Transient Offset in 14 C After the Carrington Event Recorded by Polar Tree Rings

The Carrington event of 1859 has been the strongest solar flare in the observational history. It plays a crucial role in shedding light on the frequency and impacts of the past and future Solar Energetic Particle (SEP) events on human societies. We address the impact of the Carrington event by measuring tree‐ring 14 C with multiple replications from high‐latitude locations around the event and by comparing them with mid‐ latitude measurements. A transient offset in 14 C following the event is observed with high statistical significance. Our state‐of‐the‐art 14 C production and transport model does not reproduce the observational finding, suggesting features beyond present understanding. Particularly, our observation would require partially fast transport


Introduction
The assumption of geographically coherent atmospheric 14 C concentrations forms the basis for the radiocarbon dating method.Although this assumption is considered generally true, there is an ongoing discussion regarding the potential existence of zonal gradients or regional offsets in the measured concentrations.For example, the Northern/Southern Hemisphere 14 C offset is well known (Hogg et al., 2002;McCormac et al., 1998).In addition, examples of possible intra-hemispheric offsets have been reported in the past (Stuiver et al., 1998a) as well as more recently (Pearson et al., 2020).Such effects are hypothesized to reflect the changes in the long-term atmospheric or oceanic circulation patterns or be linked to latitude effects due to different growing period conditions (Kromer et al., 2001).A common challenge in studying regional offsets is that the observed differences are often at the level of the measurement uncertainties (Bayliss et al., 2020).
In addition to such long-term and large-scale phenomena, attention has recently been given to rapid and anomalous 14 C events discovered by Miyake et al. (2012Miyake et al. ( , 2013)).The initial finding sparked considerable interest, leading to additional discoveries of rapid 14 C increases, all found through annually resolved tree-ring measurements (e.g., Bard et al., 2023;Brehm et al., 2022;Miyake et al., 2017Miyake et al., , 2021;;O'Hare et al., 2019;Paleari et al., 2022;Park et al., 2017;Terrasi et al., 2020).These events are short production increases in 14 C caused by extreme solar energetic particle (SEP) events (Cliver et al., 2022;Usoskin, 2023;Usoskin et al., 2013).The results have initiated discussions of possible latitudinal differences in 14 C atmospheric concentrations.For example, Uusitalo et al. (2018) found that the intensity of the 774 CE event measured at high-latitude Northern locations (henceforth denoted as Northern Hemisphere 1, NH1) was significantly higher than that measured at lower latitudes.Furthermore, a signal increase already in 774 CE was demonstrated by intra-annual tree-ring measurements.Similar latitude-related differences were also observed recently for the 993 CE 14 C anomaly (Miyake et al., 2022).These changes were suggested to result from the atmospheric 14 C production limited to the polar stratosphere and the stratosphere-troposphere dynamics.Recently, Zhang et al. (2022) proposed that the statistical significance of the latitudinal gradient of the 14 C signal may disappear with a larger number of sites analyzed.In their analysis, they also observed distinct patterns in the peak shapes of the 14 C anomaly event across different locations, with some exhibiting sharp increases, while others demonstrated more gradual increases over several years.Such peak shape differences probably emphasize the role of the varying stratosphere-troposphere dynamics in shaping the observed event.
However, previous studies were based on simplified box models of the carbon cycle (e.g., Büntgen et al., 2018;Güttler et al., 2015;Oeschger et al., 1975) which by design can catch neither the latitudinal/regional differences nor precise intra-annual timescales.Moreover, none of the previous studies have detected signals in cosmogenic nuclides data around the Carrington flare, the greatest solar flare observed in the last two centuries (e.g., Cliver & Dietrich, 2013;Curto et al., 2016;Hayakawa et al., 2023).
