We prepared a new piece of wood of the same individual as the one used in Miyake et al. (2012) and Miyake et al. (2013) (Figure 1 upper). The age of the Japanese cedar sample was confirmed using two independent dendrochronological methods to eliminate dating uncertainties. Particularly, the age of the sample was determined by 1) cross-dating of ring widths with a master chronology (ITRDB, https://www.ncdc.noaa.gov/paleo-search/study/15215) and 2) cross-dating of annual δ¹⁸O series with a master chronology (Nakatsuka et al., 2020; ITRDB, https://www.ncei.noaa.gov/access/paleo-search/study/28832). Recently, dendrochronology using oxygen isotopes has been rapidly advancing in Japan, and a master chronology of δ¹⁸O covering the 993 CE event has been established (Nakatsuka et al., 2020). For analyzing δ¹⁸O, a plate-shaped wood (∼1 mm thick) was prepared from the wood piece, and a series of celluloses were extracted via a chemical treatment (Kagawa et al., 2015). Each annual cellulose was wrapped in a silver foil, and the δ¹⁸O of the wood piece (256 rings) was measured using a mass spectrometer (TCEA/Delta V Advantage; ThermoFisher Scientific Bremen, Germany). The cross-dating was performed using PAST 5 software.

Cellulose for ¹⁴C analysis was extracted as described in Miyake et al. (2015) using the conventional method, that is, each annual ring was separated using a cutter knife before the chemical treatment, and each separated ring was processed with acid–alkali–acid and sodium chlorite treatments to obtain celluloses. We measured ¹⁴C concentrations in annual celluloses from 983 to 998 CE at the AMS facility at Yamagata University (YU-AMS, Tokanai et al., 2013). The years for 992, 993, 994, and 995 CE were measured twice to check reproducibility.

Previously, we obtained a good agreement in ring widths between the Japanese cedar sample and the master chronology of the Japanese cedar (tBP = 6.95 [Baillie–Pilcher t-value; Baillie and Pilcher, 1973]) (Miyake et al., 2014). In addition, the cross-dating using δ¹⁸O data showed a high correlation between the Japanese cedar sample and the master chronology (tBP = 6.17, Figure 2). As two different dating results show the same age, our sample age was highly reliable.

Figure 3A shows a measured result of ¹⁴C concentrations of the Japanese cedar sample. The duplicated data for 992–995 CE were reproduced within the errors. Figure 3B shows a comparison between the previous dataset (Miyake et al., 2013: ¹⁴C measurement was performed at the AMS in Nagoya University) and the new datasets of the Japanese cedar sample (for the duplicated data, weighted average considering the uncertainty of each data point was taken). Although the new data do not show an annual significant increase from 993 to 994 CE, the data, except for 990 CE, were reproduced well [not rejected at 95% confidence level by a chi-square test]. When the age of the rapid increase occurred in 992–993 CE, namely, the uncorrected version of the ring age reported in the first version of Miyake et al. (2013), the χ² value–evaluated difference between the previous and new data series was 21.5 (dof = 13), which was worse than that of the increase that occurred in 993–994 CE with the corrected age (χ² = 12.4, dof = 13). From this, the new dataset agrees well with the previous dataset whose age was corrected (i.e., when a significant increase occurred in 993–994 CE: Miyake et al., 2013; Miyake et al., 2014), and we confirmed the validity of the age correction in Miyake et al. (2013) and Miyake et al. (2014).

We took a weighted average for the new and previous data (Figure 3C). In the weighted average series, a significant gap between 993 and 994 CE and no significant increase between 992 and 993 CE were observed. The increment from 993 to 994 CE was 5.9‰ (average of the data errors: ∼1.2‰).

