Abstract
Radiocarbon (14C) is essential for creating chronologies to study the timings and drivers of pivotal events in human history and the Earth system over the past 55,000 years. It is also a fundamental proxy for investigating solar processes, including the potential of the Sun for extreme activity. Until now, fluctuations in past atmospheric 14C levels have limited the dating precision possible using radiocarbon. However, the discovery of solar super-storms known as extreme solar particle events (ESPEs) has driven a series of advances with the potential to transform the calendar-age precision of radiocarbon dating. Organic materials containing unique 14C ESPE signatures can now be dated to annual precision. In parallel, the search for further storms using high-precision annual 14C measurements has revealed fine-scaled variations that can be used to improve calendar-age precision, even in periods that lack ESPEs. Furthermore, the newly identified 14C fluctuations provide unprecedented insight into solar variability and the carbon cycle. Here, we review the current state of knowledge and share our insights into these rapidly developing, diverse research fields. We identify links between radiocarbon, archaeology, solar physics and Earth science to stimulate transdisciplinary collaboration, and we propose how researchers can take advantage of these recent developments.
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Main
Since its existence was confirmed in 1940 (ref. 1), radiocarbon has been both a cornerstone for dating the past 55,000 years and a fundamental tracer of Earth system processes. Here we draw together recent developments across multiple disciplines that offer new insights into the archaeological, Earth and space sciences. We discuss how the discovery of so-called Miyake events caused by ESPEs has created opportunities for more-precise radiocarbon calibration and stimulated research programmes to measure past 14C levels at annual resolution. We summarize how scientists can use ESPEs directly to obtain exact calendar dates using radiocarbon, and how they can leverage fine-scale variations in 14C identified by wider annual measurement programmes for calibration more broadly. We also survey the insights that ESPEs and consequent high-precision annual 14C measurements have provided regarding space weather and the global carbon cycle, and describe areas where further research is required to gain the greatest value from radiocarbon.
Introduction to radiocarbon
The approximately 5,700-year half-life of the radioactive 14C isotope of carbon (radiocarbon) and the ubiquitous nature of carbon in the biogeosphere make it extremely useful as a scientific tool to study the past 55,000 years. It is used both as the primary clock by which archaeologists and environmental scientists measure time, and as a probe to gain insight into key Earth system processes2,3.
Radiocarbon dating4,5 is based on the principle that while an organism is alive, it exchanges carbon with its surroundings, so it will have a ratio of 14C to stable carbon that is in equilibrium with that of its local environment; a similar situation also arises for some geological processes, such as the growth of speleothems. Once this exchange ceases, for example when an organism dies, the stable carbon incorporated into well-preserved chemical components will remain constant, but the amount of 14C will halve roughly every 5,700 years. Beyond ten half-lives (around 60,000 years), insufficient 14C remains to be measured reliably using current methods.
If the 14C concentration (the ratio of 14C to stable carbon) in the various reservoirs of the carbon cycle had been constant over time, obtaining a precise calendar age from radiocarbon dating would be straightforward. However, the 14C concentration has varied considerably over time and differs according to the carbon reservoir (for example, the atmosphere or ocean) being studied. These past fluctuations mean that all radiocarbon age measurements need to be adjusted to account for the 14C concentration when the sample stopped carbon exchange. This adjustment is known as radiocarbon calibration.
Calibrating a 14C measurement into an accurate calendar date requires comparison with reference material of known calendar age (for example, tree rings dated by dendrochronology) or with other independently dated 14C records (such as stalagmites, corals and lacustrine and marine sediments)3. These reference materials are combined into calibration curves that provide estimates of the 14C concentration of a sample that stopped exchanging in any individual calendar year6,7,8. To calibrate a sample of unknown age, we calculate which calendar dates are consistent with the observed 14C concentration of the sample. This is typically achieved using a Bayesian approach (Fig. 1 and Supplementary Video 1). Calibration leads to calendar-age estimates that are uncertain and have potentially complex, asymmetric and multimodal probability distributions. The requirement for calibration is one of the main confounding factors in 14C dating, and many important archaeological debates, such as the date of the Minoan eruption of Thera in the second millennium bc, hinge on these calendar-age probability distributions9,10,11.
