1. Introduction

Alterations and cyclic fluctuations in solar activity may be linked to periods of global warming and global cooling (Eddy, 1976; Jansen et al., 2007), extremes in weather and storm activity (Khare and Nigam 2006), and possibly even health and disease (Joseph and Wickramasinghe 2010; Wainwright et al., 2010). There is an association between reductions in sunspot activity and the development of little ice ages, as well as evidence indicating we may experience a new prolonged cycle of minimal sunspot activity.

Observational records of sunspot numbers date back to the early 17th century (Eddy, 1976), and proxy-based observations of solar activity before this time reveal quasi-periodic large-scale fluctuations in solar activity with a period of ~200 years (Stuiver & Quay, 1980; Usoskin, 2008, and references therein). These variations cause sporadic, prolonged minimal sunspot activity lasting between 30 and 150 years (Stuiver & Braziunas, 1989; Goslar, 2001; Usoskin et al., 2007). The most recent such events are the Dalton Minimum (AD 1795–1825) and the Maunder Minimum (AD 1645–1745), as recognized in the sunspot record from AD 1610 (Fig. 1).

These periods of minimal sunspot activity appear to be directly linked to previous periods of cooling world wide (Eddy, 1976; Jansen et al., 2007. Fig. 2 shows the record of a cosmogenic nuclide, carbon-14, in tree rings, which reflects the level of solar magnetic activity. These data support the occurrence of the two events identified from the sunspot record, as well as historical events that occurred prior to the 17th century including three little ice ages. However, the continuous record of carbon-14 in decadal tree rings, which is available back to ~11,000 BP (Stuiver & Braziunas, 1989; Stuiver et al., 1998; Reimer et al., 2004), suggests that the timing and duration of these solar events are somewhat irregular, and there exist millennial-scale periods without such events (Stuiver & Braziunas, 1989). However, the mean frequency of occurrence is about 200 years which correlates with periods of global cooling. For example, the four long-term intervals of minimal solar activity since the 13th century—the Wolf (AD 1282–1342), Spoerer (AD 1416–1534), Maunder (AD 1645–1715), and Dalton (AD 1795–1825) minima—correspond to the development of "Little Ice Ages" followed by periods of global warming. Although the geographical extent of the decrease in global mean temperature during this event remains debated (e.g., Jansen, 2007), these multi-centennial-scale variations in solar activity may in fact be a major cause of climate change (e.g., Eddy, 1976; Jansen et al., 2007, and the references therein).

Specifically, the "Little Ice Age" covers a cyclic period of cooling and glaciation which began in the 13th century and which continued into the 16th to 19th centuries, when glaciers began advancing southwards in Greenland and the North Atlantic, and perhaps worldwide. These episodes of global cooling appear to be linked to reduced solar activity. By contrast, the Medieval Warm Period occurred during a period of heightened solar activity. If these associations are valid, then future cyclic alterations would be expected to impact global temperatures including perhaps triggering another period of global cooling if sunspot activity is again reduced to a minimum.

The Sun is currently showing slightly different behavior compared with recent decades (Livingston & Penn, 2009). Consequently, concern has emerged regarding whether the Sun is approaching the next Maunder Minimum of reduced activity. Given this scenario, it has been suggested that global temperatures may decrease by about 0.3 °C as a result of a reduction in total solar irradiance (Feulner & Rahmstorf, 2010).

It is recognized, of course, that many factors can effect global temperatures, including the activity of microbes, humans, and stellar phenomenon. For example, climate change during the Little Ice Age, may have been directly impacted by galactic cosmic rays (Miyahara et al., 2008b, 2009). There is in fact considerable evidence indicating that global climate is effected by and correlated with decadal cycles in cosmic rays (Miyahara et al., 2008b, 2009). Specifically, it appears that climatic variability has been amplified by changes in the characteristics of solar magnetic activity (Miyahara et al., 2009). The amplification of decadal to multi-decadal climate variations may be one of several factors that contributed to the severity of climate change during the Little Ice Age. Therefore, it is prudent to consider the possibility that these and other stellar phenomenon may be impacting current global temperatures, or may do so in the future.

Given that any change in solar activity could have a great impact on modern society, it is important to establish a methodology for predicting near-future, long-term weakening or increases in solar activity as a component of forecasting possible near-future climate change.

The mean activity cycle of the Sun is ~11 years, although this is modulated by up to several years. The amplitude of these cycles, in terms of sunspot activity at cycle maxima, varies at multi-decadal to centennial time scales (Fig. 1). The possibility of a physical relation between length of the solar cycle and amplitude of the solar activity cycle has long been discussed, based on sunspot records (Clough, 1905; Solanki et al., 2002; Hathaway et al., 2003, 2004; Watari, 2008).

