Introduction

Radiocarbon (14C) is produced in the Earth’s stratosphere/troposphere mostly by thermal neutrons captured by nitrogen nuclei. Thermal neutrons are produced by nuclear reactions of high-energy cosmic rays, originating mainly from galactic sources, or to a smaller extent, from the Sun. 14C oxidizes to CO2, and tropospheric CO2 is eventually stored in tree rings through CO2 fixation by photosynthesis during growing season. Rapid events producing 14C are eventually reflected in tropospheric or tree-ring 14C measurements as peaks with an abrupt increase and a long decrease of dozens of years caused by the exchange of 14C between the atmosphere and Earth’s carbon reservoirs. Such a 14C increase was recently observed in Japanese tree rings by Miyake et al.1 from AD 774 to AD 775 (henceforth ME meaning Miyake event), followed by similar observations throughout Northern Hemisphere (NH)2,3,4,5,6 and even in New Zealand7.

The shielding effect of the geomagnetic field against charged cosmic ray particles, i.e., the geomagnetic (vertical) cutoff rigidity (RC) is the highest near the equator and decreases towards the polar regions. Therefore, particles producing cosmogenic nuclei most easily penetrate into the atmosphere at high geomagnetic latitudes8. In addition to stratospheric production, a fraction of 14C can be formed in the troposphere allowing for rapid photosynthetic fixation.

The initial atmospheric 14C pool is affected by carbon cycle dynamics. In addition to vertical transport, horizontal transport of 14C within the atmosphere alters the local 14C pool sampled by the trees. However, remnants of the original polar production and its latitudinal dependence may still be observed in the 14C signal stored into tree rings by the photosynthetic assimilation, particularly due to tropospheric production of 14C. Indeed, such subtle latitudinal differences induced by the initial production and entangled with the carbon cycle dynamics have been observed by measuring the tree-ring 14C contents9,10. Assuming a solar origin for ME, and thus initial 14C production at polar latitudes, one may observe changes in the intensity of the anomaly according to the latitude.

Here, we report the measurement of annual 14C content of a Finnish Lapland tree during the ME, so far closest to the contemporary Geomagnetic North Pole (GNP). By utilizing a peak-fitting approach and complementing our results with previously published data, we find a latitudinal tendency in the event intensities, which is consistent with a solar origin. Furthermore, based on both carbon cycle modelling and additional earlywood (EW) and latewood (LW) 14C tree-ring measurements, we find that the event occurred probably during the spring of AD 774.

Results

14C intensities

For a strong Solar Particle Event (SPE), like that of 23 February 1956, the atmospheric production of 14C can be orders of magnitude larger in polar regions compared to tropical latitudes, with high RC’s (Fig. 1). Hence, we hypothesize that the 14C intensity induced by an ME has a latitudinal tendency if the event is of solar origin because RC governs the number of solar particles that enter the Earth’s atmosphere and the tropospheric production supports rapid photosynthetic fixation. The RC values, calculated using the recent archaeomagnetic model AF_M11 (see Methods), for the epoch of AD 775 provide insight into the initial 14C production rates according to locations (see Supplementary Table 1). The location of the GNP at AD 775 (GNPAD775) can be estimated to be north-east from Svalbard at approximately 82° N, 25° E. In the vicinity of the GNPAD775, the modelled RC approaches 0 GV, implying that even low-energy particles can impinge on the atmosphere. Suggested hard particle spectrum of ME12 would likely result in partial tropospheric production of 14C (see Methods).

Fig. 1
figure 1

Map of the study region. The colour codes show the latitudinal differences of 14C production rate (14C cm−2) for a typical strong SPE (such as 23 February 1956, the strongest directly observed event, Supplementary Table 2). The 14C production model36 is described in the Methods section. The red full circles with three-letter coding show the measurement locations for 14C intensities (see text). The cross illustrates the location of the Geomagnetic North Pole in AD 775

