New data fails to replicate the small-scale radiocarbon anomalies in the early second millennium CE

Abstract

Over the last decade, the field of radiocarbon analysis has been revolutionized by the discovery of single-year anomalies, because they can be used as markers of space weather events and as time anchors for exact dating. Brehm et al. (2021) recently analyzed two new anomalies, in the years 1052 CE and 1279 CE. These candidates show consecutive year Δ¹⁴C increases of 5.9‰ and 6.5‰, respectively. In this study, we measured and analyzed dendrochronologically dated oak wood samples from northern Europe spanning both these years. Our results, although statistically consistent with those presented in the original publication, show effectively no increase in Δ¹⁴C (1 and 2.5 times the measurement error, respectively). Nonetheless, we proceed to analyze our datasets with the aid of the open-source Python package ticktack. Our modeled outputs confirm that radiocarbon production barely rose above background levels across these two periods, and no event of clearly resolvable start date or duration could be detected. Additionally, we conduct the same analyses on a new sample spanning the years 531–550 CE. Here, once again, only weak evidence was obtained for any increase in radiocarbon production, and no significant annual rise was evident. The gradual increases exhibited by all three of these samples, and the ubiquity of these patterns across the calibration curve, call into question any likely cosmic event in these cases, and illustrate how challenging it will be to distinguish lower magnitude events in the radiocarbon record.

Introduction

Radiocarbon (¹⁴C) is a cosmogenic nuclide produced in the upper layers of the atmosphere via interaction between cosmic radiation and nitrogen atoms. Its formation rate is dependent on several factors, with the flux of cosmic rays (highly energetic particles) being the main driver. The incoming cosmic rays set in train a particle shower that ultimately leads to the generation of thermal neutrons which are captured by nitrogen atoms to form ¹⁴C (Beer et al. 2012; Lingenfelter 1963; Simpson 1951). Under normal conditions, it is estimated that the incoming radiation ultimately responsible for ¹⁴C formation has almost entirely a galactic origin, and only 0.25% has a solar origin in the form of solar energetic particles (SEP) (Kovaltsov et al. 2012). On average, galactic cosmic rays (GCR) are several orders of magnitude more energetic than SEPs; therefore, despite their much lower fluence, they are more likely to penetrate the magnetic shielding of the Earth and to initiate the nuclear spallation processes (Beer et al. 2012; Kovaltsov et al. 2012). The activity of the Sun also plays a fundamental role. Specifically, the heliomagnetic and geomagnetic fields and their interaction dictate which fraction of the incoming radiation will be able to penetrate the resulting magnetic shielding and enter the atmosphere. It is when the Sun is at its maximum activity and the Earth’s magnetic shield is also intensified that ¹⁴C production is at its minimum (Damon et al. 1973; Damon and Linick 1986; Stuiver 1961; Stuiver and Braziunas 1993). However, the Sun often also exhibits violent behavior, which sporadically results in flares or coronal mass ejections (CMEs) that liberate into interplanetary space intense fluxes of SEPs, orders of magnitude more energetic than ordinary solar cosmic rays (Kovaltsov et al. 2012; Usoskin 2017). When such SEPs hit Earth, they could trigger exceptional production of cosmogenic nuclides, even though the direct observational evidence of this phenomenon is limited (Paleari et al. 2023; Pedro et al. 2012; Usoskin et al. 2020). For instance, the strongest solar storm that happened to hit the Earth in recent history, the Carrington Event of 1859 CE, left no trace in available cosmogenic nuclide records (McCracken et al. 2001; Scifo et al. 2019; Smart et al. 2006; Wolff et al. 2012).

Sudden increases in the ¹⁴C content of known-age tree rings were first discovered by Miyake et al. (Miyake et al. 2012, 2013) and have been commonly referred to as Miyake Events, but also as rapid ¹⁴C changes or ¹⁴C production events in the scientific literature. As these anomalous uplifts are observed all over the world, they cannot be considered the outcome of some regional phenomena but instead they must be analyzed at a global scale. The origin of rapid ¹⁴C changes has been linked to extreme solar activity (Mekhaldi et al. 2015; Melott and Thomas 2012; Usoskin et al. 2013). Although no consensus yet exists over the mechanism for such explosive solar behavior, some form of CME is believed to be the most likely explanation, as any correlation with astrophysical gamma ray sources appears to be weak (Dee et al. 2016; Terrasi et al. 2020). Furthermore, the latter phenomenon would also not produce major increases in ¹⁰Be (Pavlov et al. 2013), yet the most widely accepted events have been found in ice core records of ¹⁰Be and ³⁶Cl (Mekhaldi et al. 2015; O’Hare et al. 2019; Paleari et al. 2022).

