Wiggle matching is an important and powerful technique in radiocarbon dating that can be used to improve the precision of calendar age estimates. All radiocarbon determinations require calibration to provide calendar age estimates. This calibration is achieved by comparing the determinations against a calibration curve $\mu ( \cdot )$ to calculate the probability the sample arises from any particular calendar age t. Wiggle matching involves the calibration of a set of radiocarbon determinations taken from samples with known separations between their calendar ages. Since the calendar age separations between samples are known, all the calendar ages are known functions of one particular age, ${T_1}$ — commonly the most recent calendar age. Dating the sequence then reduces to considering $p({T_1} = {t_1}|data)$, the probability of the calendar age ${t_1}$ given the set of radiocarbon determinations. In previous work, a Bayesian approach has been used to derive a nice formula for this quantity under the assumption we have independent pointwise estimates of the calibration curve $\mu (t)$. In this paper, we derive a generalization of this formula showing how to incorporate covariance information from the calibration curve under an assumption of multivariate normality.

To create a reliable radiocarbon calibration curve, one needs not only high-quality data but also a robust statistical methodology. The unique aspects of much of the calibration data provide considerable modeling challenges and require a made-to-measure approach to curve construction that accurately represents and adapts to these individualities, bringing the data together into a single curve. For IntCal20, the statistical methodology has undergone a complete redesign, from the random walk used in IntCal04, IntCal09 and IntCal13, to an approach based upon Bayesian splines with errors-in-variables. The new spline approach is still fitted using Markov Chain Monte Carlo (MCMC) but offers considerable advantages over the previous random walk, including faster and more reliable curve construction together with greatly increased flexibility and detail in modeling choices. This paper describes the new methodology together with the tailored modifications required to integrate the various datasets. For an end-user, the key changes include the recognition and estimation of potential over-dispersion in 14C determinations, and its consequences on calibration which we address through the provision of predictive intervals on the curve; improvements to the modeling of rapid 14C excursions and reservoir ages/dead carbon fractions; and modifications made to, hopefully, ensure better mixing of the MCMC which consequently increase confidence in the estimated curve.

We present new updates to the calendar and radiocarbon (14C) chronologies for the Cariaco Basin, Venezuela. Calendar ages were generated by tuning abrupt climate shifts in Cariaco Basin sediments to those in speleothems from Hulu Cave. After the original Cariaco-Hulu calendar age model was published, Hulu Cave δ18O records have been augmented with increased temporal resolution and a greater number of U/Th dates. These updated Hulu Cave records provide increased accuracy as well as precision in the final Cariaco calendar age model. The depth scale for the Ocean Drilling Program Site 1002D sediment core, the primary source of samples for 14C dating, has been corrected to account for missing sediment from a core break, eliminating age-depth anomalies that afflicted the earlier calendar age models. Individual 14C dates for the Cariaco Basin remain unchanged from previous papers, although detailed comparisons of the Cariaco calibration dataset to those from Hulu Cave and Lake Suigetsu suggest that the Cariaco marine reservoir age may have shifted systematically during the past. We describe these recent changes to the Cariaco datasets and provide the data in a comprehensive format that will facilitate use by the community.

The concentration of radiocarbon (14C) differs between ocean and atmosphere. Radiocarbon determinations from samples which obtained their 14C in the marine environment therefore need a marine-specific calibration curve and cannot be calibrated directly against the atmospheric-based IntCal20 curve. This paper presents Marine20, an update to the internationally agreed marine radiocarbon age calibration curve that provides a non-polar global-average marine record of radiocarbon from 0–55 cal kBP and serves as a baseline for regional oceanic variation. Marine20 is intended for calibration of marine radiocarbon samples from non-polar regions; it is not suitable for calibration in polar regions where variability in sea ice extent, ocean upwelling and air-sea gas exchange may have caused larger changes to concentrations of marine radiocarbon. The Marine20 curve is based upon 500 simulations with an ocean/atmosphere/biosphere box-model of the global carbon cycle that has been forced by posterior realizations of our Northern Hemispheric atmospheric IntCal20 14C curve and reconstructed changes in CO2 obtained from ice core data. These forcings enable us to incorporate carbon cycle dynamics and temporal changes in the atmospheric 14C level. The box-model simulations of the global-average marine radiocarbon reservoir age are similar to those of a more complex three-dimensional ocean general circulation model. However, simplicity and speed of the box model allow us to use a Monte Carlo approach to rigorously propagate the uncertainty in both the historic concentration of atmospheric 14C and other key parameters of the carbon cycle through to our final Marine20 calibration curve. This robust propagation of uncertainty is fundamental to providing reliable precision for the radiocarbon age calibration of marine based samples. We make a first step towards deconvolving the contributions of different processes to the total uncertainty; discuss the main differences of Marine20 from the previous age calibration curve Marine13; and identify the limitations of our approach together with key areas for further work. The updated values for ΔR, the regional marine radiocarbon reservoir age corrections required to calibrate against Marine20, can be found at the data base http://calib.org/marine/.