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The hypothesis is tested by evaluating the significance of the latitudinal trend of the available ME data through Pearson’s correlation. Our tree-ring material is derived from a precisely cross-dated 7600-year long Scots pine (Pinus sylvestris) record collected from Finnish Lapland13,14,15, in particular, from Lake Kompsiojärvi (68.5N, 28.1E; hereafter LAP). We complement our results with previously published and precisely cross-dated data from Yamal/Russia (67.5° N, 70.7° E; YAM)3, Poland (50.1° N, 20.1° E; POL)4, Germany (50° N, 9° E; GER)2, Altai/Russia (47.5° N, 87.5° E; ALT)5, Japan (30.4° N, 130° E; JAP)1, USA (38.3° N, 118.7° W; CAL13 and 36.5° N, 118.8° W; CAL26) and New Zealand (36.0° S, 173.8° E; NZL)7 to analyze the latitudinal behaviour. The LAP and YAM locations are within 15° of latitude from the GNPAD775. This close vicinity is reflected as low modelled vertical cutoff rigidities of RC, LAP, YAM ~ 0.1 GV. At the southern extreme of the locations (CAL1, CAL2, JAP), the values are very high (RC, CAL, JAP ~10 GV), which should yield drastically lower initial atmospheric production of 14C, particularly in these locations (Fig. 1). We utilize peak-fitting analysis to extract the full 14C intensities related to ME to acknowledge the temporal spread of tropospheric 14C increase into several years (see Methods).

We observe a clear increase of 14C content in subfossil tree rings from LAP (Fig. 2, Supplementary Table 3) corresponding to ME. Actually, the 14C content is increased already during AD 774—it differs 5.3σ from the averaged 14C background of AD 770–773. Interestingly, YAM also shows an increase during AD 774 with respect to its 14C background. This increase is not statistically different from LAP (p = 0.24, Student’s t-test) reflecting their small latitudinal separation. The deduced 14C intensities I14C (see Methods, Supplementary Table 1) as a function of latitude are shown in Fig. 3. Our null hypothesis of a constant I14C (slope = 0) as a function of latitude is rejected with a significance level of p = 0.002 (Student’s t-test). Thus, inarguably, there is a statistically significant latitudinal trend within the data. The relation between the latitude and 14C intensity is supported by the high correlation of r(lat, I14C) = 0.87. This latitudinal trend cannot be explained by a possible seasonal variation of the tropospheric 14C concentration nor by differing growing season lengths. Although some seasonal variation may occur after an instant injection of 14C into the atmosphere16, we found its role insignificant (see Supplementary Note 1). The observed trend is consistent with the higher production rate of 14C at high latitudes and its redistribution within the atmosphere towards lower latitudes and into other carbon reservoirs. This finding implies a polar enhancement of the cosmogenic signal, which is also experimentally known for 10Be in polar ice17. The enhancement is probably mediated partially by the direct tropospheric production of 14C. The polar enhancement shown here supports our hypothesis of a charged-particle-induced 14C increase.

Fig. 2
figure 2

14C measurements of the ME from multiple locations (see main text above for abbreviations). The horizontal axis represents the calendar year of the growing season, and the vertical axis represents the age-corrected and baseline-adjusted Δ14C (see Methods, Supplementary Table 3). The baseline adjustment has been performed for easier comparison of the data. The dashed red line shows an example of the analytical type I Gumbel distribution function (GDF) fit to the JAP data. Each measurement has a standard error of typically ±3‰ as visualized in the lower right corner. Original intensities, uncertainties and fitting procedure are as described in the Methods section

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Fig. 3
figure 3

Latitude vs. the 14C intensity I14C. The red line is a linear fit to the data. The uncertainties are based on error propagation and represent one standard error, and the dashed lines indicate the 95% confident intervals for the fit. The 14C intensities are obtained by fitting a GDF with each data set and by defining the I14C as an integral of this curve (see Methods). NH1 zone has been adopted from Hua et al.18. Differences in the 14C spatial distribution are manifested by distinct zones that span through both hemispheres, latitudes North of 40°N (NH1 zone) having the highest bomb-peak 14C intensities

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Interestingly, differences within the NH Zone 1 (NH1, Fig. 3) locations (LAP, YAM, POL, GER, ALT) are relatively small, although visible. However, there are larger differences between the intensities of NH1 and non-NH1 locations (JAP, CAL1, CAL2, NZL). In fact, we see statistically significant (p = 0.008, permutation test) difference between NH1 and non-NH1 zones (see Methods). This indicates similar atmospheric circulation patterns defining the 14C spatial distributions for ME as for the bomb peak induced by atmospheric nuclear detonations in NH, and probably reflects the locations in both sides of the tropospheric Ferrel cell–Hadley cell boundary18.