Recently, the ¹⁴C production events in both 775 CE and 993 CE have been used as linchpins for ¹⁴C dating. Since their occurrence has been exactly pinpointed in time, by way of numerous dendrochronological archives (Büntgen et al. 2018), they can be used as reliable time anchors to provide exact-year dates. The first application of this sort confirmed the construction date of a church in Switzerland (Wacker et al. 2014), this was followed by dates for the Changbaishan and Katla volcanic eruptions (Büntgen et al. 2017; Oppenheimer et al. 2017), then an archeological site in Russia (Kuitems et al. 2020), and most recently the arrival of Europeans in North America (Kuitems et al. 2022).

Uncovering new rapid ¹⁴C changes is an area of active research. Multiple criteria need to be met in order for new candidates to be accepted as true events. Firstly, the measurement data need to be sufficiently precise to distinguish them from adjacent (background) data, as well as generic solar and carbon cycle induced fluctuations. Secondly, the data should be corroborated by measurements on different trees, ideally of more than one species, from more than one geographic location, and by more than one ¹⁴C laboratory ([Büntgen et al. 2018) c.f. (Wang et al. 2017; Jull et al. 2021]). Additional support must also be obtained from data on other cosmogenic isotopes, ¹⁰Be and ³⁶Cl, from ice cores, as the ³⁶Cl/¹⁰Be ratio is a good discriminator for the energy of incoming cosmic rays (Mekhaldi et al. 2015; Webber et al. 2007). Brehm et al. (2021) have analyzed two new event candidates relating to the years 1052 and 1279 CE, respectively. The 1052 CE event candidate was first proposed by Terrasi et al. (2020), although here the increase was observed in the year 1054 CE, and it was argued that the Crab Nebula supernova, documented in historical accounts in the same year, could have been the cause for the feature. Panyushkina et al. (2022) pointed to the dating discrepancy between the oak tree-ring series used by Brehm et al. (2021) and Terrasi et al. (2020) and applied DTW analysis to four ¹⁴C signatures from tree rings of California, Finland, and England and suggested that the two ¹⁴C features reported by the two studies could have been caused by a single event. These event candidates studied by Brehm et al. (2021) show a relatively small increase in Δ¹⁴C compared to other events, such as the ones already used for single-year dating. In this study, we aim to corroborate the findings of Brehm et al. (2021) by using independent tree ring samples dendrochronologically dated to the periods of time in question. We also report a new investigation into an anomalous Δ¹⁴C rise in the 540s CE, and new measurements over the 775 CE event.

In order to interpret changes in ¹⁴C/¹²C ratio in wood samples correctly, and to link them with space weather events, the ¹⁴C data must first be passed through a model of the carbon cycle, as atmospheric ¹⁴C/¹²C ratio depends on the mixing between reservoirs with different sizes and residence times, leading to a mismatch between Δ¹⁴C changes and ¹⁴C production rate changes. The most common way to do to so is using Carbon Box Models (CBM) (Oeschger et al. 1975; Siegenthaler et al. 1980; Nakamura et al. 1987). This has been done by several studies that have reported new event candidates, using in-house CBMs. However, none of those CBMs are in the public domain and therefore they are inaccessible to other research groups, making the comparison between proven and candidate events more difficult and controversial. Consequently, we welcome the release of the open-source Python package, ticktack, which encompasses CBM implementations with modern Bayesian inference tools (Zhang et al. 2022). The package allows the user to either implement one of the previously employed CBMs (Büntgen et al. 2018; Brehm et al. 2021; Güttler et al. 2015; Miyake et al. 2012) or to custom build one of your own.

