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.

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.

Radiocarbon (14C) dating is routinely used, yet occasionally, issues still arise surrounding laboratory offsets, and unexpected and unexplained variability. Quality assurance and quality control have long been recognized as important in addressing the two issues of comparability (or bias, accuracy) and uncertainty or variability (or precision) of measurements both within and between laboratories (Long and Kalin 1990). The 14C community and the wider user communities have supported interlaboratory comparisons as one of several strands to ensure the quality of measurements (Scott et al. 2018). The nature of the intercomparisons has evolved as the laboratory characteristics have changed s. The next intercomparison is currently being planned to take place in 2019–2020. The focus of our work in designing intercomparisons is to (1) assist laboratories by contributing to their QA/QC processes, (2) supplement and enhance our suite of reference materials that are available to laboratories, (3) provide consensus 14C values with associated (small) uncertainties for performance checking, and (4) provide estimates of laboratory offsets and error multipliers which can inform subsequent modeling and laboratory improvements.

Over the past 30 years, the format of the radiocarbon (14C) intercomparison studies has changed, however, the selection of sample types used in these studies has remained constant—namely, natural and routinely dated materials that could subsequently be used as in-house reference materials. One such material is peat which has been used 12 times, starting with the ICS in 1988. Peat from Iceland (TIRI), Ellanmore (TIRI), Letham Moss (ICS, VIRI, and SIRI), and St Bees, UK (FIRI and VIRI) have been used, as well as a near-background peat from Siberia. In the main, these peat samples have been provided as the humic acid fraction, with the main advantage being that the humic acid is extracted in solution and then precipitated (the solution phase providing the homogenisation) which is a key requirement for a reference material. In this paper, we will revisit the peat results and explore their findings. In addition, for the last 8 years, the Letham Moss sample has been used in the SUERC 14C laboratory as an in-house standard or reference material. This has resulted in several thousand measurements. Such a rich data set is explored to illustrate the benefits arising from the intercomparison program.

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/.

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.

Increasingly, the uses of data arc becoming more and more sophisticated as the archaeological and chronological questions being asked become more complex. Statistical models and tools for inference arc a routine part of an archaeological investigation encouraged through the availability of software, and with each release of that software, additional functionality is being added. This comes with enormous benefit but also at a cost—the dreaded black box. Therefore, this article, as the first in a series of short articles, will attempt to cover some of the things one needs to know to make the most of the power of the statistical revolution, while avoiding the pitfalls.

The Fifth International Radiocarbon Intercomparison (VIRI) continues the tradition of the TIRI (third) and FIRI (fourth) (Scott 2003) intercomparisons and operates in addition to any within-laboratory quality assurance measures as an independent check on laboratory procedures. VIRI is a phased intercomparison; results for the first phase, which employed grain samples, were reported in Scott et al. (2007). The second phase, involving bone samples, is reported here. The third and final phase, which includes samples of peat, wood, and shell, has also been completed and a companion paper appears in these proceedings.

Five bone samples were made available and included Sample E: mammoth bone (>5 half-lives); Sample F: horse bone (from Siberia, excavated in 2001; and Samples H and I: whale bones (approximately 2 half-lives). Sample G (human bone) was accessible only to accelerator mass spectrometry (AMS) laboratories because of the limited amount of sample available. More than 40 laboratories participated in Phase 2 and consensus values for the ages were as follows: Sample E = 39,305 14C yr BP (standard deviation [1 σ = 121 yr); Sample F = 2513 yr BP (1 σ = 5 yr); Sample G = 969 yr BP (1 σ = 5 yr); Sample H = 9528 yr BP (1 σ = 7 yr); and Sample I = 8331 yr BP (1 σ = 6 yr). Sample G had previously been dated by 4 laboratories and a weighted mean of 934 ± 12 yr BP had been quoted. Sample I had previously been dated at 8335 ± 25 yr BP and Sample H had been dated at 9565 ± 130 yr BP. Results for Sample H and Sample I are in good agreement with the previous results; Sample G results, however, give a value that is significantly older than the previously reported results.

Proficiency testing is a widely used, international procedure common within the analytical chemistry community. A proficiency trial (which VIRI is) often follows a standard protocol, including analysis that is typically based on z-scores, with one key quantity, σp. From a laboratory intercomparison (sometimes called a proficiency trial), we hope to gain an assessment of accuracy (in this case, from dendro-dated samples), laboratory precision (from any duplicate samples), and generally, an overall measure of performance, including measurement variability and hence realistic estimates of uncertainty. In addition, given our stated aim of creating an archive of reference materials, we also gain a determination of consensus values for new reference materials.

VIRI samples have been chosen to deliver these objectives and the sample ages included in the different stages, by design, spanned modern to background. With regard to pretreatment, some samples required intensive pretreatment (e.g. bone), while others required none (e.g. cellulose and humic acid). Sample size was not optimized, and indeed some samples were provided solely for accelerator mass spectrometry (AMS) measurement. In this sense, VIRI presented a more challenging exercise than previous intercomparisons, since by its design in stages, one can explore improvements (or deteriorations) over time in laboratory performance. At each stage, more than 50 laboratories have participated, with an increasing demographic shift towards more AMS and fewer radiometric laboratories.

The Fifth International Radiocarbon Intercomparison (VIRI) continues the tradition of the TIRI (third) and FIRI (fourth) intercomparisons (Scott 2003) and operates as an independent check on laboratory procedures in addition to any within-laboratory procedures for quality assurance. VIRI is a 4-yr project, with the first suite of samples (grain) sent out in September 2004 and the second suite (bone) sent out in December 2005. Further stages will include samples of peat, wood, and shell with a range of ages.

