Ruben, S. & Kamen, M. D. Radioactive carbon of long half-life. Phys. Rev. 57, 549 (1940).
Taylor, R. E. & Bar-Yosef, O. Radiocarbon Dating: An Archaeological Perspective (Routledge, 2014). https://doi.org/10.4324/9781315421216.
Heaton, T. J. et al. Radiocarbon: a key tracer for studying Earthâs dynamo, climate system, carbon cycle, and Sun. Science 374, eabd7096 (2021).
Arnold, J. R. & Libby, W. F. Age determinations by radiocarbon content: checks with samples of known age. Science 110, 678â680 (1949).
Libby, W. F., Anderson, E. C. & Arnold, J. R. Age determination by radiocarbon content: world-wide assay of natural radiocarbon. Science 109, 227â228 (1949).
Reimer, P. J. et al. The IntCal20 Northern Hemisphere radiocarbon age calibration curve (0â55 cal kBP). Radiocarbon 62, 725â757 (2020).
Heaton, T. J. et al. Marine20âthe marine radiocarbon age calibration curve (0â55,000 cal BP). Radiocarbon 62, 779â820 (2020).
Hogg, A. G. et al. SHCal20 Southern Hemisphere calibration, 0â55,000 years cal BP. Radiocarbon 62, 759â778 (2020).
Bronk Ramsey, C., Manning, S. W. & Galimberti, M. Dating the volcanic eruption at Thera. Radiocarbon 46, 325â344 (2004).
Pearson, C., Sbonias, K., Tzachili, I. & Heaton, T. J. Olive shrub buried on Therasia supports a mid-16th century BCE date for the Thera eruption. Sci. Rep. 13, 6994 (2023).
Bruins, H. J. et al. Geoarchaeological tsunami deposits at Palaikastro (Crete) and the Late Minoan IA eruption of Santorini. J. Archaeol. Sci. 35, 191â212 (2008).
Buck, C. E., Cavanagh, W. G. & Litton, C. D. Bayesian Approach to Interpreting Archaeological Data (John Wiley, 1996).
Bronk Ramsey, C. Bayesian analysis of radiocarbon dates. Radiocarbon 51, 337â360 (2009).
Bayliss, A. & Marshall, P. Radiocarbon Dating and Chronological Modelling: Guidelines and Best Practice (Historic England, 2022).
Bronk Ramsey, C. et al. Improved age estimates for key Late Quaternary European tephra horizons in the RESET lattice. Quat. Sci. Rev. 118, 18â32 (2015).
Bayliss, A. et al. Informing conservation: towards 14C wiggle-matching of short tree-ring sequences from medieval buildings in England. Radiocarbon 59, 985â1007 (2017).
Bard, E., Raisbeck, G. M., Yiou, F. & Jouzel, J. Solar modulation of cosmogenic nuclide production over the last millennium: comparison between 14C and 10Be records. Earth Planet. Sci. Lett. 150, 453â462 (1997).
Muscheler, R. et al. Solar activity during the last 1000 yr inferred from radionuclide records. Quat. Sci. Rev. 26, 82â97 (2007).
Stuiver, M. & Braziunas, T. F. Sun, ocean, climate and atmospheric 14CO2: an evaluation of causal and spectral relationships. Holocene 3, 289â305 (1993).
Miyake, F., Nagaya, K., Masuda, K. & Nakamura, T. A signature of cosmic-ray increase in ad 774â775 from tree rings in Japan. Nature 486, 240â242 (2012). This is the publication of the first (ad 774) Miyake event, initially assumed to be caused by a supernova.
Mekhaldi, F. et al. Multiradionuclide evidence for the solar origin of the cosmic-ray events of ad 774/5 and 993/4. Nat. Commun. 6, 8611 (2015).
Usoskin, I. G. et al. The AD775 cosmic event revisited: the Sun is to blame. Astron. Astrophys. 552, L3 (2013). This is the proof of a solar origin for the ad 774 Miyake event and the introduction of the term ESPE.
Ritter, S. et al. International legal and ethical issues of a future Carrington Event: existing frameworks, shortcomings, and recommendations. New Space 8, 23â30 (2020).