Calibration and calendar-age precision
The need for calibration means that the calendar-age precision produced by radiocarbon dating arises from two distinct components: first, the measurement precision of the 14C content of the sample; and second, the calendar-age uncertainty introduced by the calibration process. Improvements in the former without consideration of how to reduce the latter offer only limited progress in increasing calendar-age precision. For some 14C users, typically those able to obtain just a single 14C determination, the imprecision introduced through calibration may be irreducible. However, for those with access to multiple potential 14C samples, careful consideration of how and what they choose to measure and calibrate offers substantial opportunities to reduce the final calendar-age uncertainties.
Archaeologists have been quick to embrace the potential for more-precise chronologies by incorporating independent information, either on relationships between the 14C samples or with external chronologies, during calibration12,13. The routine application of Bayesian chronological modelling has led to the development of a step-by-step process to enable the selection of suites of samples for dating that can be interpreted together in formal statistical models14. Currently, relative dating known from stratigraphy, from either archaeology or environmental records, is the most widely used information incorporated into chronological models, although other kinds of sequence, such as artefact typology or seriation, are also used. This can be supplemented with tie-points provided, for example, by volcanic tephra15. Until recently, however, the decadal resolution of most of the data used to construct calibration curves has been a limitation on the types of independent archaeological and environmental information that can be used in chronological modelling16. The discovery of ESPEs has changed this.
Atmospheric 14C/12C variations
The variations in past atmospheric levels of 14C that necessitate calibration are a consequence of both changes in the rate of production over time and rearrangements in the global carbon cycle. Consequently, discoveries in the 14C record that lead to improvements in radiocarbon calibration also enable key insights in a broad range of other scientific fields.
Natural production of 14C occurs predominantly in the lower stratosphere and upper troposphere, and is driven by galactic cosmic rays (GCRs). These incoming GCRs initiate a cascade of nuclear collisions, eventually generating neutrons, which then react with atmospheric nitrogen to produce 14C. The number of GCRs that reach the atmosphere is modulated by the strength of the solar magnetic field and Earth’s geomagnetic field. Both partially shield Earth from cosmic radiation. When solar activity is high, and/or the geomagnetic field is strong, fewer GCRs reach Earth, leading to lower 14C production rates. Variations in the rate of 14C production resulting from solar activity tend to operate on short-to-moderate timescales (decadal to centennial), whereas those caused by changes in the geomagnetic field generally operate on much longer (centennial to millennial) timescales.
Until recently, no abrupt changes had been identified in the 14C record, and it was believed that the galactic cosmic-ray flux impinging on Earth varied only gradually in response to heliomagnetic and geomagnetic modulations17,18,19. Consequently, measurement of reference 14C material at annual resolution was seen as a low priority. However, in 2012, analysis of a Japanese cedar identified an unexpected 12‰ increase in atmospheric Δ14C (a decrease of more than 100 14C years) over the course of a single calendar year, ad 774–77520. Such an abrupt increase in 14C levels required an entirely unprecedented spike in 14C production, with almost four times the yearly average amount of 14C being generated that year21.
Further analysis revealed that the cause of this 14C jump was an extreme solar storm that was an order of magnitude larger than any previously estimated22. Such a storm would have created a massive short-term burst of energetic solar particles (an ESPE) that led to a huge spike in 14C production.
Impact of the discovery of ESPEs
The occurrence of similar ESPEs today could have disastrous effects on our telecommunications, electricity grids and satellite systems23,24. Understanding the frequency of such events and their possible size is therefore essential to prepare and build resilience into these systems. However, detailed instrumental measurements of the Sun’s behaviour are available only for the past few decades, during which time no ESPEs have occurred, so we are required to use the imprint they leave in cosmogenic isotope records. The discovery of the ad 774 ESPE initiated new and extensive programmes to measure 14C in tree rings at annual resolution and high precision throughout the Holocene epoch. These programmes have important implications for solar physics, enhancing our understanding of the Sun and space weather. They also provide opportunities for those seeking to calibrate radiocarbon determinations.