Origin of the event

The charged-particle flux cannot be due to Galactic Cosmic Rays (GCR) because they would not result in such a peaked 14C distribution19. This is due to perturbation of GCR by galactic magnetic fields during their travel to Earth causing dispersion and retardation. Moreover, GCR vary within the 11-year solar cycle due to the heliospheric modulation, which is too slow to produce a sharp peak. The observation also excludes the possibility of the increase being caused by supernova γ-rays1 or γ-ray bursts20,21 because they are not affected by the geomagnetic field and hence would not cause latitude-dependent effects. Furthermore, significant 10Be signal linked to the ME was found in both Greenland and Antarctic ice cores12,22. In addition, the observed I14C of NZL (Fig. 3) is consistent with bipolarity. Such bipolar effects should not occur if the isotope production was confined to only one of the hemispheres. Recently, a cometary impact was suggested to explain the anomaly23. However, a comet could explain the observed latitude effects only if it disintegrated near the GNPAD775. Even then, it should not cause any signal in 10Be. Moreover, due to the required massive size, the comet would have caused dramatic consequences to the biosphere and would not have gone unnoticed24.

Recent observations by the Kepler space telescope have shed light on the occurrence rate of these superflares on solar-like stars25,26. Maehara et al.27 analyzed the Kepler data with a high time resolution to also include shorter duration superflares. Their analysis suggests that the occurrence rate of solar flares with energies ranging from 1033 erg to 1034 erg are consistent with the ME. On the other hand, it is still unclear whether superflaring stars can be directly compared with the Sun28. The Sun’s relatively low magnetic activity around the time of the ME could be seen as problematic for the solar explanation29. However, Kilpua et al. recently found that the most extreme geomagnetic storms do not correlate well with the overall solar activity30. Hence, based on our observations and the above-described arguments, we suggest the Sun to be the cause of the event, in agreement with the recent study of Mekhaldi et al.12 using multiple cosmogenic nuclide records.

Timing of the event

Dynamics of 14C can be elucidated through atmospheric Brewer–Dobson circulation model. Stratospherically produced 14C intrudes into troposphere preferentially at mid-latitudes within residence times of 1–2 years whereas mixing of tropospherically produced 14C occurs within months31. Therefore, the latter may contribute to the observed signal immediately, whereas the assumed mid-latitude intrusion of air from stratosphere to troposphere takes place over in a longer time-scale in shaping up the observed 14C peak shape. Our adopted 11-box carbon cycle model (CCM, see Methods), accompanied with data on both growing season length and monthly thermal-time sums (TTS) (see Methods) to mimic the tree-ring 14C contents, allows us to reproduce the experimentally observed 14C peak shape generally with high correlation. Therefore, we argue that our CCM, although not containing the horizontal carbon cycle dynamics, provides us a reasonable tool to evaluate the event timing, motivated by the observation of 14C increase in LAP already at AD 774.

The LAP site is closest to the polar origin of the charged-particle induced 14C production. Furthermore, for P. sylvestris, carbon isotope signals of fresh photosynthates and tree-ring cellulose correlate strongly, indicating rapid transfer of atmospheric carbon into tree stem32. Therefore, Arctic trees of LAP are presumably able to rapidly record the assumed partial tropospheric production. In addition, the short growing season should sensitively probe the ME timing. We define the ME timing as the moment when the tropospherically produced 14C has oxidized to 14CO2 being thus available for photosynthesis (see Methods). We modelled the tropospheric 14C increases using different ME timings and compared those to the yearly data of LAP to obtain the best match. Based on Mekhaldi et al.12 and in line with Usoskin et al.2, we assumed a hard spectrum for the SPE with 70% of the 14C produced in the stratosphere and 30% in the troposphere (see Methods). The lowest residual sum of squares (RSS) between the measured and modelled data was observed assuming the ME timing during June/AD 774 (see Methods). Hence, a midsummer timing is implicated. Differing assumed tropopause height profiles can probably result in systematic shifts up to few months, particularly towards spring (see Supplementary Note 2).

