutual scaling between SOLIS and HMI is very good, and one single overall coefficient of approximately 0.8 would be a reasonable choice for those data sets. Our results suggest that the KP synoptic maps are offset by a few degrees with respect to MWO and MDI. We note that the new method gives a correct scaling for the low harmonic terms that are sufficient and necessary for coronal modeling.