Here, we further advance studies on the regional patterns of the atmospheric 14 C content by applying precise measurements and a novel direct modeling of the radiocarbon atmospheric production and transport.Particularly, we study high-latitude tree-ring 14 C intensities across the Carrington event.As a main result, we report on a statistically separable transient offset of 14 C measured in high-latitude tree rings as compared to lower-latitude locations.This offset lasted for several years after the Carrington flare of 1859.We discuss the potential origin of the disparity by considering possible solar and geomagnetic effects as well as the complex atmospheric dynamics.The finding opens new possibilities in studies of the fine structure of the past 14 C records and solar and geomagnetic phenomena within the present era of increasing numbers of annually resolved measurements.

Measurements and Other Data
The sample set contains new measurements of Δ 14 C in tree-ring material of three individual trees (Pinus sylvestris) from three distinct locations in northern Finland (Inari, Värriö, and Hetta -see Table 1 and Figure S1 in Supporting Information S1).Dendrochronological analyses and extraction of annually resolved tree-ring samples were performed by the Natural Resources Institute Finland.The samples were processed to cellulose and decay-corrected Δ 14 C values were measured by the Laboratory of Chronology/University of Helsinki (Uusitalo et al., 2022), Yamagata University (Takeyama et al., 2023) and IonBeam Lab/ETH Zurich  (Sookdeo et al., 2020;Wacker et al., 2010) as specified in Supplementary Table S1.The sample set comprises a total of 116 measurements spanning the years 1854-1870.We hereby discuss these as high-latitude data.
In addition, the analyzed data set includes data (see Table 1) from Washington (USA), Mapledurham (UK) and Sydenham House (UK), all spanning through the Carrington event period.We define these as mid-latitude data.Furthermore, for comparing the statistical significance of annual tree-ring 14 C differences between high-and midlatitude measurements, we also used data from Friedrich et al. (2019), which covers the period 382-460 CE.

Mean Calculation and Statistical Comparisons
The yearly mean 14 C values and their uncertainties for both the high-and mid-latitude zones were calculated through Monte Carlo simulation.Specifically, for each year, a mean value is calculated by simulating new values based on the errors of the individual 14 C measurements and then calculating the average of those simulated values.The previous step is repeated 100,000 times for each year.The final mean estimate and the uncertainty for each year is calculated by taking the average and standard deviation of the simulated values.The described Monte Carlo method propagates the measurement uncertainties, with the mean being derived from the observed dispersion.We note that calculated uncertainty estimates do not account for the potential over-dispersion, meaning that the final error is derived from the measurement uncertainties only.This is a well-recognized challenge facing all tree-ring-based 14 C measurements (Heaton et al., 2020;Scott et al., 2023).Our aim with the numerous replications spanning different locations, trees and measurement protocols, has been to shed light on this potential variability beyond measurement uncertainties.To further mitigate the potential effects of overdispersion, we calculated centered 3-year moving averages for both the high-and mid-latitude data sets.The moving average gives robust estimates for the central tendencies of both the high-and mid-latitude data.The centered 3-year moving averages are calculated using a similar Monte Carlo simulation approach as for the annual means.In this case, measurements within a 3-year window are combined (e.g., for the year 1855, values from 1854 to 1856 are used).The procedure is then carried out for years 1855-1869.Finally, We assess the potential presence of outliers in the annual high latitude data with the Grubbs test (Grubbs, 1969).For statistical comparisons between data sets, we use the Z-test to be consistent with the past International Radiocarbon Intercomparison studies (Scott et al., 2018) and measurements of Friedrich et al. (2019).

