The Revised Sunspot Record in Comparison to Cosmogenic Radionuclide-Based Solar Activity Reconstructions

Recent revisions in the sunspot records illustrate the challenges related to obtaining a 400-year-long observational record of past solar-activity changes. Cosmogenic radionuclides offer the possibility of obtaining an alternative and completely independent record of solar variability. Here, we illustrate that these records offer great potential for quantitative solar-activity reconstructions far back into the past, and we provide updated radionuclide-based solar-activity reconstructions for the past 2000 years. However, cosmogenic-radionuclide records are also influenced by processes independent of solar activity, leading to the need for critical assessment and correction for the non-solar influences. Independent of these uncertainties, we show a very good agreement between the revised sunspot records and the 10Be records from Antarctica and, in particular, the 14C-based solar-activity reconstructions. This comparison offers the potential of identifying remaining non-solar processes in the radionuclide-based solar-activity reconstructions, but it also helps identifying remaining biases in the recently revised sunspot records.


Introduction
Documentations of the occurrence and number of sunspots are the basis for the longest record of direct solar observations, but reliable data do not extend much further than 400 years into the past (Hoyt and Schatten, 1998). Therefore, we need to consider indirect so-called "proxy data" to extend our information about past solar variability back in time and to test the suggested revisions in the sunspot-number reconstructions. The most reliable indirect solar-proxy data come from cosmogenic radionuclides such as 10 Be, 14 C, and 36 Cl (e.g. Beer et al., 1990;Lal and Peters, 1967). These particles are produced during the interaction of galactic and solar cosmic rays with constituents of the Earth's atmosphere (Lal and Peters, 1967). Because of their sporadic nature and their on-average relatively low energies, solar-particle events are assumed to contribute negligibly to the long-term average production rate of cosmogenic radionuclides. Galactic cosmic rays, on the other hand, are considered to be mainly responsible for the production of radionuclides in the Earth's atmosphere. The varying solar magnetic shielding modulates the flux of galactic cosmic rays within the heliosphere (Lal and Peters, 1967). Therefore, cosmogenic radionuclide records can provide information about the open solar magnetic field in the past. However, cosmogenic radionuclide records not only depend on solar shielding, but also on other factors such as i) influences of the geomagnetic shielding effect, ii) transport effects in the atmosphere (e.g. in the case of 10 Be), and iii) deposition effects and/or carbon-cycle effects (in the case of 14 C) (Lal and Peters, 1967).
Despite these complications, quantitative reconstruction of solar modulation, sunspot numbers, and solar irradiance have been attempted based on cosmogenic-radionuclide data (e.g. Bard et al., 2000;Muscheler et al., 2007;Solanki et al., 2004;Steinhilber et al., 2012). Such reconstructions have provided information on, for example, the existence of the solar 11-year cycle during the Maunder minimum (Beer et al., 1990) or on longer-term cycles such as the 88-year or the 207-year solar cycles (e.g. Damon and Sonett, 1991). These reconstructions form the basis for assessing past temporal variations in solar irradiance that are used for paleoclimate model runs (e.g. Schmidt et al., 2012), and they have provided numerous examples of the coupling between past changes in solar activity and climate (e.g. Bond et al., 2001;Adolphi et al., 2014). However, there is still a debate about past solar-activity levels that is mainly based on differences in the data underlying these reconstructions. For example, Usoskin et al. (2003) favored the 10 Be record from Southern Greenland, which appears to be in good agreement with previous sunspot reconstructions. In contrast, Bard et al. (2000) and Muscheler et al. (2007) came to different conclusions about past solar activity based on 10 Be data from the South Pole and 14 C data in combination with neutron-monitor data.
In the following we review the available 10 Be and 14 C data and discuss the agreement and disagreement between the records. We show that the various ice core 10 Be records generally agree well and that there are relatively small differences that have led to the different assessments of past solar activity with respect to the recent decades. We update the solarmodulation reconstructions with the latest knowledge about the local interstellar cosmic-ray spectrum (LIS) and the related 10 Be and 14 C production rates depending on solar and geomagnetic shielding. Finally, the updated records are compared to the revised sunspot records as published recently by Clette et al. (2014) (sunspot number) and Svalgaard and Schatten (2016) (group sunspot number).