The 14C signatures left by ESPEs are unique. If one can obtain 14C samples from consecutive calendar years that bracket the ESPE (for example, by measuring individual growth rings in timbers), calibration to the exact year is possible. This step change in the precision obtainable through radiocarbon dating has the potential to extend the reach of the radiocarbon method into historical and other problems that require exact dating. Most immediately, such exact dating will be relevant to archaeologists. However, several fields of the Earth sciences also need high-precision dating when dealing with rare but dramatic events, such as earthquakes and tsunamis25, extreme weather events such as hurricanes26, or rainfall and flood events27, all of which may have varied in strength and frequency in the past. Confirming the correct identification of at least a few singular events in distant archives would demonstrate the reliability of available records in this growing field of palaeo-extreme events.
Those who study periods lacking ESPEs (or without suitable items to bracket the ESPE) may not be able to obtain exact dating using 14C, but they can still take advantage of the increased resolution in radiocarbon calibration curves enabled by annual 14C measurement programmes. Such fine-scaled understanding of atmospheric 14C structure allows relative dating information from shorter 14C sequences and/or shorter-lived 14C samples to be used more effectively and reliably in statistical models. Harnessed optimally during calibration, this indirect consequence of the search for ESPEs will improve the dating accuracy and precision of 14C more broadly (Box 1).
Recent advances in 14C and calibration
Extreme solar particle (Miyake) events
Initially, the Miyake spike of ad 774 was proposed to be the consequence of a nearby supernova. It was soon shown, however, that the only plausible cause was the Sun, specifically an ESPE with an enormous flux of solar energetic particles (SEPs) producing a spike of cosmogenic isotopes in Earth’s atmosphere22. This solar event was later confirmed by similar peaks in Δ14C from other trees around the world, as well as in other cosmogenic isotopes, 10Be and 36Cl, measured in ice cores21,28. The use of different isotopes and sophisticated modelling made it possible to identify that the event had probably occurred during the Northern Hemisphere (NH) summer of ad 774. The reconstructed SEP energy spectrum21,29 seemed to be similar to those of normal solar particle storms but several orders of magnitude greater in flux.
The identification of these huge spikes in 14C production has enabled 14C calibration at annual precision, but studying the spikes themselves is also important to better understand the behaviour of the Sun and the potential risks it poses to Earth and our technological society. The long-term behaviour of the Sun is poorly documented. Direct observational measurements of sunspots have been recorded for only a few centuries30, and more-detailed instrumental measurements for only a few decades. The largest directly observed solar storm occurred on 1–2 September in ad 1859 and is known as the Carrington Event. It led to widespread disruption, including the destruction of telegraph machines and an aurora so bright that it seemed the Sun had begun to rise31. However, so far, no identifiable increase in either Δ14C or 10Be has been detected for this event (although a transient high-latitude offset in Δ14C a couple of years after the event has been tentatively proposed32). The ad 774 Miyake Event was an entire order of magnitude greater in size than the Carrington Event, making understanding the risks of ESPEs even more important.
The discovery of the first Miyake Event stimulated research in solar physics and initiated a race for 14C measurement programmes at annual resolution to identify further ESPEs and investigate the potential for other fine-scaled solar behaviour. This work has been facilitated by advances in accelerator mass spectrometry (AMS) instrumentation33,34,35, which means that high-precision 14C measurements (less than 2‰ in Δ14C, equivalently ± 16 bp) of samples containing just a few milligrams of carbon can now be achieved much more efficiently. So far, five ESPEs have been confirmed through comparison of multiple radionuclides (7176 bc, 5259 bc, 660 bc, ad 774 and ad 993) along with four further potential candidates (12350 bc, 5410 bc, ad 1052 and ad 1279) that are yet to be confirmed20,21,36,37,38,39,40,41,42.