Modeling of 14 C Production and Transport
For this study, the production of 14 C was computed using the CRAC (Cosmic-Ray Atmospheric Cascade) model (Poluianov et al., 2016), which is the most recent and precise model of cosmogenic isotope production.Because we do not know the real energy spectrum of the Carrington event we use a hard spectrum of the second strongest and best studied SEP event of 20-Jan-2005 (GLE #69 -see http://gle.oulu.fi)computed by Koldobskiy et al. (2021).The corresponding isotope production rates were used as input parameters for the Chemical Climate Model (CCM) SOCOL-AERv2 (Chemistry-Climate Model SOlar Climate Ozone Links with AERosol module Version 2) (Feinberg et al., 2019).This model version consists of the general circulation model MA-ECHAM5 (Hommel et al., 2011) and the atmospheric chemistry module MEZON (Egorova et al., 2003), which interact with each other every two modeling hours.The CCM SOCOL-AERv2 was extended with the Carbon 14 module, as was done previously for Beryllium 7 (Golubenko et al., 2021).The exchange between different carbon reservoirs is represented through differential fluxes, and the exchange coefficients were adopted from box models (Fairhall & Young, 1985;Güttler et al., 2015;Oeschger et al., 1975), namely 7.3 and 1.8 years for the ocean and land, respectively.Carbon sinks are implemented through decay times and are dependent on the surface type (ocean or land).Depending on latitude, 14 C sinks into the land in different seasons: throughout the year in equatorial latitudes (0-30°), from April to October in middle latitudes (30-55°), from May to September in pre-polar latitudes (55-65°), and there is no sinking in polar latitudes (65-90°).The sinking into the ocean occurs throughout the year in all latitudes.More details on the model based on (Fairhall & Young, 1985;Güttler et al., 2015;Oeschger et al., 1975;Stenke et al., 2013) can be found in the Text S1 in Supporting Information S1.

Results
Data of the annually averaged Δ 14 C in high-and mid-latitude zones are depicted in Figure 1.As seen in Figure 1a, there is a systematic and statistically significant difference between the high-and mid-latitude measurements from 1861 to -1863, such that the 14 C contents measured in tree rings from northern Finland are enhanced by a few permil compared to those in the mid-latitude region.Figures 1b and 1d show all the individual measurements partitioned by the different measurement laboratories.The individual measurements display noticeable variance, attributable to measurement uncertainties, but possibly also to factors such as varying locations, tree species, and laboratory procedures.All the panels show increased values compared to the mid-latitude means around the years 1861-1863, with the tree from Hetta (panel d) showing somewhat increased values already before.The general central tendency of the difference between high-and mid-latitude data is clearer when comparing the 3-year moving averages as indicated by the bottom curve in Figure 1a.The difference has an offset of ca. 1 permil, increases to 3.5 permil ca.1862 and then gradually decreases, forming a distinct peak shape.The offset is also present in each of the individual laboratory comparisons, as illustrated in the bottom parts of Figures 1b and 1d: HEL, ETH and YU measurements reach peak offsets of 6.0, 3.1 and 3.6 permil, respectively, around years 1862-1863.1 and Methods).Each annual point includes 5-8 measurements (see Table S1).The red circles depict the mean annual values for the mid-latitude dataset.Each point includes three (for years 1855-1866) or two measurements.Uncertainties correspond to one standard error.The black and the red lines denote the 3-year moving averages of the high-and mid-latitude datasets, respectively.The bottom part of each panel shows the difference between the 3-year moving average curves, with the y-scale for this section on the right side.Panels (b)-(d) show the individual measurements of the high-latitude data versus mid-latitude average from different trees and laboratories, as detailed in Table 1 and Supplementary Table S1.For clarity, all data points are aligned with full years, though the actual growing periods are approximated to mid-year.