Production Models
The main source for the production of cosmogenic radionuclides in the Earth's atmosphere are galactic cosmic rays (GCRs). As soon as these charged particles encounter the heliospheric magnetic field (HMF), the low-energy particles are deflected, resulting in a modulation of the low-energy spectrum that strongly depends on solar activity. Thus, much higher particle intensities can be detected inside the heliosphere during solar-minimum conditions compared to phases of high solar activity. The so-called local interstellar spectrum (LIS), i.e. the particle spectrum outside the heliosphere, is of major importance for the numerical reconstruction of the production rate values (see, e.g., Herbst et al., 2010). Unfortunately, until very recently, the LIS has not been measured in situ; thus, multiple LIS models exist in the literature (e.g. Burger, Potgier, and Heber, 2000;Garcia-Munoz, Mason, and Simpson, 1975;Webber and Higbie, 2010). However, with Voyager 1 crossing the outer boundary of our solar system in 2012, the LIS of galactic protons below ≈ 500 MeV have been measured for the first time (Stone et al., 2013). On the basis of these measurements, Potgieter et al. (2014) developed a new proton LIS model (denoted as PG14), also taking into account the spacecraft-borne Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) measurements above ≈ 1 GeV.
The transport of GCRs within the heliosphere can be described by the Parker equation (Parker, 1965) giving the phase-space distribution as a function of the main modulation processes such as convection, drifts, diffusion, and adiabatic energy changes. A widely used, but only first-order approximation, is the so-called force-field approach (e.g. Gleeson and Axford, 1968;Moraal, 2013), which is a simple convection-diffusion equation neglecting, e.g., drifts as well as adiabatic energy-loss processes. Here, the transport only depends on one free parameter, the solar modulation function [ ] given by = (Ze/A)φ, with Z and A as charge and mass number of cosmic-ray nuclei. φ represents the solar-modulation parameter, which is directly linked to solar activity. The time-dependent differential GCR flux at 1 AU is given by where J LIS is the differential LIS spectrum, E the kinetic energy of the primary GCR particle, and E r the rest energy of the GCR (for protons E r ≈ 938 MeV). In addition to the HMF, once the particles arrive at Earth's vicinity, they also encounter the geomagnetic field, which shields the atmosphere from low-energy primaries. However, the particles that are able to enter the Earth's atmosphere interact with the atmospheric constituents. When the energy of the GCR particle is high enough, these interactions lead to the development of altitude-dependent secondary-particle cascades mainly consisting of hadronic particles (e.g. Simpson, 2000). Very important for the production of both short-and long-lived cosmogenic radionuclides are the secondary neutrons and protons so produced.
Numerically, the production rate [P ] of a cosmogenic radionuclide of type j can be described in the following way (see, e.g., Masarik and Beer, 1999): The production rate is a function of the density of target atoms [N ] of species i, the production cross-sections [σ ], and the secondary particle flux [J k ], which depends strongly on atmospheric depth [x] and on solar shielding [φ] and geomagnetic shielding [R C ]. R C is related to the energy E C a particle must have in order to be able to enter the atmosphere depending on the geomagnetic shielding at a certain location. The integration of P j over atmospheric depth [x] and the geographic locations gives the global production rates. In this study we investigate the global 10 Be and 14 C production rates based on the computations by Masarik and Beer (1999) and those by Kovaltsov and Usoskin (2010) and Kovaltsov, Mishev, and Usoskin (2012).  (Masarik and Beer, 1999) extended with ionization-chamber data and balloon-borne measurements of cosmic rays (McCracken and Beer, 2007) (black line). An alternative reconstruction by Usoskin, Bazilevskaya, and Kovaltsov (2011) is shown as a dotted-gray line. Both records are transferred to the LIS model of Potgieter et al. (2014).

Neutron-Monitor Data
To reconstruct solar activity over the past 2000 years, a calibration with the constantly measured cosmic-ray flux record during present conditions is required. As shown by McCracken and Beer (2007), measurements of balloon-borne ionization chambers and neutron monitors (NMs), going back to the 1930s, can be used to intercalibrate with the existing 10 Be and 14 C records on the basis of computed yield functions (see, e.g., McCracken and Beer, 2007, for further information). However, these inter-calibrations strongly depend on the applied LIS and the numerical computations. In this study we use the -reconstructions by McCracken and Beer (2007), which are based on the computations by Masarik and Beer (1999) and those by Usoskin, Bazilevskaya, and Kovaltsov (2011) to reconstruct solar activity for the past 2000 years.
As described by, e.g., Herbst et al. (2010), solar-modulation parameter values based on one LIS can be transformed into values of another LIS through linear regression. Based on their method, we transformed the -values used by McCracken and Beer (2007) (LIS model by Garcia-Munoz, Mason, and Simpson, 1975) and Usoskin, Bazilevskaya, and Kovaltsov (2011) (LIS model by Usoskin et al., 2005 on the basis of Burger, Potgier, and Heber, 2000) to values based on the newest LIS model by Potgieter et al. (2014), upon which all of the subsequent results are based. The following regression functions were used: φ PG14 = 0.995φ GM75 + 77.39 MV, 1.029φ US05 + 28.00 MV. Figure 1 shows the solar-modulation function based on NM data (Masarik and Beer, 1999) extended with ionization-chamber data and balloon-borne measurements of cosmic rays (McCracken and Beer, 2007). In addition, we show the alternative reconstruction by Usoskin, Bazilevskaya, and Kovaltsov (2011). As both were transferred to the LIS by Potgieter et al. (2014), the differences are most likely due to different yield functions (i.e. the number of secondary particles produced per incident cosmic-ray particle at a certain NM site) and/or differences in neutron-monitor data included in the calculation. As we show in the following, these different records lead to a different normalization of the 14 C-based solar-modulation records, but do not strongly affect the inferred relative changes in solar modulation.

