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 age calibration program, CALIB (Stuiver & Reimer 1986), first made available in 1986 and subsequently modified in 1987 (revision 2.0 and 2.1), has been amended anew. The 1993 program (revision 3.0) incorporates further refinements and a new calibration data set covering nearly 22,000 cal yr (≈18,400 14C yr). The new data, and corrections to the previously used data set, derive from a 6-yr (1986–1992) time-scale calibration effort of several laboratories.

If radiocarbon measurements are to be used at all for chronological purposes, we have to use statistical methods for calibration. The most widely used method of calibration can be seen as a simple application of Bayesian statistics, which uses both the information from the new measurement and information from the 14C calibration curve. In most dating applications, however, we have larger numbers of 14C measurements and we wish to relate those to events in the past. Bayesian statistics provides a coherent framework in which such analysis can be performed and is becoming a core element in many 14C dating projects. This article gives an overview of the main model components used in chronological analysis, their mathematical formulation, and examples of how such analyses can be performed using the latest version of the OxCal software (v4). Many such models can be put together, in a modular fashion, from simple elements, with defined constraints and groupings. In other cases, the commonly used “uniform phase” models might not be appropriate, and ramped, exponential, or normal distributions of events might be more useful. When considering analyses of these kinds, it is useful to be able run simulations on synthetic data. Methods for performing such tests are discussed here along with other methods of diagnosing possible problems with statistical models of this kind.

Count rates, representing the rate of 14C decay, are the basic data obtained in a 14C laboratory. The conversion of this information into an age or geochemical parameters appears a simple matter at first. However, the path between counting and suitable 14C data reporting (table 1) causes headaches to many. Minor deflections in pathway, depending on personal interpretations, are possible and give end results that are not always useful for inter-laboratory comparisons. This discussion is an attempt to identify some of these problems and to recommend certain procedures by which reporting ambiguities can be avoided.

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.

The IntCal04 and Marine04 radiocarbon calibration curves have been updated from 12 cal kBP (cal kBP is here defined as thousands of calibrated years before AD 1950), and extended to 50 cal kBP, utilizing newly available data sets that meet the IntCal Working Group criteria for pristine corals and other carbonates and for quantification of uncertainty in both the 14C and calendar timescales as established in 2002. No change was made to the curves from 0–12 cal kBP. The curves were constructed using a Markov chain Monte Carlo (MCMC) implementation of the random walk model used for IntCal04 and Marine04. The new curves were ratified at the 20th International Radiocarbon Conference in June 2009 and are available in the Supplemental Material at www.radiocarbon.org.

The focus of this paper is the conversion of radiocarbon ages to calibrated (cal) ages for the interval 24,000–0 cal BP (Before Present, 0 cal BP = AD 1950), based upon a sample set of dendrochronologically dated tree rings, uranium-thorium dated corals, and varve-counted marine sediment. The 14C age–cal age information, produced by many laboratories, is converted to Δ14C profiles and calibration curves, for the atmosphere as well as the oceans. We discuss offsets in measured l4C ages and the errors therein, regional 14C age differences, tree–coral 14C age comparisons and the time dependence of marine reservoir ages, and evaluate decadal vs. single-year 14C results. Changes in oceanic deepwater circulation, especially for the 16,000–11,000 cal BP interval, are reflected in the Δ14C values of INTCAL98.