Annual-resolution 14C measurements
Although 14C measurements of single tree rings of known age have been available for use in 14C calibration for decades, they have focused only on the past few centuries, and their extension further back in time was not seen as urgent for calibration43. Most of the reference 14C datasets used in calibration-curve construction were instead measurements of 5-, 10- or 20-year blocks of tree rings. The new measurement programmes have generated huge numbers of annual tree-ring 14C measurements, although primarily from the NH. Even in periods without ESPEs, they reveal short-term fluctuations in 14C concentrations that had been obscured in the legacy multi-year measurements. Such information can be used by anyone wishing to calibrate.
The IntCal20 NH curve6 is now based entirely on tree-ring measurements from 13,910 to 0 calendar years before present (cal bp). In this period, it draws on 10,713 14C measurements from tree-ring samples. Of these, 5,866 now correspond to single-year measurements covering 2,734 individual calendar years (Fig. 2a). Currently, these new annual-resolution sections of calibration curve tend to concentrate on hot-topic periods, specifically the most recent millennium, the two original Miyake events, the date of the Minoan eruption of Thera (Figs. 1 and 2b) and the Younger Dryas climatic event. However, IntCal20 does not include the most recently issued datasets37,38,40,41, and coverage of the Holocene with annual 14C measurements is expected to increase substantially.
The current Southern Hemisphere SHCal20 curve8 has far fewer annual 14C measurements on which to draw. It is based on 2,091 direct 14C measurements of tree rings, covering just four distinct periods: 2,140–0, 3,520–3,453, 3,608–3,590 and 13,140–11,375 cal bp. Of these, only 262 correspond to single-year 14C measurements, covering just 150 individual calendar years. The remainder of the SHCal20 curve is based on modelling (applying a 36 ± 27 14C year interhemispheric offset, to older ages, from IntCal20). Consequently, the SHCal20 curve must be considered with care if using short-term 14C fluctuations because they have mostly been inferred from the NH data.
Beyond 13,910 cal bp, the resolution of all calibration curves is much lower, owing to the limitations of our 14C archives. Here the calibration curves predominantly rely on measurements from the Hulu Cave stalagmites44,45, which are smoothed as a result of the various natural processes involved. However, new tree-ring archives are becoming available41,46,47, providing hope that annual-resolution calibration curves based on tree rings will soon extend further into the past.
Constructing calibration curves
The IntCal calibration curves6,7,8 combine all the reference 14C measurements that pass the selection criteria48. These includes both single-year and multi-year measurements, with the latter modelled as such. The current IntCal20 and SHCal20 curves are generated using Bayesian splines, generating a set of individual posterior realizations that are then summarized49. The final curves are intended to take account of, and represent, the over-dispersion observed in 14C measurements within a hemisphere (observed 14C determinations in any calendar year are more widely spread than expected from their quoted laboratory uncertainties).
The current construction methods are designed to allow more detail to be retained in time periods with large volumes of single-year measurements (Fig. 2b). However, they still implicitly model the underlying processes as smooth over time. Consequently, over ESPEs, they tend to smooth out the 14C production spikes so that the increases in Δ14C (Fig. 2c,d) occur over more than a single year, although this is also partly a consequence of the seemingly different timing of some of the events in different set of trees (Box 2).
As a result of this smoothing, those seeking exact calibration over ESPEs have predominantly used the direct mean of annual 14C measurements from a reduced set of locations50 instead of the IntCal curves. These direct-mean curves cover only short time periods and do not consider overdispersion. To demonstrate what could potentially be achieved if the international curves were modified to enable sharp ESPE discontinuities, we present a tentative MiyakeCal curve over the ad 774 event (Fig. 2c,d). MiyakeCal uses the same methodology as IntCal20 but allows an additional jump in Δ14C from ad 774–775 to be superimposed on the smooth spline processes.