Figure 2
Normalized ice-core 10 Be concentrations from Antarctica and Greenland. The black and gray lines indicate the normalized 10 Be concentration. Dotted lines bridge data gaps in each record. The red lines depict ten-year averages of each dataset. Data are shown for (from top to bottom) Siple Dome (Nishiizumi and Finkel, 2007), South Pole (Raisbeck et al., 1990), Dome Fuji (Horiuchi et al., 2008), Dome C (Beer, Raisbeck, and Yiou, 1991;Raisbeck et al., 1981), Milcent (Beer, Raisbeck, and Yiou, 1991), Dye-3 (Beer et al., 1990), Camp Century (Beer et al., 1988), GRIP (Muscheler et al., 2004;Yiou et al., 1997), and NGRIP (Berggren et al., 2009). The bottom panel indicates the temporal coverage of each record. Figure 2 shows ice core 10 Be records from Greenland and Antarctica that are used in this study. Of the publicly available records, we limited our choice to those that are longer than 500 years and provide a temporal resolution on the order of 20 years or less. This includes four Antarctic ice cores: Siple Dome (Nishiizumi and Finkel, 2007), South Pole (Raisbeck et al., 1990), Dome Fuji (Horiuchi et al., 2008), and Dome C (Beer, Raisbeck, and Yiou, 1991;Raisbeck et al., 1981). From Greenland, five ice cores fulfill our criteria: Milcent (Beer, Raisbeck, and Yiou, 1991), Dye-3 (Beer et al., 1990), Camp Century (Beer et al., 1988), GRIP (Muscheler et al., 2004;Yiou et al., 1997) and NGRIP (Berggren et al., 2009). As mentioned in the introduction, variations in ice-core 10 Be concentrations do not only reflect fluctuations in the 10 Be production rates, but may also be influenced by changes in atmospheric circulation, aerosol transport, and deposition (Adolphi and Muscheler, 2016;Field et al., 2006;Pedro et al., 2011Pedro et al., , 2012Pedro et al., , 2006. For example, it has been suggested that volcanic aerosols influence the scavenging of 10 Be, i.e. leading to enhanced 10 Be deposition following such events (Baroni et al., 2011). However, our knowledge about such effects and their influences on 10 Be records is limited. Therefore, attempts to correct for the above-mentioned non-production effects on 10 Be still contain significant uncertainties. In addition, data-quality issues might affect some of the records. This becomes apparent when correlating the records to each other, as shown in Figure 3. While most correlations are indeed significant, there are also a number of insignificant correlations between single records. Most notably, the 10 Be records from Dome C and Camp Century are not significantly correlated with any other record. Since the low correlations between single icecore records may in part be caused by a limited temporal overlap, we additionally tested the correlation of each record with the average of all other ice cores ( Figure 3, "mean"). In doing so, we found that all ice-core records except those from Dome C and Camp Century share a significant amount of covariability that most likely reflects the common production-rate signal. The averaged records are subsequently referred to as "stacks".