Radiocarbon (14C) ages cannot provide absolutely dated chronologies for archaeological or paleoenvironmental studies directly but must be converted to calendar age equivalents using a calibration curve compensating for fluctuations in atmospheric 14C concentration. Although calibration curves are constructed from independently dated archives, they invariably require revision as new data become available and our understanding of the Earth system improves. In this volume the international 14C calibration curves for both the Northern and Southern Hemispheres, as well as for the ocean surface layer, have been updated to include a wealth of new data and extended to 55,000 cal BP. Based on tree rings, IntCal20 now extends as a fully atmospheric record to ca. 13,900 cal BP. For the older part of the timescale, IntCal20 comprises statistically integrated evidence from floating tree-ring chronologies, lacustrine and marine sediments, speleothems, and corals. We utilized improved evaluation of the timescales and location variable 14C offsets from the atmosphere (reservoir age, dead carbon fraction) for each dataset. New statistical methods have refined the structure of the calibration curves while maintaining a robust treatment of uncertainties in the 14C ages, the calendar ages and other corrections. The inclusion of modeled marine reservoir ages derived from a three-dimensional ocean circulation model has allowed us to apply more appropriate reservoir corrections to the marine 14C data rather than the previous use of constant regional offsets from the atmosphere. Here we provide an overview of the new and revised datasets and the associated methods used for the construction of the IntCal20 curve and explore potential regional offsets for tree-ring data. We discuss the main differences with respect to the previous calibration curve, IntCal13, and some of the implications for archaeology and geosciences ranging from the recent past to the time of the extinction of the Neanderthals.

We undertook a strengths, weaknesses, opportunities, and threats (SWOT) analysis of Northern Hemisphere tree-ring datasets included in IntCal20 in order to evaluate their strategic fit with the demands of archaeological users. Case studies on wiggle-matching single tree rings from timbers in historic buildings and Bayesian modeling of series of results on archaeological samples from Neolithic long barrows in central-southern England exemplify the archaeological implications that arise when using IntCal20. The SWOT analysis provides an opportunity to think strategically about future radiocarbon (14C) calibration so as to maximize the utility of 14C dating in archaeology and safeguard its reputation in the discipline.

Early researchers of radiocarbon levels in Southern Hemisphere tree rings identified a variable North-South hemispheric offset, necessitating construction of a separate radiocarbon calibration curve for the South. We present here SHCal20, a revised calibration curve from 0–55,000 cal BP, based upon SHCal13 and fortified by the addition of 14 new tree-ring data sets in the 2140–0, 3520–3453, 3608–3590 and 13,140–11,375 cal BP time intervals. We detail the statistical approaches used for curve construction and present recommendations for the use of the Northern Hemisphere curve (IntCal20), the Southern Hemisphere curve (SHCal20) and suggest where application of an equal mixture of the curves might be more appropriate. Using our Bayesian spline with errors-in-variables methodology, and based upon a comparison of Southern Hemisphere tree-ring data compared with contemporaneous Northern Hemisphere data, we estimate the mean Southern Hemisphere offset to be 36 ± 27 14C yrs older.