Methods

Samples Preparation and Measurement

In this study, we analyze four different dendrochronologically dated wood samples, all of which are oak (Quercus sp.). Sample BIF-E19, spanning the years 1049–1057 CE, comes from Furness Abbey [54°8′7″N, 3°11′52″W], England. Sample APT-C02, spanning the years 1275-1283 CE, comes from Apethorpe Church [52°32′59″N, 0°29′29″W], England. Sample 14.0123.121, spanning the years 531-550 CE, comes from a plank from a water well found during archaeological excavations near present day Ruiselede [51°2′0″N, 03°23′0″E], Belgium (Doeve 2017). Sample D1600030, spanning the years 771-779 CE, comes from the archaeological site of Dorestad [51°58′30″N, 5°20′24″E], The Netherlands (Doeve and Jansma 2023). The former two samples were provided by Historic England, the second sample by the Dendrochronology Laboratory at BAAC, the fourth sample by the Cultural Heritage Agency of the Netherlands. For additional details, see Supplementary Information (SI5 and SI6). All the samples were first carefully dissected into single-year whole growth rings under a light microscope, including both early wood and late wood, and subsequently the α-cellulose fraction was extracted through a wet chemistry procedure (see Dee et al. (2020)). The α-cellulose products were combusted to CO₂, which was then trapped and graphitized in accordance with the routine procedures of the Centre for Isotope Research (CIO), University of Groningen (see Dee et al. 2020). The graphite samples were finally analyzed for their ¹⁴C content by accelerator mass spectrometry (AMS) utilizing the IonPlus MICADAS system at CIO (Dee et al. 2020; Aerts-Bijma et al. 2021). Samples BIF-E19 and APT-C02 had tree rings big enough to allow measurement of each annual sample in duplicate, in separate batches. The same procedure was only possible for a few tree rings in the case of sample 14.0123.121, while it was not possible at all for sample D1600030. These duplicate measurements are ones where the whole preparation process was entirely repeated, from wood to measurement.

Data Analysis

After obtaining the ¹⁴C/¹²C ratio of each ring, the rings measured in duplicate are tested for compatibility through the χ²-test performed at 95% probability (or at 5% significance level). Then the averaged results, expressed in terms of Δ¹⁴C, are modeled as short time series in the Python package ticktack. As stated above, this package allows the user to specify their own carbon reservoir sizes and fluxes, or to re-implement one of four models utilized in recent publications, namely the 3-box model of Miyake et al. (2012), the 11-box model of Güttler et al. (2015) or the 22-box models of Büntgen et al. (2018) and Brehm et al. (2021). In this study, we chose to analyze all our datasets using the 22-box model from Brehm et al. (2021). This decision also allowed us to compare our results directly with the ones obtained by the study proposing the new events. For more details on the structure of this box-model, see (Brehm et al. 2021). To reconstruct ¹⁴C production rates, we load the Δ¹⁴C time series together with the chosen CBM as a SingleFitter object, which can perform parametric Bayesian inference of ¹⁴C production rates for single data sets, where the sampling engine is emcee, an MIT-licensed implementation of the Affine Invariant MCMC Ensemble sampler (Goodman and Weare 2010). As three of the four datasets are shorter than twice the typical duration of the Schwabe cycle, it is not possible to fit a sinusoid to the production rate before the event candidates; therefore, we first apply the method spike only, which assumes a flat production rate for the years prior to the putative spike. Later, we apply the method flexible sinusoid affine variant, which fits a sinusoid and a trend to the data.

The model estimates various parameters of which the ¹⁴C production rate can be expressed as a function. The parameters inferred by the spike only method are Start Date (in years), Duration (in years) and Area (in atoms/cm² year/s), where the latter one refers to the area under that super-Gaussian curve, that is the total ¹⁴C production under the integrated time period (Zhang et al. 2022). The method flexible sinusoid affine variant, apart from inferring parameters such as Start Date, Duration and Area of the possible event, infers other parameters, such as Gradient, Phi, and Amplitude. It allows the model to fit the data to a sinusoid of phase Phi and amplitude Amplitude, and a trend given by the parameter Gradient. For both these methods, initial values for these parameters are estimated, and then the engine jointly scans them within a defined boundary in order to best fit the data. The exact detail of the sampling is defined by the number of burn-in and production steps. For more information on the functioning and structure of the package, see Zhang et al. (2022).

Results and Discussion

In Table 1, the averaged results for the four different wood samples are presented in the Δ¹⁴C format. Every duplicate measurement on every sample agrees, passing the χ²-test at 5% significance level, and therefore can be averaged. See Tables1-SI, 2-SI, 3-SI and Figures 1-SI, 2-SI and 3-SI in Supplementary Information (SI1) for a more detailed presentation of all the measurements.

Table 1. Averaged Δ¹⁴C results and errors obtained on the four wood samples

Figure 1. 775 CE Event. On the top (A), results of the ¹⁴C analysis over the sample D1600030 and comparison with the results of Büntgen et al. (2018). The green lines are the ticktack model results. On the bottom (B), results of the ticktack analysis over the same dataset, showing the surface distribution of the modeled posterior parameters.