Oughton, E. J., Skelton, A., Horne, R. B., Thomson, A. W. P. & Gaunt, C. T. Quantifying the daily economic impact of extreme space weather due to failure in electricity transmission infrastructure. Space Weather 15, 65â83 (2017).
Atwater, B. F. Evidence for great Holocene earthquakes along the outer coast of Washington state. Science 236, 942â944 (1987).
Winkler, T. S. et al. Revising evidence of hurricane strikes on Abaco Island (The Bahamas) over the last 700 years. Sci. Rep. 10, 16556 (2020).
Wilhelm, B. et al. Impact of warmer climate periods on flood hazard in the European Alps. Nat. Geosci. 15, 118â123 (2022).
Sukhodolov, T. et al. Atmospheric impacts of the strongest known solar particle storm of 775 AD. Sci. Rep. 7, 45257 (2017).
Koldobskiy, S., Mekhaldi, F., Kovaltsov, G. & Usoskin, I. Multiproxy reconstructions of integral energy spectra for extreme solar particle events of 7176 BCE, 660 BCE, 775 CE, and 994 CE. J. Geophys. Res. Space Phys. 128, e2022JA031186 (2023).
Clette, F. et al. Recalibration of the sunspot-number: status report. Sol. Phys. 298, 44 (2023).
Hudson, H. S. Carrington events. Annu. Rev. Astron. Astrophys. 59, 445â477 (2021).
Uusitalo, J. et al. Transient offset in 14C after the Carrington event recorded by polar tree rings. Geophys. Res. Lett. 51, e2023GL106632 (2024).
Suter, M., Huber, R., Jacob, S. A. W., Synal, H.-A. & Schroeder, J. B. A new small accelerator for radiocarbon dating. AIP Conf. Proc. 475, 665â667 (1999).
Synal, H.-A., Stocker, M. & Suter, M. MICADAS: a new compact radiocarbon AMS system. Nucl. Instrum. Methods Phys. Res. B 259, 7â13 (2007).
Synal, H.-A. & Wacker, L. AMS measurement technique after 30 years: possibilities and limitations of low energy systems. Nucl. Instrum. Methods Phys. Res. B 268, 701â707 (2010).
OâHare, P. et al. Multiradionuclide evidence for an extreme solar proton event around 2,610 B.P. (â¼660 BC). Proc. Natl Acad. Sci. USA 116, 5961â5966 (2019). This reports the discovery of a confirmed 660 bc ESPE with multi-proxy analysis.
Brehm, N. et al. Eleven-year solar cycles over the last millennium revealed by radiocarbon in tree rings. Nat. Geosci. 14, 10â15 (2021).
Brehm, N. et al. Tree-rings reveal two strong solar proton events in 7176 and 5259 BCE. Nat. Commun. 13, 1196 (2022). This paper reports the discovery of confirmed 7176 bc and 5259 bc ESPEs.
Paleari, C. I. et al. Cosmogenic radionuclides reveal an extreme solar particle storm near a solar minimum 9125 years BP. Nat. Commun. 13, 214 (2022).
Miyake, F. et al. A single-year cosmic ray event at 5410 BCE registered in 14C of tree rings. Geophys. Res. Lett. 48, e2021GL093419 (2021).
Bard, E. et al. A radiocarbon spike at 14,300 cal yr BP in subfossil trees provides the impulse response function of the global carbon cycle during the Late Glacial. Philos. Trans. A Math. Phys. Eng. Sci. 381, 20220206 (2023). This paper reports the largest annual increase in Î14C, and the only pre-Holocene event, discovered so far.
Miyake, F., Masuda, K. & Nakamura, T. Another rapid event in the carbon-14 content of tree rings. Nat. Commun. 4, 1748 (2013). This paper provides evidence of a second (ad 993) Miyake event, showing that these events recur.
Stuiver, M. A note on single-year calibration of the radiocarbon time scale, AD 1510â1954. Radiocarbon 35, 67â72 (1993).
Southon, J., Noronha, A. L., Cheng, H., Edwards, R. L. & Wang, Y. A high-resolution record of atmospheric 14C based on Hulu Cave speleothem H82. Quat. Sci. Rev. 33, 32â41 (2012).
