derived from other observatories and found similar discrepancies between model-derived and spacecraft-measured \|Br\|. In all of these studies, in-situ observations on average produced larger \|Br\| estimates than models, except Linker et al. (2016) where a correction factor of 1.5 was applied to the photospheric-field maps for the results to agree.

Riley (2007) separately applied both a constant 1.8 scaling factor and the MWO latitude-dependent correction to WSO input maps from 1976 – 2007 and calculated total open flux using the PFSS model for both sets of maps. He found that the maps with the MWO saturation correction factor applied to them pro-duced the best overall agreement with the heliospheric derived fluxes but noted significant mismatches during the periods of solar minimum, exactly when one would expect the agreement to be best. For the case of the 1.8 saturation factor applied to the WSO maps, the open-flux results agreed well with the heliospheric values only during solar minimum and under-predicted them for all other times. To explain this Riley proposed and tested the idea that interplanetary coro-nal mass ejections (ICMEs) propagating out into space yet still magnetically connected back to the Sun are detected by spacecraft in the same way that coronal hole open flux is. Riley argued that the total unsigned heliospheric flux is comprised of open coronal hole and closed ICME fluxes, especially during solar maximum. This assumption is reasonable, since distinguishing between open field lines and closed ones from ICMEs still rooted back at the Sun in spacecraft observations, especially when the front of the ICME is far beyond 1 AU, is generally very difficult. Using a simple model to estimate heliospheric ICME flux from sunspot number, Riley found an extremely good match between the combined ICME plus WSO open-flux estimates and heliospheric values. While not claiming to have settled the issue, Riley’s results nonetheless provided an alternative explanation for the temporal variation of observed heliospheric flux without having to resort to correcting the WSO magnetic field data with the MWO saturation correction factor. Owens et al., in a series of articles (Owens and Crooker, 2006; Owens et al., 2007; Owens, Crooker, and Lockwood, 2011), similarly argued that much, if not all, of the variation of heliospheric flux can be explained by a constant open solar magnetic flux baseline or floor with the addition of a time-varying, solar-cycle-dependent closed ICME magnetic-flux component.

Alternatively, total open flux can be determined by identifying coronal holes in chromospheric or coronal observations. Coronal hole areas are calculated from observations after their boundaries are determined either through manual (Harvey and Recely, 2002) or automated (e.g. Henney and Harvey, 2005; Scholl and Habbal, 2008; Krista and Gallagher, 2009; Lowder et al., 2014; Verbeeck et al., 2014; Boucheron, Valluri, and McAteer, 2016; Caplan, Downs, and Linker, 2016; Garton, Gallagher, and Murray, 2018; Hamada et al., 2018) methods. To derive open flux, coronal-hole contours are paired with corresponding synoptic photospheric-field maps. The advent of high- resolution coronal EUV images allows for an independent estimate of the open flux in comparison to model estimates and in-situ observations for the past decade. Observationally derived coronal holes also provide constraints on model-derived coronal hole boundaries.

In this article, we estimate total open magnetic flux from 1990 – 2013 in two different ways using global photospheric magnetic-field maps derived from