The thermal growing season in LAP extends from May to September (see Methods). The EW to LW transition for P. sylvestris at these latitudes occurs typically around mid-July33, which is close to the ME timing indicated above. Therefore, assuming the ME timing around midsummer in AD 774, only the LW 14C content should be elevated in the cellulose formed in AD 774. We tested this hypothesis by EW–LW measurements (Fig. 4) to confirm the ME timing. As expected, both EW and LW data show the similar peak shape as the annual LAP data (Fig. 2), consistent also in magnitude. However, only LW shows a significant (7.1σ) increase of the 14C content in AD 774, in accord with our expectations. During AD 772, the EW ring width is exceptionally wide (Supplementary Table 3). Therefore, the annual 14C signal resembles that of EWAD772. Based on large EW/LW ring width ratio, similar mechanism may also be seen in AD 775. Differences between annual and EW/LW signals will be addressed in forthcoming papers based on stable isotopic and 14C analyses.

Fig. 4
figure 4

Early- and latewood 14C measurements of the ME. The horizontal axis represents the calendar year of the growing season, and the vertical axis represents the age-corrected Δ14C. To visualize the average temporal difference between early- and latewood growth, the data points are set to June and August, respectively, for each calendar year. The baseline is defined as the average 14C of AD 770–773. The uncertainties are based on 14C counting statistic and error propagation and they represent one standard error

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Based on above, the observed 14C increase in LWAD774 is consistent with our annual data and confirms our model-based result of the event timing. Altogether, observing elevated 14C content in LWAD774 and not observing it in EWAD774 confines the event timing probably to the advent of the boreal midsummer in AD 774. It allowed for the produced 14C to be photosynthetically fixed during the late growing season of P. sylvestris in Finnish Lapland. This NH observation is in contrast with the one from the Southern Hemisphere, for which an event timing of spring/AD 775 has been proposed7, but is in agreement with estimations based on 10Be data of AD 774 occurrence34. Taking into account the uncertainties in the tropopause height profile and the assumed average atmospheric oxidation time of 14C of 1–2 months35, the solar event itself occurred few months earlier.

Discussion

In summary, the ME has been observed in tree-rings of P. sylvestris from Finnish Lapland, so far closest to the GNP of AD 775. This has allowed us to demonstrate a latitudinal trend within the available data sets. By utilizing a peak-fitting approach, we find strong correlation between the latitude and determined 14C intensities. This is consistent with the assumed solar origin of the event. The timing is confirmed by sub-annual measurements of tree-ring cellulose showing anomalous increase of the 14C content in the LW of AD 774. This study illustrates the importance of trees growing near the boreal tree limit for storing information regarding both space weather and atmospheric circulation patterns.

Methods

14C production due to an SPE

The production of 14C was calculated using the new-generation model36, which simulates, using a full Monte-Carlo technique, nucleonic cascade induced by cosmic rays in the Earth’s atmosphere and yields a 3D distribution of the 14C production. The spectrum of energetic particles for the event was considered hard2,12. The geomagnetic field was considered according to the archaeomagnetic model by Licht et al.11.

As an estimate of the tropospheric production, we applied a flat mean tropopause at the height of 150 hPa (cf. Usoskin et al.2) and found that about 30% of polar 14C is produced in the troposphere, for a hard-spectrum SPE. We note that globally about half of 14C is produced in the troposphere for such event. However, the flat-troposphere assumption may not exactly hold for the polar region, where the tropopause is typically lower, at the 200–300 hPa barometric pressure level, leading to a lower tropospheric production. When applying a local height profile of the polar tropopause37,38, we found that the fraction of tropospheric production of 14C in the polar region is about 15%. Accordingly, we used this range as an uncertainty and translated it into the uncertainty of the event’s date derivation.

The map of the study region (Fig. 1) was created using Matlab R2016b software (https://www.mathworks.com/). Specifically, the RC values from Supplementary Fig. 1 and the respective 14C production values from Supplementary Table 2 were used to define the differently coloured regions. The GNP and the measurement locations are given in Supplementary Table 1. The data and the code to reproduce the figure can be obtained from the authors.

Estimation of vertical cutoff rigidities

Although the ME took place well before the era of direct geomagnetic measurements, we are able to assess the geomagnetic cutoff rigidities at different locations for the period relying on precise archaeomagnetic reconstructions. These are based on measurements of the archaeologically dated clay samples preserving the local magnetic intensity during the time of their firing. Since the eighth century was rich for archaeological artefacts, the quality of geomagnetic field reconstructions is reasonable for that period.

