3.6 Verification of reconstructions

Because of the diversity of the methods and results of solar-activity reconstruction, it is vitally important to verify them. Even though a full verification is not possible, there are different means of indirect or partial verification, as discussed below. Several solar-activity reconstructions on the millennium timescale, which differ from each other to some degree and are based on terrestrial cosmogenic isotope data, have been published recently by various groups. Also, they may suffer from systematic effects. Therefore, there is a need for an independent method to verify/calibrate these results in order to provide a reliable quantitative estimate of the level of solar activity in the past, prior to the era of direct observations.

3.6.1 Comparison with direct data

The most direct verification of solar-activity reconstruction is a comparison with the actual GSN data for the last few centuries. However, regression-based models (see Section 3.4.1) cannot be tested in this way, since it would require a long set of independent direct data outside the “training” interval. It is usual to include all available data into the “training” period to increase the statistics of the regression, which rules out the possibility of testing the model. On the other hand, such a comparison to the actual GSN since 1610 can be regarded as a direct test for a physics-based model since it does not include phenomenological links over the same time interval. The period of the last four centuries is pretty good for testing purposes since it includes the whole range of solar activity levels from the nearly spotless Maunder minimum to the modern period of a very active sun. As an example, a comparison between the measured GSN and the 14C-based (Solanki et al., 2004Jump To The Next Citation Point) and 10Be-based (Usoskin et al., 2003cJump To The Next Citation Point) reconstructions is shown in Figure 15View Image. The agreement between the actual and reconstructed sunspot numbers is quite good, the correlation coefficient for the 14C-based series is r = 0.93 with the RMS deviation between the two series being six for the period of 1610 – 1900 (Solanki et al., 2004Jump To The Next Citation Point). We want to stress that this reconstruction is fully physics based and does not include any fitting to the whole GSN data series; thus this comparison verifies the approach in both absolute level and relative variations. The agreement between GSN and 10Be-based reconstructions (Usoskin et al., 2003cJump To The Next Citation Point) is also good (r = 0.78, RMS = 10 for 1700 – 1985). In this case, however, the comparison can only test the relative variation because of the unknown proportionality coefficient between the measured concentration of 10Be and the production rate (Section 3.3.3), which is fitted to match the overall level of the reconstructed solar activity. One can see that the reconstructed sunspot series generally follows the real GSN series, depicting the same main features, namely, the Maunder minimum, the tiny Dalton minimum, a slight decrease of activity around 1900 (known as the modern minimum) as well as a steep rise in the first half of the 20th century. Note, however, that individual 11-year cycles are poorly resolved in these reconstructions. This validates the reliability of the physics-based reconstruction of sunspot numbers.

Models focused on the reconstruction of heliospheric parameters (HMF or the modulation potential ϕ) cannot be verified in this manner since no heliospheric data exists before the 1950s. Comparison to direct cosmic-ray data after the 1950s (or, with caveats, after the 1930s – McCracken and Beer, 2007Jump To The Next Citation Point) is less conclusive, since the latter are of shorter length and correspond to a period of high solar activity, leading to larger uncertainties during grand minima.

3.6.2 Meteorites and lunar rocks: A direct probe of the galactic cosmic-ray flux

Another more-or-less direct test of solar/heliospheric activity in the past comes from cosmogenic isotopes measured in lunar rock or meteorites. Cosmogenic isotopes, produced in meteoritic or lunar rocks during their exposure to CR in interplanetary space, provide a direct measure of cosmic-ray flux. Uncertainties due to imprecisely known terrestrial processes, including the geomagnetic shielding and redistribution process, are naturally avoided in this case, since the nuclides are directly produced by cosmic rays in the body, where they remain until they are measured, without any transport or redistribution. The activity of a cosmogenic isotope in meteorite/lunar rock represents an integral of the balance between the isotope’s production and decay, thus representing the time-integrated CR flux over a period determined by the mean life of the radioisotope. The results of different analyses of measurements of cosmogenic isotopes in meteoritic and lunar rocks show that the average GCR flux remained roughly constant – within 10% over the last million years and within a factor of 1.5 for longer periods of up to 109 years (e.g., Vogt et al., 1990Grieder, 2001).

By means of measuring the abundance of relatively short-lived cosmogenic isotopes in meteorites, which fell through the ages, one can evaluate the variability of the CR flux, since the production of cosmogenic isotopes ceases after the fall of the meteorite. A nearly ideal isotope for studying centurial-scale variability is 44Ti with a half-life of 59.2 ± 0.6 yr (a lifetime of about 85 years). The isotope is produced in nuclear interactions of energetic CR with nuclei of iron and nickel in the body of a meteorite (Bonino et al., 1995Taricco et al., 2006Jump To The Next Citation Point). Because of its mean life, 44Ti is relatively insensitive to variations in cosmic-ray flux on decade (11-year Schwabe cycle) or shorter timescales, but is very sensitive to the level of CR flux and its variations on a centurial scale. Using a full model of 44Ti production in a stony meteorite (Michel and Neumann, 1998) and data on the measured activity of cosmogenic isotope 44Ti in meteorites, which fell during the past 235 years (Taricco et al., 2006Jump To The Next Citation Point), Usoskin et al. (2006cJump To The Next Citation Point) tested, in a straightforward manner, several recent reconstructions of heliospheric activity after the Maunder minimum. First, the expected 44Ti activity has been calculated from the reconstructed series of the modulation potential, and then compared with the results of actual measurements (see Figure 16View Image). It has been shown that 44Ti data can distinguish between various reconstructions of past solar activity, allowing unrealistic models to be ruled out. Presently, the Torino group (Taricco et al., 2008) is working hard on improving the quality of 44Ti measurements in meteorites, reducing the error bars in Figure 16View Image, which will allow for more precise estimates in the near future.