10 Be Data
Influences of atmospheric circulation and precipitation rate on 10 Be can be expected to differ between Greenland and Antarctica because of their large geographical separation. It is a priori unknown whether one region can be assumed to be more or less susceptible to these influences than the other. Hence, we separately produced 10 Be stacks from ice-core records from these two regions. To account for differences in the mean 10 Be deposition rates at different sites, we normalized all Greenland 10 Be records to the Dye−3 10 Be data for their overlapping periods. Similarly, we normalized all Antarctic records to the South Pole 10 Be data. Normalizing to other records has only a minor influence on the resulting stacked record. Subsequently, we created 1000 stacked 10 Be records for the two regions through bootstrapping, i.e. we randomly sampled from the available 10 Be records at each point in time and calculated the mean. Consequently, by taking the mean and standard deviation of all 1000 realizations, we obtained a Greenland and Antarctic 10 Be stack including confidence intervals (see Figure 4). It should be noted that these confidence intervals solely reflect the spread of the individual data series (and hence, they are zero when only one record covers a certain time period) and not true uncertainties, as all records from one region may be biased Figure 4 Stacked normalized decadal 10 Be variations from Greenland (orange) and Antarctica (blue). Both records are shown together with their ±1σ uncertainty (shading) based on bootstrapping (see text). a: Greenland and Antarctic 10 Be stacks of all available 10 Be records shown in Figure 2, the correlation coefficient and its p-value. b: Differences (Greenland-Antarctica) between the curves shown in panel a. c: Similar to panel a, but excluding the data from Camp Century and Dome C from the Greenland and Antarctic 10 Be stack, respectively. d: Differences between the curves shown in panel c.
in a similar way. Since the Camp Century and Dome C records do not correlate significantly with any other 10 Be record (Figure 3), we calculated the 10 Be stacks using all available records (Figure 4a), and without Camp Century and Dome C (Figure 4c). Excluding Camp Century and Dome C leads to an improved agreement between the regional 10 Be stacks (the correlation coefficient increases from 0.4 to 0.53). The differences between the two stacks are reduced especially around 1000 -1200 C.E. and 1400 -1500 C.E. when the data from Camp Century and Dome C are omitted (Figure 4b and 4d). However, systematic differences between the 10 Be stacks from both regions remain, especially from about 1600 C.E. onward. The relatively small and short-term disagreement between Antarctic and Greenland stacks for about the last 50 years is noteworthy in this context. This difference can have a major impact on the conclusions about past solar activity when relating recent solar activity to activity in the past millennium.

14 C Data and Production Rate
Figure 5 depicts the atmospheric 14 C concentration changes as inferred from tree-ring 14 C measurements compiled in the most recent IntCal13 14 C calibration record for the northern  and southern  hemisphere complemented by annual northern-hemisphere data for the past about 500 years (Stuiver, Reimer, and Braziunas, 1998). Data after 1950 C.E. are not shown, as atmospheric 14 C is heavily influenced by the anthropogenic 14 C produced during the nuclear bomb tests and therefore cannot be used to reconstruct solar activity. As we are interested in the globally averaged 14 C production rate, we used an average northern and southern hemisphere 14 C record to infer solar activity. We still retained the high-resolution annual 14 C data for the most recent period, but we corrected the absolute level for the offset induced by the time-dependent northern and southern hemisphere difference.

Figure 5
The 14 C data used in this study. The black dots show the northern-hemisphere 14 C data Stuiver, Reimer, and Braziunas, 1998), while the gray data represent the southern-hemisphere 14 C data . With a Monte Carlo approach and by using a box-diffusion carbon-cycle model , we calculated 1000 versions of the 14 C production rate consistent with the atmospheric 14 C data within its errors. The effect of fossil-fuel burning on 14 C (diluting 14 C in relation to 12 C) was accounted for by including the estimated CO 2 emissions from fossil-fuel burning . This method correctly reproduces the atmospheric CO 2 changes from 1850 to 1950 C.E., thereby supporting the estimates of the fossil-fuel-burning influence on 14 C. To eliminate large short-term scatter, which would lead to unphysical large 14 C variations, we smoothed each of the 14 C records generated in the Monte Carlo process using a Gaussian smoothing filter (σ = 2 years).
Our results generally agree well with independent calculations based on the more sophisticated carbon-cycle model of Roth and Joos (2013) (Figure 6). An upward trend in the results of Roth and Joos (2013) from 1930 to 1950 C.E. is unexpected and might be caused by the relatively slow 14 C decline in the southern hemisphere and, therefore, might overestimate the 14 C production rate during this period. This feature is less strongly expressed in the results from our calculation. One possible reason is that we used the higher-resolution annual 14 C data during this period, while Roth and Joos (2013) applied the smoothed Int-Cal 14 C record. Furthermore, Roth and Joos (2013) indicated slightly smaller amplitudes of the typical solar-induced centennial-scale 14 C production rate variations. This is probably caused by a slower 14 C uptake of the oceans in the carbon-cycle model of Roth and Joos (2013). Nevertheless, in general the different 14 C production rate results agree well within our inferred uncertainty estimates (gray band in Figure 6).