Here we use the AF_M archaeomagnetic reconstruction model11, which is provided as an ensemble of 1000 individual reconstructions of the geomagnetic field with a pseudo annual resolution. The ensemble naturally covers all the sources of uncertainties of the reconstruction (measurement errors, sample size, systematic errors, model uncertainties).

For each of the individual ensemble member reconstructions we calculated, for a given location, the geomagnetic cutoff rigidity RC, using the eccentric dipole approximation of the field, based on the first eight Gaussian spherical coefficients (see full details in the Appendix A of Usoskin et al.39). The mean RC, and its standard deviation, was finally calculated from the obtained 1000 values of individual RCs over the ensemble, as shown in Supplementary Table 1.

We choose the AF_M model because it provides a full ensemble to assess the error bars and the Gaussian coefficients, and this result is consistent, within the shown uncertainties, with the geomagnetic dipole moment provided by other recent archeomagnetic reconstructions for the period of AD 77536,40,41,42,43,44.

In the same way, we calculated a map of the RC values for the AD 775 epoch (Supplementary Fig. 1), using the mean RC values.

Tree-ring and radiocarbon analyses

A subfossil sample with well discernible rings over the study period was chosen for this analysis. The sample was tree-ring dated using statistical routines45 and visually by comparing the series of its ring widths against those of the master chronology14. The widths of the annual rings were on average 0.49 mm, with maximum and minimum widths of 0.73 and 0.37 mm, respectively. The sampling was done using a sterile surgical blade under the light microscope. No cross-contamination from one ring to the next was allowed by visual inspection. The separation of the EW and LW of the same calendar year was based on the intra-annual cellular characteristics discernible on the cross-sectional surface of the sample, generally following the established criteria46. In tree-ring laboratory, all the work to extract the isotope samples was done on cleaned sample surfaces to minimize any potential external contamination.

Tree-ring dated wood slivers were processed to α-cellulose using the batch-approach designed by Wieloch et al.47. The process consists of two alkaline extractions (5–7% NaOH), with a chlorination step (NaClO2) in between. The resulting α-cellulose was homogenized using an ultrasonic probe48 and freeze-dried. Pretreated samples were mixed with a stoichiometric excess of CuO and packed into quartz ampoules, which were evacuated and torch-sealed. The packed samples were combusted at 850 °C overnight. The released CO2 was collected and purified with liquid N2 and ethanol traps at −196 and −85 °C, respectively. The CO2 samples were converted to graphite targets49 for AMS radiocarbon measurements. AMS measurements were eventually performed at the University of Helsinki AMS facility50. The results are given as age-corrected Δ14C values51. For more detailed description of the analyses, see Helama et al.52.

Peak analysis procedure and fittings

Stratospheric mean residence times of 14C are typically 1–2 years. Therefore, it can be estimated that after, say 3 years, 5–22% of 14C remains still in stratosphere. Thus, stratosphere supplies new 14C into troposphere, and therefore for photosynthesis, several years after an abrupt event. Peak-fitting approach was chosen since it allows for quantifying the peak shape by taking into account all the available information, namely the data and its uncertainties, during the time span of this 14C supply. In addition, our approach takes into account the possible laboratory biases caused by slightly different pre-treatment procedures. These biases are typically systematic and could cause some differences in the observed baseline levels. Our method helps to mitigate this effect, since it takes into account the respective baseline of the data. Furthermore, the full peak shape contains also information on possible use of formed year photosynthetic storages.

We fitted a Type-1 Gumbel distribution function (GDF) to each of the data. The GDF has the following form:

$$y = y_0 + A{\mathrm{e}}^{\left( { - {\mathrm{e}}^{\left( { - \frac{{x - x_{\mathrm{c}}}}{w}} \right)} - \frac{{x - x_{\mathrm{c}}}}{w} + 1} \right)},$$
(1)