Cheng, H. et al. Atmospheric 14C/12C changes during the last glacial period from Hulu Cave. Science 362, 1293â1297 (2018).
Cooper, A. et al. A global environmental crisis 42,000 years ago. Science 371, 811â818 (2021).
Hogg, A. G. et al. Advances and limitations in establishing a contiguous high-resolution atmospheric radiocarbon record derived from subfossil kauri tree rings for the interval 60â27 cal kyr BP. Quat. Geochronol. 68, 101251 (2022).
Reimer, P. J. et al. Selection and treatment of data for radiocarbon calibration: an update to the international calibration (IntCal) criteria. Radiocarbon 55, 1923â1945 (2013).
Heaton, T. J. et al. The IntCal20 approach to radiocarbon calibration curve construction: a new methodology using Bayesian splines and errors-in-variables. Radiocarbon 62, 821â863 (2020).
Büntgen, U. et al. Tree rings reveal globally coherent signature of cosmogenic radiocarbon events in 774 and 993 CE. Nat. Commun. 9, 3605 (2018). This is the evidence of global ESPE signatures that enables them to be used for annual-precision 14C calibration.
Wacker, L. et al. Radiocarbon dating to a single year by means of rapid atmospheric 14C changes. Radiocarbon 56, 573â579 (2014). This is the first usage of ESPEs to provide annual-precision dating using 14C.
Hakozaki, M. et al. Verification of the annual dating of the 10th century Baitoushan volcano eruption based on an AD 774â775 radiocarbon spike. Radiocarbon 60, 261â268 (2018).
Kuitems, M. et al. Radiocarbon-based approach capable of subannual precision resolves the origins of the site of Por-Bajin. Proc. Natl Acad. Sci. USA 117, 14038â14041 (2020).
Oppenheimer, C. et al. Multi-proxy dating the âmillennium eruptionâ of Changbaishan to late 946 CE. Quat. Sci. Rev. 158, 164â171 (2017).
Meadows, J., Zunde, M., LÄÄ£ere, L., Dee, M. W. & Hamann, C. in Radiocarbon. (ed Jull, A.J.T.) https://doi.org/10.1017/RDC.2023.24 (Cambridge Univ. Press, 2023).
Philippsen, B., Feveile, C., Olsen, J. & Sindbæk, S. M. Single-year radiocarbon dating anchors Viking Age trade cycles in time. Nature 601, 392â396 (2022). This provides an annual date for the start of the Viking Age using the ad 774 ESPE.
Kuitems, M. et al. Evidence for European presence in the Americas in ad 1021. Nature 601, 388â391 (2022). This paper identifies the year that Vikings were present in North America using the ad 993 ESPE.
Black, B. A. et al. A multifault earthquake threat for the Seattle metropolitan region revealed by mass tree mortality. Sci. Adv. 9, eadh4973 (2023).
Maczkowski, A. et al. Absolute dating of the European Neolithic using the 5259 BC rapid 14C excursion. Nat. Commun. 15, 4263 (2024).
Manning, S. W., Birch, J., Conger, M. A. & Sanft, S. Resolving time among non-stratified short-duration contexts on a radiocarbon plateau: possibilities and challenges from the AD 1480â1630 example and northeastern North America. Radiocarbon 62, 1785â1807 (2020).
Nakao, N., Sakamoto, M. & Imamura, M. 14C dating of historical buildings in Japan. Radiocarbon 56, 691â697 (2014).
Capano, M. et al. Is the dating of short tree-ring series still a challenge? New evidence from the pile dwelling of Lucone di Polpenazze (northern Italy). J. Archaeol. Sci. 121, 105190 (2020).
Djamali, M. et al. An absolute radiocarbon chronology for the world heritage site of Sarvestan (SW Iran): a late Sasanian heritage in early Islamic era. Archaeometry 64, 545â559 (2022).
Jull, A. J. T., Burr, G. S. & Hodgins, G. W. L. Radiocarbon dating, reservoir effects, and calibration. Quat. Int. 299, 64â71 (2013).
Gosman, J. H., Hubbell, Z. R., Shaw, C. N. & Ryan, T. M. Development of cortical bone geometry in the human femoral and tibial diaphysis. Anat. Rec. 296, 774â787 (2013).