Improving 14C calibration
Exact dating by ESPE wiggle-matching
Almost immediately after the discovery, it was realized that the substantial jumps in 14C production during ESPEs could provide exact calendar-age precision from 14C calibration if it was possible to find timber with growth rings that spanned an event. Measurement of 14C in consecutive annual samples to discover the corresponding jump in 14C concentration allows exact identification of the ring containing the ESPE and consequently its calendar year. Counting from this growth ring to the final waney edge in the timber then reveals the precise year in which the tree was felled. This process is known as 14C wiggle-matching and can be implemented in two different ways (Box 3).
The first application of these ideas, undertaken in 2014, provided an exact date for the felling of timber used in the Holy Cross chapel of the St John the Baptist convent, a UNESCO World Heritage site in Val Müstair, Switzerland51. This has been followed by further examples52,53,54,55,56,57,58, including the exact anchoring of the stratigraphy of a Viking Age trade centre56, identification of the precise year in which Vikings were present in North America57 and evidence for a compound earthquake involving simultaneous ruptures across two fault zones near Seattle58.
The principle has the potential to be extended to any ESPE of sufficient magnitude. So far, applications have focused on identification of the ad 774 or ad 993 events, although a 2023 study has used the 5259 bc ESPE to date a floating Neolithic tree-ring chronology in Dispilio, northern Greece59. Users of the ad 993 event must proceed with care, however, because the exact timing its 14C signature in tree rings does not seem to be globally consistent (Box 2) and the choice of 14C reference data is crucial to obtaining reliable exact 14C calibration.
Leveraging annual 14C calibration curves
For archaeologists and environmental scientists not studying periods with an ESPE, or who lack preserved wood on their sites, it is still possible to take advantage of the new annual-resolution detail in 14C calibration curves. Sampling strategies that allow stratigraphic and relative calendar information to be incorporated into calibration are key. Since the advent of routine chronological modelling, the identification and inclusion of sequences of samples that can be ordered independently has been essential for maximizing dating precision. Annual-resolution calibration datasets mean that shorter sequences, and sequences of short-lived samples, may now be included in models more effectively. This can substantially increase calendar-age precision, particularly on calibration plateaux.
Instead of submitting a single sample from a seed, one may aim to calibrate a sequence obtained from a charcoal fragment60. Short wiggle-matches may also be obtained from timbers in historic or proto-historic buildings that are unsuitable for dendrochronology61,62,63. Studies of human bone provide a further example, although modelling is complicated by the potential for dietary reservoir effects64 and bone-collagen turnover65, for which more research is sorely needed66. Sampling single teeth from several individuals who died at the same time but were of different ages when they died enables a relative sequence of samples to be elicited from a group of burials67. Differences in the formation times of different bones in a human skeleton, such as the petrous and rib, can also be used to produce a sequence of 14C measurements from a dated individual68. Box 4 combines the sampling of teeth and bone from multiple individuals into a sequence of six 14C determinations with varying calendar-age gaps69,70. Increasingly, studies of ancient DNA are not only providing phylogenetic trees71, but also kinship relationships between individuals72. These relationships can also provide short sequences for chronological models, based on either the degree of kinship73 or reconstructed pedigrees72,74.
Future directions and opportunities
Understanding the Sun
For the period before telescopes were invented in the early seventeenth century, cosmogenic isotopes provide the only quantitative information on solar variability, particularly 14C owing to its high resolution. Models that link cosmogenic production and solar variability can be verified using direct instrumental data on the Sun obtained over the past four centuries37,75,76.
All eight Holocene ESPEs identified so far were 20–100 times stronger than the strongest solar storm directly recorded over the past decades (on 23 February in ad 1956). The event of 12,350 bc still needs detailed analysis but has the largest Δ14C increase of all41. However, smaller ESPEs cannot be resolved in the existing 14C data series77,78. Presently, only about one-sixth of the Holocene is covered by high-resolution 14C data6,38. It is therefore likely that more ESPEs will be found as the coverage of precise annual 14C measurements increases.