Geomagnetic Field Data
For solar-activity reconstructions based on cosmogenic-radionuclide records, we need to correct for the geomagnetic-field influence as the atmospheric production rate of cosmogenic radionuclides is inversely related to the strength of the geomagnetic-field intensity. As the cosmic-ray modulation is most important far away from the Earth's surface, where the higher moments of the geomagnetic field do not significantly contribute to the shielding, the production rate is predominantly influenced by the geomagnetic dipole moment. Internally driven geomagnetic-field changes are usually associated with changes in the production rate on millennial timescales, 2000 -3000 years and longer Wagner et al., 2000), but they probably already start to play a significant role on timescales of 500 years (Korte and Muscheler, 2012).
To determine the dipole moment, it is necessary to filter out regional differences in geomagnetic-field intensities, which requires data with good global coverage. This has traditionally been done by averaging, or in some other way combining, all available archaeointensity data (including data from igneous rocks) assuming that all non-dipole field contributions will be minimized in the process (e.g. Knudsen et al., 2008 shown in Figure 7). However, the effectiveness of this approach has been questioned because of the strong geographical bias in the data distribution, with the majority of the measurements concentrated on Europe and the northern hemisphere (e.g. Korte and Constable, 2005;Nilsson, Muscheler, and Snowball, 2011). Efforts to construct global geomagnetic-field models have, to a certain extent, overcome this problem by including directional data as well as intensities and allowing for more complex field structures; see A_FM (Licht et al., 2013) shown in Figure 7. To reduce the geographical bias in the data distribution, sedimentary palaeomagnetic data are sometimes also included, which provide a vastly improved data coverage but lead to models with lower temporal resolution; see pfm9k.1b (Nilsson et al., 2014) in Figure 7. The low temporal resolution is due to the generally large chronological uncertainties of sedimentary palaeomagnetic data and potential smoothing associated with the gradual processes by which the magnetization is acquired over time in the sediments (Roberts and Winklhofer, 2004).
Despite recent advances in geomagnetic-field modeling, reconstructing past changes in the dipole moment beyond historical observations is still proving to be a challenge (Panovska et al., 2015). Figure 7 shows that the different geomagnetic-field reconstructions largely agree in their broad trend, i.e. all records show a similar long-term trend gradually decreasing toward the present. In addition, the most recent dipole estimates agree mostly within their respective error estimates. Nevertheless, for solar-activity reconstruction it also implies that there are still unresolved (possibly systematic) differences in the geomagneticfield reconstructions that directly translate into uncertainties in the estimates of solar modulation.
To provide the best possible continuous dipole-moment reconstruction for the past 2000 years, we spliced together the dipole-moment estimates from two recent archaeo/ palaeomagnetic field models, A_FM (Licht et al., 2013) and pfm9k.1b (Nilsson et al., 2014) based on 1000 and 2000 bootstrap models, respectively, with predictions of models based on historical field observations: gufm1 (Jackson, Jonkers, and Walker, 2000) between 1840 -1990 C.E. and IGRF 12th generation (Thebault et al., 2015) up to 2000 C.E. To avoid discontinuities in the transition, each individual bootstrap model was joined together with the historical field estimate by spline interpolation over a 100-year period (1740 -1840 C.E.); see Figure 7.