Available datasets for the 993 CE event are listed in Table 1. Table 1 shows radiocarbon zones for each tree sample too. Radiocarbon zones were originally introduced to explain ¹⁴C differences during the bomb peak, and have been defined as four regions in the northern hemisphere, that is, NH0, NH1, NH2, and NH3 zones (Hua et al., 2013, 2021; Büntgen et al., 2018). Boundaries of the radiocarbon zones were defined as 60°N between NH0 and NH1 (Büntgen et al., 2018), Ferrel cell–Hadley cell boundaries (around 40°N) between NH1 and NH2, and the mean summer position of the ITCZ between NH2 and NH3 (Hua et al., 2013; Hua et al., 2021). Figures 4A–C shows the Δ¹⁴C series in Table 1 for radiocarbon zones NH0, NH1, and NH2. Previous studies have reported offset trends in ¹⁴C data due to differences in radiocarbon zones, that is, Δ¹⁴C differences of radiocarbon zones NH2–NH0 and NH1–NH0 were observed at ∼3‰ and ∼2‰, respectively, around 774 CE, 993 CE, and 5410 BCE (Büntgen et al., 2018; Miyake et al., 2021). Figure 4D shows a comparison of the average series of Table 1 between different radiocarbon zones. The difference between the mean values of each radiocarbon zones is 2.8 ± 0.4‰ (NH2–NH0) and 1.2 ± 0.3 ‰ (NH1–NH0), respectively (the errors were calculated via error propagation). These offsets agree with the previous results, and basically, it is considered to reflect the difference in the baseline for each radiocarbon zone as described in previous studies (Büntgen et al., 2018; Miyake et al., 2021). However, the differences in 993 CE between each zone are particularly large.

These differences in 993 CE reflect the differences in the timing of increase, as mentioned in the introduction, that is, some series started to increase significantly from 993 to 994 CE including the Japanese cedar sample, or from 992 to 993 CE (Büntgen et al., 2018). Table 1 summarizes the ages when each series shows a significant increase in 992–993 CE and 993–994 CE. Focusing on the NH0 zone (four series) and NH2 zone (four series) in particular, the NH0 zone started to increase in 992–993 CE for all series (>2σ), whereas the NH2 zone started to increase in 993–994 CE in three series except the Qilian juniper (note that the Qilian juniper is a sample taken from 37°N and may be located near the NH1–NH2 boundary). The Japanese cedar series is consistent with the Douglas-fir series (USA07 in Figure 4C) which showed a different variation from the other series of Büntgen et al. (2018). The NH1 zone is not used to clarify the discussion because the NH1–NH2 boundaries may vary by longitude, that is, between 36°N and 42°N (Hua et al., 2013). Figure 5 shows a comparison of the average series of NH2 and NH0 zones (the Japanese cedar series is also shown for reference), where we assumed the baseline of each radiocarbon zone is the average of 990–992 CE and adjusted each average to zero on the vertical axis of Figure 5. In this comparison, the data series agree well within the error except for 993 CE. Such a precursor to the ¹⁴C increases at high latitude was also pointed out by Park et al. (2017) and Uusitalo et al. (2018) for the 774 CE event, that is, the Finnish Lapland and Yamal datasets from the NH0 zone show a significant increase from 773 to 774 CE, whereas lower latitudes data do not show the same.

Although differences in ¹⁴C concentrations with latitude have been discussed in previous studies, that is, the baseline offset of ¹⁴C concentrations (Büntgen et al., 2018) and the latitudinal dependence of ¹⁴C increase intensity during the event (Uusitalo et al., 2018), the difference of increase timing cannot be explained by these effects. Given that there is no large difference in tree growth between the NH0 and NH2 zones (e.g., June–August and May–September for the NH0 and NH2 zones, respectively: Büntgen et al., 2018), the timing difference in the ¹⁴C increase may reflect atmospheric transport. Originally, almost all ¹⁴C production by SEPs occurs at high latitudes (>60°) in the stratosphere, and a fraction of nuclide production in high latitude to the global is much higher for SEPs than galactic cosmic rays (Poluianov et al., 2016; Miyake et al., 2019a). Subsequently, ¹⁴C produced in the stratosphere is taken up by trees in the troposphere through the stratosphere–troposphere exchange (STE). Generally, it is considered that the STE dominantly occurred in the midlatitudes (e.g., 30–70°N: Stohl et al., 2003; Liang et al., 2009). If the observed difference in the timing of ¹⁴C increases reflects the effect of atmospheric transport, it would suggest that the STE of stratospheric high-latitude atmosphere occurs mainly in high latitudes (NH0 zone) and an atmosphere with a high ¹⁴C concentration is transported from high latitudes to low latitudes in the troposphere, or the STE in high latitudes (NH0) occurs earlier than that in low latitudes (NH2).