Increasing annual coverage is crucial to fully understand ESPEs. It is still unclear whether they correspond to the extreme energetic tail of rare but normal solar storms, metaphorical Black Swan events79, or whether they represent an entirely new solar eruptive process, metaphorical Dragon King events (Fig. 3). In 2012, super-flares on Sun-like stars that are 100–1,000 times stronger than all known solar flares were also discovered80. It has been proposed that ESPEs and super-flares are related phenomena. However, a projection of super-flare results to the Sun does not match the ESPE statistics81. To resolve these questions, more high-precision 14C measurements, reproduced over multiple records at annual resolution, are needed.
Solar activity is organized in approximately 11-year cycles of slightly variable length and highly variable amplitude82. These cycles are usually studied by sunspot number. Counting of sunspots began in ad 1610 and form the longest dataset of direct astronomical observations, covering 36 solar cycles including the Maunder minimum of activity (ad 1645–1715) and a Modern grand maximum (ad 1940–2008). This time series allows some empirical regularities of the solar cycle to be identified82 but is highly limited because the number of cycles is small.
Annual 14C data have been used to study solar cycles beyond the observational sunspot record for some time19, but were previously hampered by insufficient measurement resolution. In 2021, 14C measurements for the past millennium were obtained with sufficient precision to reconstruct individual solar cycles37,75. This nearly tripled the number of known solar cycles to 96 and allowed some empirical rules to be confirmed. Further reconstruction of 11-year solar cycles on longer multi-millennial time scales, which requires high-precision annual 14C measurements, is critical to understanding the solar dynamo83.
So far, excluding the 12,350 bc event41, ESPEs have been found only in Holocene subfossil trees. Solar variability beyond the Holocene remains terra incognita, although existing tree-ring 14C data and ice-core 10Be and 36Cl are seen to exhibit high-frequency structures46,84,85,86. Extending the solar record beyond the Holocene will require dedicated efforts to find relatively rare subfossil trees from Glacial and Late Glacial periods. Ancient New Zealand kauri trees (Agathis australis) show considerable promise beyond the Last Glacial Maximum46,47. The AMS analyses of these trees will need to be optimized through careful controls on uncertainty87 to detect small and rapid 14C changes. The Glacial and Late Glacial periods were characterized by rapid variations of the carbon cycle, as illustrated by changes in atmospheric 12CO2 (ref. 88) and 13CO2 (ref. 89). These findings emphasize the need to reconstruct abrupt 14C changes in trees from both hemispheres. Abrupt solar variations should be recorded in all trees, whereas rapid carbon-cycle changes may lead to changes in the interhemispheric 14C gradient90,91.
Understanding environmental processes
Abrupt spikes in 14C production enable insight into Earth and environmental processes. Sub-annual 14C measurements across the ad 774 and ad 993 Miyake events from the mid to high latitudes of both hemispheres have helped to identify the seasonal timing and a latitudinal gradient of radiocarbon preserved in contemporary trees50. Intriguingly, these early results indicate that there may be regional differences in the precise timings of some ESPE 14C signatures (Box 2) and in the interhemispheric 14C gradient between the events, possibly modulated by changes in the ocean–atmospheric circulation and the carbon cycle50.
To improve our understanding of Earth system processes, high-precision annual (or even sub-annual) 14C measurements must be accompanied by the development of a carbon-cycle dynamic model with sufficient spatio-temporal accuracy to account for detailed processes, including latitudinal gradients, orography, proximity to the ocean and the growth period of trees. Although the standard carbon-cycle box model92 works well for slow decadal changes, large-scale ‘boxes’ that do not resolve uneven patterns of 14C production and transport may lead to inaccurate results for annual and sub-annual scales, especially during ESPE production spikes93. One prospective direction is coupling a detailed climate-chemistry dynamic atmospheric model, such as SOCOL94, ECHAM-HAM or GEOS-Chem95, with the dynamic ocean96 and a realistic biosphere, including growth and carbon uptake of specific tree species.