Firstly, we present new ¹⁴C measurements over the period from 771–779 CE, spanning the years of the 775 CE event. Our results show the same sharp rise shown by Miyake et al. (2012), even though the Δ¹⁴C values are on average higher than the ones reported from the original study. Our results do not appear to be anomalous when compared with all the data from the Northern Hemisphere reported by the survey over this event by Büntgen et al. (2018) (Figure 1A). We also observe that the Δ¹⁴C rise spans a two-year period; this has been observed before in some datasets, although it is still not clear what causes a difference between a sharp and a prolonged rise for this event, as both phenomenologies can be seen in trees from different locations and growing conditions (Büntgen et al. 2018; Zhang et al. 2022).

Regarding the 1052 CE event candidate, our results across sample BIF-E19 are directly compared with those published by Brehm et al. (2021) (Figure 2A). Brehm et al. (2021) measured a Δ¹⁴C increase of 5.9 ± 1.1‰ between the calendar years 1052 and 1053 CE, and points to a possible connection between such an increase and an SEP event. All the data points of our time series agree with those of Brehm et al. (2021) at 1σ probability, apart from the points at 1052 and 1057 CE, which are nevertheless consistent at 2σ probability; indeed all the sets of same-year measurements pass the χ²-test at 5% significance level. Thus, our results are statistically compatible with Brehm et al. (2021), and both data sets can also be averaged (see Supplementary Information, SI2). Looking at the results from our study alone, we could point to a slight increase in Δ¹⁴C between the years 1054 and 1055 CE, namely of 4.4 ± 1.7 ‰. Such an increase is only around two and a half times the measurement error, and so would routinely be regarded as negligible. However, it is somewhat comparable to the increase inferred by Brehm et al. (2021) between 1052 and 1053 CE, although not co-eval. This temporal disparity was also found between Brehm et al. (2021) and Terrasi et al. (2020). However, Panyushkina et al. (2022), performing DTW analyses over ¹⁴C time series, points out that those two features are possibly one and the same. In Supplementary Information 3 (SI3) we briefly show that even if one hypothesizes that there was a mistake in one of the dendrochronologies, the two datasets are still statistically compatible.

Figure 2. 1052 CE event candidate. On the top (A), results of the ¹⁴C analysis over the sample BIF-E19 and comparison with the results of Brehm et al. (2021), and the average between the two datasets. The green lines are the ticktack model results. On the bottom (B), results of the ticktack analysis over the same dataset, showing the surface distribution of the modeled posterior parameters.

Regarding the 1279 CE event candidate, our results over sample APT-C02 are directly compared with the results published by Brehm et al. (2021) (Figure 3A). Brehm et al. (2021) measured a Δ¹⁴C increase of 6.5 ± 1.6‰ between the calendar years 1279 and 1280 CE, again suggesting a possible connection with an SEP event. Once more, all the data points of our time series agree with those of Brehm et al. (2021) at 1σ probability, apart from the last three at 1281, 1282 and 1283 CE. Again, all the sets of same-year measurements pass the χ²-test at 5% significance level, apart from the year 1281, which passes the test at 2.5% significance level. Thus, our results are again statistically compatible with Brehm et al. (2021), and both data sets can also be averaged (see Supplementary Information, SI2). Nevertheless, the increase reported in their study is not noticeable in this study, as between those years we report a change of just 1.7 ± 1.6‰. Alternatively, we could consider a time interval of 2 years, say between 1278 and 1280 CE, but even in that case the rise becomes only 3.3 ± 1.6‰. This latter value is in agreement with a recent analysis of the same event candidate (Miyahara et al. 2022).

Figure 3. 1279 CE event candidate. On the top (A), results of the ¹⁴C analysis over the sample APT-C02 and comparison with the results of Brehm et al. (2021), and the average between the two datasets. The green lines are the ticktack model results. On the bottom (B), results of the ticktack analysis over the same dataset, showing the surface distribution of the modeled posterior parameters.

Finally, we present a comparison case: new ¹⁴C measurements over the time period from 531 to 550 CE (Figure 4A). This time series shows a relatively flat trend for the first 11 years, with a subsequent gradual and slow rise starting on year 541 CE. To reiterate, we do not observe a single-year rise in this data either. However, a relatively steep rise endures for several years, peaking in 546 CE. The magnitude of the rise, taken over the period from 541 to 546 CE, amounts to 6.3 ± 1.6‰, which is of a similar to the magnitude of the rise shown in the two previous examples, only on a multiple-year basis, as this signal could be part of an 11-year cycle.