The statistical significance of the difference between high-and mid-latitude annual data at the time around the Carrington flare is further explored in Figure 2a.The difference appears systematic and highly significant (pvalue is below 0.01) for the years 1862 and 1863, and significant (p < 0.05) for the year 1861.For all other analyzed years, the difference is insignificant (p > 0.05) except for years 1856 and 1859 when the difference is significant (p ≈ 0.02).With regards to p-values, it is important to note that they are calculated based on the annual mean values and their standard errors, which are propagated from the individual measurement errors.Although this is a common practice, the final uncertainty may not fully represent the underlying distribution, thereby possibly affecting the individual p-value comparisons.Hence, it is better to look at the overall behavior, rather than individual points.The fact that the p-value is low on multiple adjacent points strengthens the interpretation that the difference is real and not a statistical anomaly.Furthermore, based on the two-sided Grubbs test (see Methods), the high-latitude measurements show internal consistency with no significant outliers at the p = 0.05 level, apart from years 1854 and 1864.For 1864, the apparent outlier results from low variance and fewer measurements, with four out of five falling within 1 permil.The measurement identified as an outlier is 1.7 permil above that year's average, a normal fluctuation within single measurements.In 1854, an outlier is detected as 6.3 permil below the average.However, we retained this outlier in the analysis as it did not occur during key years and does not affect the interpretation of the results.Finally, although the high-latitude measurements are consistent as a group, there are occasional differences in pair-wise comparisons between laboratories.Furthermore, the HEL measurements display a more pronounced offset.To assess whether the offset is influenced by extremities, we have performed sensitivity analyses where, for each year in the high-latitude data, the value furthest from the mean is excluded, and as a separate test where both extremes (min-max) are excluded.We found that the 14 C difference remained essentially unchanged (see Figure S2 in Supporting Information S1).Furthermore, the transient offset persists even if the HEL measurements are excluded altogether from the comparison (see Figure S3 in Supporting Information S1).In addition, we have calculated the 3-year moving median of the high-latitude data and its difference from the mid-latitude data.As the median is the value in the middle of the data set, it is not sensitive to extreme values.The resulting graph (see Figure S2 in Supporting Information S1) of the difference is essentially the same as the one calculated using the moving means shown in Figure 1a.This consistency between the two methods reinforces our observation that the transient offset is robust against the influence of individual values.
Although the difference is statistically significant, it may potentially arise from a general bias between the highand mid-latitude 14 C concentrations or incorrectly estimated natural variability inherent to each latitude zone.To test this, we performed a similar comparison between high-and mid-latitude 14 C data (Friedrich et al., 2019) spanning years 382-460 CE (Figure 2b).As seen, none of the 79 points appears significant at p < 0.05 level suggesting that annual differences as significant as those observed after the Carrington flare are not common among measurements with similar latitude profiles.However, to our knowledge, the annual data is not comprised of as many and as varied measurements as in our comparison, leading to larger uncertainties in estimation of the mean.This is further demonstrated in Figures 2c and 2d, which show the absolute difference for the Carrington and 382-460 periods, respectively.From the comparison, the latter clearly exhibits more variance.Although the data shows occasional diversions being as large or even larger than during the Carrington period, they appear to be more random in nature, as demonstrated by their scatter on both sides of the baseline.On the other hand, the Carrington era difference shows remarkable stability, with most values residing on the baseline, except for the years 1861-1864.In summary, the data of Friedrich et al. does not show evidence for excursions like what is observed around the Carrington event.However, the existence of such transient differences cannot be completely ruled out, as the annual sample size of Friedrich et al.'s measurements may not be sufficiently large to provide the necessary statistical power.

Discussion
We show that a statistically significant difference exists between 14 C abundances at high-and mid-latitude following the Carrington flare.The found divergence is a short-term (several years) transient phenomenon and appears distinct from more persistent offsets due to geographical growth-period differences (Stuiver & Braziunas, 1998).Independent measurements of the samples by multiple laboratories make the results robust against possible biases related to statistics or measurement processes, an issue typically affecting annual 14 C comparisons.Below we discuss the potential origin of the observed difference by considering geomagnetic effects, the Carrington event, atmospheric circulations and the solar cycle.
The years around the Carrington event -and during the solar cycle 10 -were geomagnetically unusually active.The Helsinki magnetic observatory measured enhanced numbers of geomagnetic storm days around 1860-1866 and auroral intensities were similarly elevated (Nevanlinna & Kataja, 1993).Moreover, the wandering of the north magnetic pole (https://www.ngdc.noaa.gov/geomag/data/poles/NP.xy) changed its direction around 1860 and similar phenomena occurred in 1730 (Kovalyov, 2019).The increased and dynamic activity is also demonstrated by geomagnetic jerks observed around those years (e.g., 1861/1870; 1730/1741) (Alexandrescu et al., 1997;Korte et al., 2009).Interestingly, these geomagnetic jerks essentially coincide with the historically observed geomagnetic storms induced by the Carrington flare and that of the year 1730 (Hayakawa et al., 2018).These simultaneous phenomena may indicate a solar-terrestrial connection within the dynamic development of the geomagnetic field.