Connecting calendar ages to radiocarbon (14C) ages, i.e. constructing a calibration curve, requires 14C samples that represent, or are closely connected to, atmospheric 14C values and that can also be independently dated. In addition to these data, there is information that can serve as independent tests of the calibration curve. For example, information from ice core radionuclide data cannot be directly incorporated into the calibration curve construction as it delivers less direct information on the 14C age–calendar age relationship but it can provide tests of the quality of the calibration curve. Furthermore, ice core ages on 14C-dated volcanic eruptions provide key information on the agreement of ice core and radiocarbon time scales. Due to their scarcity such data would have little impact if directly incorporated into the calibration curve. However, these serve as important “anchor points” in time for independently testing the calibration curve and/or ice-core time scales. Here we will show that such information largely supports the new IntCal20 calibration record. Furthermore, we discuss how floating tree-ring sequences on ice-core time scales agree with the new calibration curve. For the period around 40,000 years ago we discuss unresolved differences between ice core 10Be and 14C records that are possibly related to our limited understanding of carbon cycle influences on the atmospheric 14C concentration during the last glacial period. Finally, we review the results on the time scale comparison between the Greenland ice-core time scale (GICC05) and IntCal20 that effectively allow a direct comparison of 14C-dated records with the Greenland ice core data.

Terrestrial plant macrofossils from the sedimentary record of Lake Suigetsu, Japan, provide the only quasi-continuous direct atmospheric record of radiocarbon (14C) covering the last 50 ka cal BP (Bronk Ramsey et al. 2012). Since then, new high precision data have become available on U-Th dated speleothems from Hulu Cave China, covering the same time range (Cheng et al. 2018). In addition, an updated varve-based chronology has also been published for the 2006 core from Lake Suigetsu (SG06) based on extended microscopic analysis of the sediments and improved algorithms for interpolation (Schlolaut et al. 2018). Here we reanalyze the radiocarbon dataset from Suigetsu based on the new varve counting information and the constraints imposed by the speleothem data. This enables the new information on the calendar age scale of the Suigetsu dataset to be used in the construction of the consensus IntCal calibration curve. Comparison of the speleothem and plant macrofossil records provides insight into the mechanisms underlying the incorporation of carbon into different types of record and the relative strengths of different types of archive for calibration purposes.

Beyond ~13.9 cal kBP, the IntCal20 radiocarbon (14C) calibration curve is based upon combining data across a range of different archives including corals and planktic foraminifera. In order to reliably incorporate such marine data into an atmospheric curve, we need to resolve these records into their constituent atmospheric signal and marine reservoir age. We present results of marine reservoir age simulations enabling this resolution, applying the LSG ocean general circulation model forced with various climatic background conditions and with atmospheric radiocarbon changes according to the Hulu Cave speleothem record. Simulating the spatiotemporal evolution of reservoir ages between 54,000 and 10,700 cal BP, we find reservoir ages between 500 and 1400 yr in the low- and mid-latitudes, but also more than 3000 yr in the polar seas. Our results are broadly in agreement with available marine radiocarbon reconstructions, with the caveat that continental margins, marginal seas, or tropical lagoons are not properly resolved in our coarse-resolution model.

This research investigates two factors influencing the ability of tree-ring data to provide accurate 14C calibration information: the fitness and rigor of the statistical model used to combine the data into a curve; and the accuracy, precision and reproducibility of the component 14C data sets. It presents a new Bayesian spline method for calibration curve construction and tests it on extant and new Southern Hemisphere (SH) data sets (also examining their dendrochronology and pretreatment) for the post-Little Ice Age (LIA) interval AD 1500–1950. The new method of construction allows calculation of component data offsets, permitting identification of laboratory and geographic biases. Application of the new method to the 10 suitable SH 14C data sets suggests that individual offset ranges for component data sets appear to be in the region of ± 10 yr. Data sets with individual offsets larger than this need to be carefully assessed before selection for calibration purposes. We identify a potential geographical offset associated with the Southern Ocean (high latitude) Campbell Island data. We test the new methodology for wiggle-matching short tree-ring sequences and use an OxCal simulation to assess the likely precision obtainable by wiggle-matching in the post-LIA interval.

The IntCal09 and Marine09 radiocarbon calibration curves have been revised utilizing newly available and updated data sets from 14C measurements on tree rings, plant macrofossils, speleothems, corals, and foraminifera. The calibration curves were derived from the data using the random walk model (RWM) used to generate IntCal09 and Marine09, which has been revised to account for additional uncertainties and error structures. The new curves were ratified at the 21st International Radiocarbon conference in July 2012 and are available as Supplemental Material at www.radiocarbon.org. The database can be accessed at http://intcal.qub.ac.uk/intcal13/.