Figure 4. 540s ¹⁴C feature. On the top (A), results of the ¹⁴C analysis over the sample 14.0123.121. The green lines are the ticktack model results. On the bottom (B), results of the ticktack analysis over the same dataset, showing the surface distribution of the modelled posterior parameters.

To gain further insights into the possibility that real disturbances occurred in atmospheric Δ¹⁴C levels over these time periods we need to take into account the ¹⁴C cycle, employing a global CBM, and we do so by using of the ticktack package. This package passes the ¹⁴C data through the chosen carbon box model, takes for granted that a ¹⁴C production event happened within the dataset, and tries to best fit the ¹⁴C production rate to the data varying its parameters. In the bottom part of each Figure, noted by the letter B, corner plots of the inferred parameters, directly produced by ticktack, are shown for each of the periods in question. In dark blue are the 68.2% likelihood intervals of highest posterior density, and in light blue the 95.4% likelihood intervals. In the upper part of each Figure, noted by the letter A, the green lines represent the results of the model expressed in terms of Δ¹⁴C. In our study we first perform a ticktack analysis applying the spike only method to the datasets presented in Table 1. Then we perform a second ticktack analysis applying the flexible sinusoid affine variant method. In order to allow a sinusoidal fit of approximately 11 years, the datasets need to be long enough to incorporate at least two full periods. As this was not possible with the new datasets presented in this study, we overcame this obstacle by analyzing additional datasets. For the 775 CE Event, we use the dataset originally published by Miyake et al. (2012). For the 1052 CE event candidate, we merge our dataset with the dataset from Eastoe et al. (2019), averaging those measurements corresponding to same growth years. We could not use the dataset from Brehm et al. (2021) as it has a gap between the years 1042 and 1049 CE. For the 1279 CE event candidate, the same procedure as above is done using the dataset from Brehm et al. (2021). For the 540s CE feature, we use the same datasets we used in the first analysis.

First, we show the results over the new measurements of the 775 Event (Figure 1B). The spike only analysis points to an increase in ¹⁴C production of around 6.4 atoms/cm²/s per year, value that fits the estimate proposed by Güttler et al. (2015), with a start date estimated within the year 774 CE and an event duration that hits the minimum resolution of the model, which is around 11 days, hinting to an event duration of less than a month. All the 68.2% likelihood intervals are well constrained with a narrow margin around distinct values. Furthermore, the analysis of this event with the flexible sinusoid affine variant shows results in agreement with the spike only analysis (Figure 5-SI, Supplementary Information 4).

Second, we show the results over our new measurements of the 1052 CE event candidate (Figure 2B). The modeled increase in ¹⁴C production to fit the data is in this case of just 1.4 atoms/cm²/s per year, with a start date estimated to be around the year 1054 CE, instead of the year 1052 showed by the data in Brehm et al. (2021), even though the 68.2% likelihood interval is less well defined, as it ranges from middle of year 1053 CE to the beginning of year 1055 CE. Event duration peaks again around the minimum resolution of the model, but with a larger spread, as in general all probability regions result more widespread. The analysis of this event with the flexible sinusoid affine variant shows an even lower estimated production rate, and an unresolved start date for the possible event (Figure 6-SI, Supplementary Information 4).

Third, we show the results over our new measurements of the 1279 CE event candidate (Figure 3B). The modeled increase in ¹⁴C production to fit the data is in this case of just 1.1 atoms/cm²/s per year, with a start date estimated to be between 1277 and 1279 CE. The event duration peaks once again around the minimum resolution of the model, with again the 1σ probability densities for Start Date and Event Duration being more widespread. Also in this case, the analysis of this event with the flexible sinusoid affine variant shows an even lower estimated production rate, and an unresolved start date for the possible event (Figure 7-SI, Supplementary Information 4).