However, the Carrington event itself has been considered one of the most significant geomagnetic storms.Whereas the model discussed here assumes a constant eccentric-dipole geomagnetic field during the period in question, the Carrington flare induced an extreme geomagnetic disturbance of the Disturbance H variations of 917 to 989 nT according to the Colaba magnetometer (Hayakawa et al., 2022).Considering the Colaba magnetogram data for the September 1-2 storm, the decrease in the horizontal geomagnetic field seems small.
Averaging over the full year, the decrease of the geomagnetic field strength was still less than 1% of the full horizontal field strength.Moreover, the observed latitudinal gradient is difficult to conceive due to such a global geomagnetic field disturbance.Thus, we consider the contemporary GM field change to be of minor importance in our observation.
Although no definite quantitative explanations can be given to the observed excess of high-latitude 14 C atmospheric abundances over the mid-latitude ones in the early 1860s, some qualitative understanding can be proposed.Given the concurrent timing, the first idea would be that the observed 14 C polar enhancement was caused by a solar energetic particle (SEP) event associated with the Carrington flare, since 14 C production by SEPs mostly occurs at higher latitudes (Golubenko et al., 2022).To check this idea, we utilized a CCM SOCOL (see Methods) to determine whether the observed divergence could be explained in the model's framework.However, according to the model simulations made assuming a constant geomagnetic dipole field and the hard energy spectrum of the strong SEP event of 20-Jan-2005 (GLE #69), we were unable to reproduce the observation of enhanced tropospheric 14 C content at high latitudes (see Figure S4 and Text S1 in Supporting Information S1).Thus, the statistically significant polar enhancement needs further explanation beyond the used model assumptions.
This enhancement took place a few years after the Carrington flare in September 1859.The flare magnitude has been indirectly estimated as ≈X64.4 ± 7.2 (≈5 × 10 32 erg of bolometric energy) from the magnitude of the geomagnetic crochet (solar-flare effect) (Cliver et al., 2022).Recent assessments have revised the magnitude estimate even upward ≈X80 (X46-X126) and ≈(5.77 ± 2.89) × 10 32 erg on the basis of areas of white-light flaring regions, flare duration, and brightness descriptions (Hayakawa et al., 2023).This means that the Carrington flare was more intense than the most intense solar flares in observational history.Moreover, the auroral reports indicate a precursor solar flare with significant intensity in late August 1859 (Cliver & Dietrich, 2013;Hayakawa et al., 2019).As such, the upward revision for the Carrington flare and the presence of the August flare are rather supportive for an expectation of an extreme SEP event causing Δ 14 C enhancements in the Arctic tree rings.In addition, a total solar eclipse on 18 July 1860 allowed contemporaneous astronomers to witness the earliest coronal mass ejection in observational history (Eddy, 1974;Hayakawa et al., 2021).This probable interplanetary coronal mass ejection launched from the southwestern quadrant of the solar disk which is favorable for a geoeffective SEP event.This may have contributed to the observation, although we need to be cautious not to overinterpret the associations of the indirectly observed flares with the Δ 14 C enhancements.Particularly, the enhancement observed in tree-rings would require mostly stratospheric 14 C excess to be transported to ground level for photosynthetic fixation.