A new calibration curve for the conversion of radiocarbon ages to calibrated (cal) ages has been constructed and internationally ratified to replace IntCal98, which extended from 0–24 cal kyr BP (Before Present, 0 cal BP = AD 1950). The new calibration data set for terrestrial samples extends from 0–26 cal kyr BP, but with much higher resolution beyond 11.4 cal kyr BP than IntCal98. Dendrochronologically-dated tree-ring samples cover the period from 0–12.4 cal kyr BP. Beyond the end of the tree rings, data from marine records (corals and foraminifera) are converted to the atmospheric equivalent with a site-specific marine reservoir correction to provide terrestrial calibration from 12.4–26.0 cal kyr B P. A substantial enhancement relative to IntCal98 is the introduction of a coherent statistical approach based on a random walk model, which takes into account the uncertainty in both the calendar age and the 14C age to calculate the underlying calibration curve (Buck and Blackwell, this issue). The tree-ring data sets, sources of uncertainty, and regional offsets are discussed here. The marine data sets and calibration curve for marine samples from the surface mixed layer (Marine04) are discussed in brief, but details are presented in Hughen et al. (this issue a). We do not make a recommendation for calibration beyond 26 cal kyr BP at this time; however, potential calibration data sets are compared in another paper (van der Plicht et al., this issue).

People usually study the chronologies of archaeological sites and geological sequences using many different kinds of evidence, taking into account calibrated radiocarbon dates, other dating methods and stratigraphic information. Many individual case studies demonstrate the value of using statistical methods to combine these different types of information. I have developed a computer program, OxCal, running under Windows 3.1 (for IBM PCs), that will perform both 14C calibration and calculate what extra information can be gained from stratigraphic evidence. The program can perform automatic wiggle matches and calculate probability distributions for samples in sequences and phases. The program is written in C++ and uses Bayesian statistics and Gibbs sampling for the calculations. The program is very easy to use, both for simple calibration and complex site analysis, and will produce graphical output from virtually any printer.

This paper highlights some of the main developments to the radiocarbon calibration program, OxCal. In addition to many cosmetic changes, the latest version of OxCal uses some different algorithms for the treatment of multiple phases. The theoretical framework behind these is discussed and some model calculations demonstrated. Significant changes have also been made to the sampling algorithms used which improve the convergence of the Bayesian analysis. The convergence itself is also reported in a more comprehensive way so that problems can be traced to specific parts of the model. The use of convergence data, and other techniques for testing the implications of particular models, are described.

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.

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/.

OxCal is a widely used software package for the calibration of radiocarbon dates and the statistical analysis of 14C and other chronological information. The program aims to make statistical methods easily available to researchers and students working in a range of different disciplines. This paper will look at the recent and planned developments of the package. The recent additions to the statistical methods are primarily aimed at providing more robust models, in particular through model averaging for deposition models and through different multiphase models. The paper will look at how these new models have been implemented and explore the implications for researchers who might benefit from their use. In addition, a new approach to the evaluation of marine reservoir offsets will be presented. As the quantity and complexity of chronological data increase, it is also important to have efficient methods for the visualization of such extensive data sets and methods for the presentation of spatial and geographical data embedded within planned future versions of OxCal will also be discussed.

New radiocarbon calibration curves, IntCal04 and Marine04, have been constructed and internationally ratified to replace the terrestrial and marine components of IntCal98. The new calibration data sets extend an additional 2000 yr, from 0–26 cal kyr BP (Before Present, 0 cal BP = AD 1950), and provide much higher resolution, greater precision, and more detailed structure than IntCal98. For the Marine04 curve, dendrochronologically-dated tree-ring samples, converted with a box diffusion model to marine mixed-layer ages, cover the period from 0–10.5 cal kyr BP. Beyond 10.5 cal kyr BP, high-resolution marine data become available from foraminifera in varved sediments and U/Th-dated corals. The marine records are corrected with site-specific 14C reservoir age information to provide a single global marine mixed-layer calibration from 10.5–26.0 cal kyr BP. A substantial enhancement relative to IntCal98 is the introduction of a random walk model, which takes into account the uncertainty in both the calendar age and the 14C age to calculate the underlying calibration curve (Buck and Blackwell, this issue). The marine data sets and calibration curve for marine samples from the surface mixed layer (Marine04) are discussed here. The tree-ring data sets, sources of uncertainty, and regional offsets are presented in detail in a companion paper by Reimer et al. (this issue).