Detailed studies have revealed a possible connection between the length and amplitude of sunspot cycles. A lengthening of the solar cycle appears to precede intervals of weak sunspot activity (Solanki et al., 2002; Hathaway et al., 2003, 2004; Watari, 2008), although there seems to be a time lag of up to several cycles, which could also vary over time (Solanki et al., 2002).

2. The Present Study

In previous studies, we investigated the possible relationship between length of the solar cycle and solar activity, based on measurements of annual carbon-14 contents in tree rings (Miyahara et al., 2008b). Carbon-14 is produced by incident galactic cosmic rays and is absorbed by trees in the form of carbon dioxide; thus, its abundance in tree rings provides a record of solar magnetic activity. Given that tree rings provide a definite time scale, measurements of carbon-14 content in annually resolved tree rings enable reconstruction of the length of solar cycles with absolute ages. Using current technology, the standard statistical error of carbon-14 measurements by accelerator mass spectrometer is too large to determine the exact length of each 11-year solar cycle. However, precisely measured carbon-14 values show cyclic variations corresponding to solar cycles (Miyahara et al., 2008a), thereby providing information on shortening or lengthening of the solar cycle by several years. Frequency analyses of carbon-14 records back to ~1100 years ago have revealed that the length of the solar cycle is modulated within ~9–15 years and that there exists an inverse correlation between the mean length of the solar cycle and the level of long-term solar activity (Miyahara et al., 2008b).

The characteristics of previous grand solar minima have been studied based on carbon-14 content in tree rings with decadal resolution back to ~11,000 years ago. It has been suggested that intervals of prolonged sunspot absence may be categorized into three types: the Wolf, Maunder, and Spoerer types (Stuiver & Braziunas, 1989; Goslar, 2002; Usoskin et al., 2007), which have an overall mean duration of ~70 years (Usoskin et al., 2007). It seems that the Spoerer-type minimum, with a duration of more than 100 years, is the longest type, and is likely to differ in character from the shorter Wolf-type and Maunder-type minima, which have durations of between 30 and 90 years.

Our previous studies on solar cycles during the Maunder and Spoerer minima, based on carbon-14 records that extend back to AD 1413, indicate that the evolution of the solar cycle may differ for the different types of grand minima. In the case of the Maunder Minimum, the solar cycle displayed a largely stable increase to ~14 years during a 70-year interval of sunspot absence (Miyahara et al., 2004), whereas such an increase was not observed for the Spoerer Minimum (Miyahara et al., 2006). Only a slight extension and suppression of the solar cycle was detected in the frequency spectrum for the interval AD 1460–1500, which represents the middle part of the ~120-year event.

Beryllium-10 content in ice cores from Polar Regions also changes with variations in solar activity (Beer et al., 1998; Berggren et al., 2009). However, uncertainty exists in dating annual ice layers (although the uncertainly is probably as small as several years), meaning that ice samples are unsuitable for analyses of shortening/lengthening of the solar cycle by magnitudes of just several years.

3. Methods

To examine the possibility of empirical predictions of long-term weakening of solar activity, we extended our annual carbon-14 record back to AD 1374, thereby enabling a discussion on the detailed features of solar cycles around the onset of the Spoerer minimum as well as the Maunder minimum. Annual carbon-14 record for the Maunder Minimum has also been obtained by Stuiver et al. (1998) with higher precision. Accordingly, our measurements allow for the first time the comparisons of precursors among three grand solar minima with the different durations.

For this study, we analyzed a Japanese cedar tree from Yaku Island, Japan (130°N, 30°E). The annually separated tree rings were washed in solutions of hydrochloric acid (HCl) and sodium hydroxide (NaOH) before being combusted and converted into graphite for analysis using accelerator mass spectrometers housed at Nagoya University, Japan, and the University of Tokyo, Japan. Values of Delta ¹⁴C were obtained according to the calculation method proposed by Stuiver and Polach (1977). Since variations in carbon-14 content due to the 11-year cycle of galactic cosmic ray (GCR) intensity (which involves variations of ~30%) would be attenuated by a factor of ~90 in the carbon cycle (Siegenthaler & Beer 1988), high-precision measurements of carbon-14 content were conducted to achieve an accuracy of 0.3–0.4%. This accuracy enables the determination of solar cycle lengths with an error of ± ~1 year.

4. Results and Discussion

Fig. 3a shows the measured carbon-14 contents in annual tree rings. We had previously obtained data for the interval since AD 1413 (Miyahara et al., 2006); the new data cover the period AD 1374–1413. For re-measured and duplicated points, the data were averaged by weighting according to statistical significance. The dashed line in Fig. 3a shows the decadal carbon-14 content obtained based on analyses of trees from the Pacific Northwest of the United States and Canada (Stuiver et al., 1998).