According to atmospheric ozone tracking studies, the injection of stratospheric air into the troposphere occurs primarily as the stratospheric-tropospheric exchange (STE) during the spring season at latitudes between 40 and -80°N, with 19-33% of air mass exchange taking place at latitudes above 70°N (Liang et al., 2009).The atmospheric Brewer-Dobson circulation is typically referred to in relation to the 14 C tree-ring studies as the main mechanism behind the global STE.Although this circulation controls the downwelling of air into the lower stratosphere, the air exchange across the tropopause occurs through smaller scale processes, such as tropopause folds near the jet streams (Rao & Kirkwood, 2005), especially at mid-latitudes.Significant STE also occurs at the high Arctic latitudes of around 70°N, often referred to as the "Arctic Front" (Dibb et al., 1992(Dibb et al., , 1994(Dibb et al., , 2003;;Shapiro et al., 1987).This region is zonally close to the high-latitude region where our analyzed trees grew.Furthermore, according to a recent stratospheric ozone intrusion study with measurements from North American locations, there is a tendency for larger stratospheric contributions to the middle and upper tropospheric layers for latitudes north of 60°N compared to lower latitude zones, likely because the Arctic tropopause resides at lower altitudes compared to the more southern latitudes (Tarasick et al., 2019).
The above-described fast Arctic STE has potentially gained supporting evidence from recent studies of SEP events of 774 and 993 CE.A fast rise of 14 C level in high-latitude trees in Finnish Lapland (Uusitalo et al., 2018) and Yamal (Jull et al., 2014) has been observed in 774 CE.Furthermore, an early elevated signal in high-latitude trees has been observed in 993 CE (Miyake et al., 2022).Such observations cannot be understood assuming that atmospheric 14 C transport occurs solely through mid-latitudes, unless production occurred near ground levels at high latitudes.In fact, considering the 993 CE event, it is puzzling why there is no increase at all in the mean values of the low latitude zone (NH2) for the year 993 CE, as opposed to the more northern locations of NH1 and particularly of NH0 (Figure 4d of Miyake et al., 2022).All the above indicate fast high-latitude transport of stratospheric air to troposphere consistent with Liang et al. (2009).
Eventually, the peak maxima are reached 2-3 years after the 774 and 993 CE events.We note a similarity with our observed divergence, where the difference forms a trend that keeps increasing and peaks 3 years after the event.For all the events, the stratosphere appears injecting 14 C to the high-latitude troposphere for several years after the event.Thereby, we consider the possibility that the underlying mechanism for the observed divergence may share similarities to those suggested for the 774 and 993 CE events.Namely that part of the initial Arctic stratospheric/ upper tropospheric 14 C excess transports relatively quickly to the ground level at high latitudes and gets fixated to the trees before the signal gets diluted by the greater atmospheric volumes in mid-and low-latitude regions.Only later, after a more complete stratospheric mixing, would the tropospheric concentrations be dominated by the mid-and high-latitude air injections.Meanwhile, the midlatitude 14 C, with larger air masses, would be dominated by changes in galactic cosmic ray (GCR) intensity caused by the Schwabe cycle (Golubenko et al., 2022), leading to decreasing concentrations.Those decreases would be countered by the Carrington event excess in the highlatitude trees thus forming the observed divergence.
Furthermore, we note that to make this hypothesis feasible, the Arctic upper atmosphere needs to be isolated long enough to allow for the 14 C excess to affect the troposphere for a few years before fully mixing with the larger stratosphere.Similar behavior has indeed been observed before, following the Soviet nuclear bomb tests at Novaya Zemlya (73°N) that injected huge amounts of 14 C into the Arctic stratosphere during 1961/1962.After the largest detonations, it took several years for the stratospheric concentrations to get well mixed, with the Arctic stratosphere demonstrating larger concentrations altitude-wise compared to the more southern regions (see Figure 33 and onwards in Telegadas, 1971).However, we note that in general, the 14 C bomb peak proves suboptimal as an analog for the Carrington event and the subsequent tropospheric excess, due to the diverse geographies, differing latitude zones, and varied altitude ranges associated with the numerous nuclear tests conducted by several nations during the late 1950's and early 1960's.