Because of the long life time of the 44Ti nuclide (about 85 years), this method does not allow for the reconstruction of solar/heliospheric activity, but it serves as a direct way to test existing reconstructions independently. Most of the reconstructions appear consistent with the measured 44Ti activity in meteorites, including the last decades, thus validating their veracity. The only apparently-inconsistent model is the one by Muscheler et al. (2005Jump To The Next Citation Point), which is based on erroneous normalization (as discussed in Solanki et al., 2005Jump To The Next Citation Point). In particular, the 44Ti data confirms significant secular variations of the solar magnetic flux during the last century (cf. Lockwood et al., 1999Solanki et al., 2000Wang et al., 2005Jump To The Next Citation Point).

View Image

Figure 16: Immediate 44Ti activity in stony meteorites as a function of time of fall. Dots with error bars correspond to measured values (Taricco et al., 2006). Curves correspond to the theoretically expected 44Ti activity, computed using the method of Usoskin et al. (2006c) and different reconstructions of ϕ shown in Figure 12View Image.

3.6.3 Comparison between isotopes

As an indirect test of the solar-activity reconstruction, one can compare different isotopes. The idea behind this test is that two isotopes, 14C and 10Be, have essentially different terrestrial fates, so that only the production signal, namely, solar modulation of cosmic rays, can be regarded as common in the two series. Processes of transport/deposition are completely different (moreover, the 14C series is obtained as an average of the world-wide–distributed samples). The effect of changing geomagnetic fields is also different (although not completely) for the two isotopes, since radiocarbon is globally mixed, while 10Be is only partly mixed before being stored in an archive. Even comparison between data of the same 10Be isotope, but measured in far-spaced ice cores (e.g., Greenland and Antarctica), may help in separating climatic and extraterrestrial factors, since meteorology in the two opposite polar areas is quite different.

The first thorough consistent comparison between 10Be and 14C records for the last millennium was performed by Bard et al. (1997Jump To The Next Citation Point). They assumed that the measured 10Be concentration in Antarctica is directly related to CR variations. Accordingly, 14C production was considered as proportional to 10Be data. Then, applying a 12-box carbon-cycle model, Bard et al. (1997) computed the expected Δ14C synthetic record. Finally, these 10Be-based Δ14C variations were compared with the actual measurements of Δ14C in tree rings, which depicted a close agreement in the profile of temporal variation (coefficient of linear correlation r = 0.81 with exact phasing). Despite some fine discrepancies, which can indicate periods of climatic influence, that result has clearly proven the dominance of solar modulation of cosmogenic nuclide production variations during the last millennium. This conclusion has been confirmed (e.g., Usoskin et al., 2003cJump To The Next Citation PointMuscheler et al., 2007Jump To The Next Citation Point) in the sense that quantitative solar-activity reconstructions, based on 10Be and 14C data series for the last millennium, yield very similar results, which differ only in small details. However, a longer comparison over the entire Holocene timescale suggests that, while centennial variations of solar activity reconstructed from the two isotopes are very close to each other, there might be a discrepancy in the very long-term trend (Vonmoos et al., 2006Jump To The Next Citation PointMuscheler et al., 2007), whose nature is not clear (climate changes, geomagnetic effects or model uncertainties).

Recently, Usoskin et al. (2009b) studied frequency ranges in which the solar signal dominates in different cosmogenic isotope data. They compared the expected 10Be variations computed from 14C-based reconstruction of cosmic ray intensity with the actually measured 10Be abundance at the sites and found that: (1) There is good agreement between the 14C and 10Be data sets, on different timescales and at different locations, confirming the existence of a common solar signal in both isotope data; (2) The 10Be data are driven by the solar signal on timescales from about centennial to millennial time scales; (3) The synchronization is lost on short (< 100 years) timescales, either due to local climate or chronological uncertainties (Delaygue and Bard, 2010) but the solar signal becomes important even at short scales during periods of Grand minima of solar activity, (4) There is an indication of a possible systematic uncertainty in the early Holocene (cf., Vonmoos et al., 2006), likely due to a not-perfectly-stable thermohaline circulation. Overall, both 14C- and 10Be-based records are consistent with each other over a wide range of timescales and time intervals. UpdateJump To The Next Update Information

Thus, comparison of the results obtained from different sources implies that the variations of cosmogenic nuclides on the long-term scale (centuries to millennia) during the Holocene are primarily defined by the solar modulation of CR.


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