Ubelaker, D. H. et al. Lag time of modern bomb-pulse radiocarbon in human bone tissues: new data from Brazil. Forensic Sci. Int. 331, 111143 (2022).
Rose, H. A., Meadows, J. & Bjerregaard, M. High-resolution dating of a medieval multiple grave. Radiocarbon 60, 1547â1559 (2018).
Chmielewski, T. J. et al. Increase in 14C dating accuracy of prehistoric skeletal remains by optimised bone sampling: Chronometric studies on eneolithic burials from Mikulin 9 (Poland) and Urziceni-Vada Ret (Romania). Geochronometria 47, 196â208 (2020).
Millard, A. Palace Green Library Excavations 2013 (PGL13): Chronology of the Burials. https://durham-repository.worktribe.com/output/1636149 (Durham University, 2015).
Gerrard, C., Graves, P., Millard, A., Annis, R. & Caffell, A. Lost Lives, New Voices: Unlocking the Stories of the Scottish Soldiers at the Battle of Dunbar, 1650 (Oxbow, 2018).
Douka, K. et al. Age estimates for hominin fossils and the onset of the Upper Palaeolithic at Denisova Cave. Nature 565, 640â644 (2019).
Fowler, C. et al. A high-resolution picture of kinship practices in an Early Neolithic tomb. Nature 601, 584â587 (2022).
Meadows, J. et al. High-precision Bayesian chronological modeling on a calibration plateau: the Niedertiefenbach gallery grave. Radiocarbon 62, 1261â1284 (2020).
Sedig, J. W., Olalde, I., Patterson, N., Harney, Ã. & Reich, D. Combining ancient DNA and radiocarbon dating data to increase chronological accuracy. J. Archaeol. Sci. 133, 105452 (2021).
Usoskin, I. G. et al. Solar cyclic activity over the last millennium reconstructed from annual 14C data. Astron. Astrophys. 649, A141 (2021).
Wu, C.-J., Krivova, N. A., Solanki, S. K. & Usoskin, I. G. Solar total and spectral irradiance reconstruction over the last 9000 years. Astron. Astrophys. 620, A120 (2018).
Usoskin, I. G. et al. Revisited reference solar proton event of 23 February 1956: assessment of the cosmogenic-isotope method sensitivity to extreme solar events. J. Geophys. Res. Space Phys. 125, e2020JA027921 (2020).
Mekhaldi, F., Adolphi, F., Herbst, K. & Muscheler, R. The signal of solar storms embedded in cosmogenic radionuclides: detectability and uncertainties. J. Geophys. Res. Space Phys. 126, e2021JA029351 (2021).
Usoskin, I. G. A history of solar activity over millennia. Living Rev. Sol. Phys. 20, 2 (2023).
Maehara, H. et al. Superflares on solar-type stars. Nature 485, 478â481 (2012).
Cliver, E. W., Schrijver, C. J., Shibata, K. & Usoskin, I. G. Extreme solar events. Living Rev. Sol. Phys. 19, 2 (2022).
Hathaway, D. H.The solar cycle. Living Rev. Sol. Phys. 12, 4 (2015).
Biswas, A., Karak, B. B., Usoskin, I. & Weisshaar, E. Long-term modulation of solar cycles. Space Sci. Rev. 219, 19 (2023).
Adolphi, F. et al. Radiocarbon calibration uncertainties during the last deglaciation: insights from new floating tree-ring chronologies. Quat. Sci. Rev. 170, 98â108 (2017).
Raisbeck, G. M. et al. An improved northâsouth synchronization of ice core records around the 41 kyr 10Be peak. Clim. Past 13, 217â229 (2017).
Turney, C. S. M. et al. High-precision dating and correlation of ice, marine and terrestrial sequences spanning Heinrich Event 3: testing mechanisms of interhemispheric change using New Zealand ancient kauri (Agathis australis). Quat. Sci. Rev. 137, 126â134 (2016).
Wacker, L. et al. Findings from an in-depth annual tree-ring radiocarbon intercomparison. Radiocarbon 62, 873â882 (2020).