The 4 grain samples included 2 samples (A and C) of barley mash (20 g for radiometric analysis and 2 g for AMS), a grain (barley) byproduct from the manufacture of Glengoyne malt whiskey. The 2 remaining charred grain samples (B and D) were from excavations at Beth Saida and Tel Hadar, respectively (10 g for radiometric analysis and 4 seeds for AMS) and were provided by Elisabetta Boaretto of the Weizmann Institute. Consensus values for samples A and C are 109.2 (standard deviation [1 σ] = 2.73) and 110.6 pMC (1 σ = 2.48), and 2805 (1 σ = 162.7) and 2835 BP (1 σ = 190.8) for samples B and D, respectively. Sample A is a new sample that was collected in 2001, while sample C was used in the FIRI trial as samples G & J (consensus value 110.7 pMC) and was collected in 1998. The expected ages (on archaeological grounds) of samples B and D are 2800 BP and 2850–2900 BP, respectively. The second suite of samples comprises bone, ranging in age from Medieval to “close to background,” and was distributed in December 2005. Samples for both radiometric and AMS laboratories include E: mammoth bone (>5 half-lives); F: horse bone (from Siberia, excavated in 2001); and H, I: whalebone. Finally, sample G (human bone) was only for AMS laboratories. Some of the issues related to using bone in a laboratory intercomparison will be discussed.

All measurement is subject to error, which creates uncertainty. Every time that an analytical radiocarbon measurement is repeated under identical conditions on an identical sample (even if this were possible), a different result is obtained. However, laboratories typically make only 1 measurement on a sample, but they are still able to provide an estimate of the analytical uncertainty that reflects the range of values (or the spread) in results that would have been obtained were the measurement to be repeated many times under identical conditions. For a single measured 14C age, the commonly quoted error is based on counting statistics and is used to determine the uncertainty associated with the 14C age. The quoted error will include components due to other laboratory corrections and is assumed to represent the spread we would see were we able to repeat the measurement many times.

Accuracy and precision in 14C dating are much desired properties. Accuracy of the measurement refers to the deviation (difference) of the measured value from the true value (or sometimes expected or consensus value), while precision refers to the variation (expected or observed) in a series of replicate measurements. Quality assurance and experimental assessment of these properties occupy much laboratory time through measurement of standards (primary and secondary), reference materials, and participation in interlaboratory trials. This paper introduces some of the most important terms commonly used in 14C dating and explains, through some simple examples, their interpretation.

It is now almost 10 yr since radiocarbon dating of cremated bone was first developed using the small carbonate component contained within the hydroxyapatite-based inorganic fraction. Currently, a significant number of 14C laboratories date cremated bone as part of their routine dating service. As a general investigation of cremated bone dating since this initial development, a small, cremated bone intercomparison study took place in 2005, involving 6 laboratories. Six cremated bone samples (including 2 sets of duplicates), with ages spanning approximately 1500–2800 BP, were sent to the laboratories. The results, which showed relatively good agreement amongst the laboratories and between the duplicate samples, are discussed in detail.

Radiocarbon ages were measured on replicate samples of burnt grain and 5 mollusk species collected from a single sealed layer at an archaeological site (Hornish Point) on the west coast of South Uist, Scotland. The aim was to examine the impact of using different mollusk species on ΔR determinations that are calculated using the paired terrestrial/marine sample approach. The mollusk species examined inhabit a range of environments and utilize a variety of food sources within the intertidal zone. Several authors have suggested that these factors may be responsible for observed variations in the 14C activity of mollusk shells that were contemporaneous in a single location. This study found no significant variation in the 14C ages of the mollusk species, and consequently, no significant variation in calculated values of ΔR. The implication is that in an area where there are no carboniferous rocks or significant local inputs of freshwater to the surface ocean, any of a range of marine mollusk species can be used in combination with short-lived terrestrial material from the same secure archaeological context to accurately determine a ΔR value for a particular geographic location and period in time.

We assessed the evidence for variations in the marine radiocarbon reservoir effect (MRE) at coastal, archaeological Iron Age sites in north and west Scotland by comparing AMS measurements of paired marine and terrestrial materials (4 pairs per context). ΔR values were calculated from measurements on material from 3 sites using 6 sets of samples, all of which were deposited around 2000 BP. The weighted mean of the ΔR determinations was −79 ± 17 14C yr, which indicates a consistent, reduced offset between atmospheric and surface ocean 14C specific activity for these sites during this period, relative to the present day (ΔR = ∼0 14C yr). We discuss the significance of this revised ΔR correction by using the example of wheelhouse chronologies at Hornish Point and their development in relation to brochs. In addition, we assess the importance of using the concepts of MRE correction and ΔR variations when constructing chronologies using 14C measurements made on materials that contain marine-derived carbon.

The radiologic impact of 14C produced by the nuclear fuel cycle is assessed at both global and local levels. In the former context, it is predicted here that the specific activity of atmospheric CO2 in the year 2050 will be ca 7.6 pCig-1 C. Although this is similar to the present level, the subsequent collective dose commitment could be highly significant.

The enhancement of 14C concentrations around the nuclear fuel-reprocessing plant at Sellafield (Windscale) in Cumbria, U K has been monitored over recent years. For example, maximum levels of 27.2 pCig-1C (∼350% above natural) during 1984 were observed < 1 km from the plant, with enhanced activities detectable to at least 29km. Nevertheless, it is clear that the radiologic significance to the local population is low. The spatial distribution of the excess 14C allows atmospheric dispersion models to be tested in the context of continuous releases and the results thus far show that the Gaussian plume model performs successfully.