Solar Modulation [ ] Reconstruction
By combining theoretical production-rate models, cosmogenic-radionuclide records, and geomagnetic-field reconstructions, we can infer cosmogenic radionuclide-based solaractivity reconstructions. However, a direct transfer of absolute production-rate estimates to solar-modulation estimates is currently uncertain owing to i) carbon-cycle uncertainties for 14 C, ii) deposition uncertainties for 10 Be, and iii) production-rate uncertainties in the computations that are due to the uncertainties in the LIS of cosmic rays and uncertainties in the production cross sections for cosmogenic radionuclides. We note that both LIS and production cross sections are not well known, but they play a crucial role for the numerical computations. Changing to a different LIS model can result in differences of up to 20 %, while differences in the cross sections (in particular the neutron cross sections; see, e.g., Caffee et al., 2013) can lead to systematic differences of up to 25 % (Herbst, 2013). Hence, we applied the more reliable approach of connecting (normalizing) the radionuclide variations to the absolute solar-modulation estimates inferred from the neutron-monitor data (Figure 1).
In the case of 14 C, we normalized the 14 C production-rate record to obtain the same average solar-modulation function in the period from 1937 to 1948 (covering one average solar cycle), as indicated by the extended neutron-monitor data. This was done with randomly selected realizations of the Monte Carlo inferred 14 C production records and randomly selected geomagnetic-field realization. By repeating this procedure 1000 times and averaging the resulting curves, we could infer an average 14 C-based solar-modulation function with its corresponding error inferred from the spread of the different results. The 10 Be records were normalized in a similar way. However, in this case we took the full period of overlap with the neutron-monitor data to normalize the 10 Be record. In this calculation we assumed that the 10 Be stacks reflect the globally averaged relative changes in the 10 Be production rate. The range of uncertainty based on the geomagnetic-field and 10 Be data was included in the same way as for 14 C. This procedure was carried out for the production-rate models and neutron-monitor-based records mentioned above, i.e. Beer (1999) combined with McCracken and and Kovaltsov, Mishev, and Usoskin (2012), Kovaltsov and Usoskin (2010) combined with Usoskin, Bazilevskaya, and Kovaltsov (2011). All solar-modulation functions are reported using the LIS model of Potgieter et al. (2014). Figure 8 shows the three independent reconstructions of the solar modulation based on Greenland 10 Be, Antarctic 10 Be, and 14 C. For the Greenland and Antarctic 10 Be based reconstructions, we used the 10 Be stacks without Camp Century and Dome C, respectively, as shown in Figure 4c. The relatively large 10 Be decrease toward today in the Greenland data leads to an inferred strong increase in solar modulation toward today. However, this reconstruction also shows negative (i.e. unphysical) solar-modulation values during the large solar minima of the last millennium, illustrating the challenges of inferring exact amplitudes of past solar-activity variations from this record. The Antarctic 10 Be data do not show such a large trend, leading to the conclusion that these records do not indicate exceptionally high solar activity during recent decades . It can also be seen that Antarctic-and Greenland-based solar-activity reconstructions do not agree during the last 50 years (Figures 4 and 8), leading to the conclusion that at least one of the records also contains a non-production signal. As discussed before, this is not unexpected considering the noise that is present in 10 Be records (Figure 4). This emphasizes that we need to be careful to avoid overinterpreting the 10 Be data, especially when attempting quantitative solar-activity reconstructions. Nevertheless, both 10 Be stacks agree with respect to the main features such as, e.g., the three large solar minima from 1300 to 1750 C.E. (Maunder, Spörer, and Wolf minima). Applying the production-rate calculations of Kovaltsov and Usoskin (2010) leads to similar conclusions, although the range of variability in solar modulation is generally slightly smaller.

Results
The 14 C-based record shares these common large-scale features with the 10 Be record. It shows a similar long-term trend throughout most of the past 2000 years, culminating in the Figure 8 The different -reconstructions based on the Greenland 10 Be data (top panel), the Antarctic 10 Be data (middle panel), and the 14 C data combined with the neutron-monitor-based data (lower panel). The records were calculated with the pfm9k.1b geomagnetic-field model results and the production-rate calculation from Masarik and Beer (1999). The horizontal-dashed lines show the average solar modulation inferred from the instrumental data from 1950 to 2000 C.E. three deep solar minima mentioned above. These are followed by a general increase in solar activity toward the second part of the twentieth century. In agreement with the Antarcticbased record, solar activity in the second part of the twentieth century is high, but similar levels are reached during several periods in the past 2000 years.

Uncertainties in the Solar Modulation Reconstruction
As shown, there are unresolved differences in the 10 Be records. This makes quantitative 10 Be-based solar-activity reconstructions somewhat uncertain at present (see Figure 4d). For example, the differences between the Greenland and Antarctic 10 Be stack during the past 50 years (i.e. the normalization period) have an influence on the complete record when focusing on the comparison of recent to past solar activity. More specifically, this can lead to the conclusion of exceptional high solar activity in recent decades (Usoskin et al., 2003) compared to high, but not exceptional, solar activity during this period (Bard et al., 2000;Muscheler et al., 2007). The unphysical negative solar modulation inferred from the Greenland stack illustrates that this record very likely shows changes that are too strong to be explained by solar modulation alone. Using the production-rate calculations of Kovaltsov and Usoskin (2010) leads to less (but still) negative inferred solar modulation. In combination with the hypothesis of a so-called polar amplification (i.e. polar 10 Be records rather reflecting the polar production and not a global production signal (Mazaud, Laj, and Bender, 1994)), it might be argued that the Greenland 10 Be record is within the expected range of variability due to solar modulation. However, several arguments indicate problems in this reasoning: The real 10 Be range is even larger since we discuss a smoothed record (ten-year averages), i.e. eliminating the variability that is due to the 11-year cycle (Beer et al., 1990). In addition, there is no indication of a systematic polar bias in Greenland 10 Be records (Adolphi and Muscheler, 2016). Furthermore, the direct comparison of neutron monitor and 10 Be data illustrates the non-production influences in the Greenland 10 Be records during the past 60 years (e.g. Pedro et al., 2012).
Focusing on 14 C instead, Figure 9 shows the influence of different geomagnetic-field estimates and the differences arising from applying different production rate models. As mentioned, all curves are based on the same LIS spectrum (Potgieter et al., 2014). There is only a very small difference between the results using the two recent geomagnetic-field records (Licht et al., 2013;Nilsson et al., 2014). This is mainly due to the low sensitivity of cosmogenic-radionuclide production rate changes to variations in the geomagnetic field in periods of generally high geomagnetic-field intensities. The two resulting curves agree very well within the combined errors (blue and red lines in Figure 9). However, we note that potential systematic errors in the geomagnetic-field models could still be a significant source of uncertainty in the reconstructions. Figure 9 also illustrates that the differences in the production rate calculations have an influence on the absolute levels of solar modulation (mainly due to a normalization difference as shown in Figure 1). The absolute numbers for the solar-modulation function differ by about 10 % for the results from the different production models. However, without the normalization difference, the 14 C-based solar-modulation records are only slightly different.

