Caveat emptor!—wiggle-matching European wood samples (AD 46–AD 286)

Abstract

This study suggests that there may be considerable difficulties in providing accurate calendar age estimates in the Roman period in Europe, between ca. AD 60 and ca. AD 230, using the radiocarbon calibration datasets that are currently available. Incorporating the potential for systematic offsets between the measured data and the calibration curve using the ΔR approach suggested by Hogg et al. (2019), only marginally mitigates the biases in calendar date estimates observed. At present, it clearly behoves researchers in this period to “caveat emptor” and validate the accuracy of their calibrated radiocarbon dates and chronological models against other sources of dating information.

Introduction

The current radiocarbon calibration curve for the Northern Hemisphere, IntCal20 (Reimer et al. 2020), represents a major update of previous calibration curves (Reimer et al. 2004; Reimer et al. 2013). Over the first half of the first millennium AD, IntCal20 is based on over 550 calibration datapoints, in comparison to IntCal13, which was based on just over 100 (Figure 1 [upper]). The data included in IntCal13 were measured on decadal and bi-decadal blocks of wood, whereas IntCal20 also includes measurements on 5-year blocks for the entire half millennium, and measurements on single-year tree-rings between AD 290 and AD 486. A new statistical approach for the construction of the curve has also been adopted (Heaton et al. 2020).

Figure 1. IntCal20 (magenta-pink) and IntCal13 (grey) with the calibration datasets on which they are based; those from Seattle (QL; Stuiver and Braziunas 1993; Stuiver et al. 1998), Belfast (UB; McCormac et al. 2004; Pearson et al. 1986) and Waikato (Wk; Hogg et al. 2009) are included in both curves, those from Groningen (GrA; Sakamoto et al. 2003), Mannheim (MAMS-; Friedrich et al. 2019) and Palaeo Labo Co. Ltd (Sakamoto et al. 2003; Okuno et al. 2018) only in IntCal20. Measurements on Irish oak undertaken for this study are shown in blue (ETH- and GrM-). The first half of the first millennium AD (upper), the period of this study (lower).

In general, the calibration data and, thus, the two curves follow each other closely. There is, however, a more appreciable divergence between ca. AD 60 and ca. AD 230. As previously observed (Haneca et al. 2021; Staff and Liu 2021), this can lead to archaeologically meaningful differences in calibrated radiocarbon dates in this period. Modeling can exacerbate this issue, as demonstrated recently for a small cemetery (Group A) at Stanwick, Northamptonshire, which falls in the decades around AD 130 if modeled using IntCal13 or in the decades around AD 200 if modeled using IntCal20 (Fleming et al. submitted, fig. 5; Figure 2). The results from the two models are clearly incompatible, and both cannot be correct.

Figure 2. Probability distributions of dates from burials in Group A at Stanwick, Northamptonshire, UK, derived from the model defined in Fleming et al. (submitted, fig 5). Each distribution represents the relative probability that an event occurs at a particular time. Distributions in magenta-pink derive from the model calculated using IntCal13 (Reimer et al. 2013), and those in black from the model calculated using IntCal20 (Reimer et al. 2020). Crosses indicate the medians of the posterior distributions.

The Dataset

In order to compare the effectiveness of IntCal13 and IntCal20 for producing accurate calibration in the Roman period in Europe, a series of wiggle-match models were constructed using ¹⁴C measurements on known-age tree-rings from the Irish oak chronology (Baillie 1982; Brown and Baillie 2012; Pilcher et al. 1984).

The samples were of latewood from single tree-rings that have been dated by dendrochronology as forming between AD 46 and AD 286. Every fifth ring was dated, except in two cases where the gap was seven and three rings respectively (Appendix 1). The samples came from four bog oaks (Q815, Q821, Q837, and Q1081) recovered from a demolished cottage at Balloo, Co Down (52.47°N, 5.71°W), four bog oaks (Q9881, Q9985–6, and Q9888) from the lake edge at Ballinderry, Co Antrim (54.55°N, 6.28°W), and a single waterlogged oak (Q451) from those recovered from Allistragh, Co Armagh (54.23°N, 6.40°W). Details of the dendrochronological dating and sub-sampling for radiocarbon dating of the timbers from Balloo and Ballinderry can be found in Supplementary Material; details for the timber from Allistragh are published elsewhere (Wacker et al. 2020, Supplementary Material).