Marcott, S. A. et al. Centennial-scale changes in the global carbon cycle during the last deglaciation. Nature 514, 616â619 (2014).
Bauska, T. K. et al. Carbon isotopes characterize rapid changes in atmospheric carbon dioxide during the last deglaciation. Proc. Natl Acad. Sci. USA 113, 3465â3470 (2016).
Hogg, A. et al. Punctuated shutdown of Atlantic meridional overturning circulation during Greenland Stadial 1. Sci. Rep. 6, 25902 (2016).
Capano, M. et al. Onset of the Younger Dryas recorded with 14C at annual resolution in French subfossil trees. Radiocarbon 62, 901â918 (2020).
Oeschger, H., Siegenthaler, U., Schotterer, U. & Gugelmann, A. A box diffusion model to study the carbon dioxide exchange in nature. Tellus 27, 168â192 (1975).
Zhang, Q. et al. Modelling cosmic radiation events in the tree-ring radiocarbon record. Proc. Math. Phys. Eng. Sci. 478, 20220497 (2022).
Golubenko, K., Rozanov, E., Kovaltsov, G. & Usoskin, I. Zonal mean distribution of cosmogenic isotope (7Be, 10Be, 14C, and 36Cl) production in stratosphere and troposphere. J. Geophys. Res. Atmos. 127, e2022JD036726 (2022).
Zheng, M. et al. Modeling atmospheric transport of cosmogenic radionuclide 10Be using GEOS-Chem 14.1.1 and ECHAM6.3-HAM2.3: implications for solar and geomagnetic reconstructions. Geophys. Res. Lett. 51, e2023GL106642 (2024).
Roth, R. & Joos, F. A reconstruction of radiocarbon production and total solar irradiance from the Holocene 14C and CO2 records: implications of data and model uncertainties. Clim. Past 9, 1879â1909 (2013).
Friedlingstein, P. et al. Global carbon budget 2023. Earth Syst. Sci. Data 15, 5301â5369 (2023).
Ciais, P. et al. Five decades of northern land carbon uptake revealed by the interhemispheric CO2 gradient. Nature 568, 221â225 (2019).
Basu, S. et al. Estimating US fossil fuel CO2 emissions from measurements of 14C in atmospheric CO2. Proc. Natl Acad. Sci. USA 117, 13300â13307 (2020).
Byrne, B. et al. National CO2 budgets (2015â2020) inferred from atmospheric CO2 observations in support of the global stocktake. Earth Syst. Sci. Data 15, 963â1004 (2023).
Hua, Q. et al. Atmospheric radiocarbon for the period 1950â2019. Radiocarbon 64, 723â745 (2022).
Delaygue, G., Bekki, S. & Bard, E. Modelling the stratospheric budget of beryllium isotopes. Tellus B Chem. Phys. Meteorol. 67, 28582 (2015).
Baroni, M., Bard, E., Petit, J.-R., Magand, O. & Bourlès, D. Volcanic and solar activity, and atmospheric circulation influences on cosmogenic 10Be fallout at Vostok and Concordia (Antarctica) over the last 60 years. Geochim. Cosmochim. Acta 75, 7132â7145 (2011).
Panovska, S., Korte, M. & Constable, C. G. One hundred thousand years of geomagnetic field evolution. Rev. Geophys. 57, 1289â1337 (2019).
Green, P. J. & Silverman, B. W. Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach (Chapman and Hall/CRC, 1993). https://doi.org/10.1201/b15710.
Bayliss, A. et al. IntCal20 tree rings: an archaeological Swot analysis. Radiocarbon 62, 1045â1078 (2020).
Kromer, B. et al. Regional 14CO2 offsets in the troposphere: magnitude, mechanisms, and consequences. Science 294, 2529â2532 (2001).
Manning, S. W. et al. Mediterranean radiocarbon offsets and calendar dates for prehistory. Sci. Adv. 6, eaaz1096 (2020).
Kimak, A. & Leuenberger, M. Are carbohydrate storage strategies of trees traceable by earlyâlatewood carbon isotope differences? Trees 29, 859â870 (2015).