With the carbon cycle currently experiencing extreme disruption97, inverse 3D-transport modelling is being used to identify CO2 emission sources and sinks based on the time-varying spatial evolution of 12CO2, 13CO2 and 14CO2 (refs. 98,99,100). Application of this approach using 14C records of ESPE spikes and other rapid 14C changes at different locations may improve knowledge on natural 14C atmospheric dispersal and carbon sinks, extending the insights afforded by the 1960s nuclear ‘bomb spike’101. Complemented by an expanded global network of 14C measurements, such an approach would allow the use of observed latitudinal gradients in the amplitude of ESPEs50. Similar chemical transport models could be used to simulate the dispersal and fallout of 10Be and 36Cl on polar ice caps95,102. This is crucial because aerosols from volcanic eruptions can increase the deposition of 10Be and 36Cl, generating abrupt spikes that may be confused with ESPEs103. Accurate geomagnetic records104 are also necessary to model the amplitude of cosmogenic production associated with ESPEs.
Statistical considerations
Harnessing annual-resolution calibration datasets will require statistical hurdles to be overcome. Calibration-curve construction must be adapted to better represent abrupt ESPE 14C production changes. This is a challenge because regression methods typically assume that the underlying function is smooth105 to prevent overfitting. Ensuring one does not overfit to spurious 14C artefacts is particularly important for calibration curves because the underlying reference data consist of overlapping trees from different locations, species and laboratories, all of which introduce considerable extra variability106,107,108.
Such smoothness does not easily allow representation of ESPEs, however. One solution might incorporate extra ESPE-specific basis functions, placed at fixed times, into the regression to represent the temporal atmospheric Δ14C response of an ESPE. These functions could be informed by the atmospheric models discussed above94,95. This will require agreement on where such additional basis functions should be located and, until coverage with annual 14C data becomes complete, leaves the possibility that some ESPE variations will be missed in the calibration curves38.
With increasing calibration precision, it is essential to fully understand all sources of potential variations in the measurement of 14C samples, including shared offsets and biases106. This is particularly relevant for annual measurements, owing to 14C differences during the growing season50,108,109. Current tree-ring data exhibit overdispersion with 14C measurements in any calendar year more highly spread than their quoted laboratory-reported uncertainties should indicate49. Furthermore, consistent 14C offsets have been observed between contemporaneous tree rings from different locations. In case study I (Box 2), for example, as well as a difference in ESPE timing, the 14C measurements from any region tend to stay above or below those of other regions. Understanding the causes of extra variations and shared biases in 14C is critical to accurate calibration, particularly when calibrating sequences of 14C samples (Fig. 4 and Box 2).
The 14C research community has undertaken considerable work to assess and improve the accuracy and precision of their measurements through laboratory intercomparisons87,110. This work has begun to apportion the sources of variation observed in 14C measurements, such as pre-treatment methods. Identification of offsets and their sources is challenging, however, because they are typically of a similar size to measurement precision. Furthermore, many offsets will not be constant over time106. We require a dedicated programme of work, engaging with a broad set of laboratories, to improve our understanding of regional, altitudinal and laboratory sources of extra uncertainty, aided by high-precision AMS.
Calibration-curve usage could potentially be improved by the use of covariance information on the 14C ages in adjacent calendar years. This is currently lost when providing point-wise curve summaries49,111. Furthermore, as calibration curves become wigglier, the possibility of highly multimodal fits when calibrating models increases substantially. The use of robust assessment metrics13,112,113,114,115 to ensure that calibration models have properly converged before inference is made will be even more important than it is now. More-advanced Markov chain Monte Carlo approaches, such as parallel tempering49,116, slice sampling117,118 or Hamiltonian Monte Carlo119, may be required.
To ensure uptake in the radiocarbon community, all these statistical considerations must be integrated into user-friendly software, accompanied by educational support.