An alternative explanation can be related to the solar cycle.According to models (e.g., Golubenko et al., 2022;Kovaltsov et al., 2012), the global production rate of 14 C changes by 15-20% over a typical solar cycle, leading to 1-3‰ fluctuations in mid-latitude Δ 14 C tree-ring data (Brehm et al., 2021;Friedrich et al., 2019;Kudsk et al., 2022).Potentially, such fluctuations may also result in short-term inhomogeneities of the order of several permille in ground-level concentrations.This would require stratospheric production gradients and rapid STE at high latitudes in a similar manner to what was hypothesized in relation to the Carrington flare.Although this is not supported by direct modeling, such a mechanism can suggestively lead to occasional asynchronicity in the solarcycle Δ 14 C minima and maxima observed in high-and mid-latitude records (Friedrich et al., 2019).Our high statistical precision based on multiple measurements demonstrates that it is possible to detect several-permille variations in the tree-ring Δ 14 C signals.
As a summary, we report a robust observational result of a transient Δ 14 C offset after the Carrington event.The offset cannot be understood in the framework of the current paradigm, as demonstrated by the modeling results.We have discussed the observation through the recent upscaled magnitude of the Carrington flare in combination with the less well-understood Arctic STE dynamics, to help explain both the offset, as well as the rapid highlatitude signals in the 774 CE and 993 CE events.We note that additional measurements from high-and midlatitude locations are needed to be more conclusive of the exact cause.To pinpoint the exact cause, we propose replicated measurements across multiple solar cycles and further study of potential analogous events from for example, years 1052/1054, 1279, 1582, 1730 and 1770 (Brehm et al., 2021;Hattori et al., 2019;Hayakawa et al., 2017Hayakawa et al., , 2018;;Terrasi et al., 2020).If such transient offsets are prevalent, they could provide a novel method for studying past solar, geomagnetic and atmospheric phenomena.By improving the detection of smaller SEP events, they could help bridge the gap (Usoskin & Kovaltsov, 2021) between the very large/medium-sized events (e.g., 774 and 993 CE) and the much smaller ones observed through modern instrumental methods.An improved understanding of the statistics of extreme solar events would be valuable when assessing the potential societal risks they pose.Furthermore, they may provide important insights into the multifaceted atmospheric dynamics and STE processes free of the contaminations of the modern era with anthropogenic radionuclide and fossil carbon signals.(Uusitalo et al., 2024).The mid-latitude tree-ring 14 C data for the Carrington period can be accessed from the original publications of Stuiver et al. (1998b), Scifo et al. (2019), andBrehm et al. (2021), and also from Table S1 of this article.The high-and mid-latitude tree-ring 14 C data for the period 382-460 CE can be accessed from Friedrich et al. (2019).

Figure 1 .
Figure 1.Panel (a) shows the Δ 14 C data measured around the Carrington event, denoted by the vertical dashed line.The black squares show the mean of the high latitude data as measured from three different trees (see Table1 and Methods).Each annual point includes 5-8 measurements (see TableS1).The red circles depict the mean annual values for the mid-latitude dataset.Each point includes three (for years 1855-1866) or two measurements.Uncertainties correspond to one standard error.The black and the red lines denote the 3-year moving averages of the high-and mid-latitude datasets, respectively.The bottom part of each panel shows the difference between the 3-year moving average curves, with the y-scale for this section on the right side.Panels (b)-(d) show the individual measurements of the high-latitude data versus mid-latitude average from different trees and laboratories, as detailed in Table1and Supplementary TableS1.For clarity, all data points are aligned with full years, though the actual growing periods are approximated to mid-year.

Figure 2 .
Figure 2. Comparison of the high-versus mid-latitude Δ 14 C differences across two different time periods.Panels (a) and (b) depict the statistical significance (in terms of p-value) of the differences in Δ 14 C for two time periods: (a) around the Carrington flare, and (b) for the period of 382-460 CE (see Methods).The dashed horizontal lines mark the 0.05 significance level.The y-axis is inverted and logarithmic.Panels (c) and (d) present the absolute Δ 14 C differences for the same time periods as those depicted in panels (a) and (b), with the dashed horizontal line marking the baseline.

Table 1
List of Tree-Ring 14 C Datasets Used for the Present Study