Figure 9
Comparison of the different 14 C-based solar-modulation records. The dark-blue line with light-blue error band shows the results based on the production-rate calculations from Masarik and Beer (1999) and the pfm9k.1b geomagnetic-field model (Nilsson et al., 2014) connected to the neutron-monitor based solar modulation from McCracken and Beer (2007). The dashed-red curve shows the same calculation but using the AFM geomagnetic-field model (Licht et al., 2013). It largely overlaps with the blue line.
The dotted-black curve shows the results using the production-rate calculations from Kovaltsov, Mishev, and Usoskin (2012) connected to the neutron-monitor-based solar modulation from Usoskin, Bazilevskaya, and Kovaltsov (2011) and the pfm9k.1b geomagnetic field model. Note that for this record the y-axis labels are indicated in the brackets, i.e. largely correcting for the 10 % offset in neutron-monitor-based solar-modulation reconstruction shown in Figure 1. The horizontal-dashed line indicates the average neutron-monitor based solar-modulation function for the second part of the twentieth century.

Comparison to the Revised Sunspot Record
In the following we compare the Greenland, Antarctic, and 14 C-based solar-modulation records to the revised sunspot records (Clette et al., 2014;Svalgaard and Schatten, 2016). As sunspot and radionuclide records react to different expressions of solar variability (magnetic fields on the Sun and the open magnetic flux), it is not a priori obvious that there should be a perfect correlation between these records. Nevertheless, there have been efforts to convert one into the other (Usoskin et al., 2003), and these reconstructed sunspot records correlate linearly to the radionuclide-based solar-modulation records from which they were derived. Therefore, we limit our comparison in the following to a direct linear comparison between solar modulation and revised sunspot records. Figure 10 shows the comparison between these records on timescales longer than 11 years. This comparison indicates a very close linear correlation between the two completely independent records of radionuclide-based solar modulation and sunspot numbers. Especially the record based on the production computations of Masarik and Beer (1999) (C14 MB ) shows very close agreement with the sunspot record. Around 1750 C.E., the 14 C-based record agrees better with the sunspot record (Clette et al., 2014), while the group sunspot numbers are systematically higher (Svalgaard and Schatten, 2016). Around 1950 C.E., there is some additional shortterm disagreement that might indicate an underestimation of the solar modulation based on the extended neutron-monitor record before 1950 C.E. and a possible underestimation of the solar modulation based on 14 C around this period (i.e. offsetting biases in the 14 C production rate and the extended neutron-monitor data). Comparing the sunspot records to the 14 C-based results using the normalization based on Usoskin, Bazilevskaya, and Kovaltsov (2011) and the calculations of Kovaltsov, Mishev, and Usoskin (2012) (C14 KU ) leads to systematically lower solar-modulation values. We therefore scaled the y-axis differently (numbers in brackets in Figure 10) to minimize this systematic offset. This record also supports Figure 10 Comparison of the 14 C based solar-modulation function with the revised sunspot (black) and group sunspot (dashed-dark blue) numbers. All records show the running 11-year average. The red (orange) curve shows the 14 C (neutron monitor)-based results using the production calculations of Masarik and Beer (1999) (labeled C14 MB ). The dashed-orange curves show the results based on Kovaltsov, Mishev, and Usoskin (2012) normalized to the neutron-monitor-based reconstruction of Usoskin, Bazilevskaya, and Kovaltsov (2011) (labeled C14 KU ). Note the two different left y-axes, where the numbers for the solar-modulation potential in brackets refer to C14 KU . It indicates that the relative changes in solar modulation are similar, but the different production rate models lead to about 10 % different values in the absolute number of the solar-modulation potential. Similarly, the sunspot data have been rescaled (−34 %) to allow for a direct comparison to the Group Sunspot Number data. The old group sunspot record from Hoyt and Schatten (1998) is shown as the black dotted curve. the high solar-activity values around 1780 on a level comparable to the second part of the twentieth century. For reference we also plot the outdated group sunspot record published by Hoyt and Schatten (1998). It is apparent that this record suggests significantly lower solar-activity levels before about 1900 C.E. compared to the revised sunspot records and the 14 C-based solar-activity reconstruction. Figure 11 shows the comparison of the different 10 Be-based solar-modulation records with the sunspot records (same scaling as in Figure 10). The Antarctic 10 Be-based record and the sunspot records agree well. The normalization procedure in combination with the large 10 Be trend in the Greenland record over the past 100 years leads to a generally much lower solar modulation based on this record. To use these 10 Be-based records to test the revised sunspot record appears problematic since these records do not show a prefect agreement with the instrumental neutron-monitor data (see the black line in comparison to the 10 Be-based solar modulation in Figure 11). Therefore, apparent climate or weather influences in the records are already visible in the 10 Be record for the normalization period. The aforementioned differences between Greenland and Antarctic 10 Be data indicate that such influences are also present further back in time. We currently do not have adequate models to independently correct for such influences in the 10 Be record.