where y0 is the baseline level (also used when adjusting the peaks to zero baseline), A is the amplitude of the peak, xc is the time of the peak maximum and w is the width of the peak. GDF is normally used in extreme event statistics53 and its shape is characterized by a rapid rise and an exponential tail. Therefore, it is suitable for deducing intensities of rapidly increasing and slowly decreasing events occurring together with a relatively constant background, such as 14C intensity increase due to an SPE. Other distributions with similar shapes, such as Log-Normal and Exponentially Modified Gaussian that are often used in peak analysis54 were also considered, but GDF was found to be superior because of its overall convenience of use, simplicity of equation and property to not over-fit to statistical noise. Furthermore, GDF has been used before in peak analyses in a similar fashion to what is done here55. The GDF fit to each of the ME measurement can be seen in Supplementary Figs 3–10. Additionally, Supplementary Fig. 11 shows a GDF fit to a typical Δ14C profile due to instant injection of 14C into the atmosphere modelled by our adopted CCM.

To get the peak intensities, we analytically integrate the GDF in Eq. (1), which then becomes

$$y = {\int} {A{\mathrm{e}}^{\left( { - {\mathrm{e}}^{\left( { - \frac{{x - x_{\mathrm{c}}}}{w}} \right)} - \frac{{x - x_{\mathrm{c}}}}{w} + 1} \right)}} {\mathrm d}x = Aw{\mathrm{e}}^{\left( {1 - {\mathrm{e}}^{\left( {\frac{{x_{\mathrm{c}} - x}}{w}} \right)}} \right)} + C.$$
(2)

The interval used to calculate the integral for each of the data sets is bound to be from 770 to 779. The interval was chosen since it covers the event occurrence and the tropospheric near-event time distribution of 14C but not the long tail influenced merely by carbon cycle characteristics. Thus, the equation for the 14C intensity I14C becomes

$$I_{14{\mathrm{C}}} = \mathop {\smallint }\limits\int_{770}^{779} A{\mathrm{e}}^{\left( { - {\mathrm{e}}^{\left( { - \frac{{x - x_{\mathrm{c}}}}{w}} \right)} - \frac{{x - x_{\mathrm{c}}}}{w} + 1} \right)}{\mathrm d}x = Aw{\mathrm{e}}^{\left( {1 - {\mathrm{e}}^{\left( {\frac{{x_{\mathrm{c}} - 779}}{w}} \right)}} \right)} - Aw{\mathrm{e}}^{\left( {1 - {\mathrm{e}}^{\left( {\frac{{x_{\mathrm{c}} - 770}}{w}} \right)}} \right)}.$$
(3)

In addition, an error estimate σ of the I14C is calculated. This is done by propagating errors for the known values of A, xc, w and their standard errors in Eq. (3). The integrated 14C intensities can be seen in Supplementary Table 1.

To be confident on the capability of the peak-fitting method to capture the underlying 14C intensity, we tested our method by comparing simulated and peak-fitted peak sizes to the theoretically expected ones (Supplementary Fig. 2). The CCM provides a theoretically expected 14C intensity (red line in Supplementary Fig. 2) based on the underlying 14C production. The Monte Carlo simulation provides 14C peaks (105 runs) for each underlying 14C intensity by assuming 3% statistical measurement errors. These were peak-fitted individually to obtain simulated 14C intensities (open squares in Supplementary Fig. 2). This sensitivity analysis demonstrated that the peak-fitting method captures the underlying relative 14C intensities extremely well. Hence, the peak-fitting method can be considered robust.

14C intensities in NH1 and non-NH1 zones

Atmospheric 14C analyses based on bomb peak have demonstrated distinct zones of varying 14C contents within the NH18. These are related to the observed circulation cells within the atmosphere. Visually, the 14C intensities of NH1 and non-NH1 zones for ME seem to form two latitudinally separate groups (Fig. 3). We tested whether this difference is statistically meaningful. Because the individual 14C intensities do not necessarily follow a normal distribution, we could not use Student’s t-test or any other test that assumes normality. Hence, we used a resampling method to perform an exact significance test. Specifically, this was done as follows. First, we calculated the test statistic (e.g., difference of means) using groups NH1 and non-NH1. Second, we combined the values of NH1 and non-NH1 into a single pool. Third, we performed a Monte Carlo simulation (105 runs) where we randomly recombined these values into two groups with sizes of NH1 (5) and non-NH1 (4) groups. Fourth, we calculated the probability (p-value) of finding values more extreme than our test statistic. The above analysis was performed using both the “difference of means between group1 and group2” and the “sum of variances of group1 and group2” as test statistics. In both cases, the probability of finding value as extreme or more extreme than our test statistic is p = 0.008. This analysis shows it is unlikely that the observed 14C intensities of NH1 and non-NH1 groups originate from the same probability distribution, thus indicating latitudinal differences.