Archaeological interpretations
Since 14C dating was first developed, the adoption of new developments by archaeologists has been rapid. The possibility of obtaining exact chronologies by fitting series of measurements on single-year tree rings to the abrupt changes in atmospheric 14C at ESPEs is the latest example51,52,53,54,55,56,57. This methodology can provide precise calendar dating for particular sites that fits them exactly into historical narratives, thereby providing fixed points in wider archaeological discussion. It also has the potential to securely anchor floating historical sequences, such as those of the Near East and Central America, to the calendar scale120. The search for key timbers, intact to waney edge and securely tied to these historical sequences, runs parallel with the hunt for new ESPEs.
For archaeologists studying sites or periods containing known ESPEs, dating a series of single tree rings containing the specific ESPE signature may provide an exact anchoring for that chronology, although the relationship between the dated sample and the archaeological question remains paramount14,121. For long periods, however, there are no such events. As more single-year data become available, changes to the calibration curve in some periods will be substantial, particularly if there is a currently undetected ESPE38. In most places, however, changes will be more modest, with small wiggles and steps becoming visible that cannot be resolved in the current coarser-resolution data87. This extra structure, even on a small scale, can nevertheless still have a substantive impact on modelled chronologies.
Archaeologists have long focused on the in-built age and taphonomy of the material selected for dating122, and the advent of AMS brought a focus on dating short-life, single-entity samples123. The current Bayesian process14 provides a framework to select suites of samples for dating that can be interpreted together in formal statistical models. This process will need to develop alongside a much more detailed annual calibration curve, in particular the possibility to more effectively leverage information from short 14C sequences and/or sequences of short-lived 14C samples (Box 4). In undertaking such studies, high-precision measurement of the unknown samples is vital124. Increases in the modelling of suites of 14C samples may be supported by the development of model-selection approaches, building on existing individual and model agreement indices115. Such approaches could provide more-robust inference in the presence of model uncertainty125,126 and help to select between multiple potential interpretations.
Finally, the increase in the detail and precision of calibration data mean it is essential to ensure the reproducibility of 14C modelling. Each update to the calibration datasets affects the calibrated dates in previous studies. There is a need to develop model repositories in which, as calibration curves are improved, previous studies can be recalibrated with the state-of-the-art knowledge. This will ensure that research remains comparable, and that archaeological and geoscientific knowledge is continuously updated.
Conclusions
The unexpected discovery of ESPEs in the 14C record has brought together archaeologists, environmental scientists and solar physicists in pursuit of common research objectives. ESPEs, and the extensive high-precision annual 14C measurement programmes their discovery initiated, are enabling substantial advances across numerous fields of endeavour. As well as improvements in the dating precision achievable using radiocarbon, including the potential calibration to an exact year, we are now gaining deep insights into the extreme behaviour of the Sun, societal evolution and the archaeological record, as well as the operation of the Earth system. Whether used for precise dating, solar physics, or as a tracer of carbon dynamics, radiocarbon has shown itself to remain fundamental to understanding the world in which we live.
Reporting summary
Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.
Data availability
All data are available in the references.
Code availability
The code used is available at https://github.com/TJHeaton/Quest-Exact-Radiocarbon-Dating.
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Acknowledgements
We thank Z. Apala and J. Apals for the photograph in case study II; J. Veitch (Department of Archaeology, Durham University) for the photograph in case study III; and K. Hemer, J. Meadows, A. Millard, E. M. Scott and G. Stone for feedback. I.U. benefited from the visiting fellowship programme at ISSI (Bern). T.J.H. was supported by APX\R1\231120, NE/X009815/1 and EP/X032906/1; E.B. was funded by ANR MARCARA; C.B.R. was supported by NE/X009815/1 and as part of the National Environmental Isotope Facility; and I.U. acknowledges partial support from the Research Council of Finland (project 354280).
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Calibrating a single 14C determination.
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Bayesian wiggle-matching a sequence of 14C samples.
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Heaton, T.J., Bard, E., Bayliss, A. et al. Extreme solar storms and the quest for exact dating with radiocarbon. Nature 633, 306–317 (2024). https://doi.org/10.1038/s41586-024-07679-4
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DOI: https://doi.org/10.1038/s41586-024-07679-4
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