The 11-Year Cycle in the 14 C Data
The revised group-sunspot record exhibits more counts during the Maunder minimum from about 1650 to 1700 C.E. compared to the previously published group sunspot record. In the following we investigate whether the 14 C record can be used to test this short-term variability during the last, and only directly observed, grand solar minimum. The upper panel of Figure 12 shows the revised group-sunspot record in comparison with the 14 C-based solar Figure 11 Comparison of revised sunspot records (black and dashed-blue curves) to 10 Be-based solar modulation records. The sunspot data show running 11-year averages and the 10 Be data is based on the ten-year averages shown in previous figures. The 10 Be-based records are normalized to obtain agreement between neutron monitor and 10 Be-based solar modulation in the period of overlap. The dark-and light-green curves show the solar modulation based on the Antarctic 10 Be data using the production-rate calculations of Masarik and Beer (1999) and Kovaltsov and Usoskin (2010), respectively. The red and orange curves show the solar modulation based on the Greenland 10 Be data using the production rate calculations of Masarik and Beer (1999) and Kovaltsov and Usoskin (2010), respectively. The unphysical range (negative solar modulation) is indicated by the shading. The scaling between sunspots and solar modulation is the same as in Figure 10 and the numbers for the solar-modulation potential in brackets refer to the calculations based on Kovaltsov and Usoskin (2010). The old group sunspot record from Hoyt and Schatten (1998) is shown as the dotted-black curve. modulation record calculated in this study. The lower panel shows the comparison of the two time series for variability only on timescales from 5 to 20 years (FFT band-pass filter). Considering the smoothing of the atmospheric 14 C variations connected to short-term changes, it is notable that most of the 11-year variability is reflected in the 14 C-based record and that the timing of the changes is mostly synchronous with the sunspot record. In particular, focusing on the Maunder minimum shows a reasonable agreement. As has been observed in 10 Be data (Beer et al., 1990), the 14 C record shows continued solar modulation during the Maunder minimum. An exact comparison of the 11-year cycle variability in 14 C and group sunspots is challenged by the relatively small amplitude of the 11-year cycle during the Maunder minimum, which decreases the signal-to-noise ratio in both records. Occasional periods of disagreement could hence indicate uncertainties in either record. Nevertheless, the 14 C record lends some support to the short-term variability in the group sunspot record during the Maunder minimum.

Conclusions
We presented an update of 10 Be and 14 C-based solar modulation reconstructions for the past 2000 years and a comparison to the revised sunspot records. We note that the difference in Greenland and Antarctic 10 Be data can lead to disagreeing conclusions about past solaractivity levels. This difference is most likely due to weather and climate influences on the records. 14 C is less strongly affected by such influences, but the 14 C-based solar modulation includes some additional uncertainty owing to the necessity to connect the data to the more uncertain pre-1950 extended neutron-monitor data. The 14 C and the Antarctic 10 Be data both lead to similar solar-activity reconstructions, while the Greenland 10 Be records show changes in recent centuries that are too large to be explained by solar modulation alone. In general, the sunspot and radionuclide records agree well. Especially the 14 C-based record agrees very well with the revised sunspot data, lending strong support to these revisions.