We updated annual mean reconstructions of near-Earth interplanetary conditions and (signed) open solar flux FS for the past 186 years. Furthermore, we added observations for solar cycle 24 to refine regressions and improved allowance for orthogardenhose and folded (a.k.a., switchback) heliospheric flux from studies using strahl electrons. We also improved the allowance made for the annual mean gardenhose angle of the interplanetary magnetic field. We used both multiple regression with interplanetary magnetic field B and solar wind speed VSW and linear regression with the function BVSWn and demonstrated that the latter gives correlations that are not significantly lower than those given by the former. We conducted a number of tests of the geomagnetic indices used, of which by far the most important is that all four usable pairings of indices produce almost identical results for B, VSW, and FS. All reconstructions were given full 2σ uncertainties using a Monte Carlo technique that generates an ensemble of 1 million members for each pairing of indices. The long-term variations of near-Earth interplanetary field B and open solar flux FS were found to closely match those of the international sunspot numbers but VSW show a significantly different variation. This result explains why of the two peaks of 20th-century grand solar maximum, the range geomagnetic indices give a larger second peak, whereas the diurnal variation indices give a first peak that is larger, as it is for sunspots. We found that the increase in solar cycle averages of FS was between 2.46 × 1014 Wb in 1906 and 4.10 × 1014 Wb in 1949, the peak of the grand maximum, and hence, the rise in open flux was by a factor of 67%.

A fraction of the magnetic flux threading the solar photosphere extends to sufficient heliocentric distances that it is dragged out by the solar wind. Understanding this open solar flux (OSF) is central to space weather, as the OSF forms the heliosphere, magnetically connects the Sun to the planets, and dominates the motion of energetic particles. Quantification of OSF is also a key means of verifying global coronal models. However, OSF estimates derived from extrapolating the magnetic field from photospheric observations are consistently smaller than those based on heliospheric magnetic field (HMF) measurements, by around a factor two. It is therefore important to understand the uncertainties in estimating OSF from in-situ HMF measurements. This requires both an assumption of latitudinal invariance in the radial component of the HMF in the heliosphere, and that structures without an immediate connection to the Sun, such as local magnetic field inversions (or ‘switchbacks’), can be correctly accounted for. In this study, we investigate the second assumption. Following an established methodology, we use in-situ electron and magnetic data to determine the global topology of the HMF and correct for inversions that would otherwise lead to an overestimation of the OSF. The OSF estimation is applied to the interval 1994 – 2021 and combines measurements from the Wind and ACE spacecraft. This extends the time range over which this methodology has previously been applied from 13 years (1998 – 2011) to 27 years. We find that inversions cannot fully explain the discrepancy between heliospheric and photospheric OSF estimations, with the best heliospheric estimate of OSF still, on average, a factor 1.6 higher than the values extrapolated from photospheric observations.