There appears to be a slight offset between the carbon-14 contents in trees from Japan and those from the West Coast of the United States at around AD 1374–1415. The average carbon-14 contents in trees from Japan and the West Coast also deviate during the interval between the end of the Spoerer Minimum and the beginning of the Maunder Minimum (Miyahara et al., 2008a). Given that the timings of the deviations and the ~200-year solar cycle are similar among the two events, the offsets are probably due to a change in the carbon cycle; e.g., a change in oceanic circulation caused by climate change with a ~200-year period. The carbon-14 contents in trees from Japan are lower than those in trees from the West Coast for both events, suggesting that the effect of CO₂ emissions from the deep ocean, which has low carbon-14 concentrations, was more significant in Japan during the warmer phase of the ~200-year cycle. Despite the occurrence of such regional offsets of carbon-14 content at a centennial time scale, the decadal-scale variations of the two carbon-14 records are consistent with each other (Miyahara et al., 2007), and both records consistently show decadal solar cycles (for a comparison of carbon-14 data with sunspot numbers, see Miyahara et al., 2008a).

To examine the features of decadal variations in the carbon-14 record at around the Spoerer Minimum, we performed a frequency analysis using the S-transform (Stockwell et al., 1996), which is an advanced method related to the wavelet transform. Fig. 3b shows variations in the length of the 11-year solar cycle at around the onset of the Spoerer Minimum, which is defined as the time when sunspots started to disappear. The year of onset of this event has been estimated to be around AD 1416 (Stuiver & Quay, 1980). The spectrum outside of the black curve in Fig. 3b is less reliable due to inherent features of the wavelet analysis. The spectrum shows a continuous signal of decadal cycles at around AD 1390–1435, although with a period of ~13 years. The significance level of the signal for AD 1395–1435 is 3 sigma.

Fig. 3c shows the band-pass filtered carbon-14 record, filtered with a band width of 1–25 years (dashed line) and 10–25 years (solid line). These data indicate that the first solar cycle had started by around AD 1416, consistent with the estimation by Stuiver & Quay (1980). Note that the abundance of carbon-14 is inversely correlated with sunspot activity, and that the signals of the decadal cycles in carbon-14 are delayed by 2–3 years compared with the actual phase of solar cycles, due to the carbon cycle. This lag has not been corrected in Fig. 3. The frequency spectrum of our previous carbon-14 record for the Spoerer Minimum, which did not fully cover the event, showed no significant lengthening of the solar cycle (Miyahara et al., 2006). However, the spectrum of the extended record in Fig. 3b indicates a continuous lengthening of the solar cycle from around the beginning of the Spoerer Minimum, as also reported for the Maunder Minimum (Miyahara et al., 2004). In addition, the frequency spectrum shows that lengthening of the solar cycle had already started at around AD 1390, at least two cycles before the onset of the Spoerer Minimum.

Similar precursory lengthening of the solar cycle is also seen in the carbon-14 content for the Maunder Minimum (Fig. 4). For this event, Fig. 4 shows (a) sunspot activity from AD 1610 (Hoyt & Schatten 1998); (b) the carbon-14 content in tree rings, as determined by Stuiver et al. (1998); and (c) the frequency spectrum. The spectrum indicates that the length of the solar cycle was ~10 years at around AD 1600–1610 but subsequently increased to ~12–13 years, and was constant at ~14 years from AD 1660, during the Maunder Minimum. The signal of the solar cycle is extremely weak at around AD 1645–1655; however, the band-pass filtered carbon-14 record of our data (Miyahara et al., 2004) depicts decadal-scale variations during this period (Miyahara et al., 2007, 2009), in phase with variations in scarce sunspot data (Fig. 5).

A comparison of the sunspot record in Fig. 4a with the spectrum of the carbon-14 record in Fig. 4c suggests that the precursory feature starts with considerable sunspot numbers, at about two cycles ahead of the full onset of the prolonged sunspot absence at AD 1645. It should also be noted that the carbon-14 content in tree rings is already in the ascending phase during such precursory periods (Fig. 4b), indicating that the intensity of galactic cosmic rays had started to increase to some extent and that the solar poloidal magnetic field was in the weakening phase.

In the case of the Dalton Minimum, which is probably the faintest and shortest example of prolonged sunspot absence (Fig. 6), the preceding solar cycle is ~13–14 years, although only for a single cycle starting at around AD 1784. It has been suggested that this long cycle is in fact two short cycles (Usoskin et al., 2001a, 2009); however, reconstruction of the polarity of the solar dipole magnetic field back to the Maunder Minimum (Miyahara et al., 2005, 2008) (Fig. 5) indicates that the suggested additional cycle at late Solar Cycle 4 was unaccompanied by a magnetic reversal (see the discussion in Miyahara, 2009). Thus, this cycle is interpreted as a long, single cycle in terms of the solar magnetic cycle.

