Lockwood (2001) noted that the open solar flux reconstruction of Lockwood et al. (1999a) overlapped with cosmogenic isotope records, in a way that modern data on cosmic rays from neutron monitors (Simpson, 2000) did not. A good anticorrelation was found by Lockwood (2001, 2003) on both solar cycle and centennial timescales, with the upward drift in open solar flux reflected in the downward drift in cosmogenic isotope abundances in terrestrial reservoirs, and also the drift in results from early ionisation chambers (Forbush, 1958; Neher et al., 1953; McCracken and McDonald, 2001). This trend can also be detected in the cosmogenic 44Ti isotope found in meteorites (Bonino et al., 1995; Taricco et al., 2006; Usoskin et al., 2006) which is significant as it finally removes any possibility that the trend is associated with climate change influence on deposition into terrestrial reservoirs. Usoskin et al. (2006) use the 44Ti isotope data to give strong support to models of the evolution of heliospheric fields based on sunspot number (first introduced by Solanki et al., 2000), as discussed Section 11. This work showed that the well-known Hale cycle variation in cosmic ray fluxes detected using neutron monitors (with alternately peaked and then plateau-like maxima at sunspot minimum) was also well matched by the inverse of the open solar flux variation (see, in particular, Figure 2 of Rouillard and Lockwood, 2004). The anticorrelation with near-Earth IMF had been noted by Cane et al. (1999) and Belov (2000). Furthermore, Thomas et al. (2013) has shown that this feature is also present in the and reconstructions from geomagnetic activity. This raises an interesting question, which remains largely unresolved, as to the relative influences of cosmic ray drifts in the heliosphere and of the open solar flux on the modulation of cosmic rays arriving at Earth, both on decadal and centennial time scales. That the open solar flux is a factor is not a surprise as cosmic rays are scattered off irregularities in the heliospheric field and those irregularities are known to scale in amplitude with the average field value and, as shown for near-Earth space by Figure 29, that field scales with the . The drift theory is very well established (e.g., Jokipii et al., 1977; Jokipii, 1991; McDonald et al., 1993) and has some notable successes; for example, the antiphase Hale cycle seen in electrons (Evenson, 1998) and positrons (Clem and Everson, 2002) and their latitudinal variations (Heber et al., 1999). If it is assumed that these drift effects contribute to the Hale cycle but not the secular drift, their effect can be averaged out by taking means over the Hale cycle (Steinhilber et al., 2008). Using ice core records of the abundance of the 10Be cosmogenic isotope and a simple theory of cosmic ray shielding, Steinhilber et al. (2010) (SEA10) have reconstructed 25-year means of the IMF over the last 9300 years. The results since the Maunder minimum are shown in Figure 34 and compared with 11-year running means of from the reconstructions discussed in Section 9.1.
The general agreement between the geomagnetic and cosmogenic isotope reconstructions is extremely good although there are obvious differences and there may be some timing errors which may turn out to be attributable to dating problems with the ice cores. The agreement is very good after 1900 but less good before then. Between 1850 and 1875 the SC10 reconstruction agrees well with the average level of the SEA10 reconstruction, although showing oscillations that are not found in the SEA10 data. However, SC10 yields higher values of in the intervals 1875 – 1905 and 1835 – 1850. The 25-year means of the SEA reconstruction of remain above the SC10 postulated floor level for annual means, even in the Dalton minimum (DM). However, this is not true of the Maunder minimum (MM) where they fell well below it. Even in 25-year means the SEA10 estimate fell to by the end of the Maunder minimum, which is still lower than the downward revision of the floor estimate to 2.8 nT by Cliver and Ling (2011). Extending the sequence over 9300 years, SEA10 find 14 grand solar minima in which the reconstructed fell to even lower values in 25 year means. The SEA10 value of (and its uncertainty) at the end of the Maunder minimum is marked by the white dot in Figure 29, and using the polynomial fit shown, this yields an estimate of the signed open solar flux at the end of the Maunder minimum of .
The open flux continuity model discussed in Section 11, which was derived to explain and fit the open solar flux reconstructions from geomagnetic activity data, has been used to estimate the variation of sunspot numbers from the cosmogenic data isotope data for the last millennium (Usoskin et al., 2003; Solanki et al., 2004). These studies found that the recent grand maximum contained unusually high sunspot numbers in the past 11 000 years, a conclusion that generated some debate (Raisbeck and Yiou, 2004; Usoskin et al., 2004; Muscheler et al., 2005; Solanki et al., 2005). Using the composite of cosmogenic isotope data compiled by Steinhilber et al. (2008), Abreu et al. (2008) found that the recent grand solar maximum may not have been the largest in the sequence, but it was the longest in duration.