Carbon cycle model

We adopted a 11-box CCM from Güttler et al.7. Their model has an advantage of having a resolution of 1 month instead of 1 year used in most studies regarding the ME. Hence, it is especially suitable in assessing the timing of the event.

The carbon reservoir masses (a unit corresponds to 1012 kg) and the annual fluxes (1012 kg yr−1) between them can be seen in Supplementary Fig. 12. A mean atmospheric 14C production rate of 1.88 14C cm−2 s−1 atoms, which corresponds to an excess of 7.0 kg yr−1, was used to obtain the atmospheric 14C concentrations at around AD 775. In our model runs, we assume an event production rate of 83 14C cm−2 s−1 over 1 month totalling to 25.8 kg of 14C. Seventy percent of the total 14C production is assumed to have taken place in the stratosphere and 30% in the troposphere, which is also in line with Usoskin et al.2.

The model assumes that the 14C is in the form of 14CO2, which is not true immediately after the 14C production. Although 14CO is formed very rapidly, the mean oxidation time τ for 14CO is approximately 1–2 months35. Since oxidation is a statistical process, some 14CO molecules get oxidized almost immediately, whereas it takes a long time for all the molecules to be oxidized. The rate of oxidation can be calculated using the exponential decay equation \(N\left( t \right) = 1 - {\mathrm{e}}^{ - \frac{t}{\tau }}\), where t is the elapsed time and τ is the mean oxidation time. Assuming t = τ = 2 months, we find that \(1 - \frac{1}{{\mathrm{e}}}\) (~2/3) of the initially produced 14C has oxidized to 14CO2. Hence, we define our use of word timing to mean the moment, when \(1 - \frac{1}{\mathrm e}\) of the originally produced 14C has oxidized to 14CO2. In addition to being compatible with the model output, this definition is compatible with tree-ring measurements, since most of the original 14C is in a form that can be photosynthetically sampled by trees. However, it is noted that the non-zero mean oxidation time adds up to 2 months systematic uncertainty as to when the initial 14C production occurred.

Growing seasons and TTS

To estimate whether the climate around AD 775 was different from the modern era, we made a comparison between (a) the year AD 1959–2015 average TJuly (Finnish Meteorological Institute data, http://en.ilmatieteenlaitos.fi/open-data-manual) for Inari (68.9N, 27.0E) and (b) the tree-ring width-based reconstructed temperatures of Finnish Lapland during AD 750–80056. The averages were TJuly 1959–2015 = 13.7 ± 1.8 °C and TJuly, rec 750–800 = 13.1 ± 0.9 °C. These values are identical within the uncertainties. Thus, we assumed similarity of the climate and thus the growing seasons for the era of the ME and of modern times.

To mimic the actual tree growth mediated by photosynthetic assimilation during the growing season within our model, we took into account the average (AD 1959–2015 from Inari) TTS and weighted the monthly 14C concentration (given by the model) by monthly fractions of TTS to obtain the peak shape in tree rings. These values can be seen in Supplementary Fig. 13.

Timing of the event by carbon cycle modelling

To estimate the timeframe for the event occurrence, we analyzed the data of the northernmost location LAP in more detail. The adopted CCM reproduces reasonably well the observed individual 14C peak shapes (Supplementary Figs. 3–10). Moreover, we can reproduce the observed changes in the 14C intensities with the model. Therefore, we adopted the modelled peak shape also for comparison to estimate the timeframe of the event. We weighted the modelled tropospheric 14C content within the assumed growing season by monthly TTS to get an average 14C content of tree rings for each year (AD 770–779). These modelled data, assuming different occurrence times of the event with a monthly resolution, were then compared with the measured data to find the lowest RSS, which is defined as follows:

$${\mathrm{RSS}} = \mathop {\sum }\limits_{i = 1}^n \left( {y_{i} - f(x_{i})} \right)^2,$$
(4)

where yi is the measured Δ14C and f(xi) is the modelled Δ14C for each year through 770–779. These RSS values can be seen in Supplementary Fig. 14.

Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.