Records of carbon-14 content suggest that lengthening of one or more solar cycles is a common feature leading up to intervals of prolonged sunspot absence, although the exact features of these precursor events are likely to differ depending on the type of event, including the duration, magnitude, and evolution of solar activity, among other factors. We propose that the Spoerer and Maunder minima were preceded by at least two premonitory solar cycles, in contrast to the Dalton Minimum. The two consecutive lengthened cycles identified in this study have not been recognized in the sunspot or carbon-14 records from periods other than those around intervals of prolonged sunspot absence. Therefore, we speculate that such cycles are peculiar to these long-term events. Although the characteristic features of and differences between the precursors associated with the Maunder and Spoerer minima require further investigation, it could be suggested that smaller events are marked by shorter precursors.

There are a number of theoretical works trying to reproduce the grand solar minima such as the Maunder Minimum by either a simple model or the mean-field dynamo model (e.g. Wilmont-Smith et al., 2005; Charbonneau et al., 2004; Brandenburg & Spiegel, 2008; Choudhuri & Binay, 2009). One of the possible key parameters of solar dynamo that is related to solar cycle length is the speed of meridional circulation. Although the connections among meridional flow, solar poloidal field, and the sunspot activity need further investigations, our results suggests the beginning of a change in the meridional circulation two cycles ahead of the onset of prolonged sunspot absence.

The characteristic features of the evolution of the solar cycle during the Spoerer Minimum also require further analysis, although our carbon-14 record shows that the ~14 year (or less) period of the solar cycle during the initial decades of the Spoerer Minimum recovered to the normal state but again fell into a weak or lengthened phase. This finding may indicate that Spoerer-type minima, which have an unusually long duration of ~120 years, consist of two smaller events; e.g., a Maunder-type minimum followed by a faint event such as the Dalton minimum. This hypothesis is supported by the observation that the carbon-14 content in tree rings shows a plateau only in the case of the Spoerer Minimum.

5. Implications for the Near-Future Solar Activity

The minimum of the most recent solar cycle (onset of Solar Cycle 23) occurred in May 1996; hence, the onset of Solar Cycle 24 should have occurred at around mid-2007 according to the typical 11-year sunspot cycle. However, the number of sunspots was lowest in 2009, and the start of Solar Cycle 24 was delayed by about 2 years. Consequently, the length of the solar cycle has increased, as occurred during past grand solar minima. In addition, the intensity of solar wind observed by the Ulysses spacecraft in 2008 was the lowest of the past ~50 years (McComas et al., 2008), which is probably related to weakening of the solar polar field (Svalgaard et al., 2005). Likewise, the flux of cosmic rays in 2009 reached its highest level over the past ~50 years (see neutron monitoring data; e.g., from the Cosmic Ray Station of the University of Oulu in Finland (http://cosmicrays.oulu.fi/).

The above features indicate that solar activity is now at its lowest level of the satellite-based observational era of several decades, possibly even of the past century. However, our carbon-14 based observations do not indicate the imminent occurrence of the Maunder Minimum (i.e., sunspot disappearance lasting several decades), although there exists the possibility that the sunspot number at the next maximum in solar activity would approach the level during the Dalton Minimum. The likelihood of the imminent occurrence of the next long-lasting grand solar minima would increase if the next solar cycle (Solar Cycle 24) is lengthened by several years.

6. Conclusions

Tree rings provide a powerful tool in detecting past lengthening/shortening of the solar cycle. Carbon-14 in tree rings provides important information on past changes in the length of the 11-year solar cycle, thereby providing insight into the precursory features of intervals of prolonged sunspot absence. Our carbon-14 record, which extends back to before the Spoerer Minimum, suggests that the increased duration of at least two preceding solar cycles, as well as the cycles during the event itself, is a common feature of long-lasting intervals of sunspot disappearance such as the Maunder and Spoerer minima. The Dalton Minimum, which lasted for several decades, was preceded by only a single lengthened cycle. Accordingly, it could be suggested that the precursor events differ depending on the magnitude or duration of the interval of sunspot absence.

Further investigations based on precise measurements are needed to clarify the differences between the onsets of the Maunder and Spoerer minima. Such detailed analyses of carbon-14 content in tree rings would assist not only in constraining the solar dynamo model and in empirically predicting the next interval of prolonged sunspot absence, but also in forecasting changes in the near-space environment and in Earth’s climate. This is important because if the solar activity were to become reduced to levels comparable to the Maunder Minimum, our current episode of global warming could be followed by another Little Ice Age.

Acknowledgments: This work was supported by a Grant-in-Aid for Young Scientists (B), MOE (Global Environment Research Fund), and 21COE at Nagoya University.