Finally, we show the results over our new measurements of the ¹⁴C feature around the years 540s CE (Figure 4B). In this case, the modeled increase in ¹⁴C production is of 1.7 atoms/cm²/s per year, with a start date centered around year 542 CE and an event duration once more peaking around the minimum resolution of the model, but with the biggest time spread so far between these analyses, suggesting a possible long-lasting increase in ¹⁴C production, that would match the longer rise seen in the data. Once more, the analysis of this event with the flexible sinusoid affine variant shows results in agreement with the spike only analysis (Figure 7-SI, Supplementary Information 4). The result of this analysis in terms of estimated production rate is comparable to those obtained in the two previous cases. However, the cause of this feature is to be deemed uncertain, as the small increase spreads over multiple years, where a normal change in solar modulation could explain the feature. However, a totally different phenomenon could be the cause of this increase; for instance, it has been shown that a major cooling event would reduce deep-water circulation, and such an occurrence can be associated with a higher atmospheric ¹⁴C/¹²C ratio (Goslar et al. 1995; Muscheler et al. 2008; Stocker and Wright 1996). Curiously, this rise in atmospheric Δ¹⁴C coincides with coolest period in the Northern Hemisphere during the Common Era, widely attributed to volcanic eruptions in 536 and 540 CE (Sigl et al. 2015; Smith et al. 2020).

Comparing these different datasets and analyzes, a clear distinction can be made between the 775 CE event and the other analyzed time periods; the former can be clearly recognized as a sudden spike in Δ¹⁴C, as it corresponds to an increase in ¹⁴C production rate of about 6.37 ¹⁴C atoms/cm²/s (parameter “Area” from ticktack model), or 3 to 4 times the production rate in normal conditions (Kovaltsov et al. 2012). The other three features, while they still show an increase in Δ¹⁴C, only do so for a magnitude comparable to 1 or 2 times the measurement error of the baseline before the supposed event, and furthermore the estimated total excess ¹⁴C production generated during these uplifts is less than double what would be expected from normal background cosmic radiation (Kovaltsov et al. 2012), and this could easily be caused by normal variations in solar modulation. Clearly all three periods do represent increases in the ¹⁴C/¹²C ratio in the atmosphere but there is scant evidence here for what might be described as an instantaneous production event, let alone a phenomenon comparable with a ¹⁴C production event. Another point to be made is about reproducibility of results. The biggest global occurring SEP events, like the 775 CE and 994 CE events, are characterized, amongst other factors, by the fact they have roughly the same excursion signature detectable in tree rings from all over the world. In the case of these event candidates, the proposed signature is so minute that clear reproducibility between independent studies is unobtainable. For instance, as previously mentioned, Miyahara et al. (2022) reports the 1279 CE event candidate to be a Δ¹⁴C increase of about 3‰ between the years 1279 and 1280 CE, instead of the 5‰ reported by Brehm et al. (2021), while in this study we report an increase of about 2‰. This means that between the studies, the same ¹⁴C feature differs by up to 60% of the initially proposed value. When considering measurement errors and geographical variability, it appears evident that distinguishing lower magnitude events in the ¹⁴C record is a challenging and uncertain task. We argue that some caution needs to be used when dealing with Δ¹⁴C increases of this small magnitude, and we stress the importance of cross-checking every proposed event with additional analysis from other groups and samples, like in the case of this study. However, to resolve such small features, this may not be enough, as supporting evidence from ¹⁰Be and ³⁶Cl data would be needed to definitively pinpoint the origin of these features, even though an additional challenge would be that for such small features, such ice core data is often too noisy and poorly resolved, to properly detect them (Mekhaldi et al. 2021). Although we do not wholeheartedly challenge the existence of these features, we only question the attribution of their origin, as such excursions could be potentially be caused by normal changes in solar modulation or by other climatic phenomena.

Conclusions

In an attempt to replicate the results shown by Brehm et al. (2021) regarding the proposed event candidates of 1052 CE and 1279 CE, we measured and analyzed samples spanning the years concerned. Our results, despite being statistically consistent with the one published in the first study, do not show a clear change in Δ¹⁴C from one year to the next. We suggest that such small increases in Δ¹⁴C cannot be claimed as radiation events with absolute certainty on the basis of the current evidence, and certainly cannot be reliably used for exact-year dating, for two main reasons. Firstly, in order to confidently claim them as globally attested radiation events, the signature of their ¹⁴C excursions should be clearly replicable from multiple studies, and from different datasets; however, the low magnitude of these features makes it challenging to distinguish unequivocally between the influence of production rate changes, the intrinsic variability of the measurement, and the geographically dependent variability of atmospheric ¹⁴C/¹²C ratio; furthermore, additional support from other cosmogenic isotopes analysis, such as ¹⁰Be and ³⁶Cl, would be needed to support such hypotheses. Secondly, these excursions reflect a relatively small increase in ¹⁴C production rate, which is very different from the increases demonstrated by the established extreme SEP events. Indeed, they are perhaps more compatible with divergences caused by environmental events, a different mechanism altogether, or by variations in solar modulation.