Carbon cycle box models used in the past are unsuitable for discussing atmospheric transport as the box of the atmosphere is only divided into the stratosphere and troposphere (e.g., Güttler et al., 2015). Therefore, the development of a three-dimensional transport model and using it for evaluation will be crucial in the future. However, the ¹⁴C data of 993 CE show a significant difference between NH0 and NH2 zones. This can be explained by a few months’ delay (<∼half a year) of the NH2 zone with respect to the NH0 zone because an occurrence of the SEP event of 993 CE was estimated in April 993 CE using ¹⁴C data of tree samples in both hemispheres (Büntgen et al., 2018), and trees finish carbon fixation in around September. Considering that it takes up to 6 months for the hemispheric troposphere to become uniform (Miyake et al., 2019a), the few months’ delay is considered a reasonable explanation.

As described, most differences in the timing of the increase in reported ¹⁴C data may be explained by such an atmospheric transport effect. However, from the timescale that the hemisphere becomes uniform (∼6 months: Miyake et al., 2019a), the ¹⁴C concentration should be increased in 994 CE, which cannot explain the low concentration of the earlywood of the Danish oak in 994 CE (Fogtmann-Schltz et al., 2017). This may be explained by the characteristics of the tree species. Most data in Table 1 are conifers; in addition, three series used hard woods (Danish oak and English oak: Fogtmann-Schltz et al., 2017; Rakowski et al., 2018; Brehm et al., 2021). The earlywood formation in deciduous broad-leaved trees with ring-porous wood begins before bud burst and is completed before the leaves are fully expanded (Ladefoged 1952; Kozlowski 1992; Catesson and Lachaud 1993; Pilcher 1995). Such earlywood formation originated from the stored carbon (before the previous year) and has also been shown by isotope analysis (Helle and Schleser, 2004). Earlywood data of the Danish oak series may also show such a difference in the carbon fixation time. Further studies on tree species and the fixation time of carbon will be required. Although we considered a simple delay effect due to atmospheric transport above, a dilution effect of the ocean may differ from region to region even if the latitude is the same (i.e., the closer to the ocean, the more affected by the ocean with a low ¹⁴C concentration: e.g., Nakamura et al., 2013). For example, in a comparison of the Qilian juniper (inland in China) and Asunaro (Japan: close to the ocean), which are located around the NH1–NH2 boundary, the Qilian juniper shows a ¹⁴C increase from 992 to 993 (relatively sharp change); on the other hand, the Asunaro shows a gradual change. In the future, it will be necessary to consider each of these factors affecting ¹⁴C concentrations in tree rings.

The 993 CE event was detected as a significant ¹⁴C increase in most trees and can be dated by ¹⁴C spike matching. However, as mentioned above, there are differences in the absolute value and timing of an increase in ¹⁴C concentration depending on the region (or tree species) of using the tree sample, namely, a 1-year age-determination error may occur in the case of the spike matching using the 993 CE event. Therefore, it is crucial to understand and apply the regional characteristics of the trees used for dating. That said, the 993 CE spikes can be dated in ±1 year, so it is definitely a breakthrough compared with conventional radiocarbon dating.