Scott, E. M., Naysmith, P. & Cook, G. T. Why do we need 14C inter-comparisons?: The Glasgow –14C inter-comparison series, a reflection over 30 years. Quat. Geochronol. 43, 72â82 (2018).
Blackwell, P. G. & Buck, C. E. Estimating radiocarbon calibration curves. Bayesian Anal. 3, 225â248 (2008).
Geweke, J. in Bayesian Statistics 4 (eds Bernardo, J. M. et al.) 169â194 (Oxford Univ. Press, 1992).
Brooks, S. P. & Roberts, G. O. Convergence assessment techniques for Markov chain Monte Carlo. Stat. Comput. 8, 319â335 (1998).
Gelman, A. & Rubin, D. B. Inference from iterative simulation using multiple sequences. Statist. Sci. 7, 457â472 (1992).
Bronk Ramsey, C. Radiocarbon calibration and analysis of stratigraphy: the OxCal program. Radiocarbon 37, 425â430 (1995).
Geyer, C. J. Markov chain Monte Carlo maximum likelihood. In Computing Science and Statistics: Proc. 23rd Symposium on the Interface (ed. Keramidas, E. M.) 156â163 (Interface Foundation, 1991).
Robert, C. P. & Casella, G. Monte Carlo Statistical Methods (Springer, 2004). https://doi.org/10.1007/978-1-4757-4145-2.
Heaton, T. J. Nonâparametric calibration of multiple related radiocarbon determinations and their calendar age summarisation. J. R. Statist. Soc. C 71, 1918â1956 (2022).
Betancourt, M. A conceptual introduction to Hamiltonian Monte Carlo. Preprint at https://arxiv.org/abs/1701.02434 (2017).
Dee, M. W. & Pope, B. J. S. Anchoring historical sequences using a new source of astro-chronological tie-points. Proc. Math. Phys. Eng. Sci. 472, 20160263 (2016).
Weiner, S. Microarchaeology: Beyond the Visible Archaeological Record (Cambridge Univ. Press, 2010). https://doi.org/10.1017/CBO9780511811210.
Waterbolk, H. T. Working with radiocarbon dates. Proc. Prehist. Soc. 37, 15â33 (1971).
Ashmore, P. J. Radiocarbon dating: avoiding errors by avoiding mixed samples. Antiquity 73, 124â130 (1999).
McDonald, L. & Manning, S. W. A simulation approach to quantify the parameters and limitations of the radiocarbon wiggle-match dating technique. Quat. Geochronol. 75, 101423 (2023).
Dellaportas, P., Forster, J. J. & Ntzoufras, I. On Bayesian model and variable selection using MCMC. Stat. Comput. 12, 27â36 (2002).
Amaral Turkman, M. A., Paulino, C. D. & Müller, P. Computational Bayesian Statistics (Cambridge Univ. Press, 2019). https://doi.org/10.1017/9781108646185.
Reimer, P. J. et al. IntCal13 and Marine13 radiocarbon age calibration curves 0â50,000 years cal BP. Radiocarbon 55, 1869â1887 (2013).
Raukunen, O., Usoskin, I., Koldobskiy, S., Kovaltsov, G. & Vainio, R. Annual integral solar proton fluences for 1984â2019. Astron. Astrophys. 665, A65 (2022).
Mook, W. G. Business meeting: recommendations/resolutions adopted by the Twelfth International Radiocarbon Conference. Radiocarbon 28, 799 (1986).
Stuiver, M. & Polach, H. A. Discussion reporting of 14C data. Radiocarbon 19, 355â363 (1977).
Miyake, F. et al. Verification of the cosmic-ray event in ad 993â994 by using a Japanese hinoki tree. Radiocarbon 56, 1189â1194 (2014).
Oswald, A. Clay Pipes for the Archaeologist (BAR, 1975).
AlQahtani, S. J., Hector, M. P. & Liversidge, H. M. Brief communication: the London atlas of human tooth development and eruption. Am. J. Phys. Anthropol. 142, 481â490 (2010).
Bronk Ramsey, C. Development of the radiocarbon calibration program. Radiocarbon 43, 355â363 (2001).
Reimer, P. J. & Reimer, R. W. A marine reservoir correction database and on-line interface. Radiocarbon 43, 461â463 (2001).