The wide availability of precise radiocarbon dates has allowed researchers in a number of disciplines to address chronological questions at a resolution which was not possible 10 or 20 years ago. The use of Bayesian statistics for the analysis of groups of dates is becoming a common way to integrate all of the 14C evidence together. However, the models most often used make a number of assumptions that may not always be appropriate. In particular, there is an assumption that all of the 14C measurements are correct in their context and that the original 14C concentration of the sample is properly represented by the calibration curve.

In practice, in any analysis of dates some are usually rejected as obvious outliers. However, there are Bayesian statistical methods which can be used to perform this rejection in a more objective way (Christen 1994b), but these are not often used. This paper discusses the underlying statistics and application of these methods, and extensions of them, as they are implemented in OxCal v 4.1. New methods are presented for the treatment of outliers, where the problems lie principally with the context rather than the 14C measurement. There is also a full treatment of outlier analysis for samples that are all of the same age, which takes account of the uncertainty in the calibration curve. All of these Bayesian approaches can be used either for outlier detection and rejection or in a model averaging approach where dates most likely to be outliers are downweighted.

Another important subject is the consistent treatment of correlated uncertainties between a set of measurements and the calibration curve. This has already been discussed by Jones and Nicholls (2001) in the case of marine reservoir offsets. In this paper, the use of a similar approach for other kinds of correlated offset (such as overall measurement bias or regional offsets in the calibration curve) is discussed and the implementation of these methods in OxCal v 4.0 is presented.

The detailed radiocarbon age vs. calibrated (cal) age studies of tree rings reported in this Calibration Issue provide a unique data set for precise 14C age calibration of materials formed in isotopic equilibrium with atmospheric CO2. The situation is more complex for organisms formed in other reservoirs, such as lakes and oceans. Here the initial specific 14C activity may differ from that of the contemporaneous atmosphere. The measured remaining 14C activity of samples formed in such reservoirs not only reflects 14C decay (related to sample age) but also the reservoir 14C activity. As the measured sample 14C activity figures into the calculation of a conventional 14C age (Stuiver & Polach 1977), apparent 14C age differences occur when contemporaneously grown samples of different reservoirs are dated.

A re-evaluation of the Longin collagen-extraction method shows that a lower reflux temperature reduces degradation of protein (“collagen”) remnants. This allows additional purification through ultrafiltration to isolate the >30kDalton fraction of the reflux product.

Single-year and decadal radiocarbon tree-ring ages are tabulated and discussed in terms of 14C age calibration. The single-year data form the basis of a detailed 14C age calibration curve for the cal ad 1510–1954 interval (“cal” denotes calibrated). The Seattle decadal data set (back to 11,617 cal BP, with 0 BP = ad 1950) is a component of the integrated decadal INTCAL98 14C age curve (Stuiver et al. 1998). Atmospheric 14C ages can be transformed into 14C ages of the global ocean using a carbon reservoir model. INTCAL98 14C ages, used for these calculations, yield global ocean 14C ages differing slightly from previously published ones (Stuiver and Braziunas 1993b). We include discussions of offsets, error multipliers, regional 14C age differences and marine 14C age response to oceanic and atmospheric forcing.

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.

Bayesian models have proved very powerful in analyzing large datasets of radiocarbon (14C) measurements from specific sites and in regional cultural or political models. These models require the prior for the underlying processes that are being described to be defined, including the distribution of underlying events. Chronological information is also incorporated into Bayesian models used in DNA research, with the use of Skyline plots to show demographic trends. Despite these advances, there remain difficulties in assessing whether data conform to the assumed underlying models, and in dealing with the type of artifacts seen in Sum plots. In addition, existing methods are not applicable for situations where it is not possible to quantify the underlying process, or where sample selection is thought to have filtered the data in a way that masks the original event distribution. In this paper three different approaches are compared: “Sum” distributions, postulated undated events, and kernel density approaches. Their implementation in the OxCal program is described and their suitability for visualizing the results from chronological and geographic analyses considered for cases with and without useful prior information. The conclusion is that kernel density analysis is a powerful method that could be much more widely applied in a wide range of dating applications.