The Southern Hemisphere SHCal04 radiocarbon calibration curve has been updated with the addition of new data sets extending measurements to 2145 cal BP and including the ANSTO Younger Dryas Huon pine data set. Outside the range of measured data, the curve is based upon the ern Hemisphere data sets as presented in IntCal13, with an interhemispheric offset averaging 43 ± 23 yr modeled by an autoregressive process to represent the short-term correlations in the offset.

We present a new record of radiocarbon ages measured by accelerator mass spectrometry (AMS) on a deep-sea core collected off the Pakistan Margin. The 14C ages measured on the planktonic foraminifera Globigerinoides ruber from core MD04-2876 define a high and stable sedimentation rate on the order of 50 cm/kyr over the last 50 kyr. The site is distant from the main upwelling zone of the western Arabian Sea where 14C reservoir age is large and may be variable. Many independent proxies based on elemental analyses, mineralogy, biomarkers, isotopic proxies, and foraminiferal abundances show abrupt changes correlative with Dansgaard-Oeschger and Heinrich events. It is now common knowledge that these climatic events also affected the Arabian Sea during the last glacial period through changes in the Indian monsoon and in ventilation at intermediate depths. The stratigraphic agreement between all proxies, from fine- to coarse-size fractions, indicates that the foraminiferal 14C ages are representative of the different sediment fractions.

To build a calendar age scale for core MD04-2876, we matched its climate record to the oxygen isotopic (δ18O) profile of Hulu Cave stalagmites that have been accurately dated by U-Th (Wang et al. 2001; Southon et al. 2012; Edwards et al., submitted). Both archives exhibit very similar signatures, even for century-long events linked to monsoonal variations. For comparison, we have also updated our previous work on core MD95-2042 from the Iberian Margin (Bard et al. 2004a,b,c), whose climate record has likewise been tuned to the high-resolution δ18O Hulu Cave profile. Sophisticated and novel statistical techniques were used to interpolate ages and calculate uncertainties between chronological tie-points (Heaton et al. 2013, this issue). The data from the Pakistan and Iberian margins compare well even if they come from distant sites characterized by different oceanic conditions. Collectively, the data also compare well with the IntCal09 curve, except for specific intervals around 16 cal kyr BP and from 28 to 31 cal kyr BP. During these intervals, the data indicate that 14C is somewhat older than indicated by the IntCal09 curve. Agreement between the data from both oceanic sites suggests that the discrepancy is not due to local changes of sea-surface 14C reservoir ages, but rather that the IntCal09 curve needed to be updated in these intervals as has been done in the framework of IntCal13 (Reimer et al. 2013a, this issue).

High-quality data from appropriate archives are needed for the continuing improvement of radiocarbon calibration curves. We discuss here the basic assumptions behind 14C dating that necessitate calibration and the relative strengths and weaknesses of archives from which calibration data are obtained. We also highlight the procedures, problems, and uncertainties involved in determining atmospheric and surface ocean 14C/12C in these archives, including a discussion of the various methods used to derive an independent absolute timescale and uncertainty. The types of data required for the current IntCal database and calibration curve model are tabulated with examples.

We consider a general methodology for the transferral of chronologies from a master reference record containing direct dating information to an undated record of interest that does not. Transferral is achieved through the identification, by an expert, of a series of tie-points within both records that are believed to correspond to approximately contemporaneous events. Through tying of the 2 records together at these points, the reference chronology is elastically deformed onto the undated record. The method consists of 3 steps: creation of an age-depth model for the reference record using its direct dating information; selection of the tie-points and translation of their age estimates from the reference to the undated record; and finally, creation of an age-depth model for the undated record using these uncertain tie-point age estimates. Our method takes full account of the uncertainties involved in all stages of the process to create a final chronology within the undated record that allows joint age estimates to be found together with their credible intervals. To achieve computational practicality, we employ a Gaussian process to create our age-depth models. Calculations can then be performed exactly without resort to extremely slow Monte Carlo methods involving multiple independent model fits that would be required by other age-depth models.