Radiocarbon dating of the samples of Irish oak was undertaken by the Centre for Isotope Research, University of Groningen (GrM-), the Netherlands, and at the Laboratory of Ion Beam Physics, ETH Zürich (ETH-), Switzerland in 2022. In Groningen, each ring was converted to α-cellulose using an intensified acid-base-acid-oxidation pretreatment (Dee et al. 2020) and combusted in an elemental analyser (IsotopeCube NCS), coupled to an Isotope Ratio Mass Spectrometer (Isoprime 100). The resultant CO₂ was graphitised by hydrogen reduction in the presence of an iron catalyst (Hut et al. 1986; Aerts-Bijma et al. 1997). The graphite was then pressed into aluminium cathodes and dated by Accelerator Mass Spectrometry (AMS) (Synal et al. 2007; Salehpour et al. 2016). In Zürich, cellulose was extracted from each ring using the base-acid-base-acid-bleaching (BABAB) method described by Němec et al. (2010), combusted and graphitised as outlined in Wacker et al. (2010c) and dated by accelerator mass spectrometry (Synal et al. 2007; Wacker et al. 2010a). At both laboratories data reduction was undertaken as described by Wacker et al. (2010b), and both facilities maintain continual programmes of quality assurance procedures (Aerts-Bijma et al. 2021, Sookdeo et al. 2020), in addition to participation in international inter-comparison exercises (Wacker et al. 2020).

The results are conventional ¹⁴C ages, corrected for fractionation using δ¹³C values measured by accelerator mass spectrometry (Stuiver and Polach 1977; Appendix 1). Fifteen tree-rings were measured by both laboratories, all pairs being consistent at the 5% significance level (Ward and Wilson 1978). The weighted mean difference between these replicates is −7.97±6.36 BP (ETH younger), and χ² _red is 0.75 (Bevington and Robertson 1992, equation 4.19; Bevington 1969, 69).

Wiggle-Matching

Wiggle-matching has been undertaken using the Bayesian approach first described by Christen and Litton (1995), implemented using OxCal v4.4 (Bronk Ramsey et al. 2001; Bronk Ramsey 2009). This method assumes that we have independent pointwise estimates of the calibration curve: covariance information from the calibration curve is not used (Millard 2008; Muzikar and Heaton 2022).

The models all contain measurements on seven tree-rings, spaced five years apart and spanning 31 calendar years (except those between AD 166–198 and AD 176–206 and those between AD 198–226 and AD 208–236 which span 33 calendar years and 29 calendar years respectively and contain some measurements spaced three years apart and seven years apart). This short span of calendar dating has been chosen to replicate archaeological reality, for example when wiggle-matching tree-ring sequences that are usually undatable by ring-width or oxygen isotope dendrochronology (Bayliss et al. 2017), or when wiggle-matching different elements of a human skeleton (Millard et al. 2020). All models calculate the date when the ring for AD 286 formed. Replicate measurements have been combined by taking a weighted mean before inclusion in the model. The 43 wiggle-matches run from AD 46−AD 76, AD 51−AD 81 etc. to AD 256−AD 286. Each model has been calculated three times: once using IntCal13, once using IntCal20, and once using IntCal20 allowing for a potential systematic offset between the new data and the calibration curve (applying the “Delta_R” function of OxCal with a uniform prior of −20 to +20 BP; Hogg et al. 2019). All models have been run at a resolution of 1 and for 20M iterations.

Figure 3 shows the wiggle-match model that includes measurements on samples dating to between AD 76 and AD 106, and so there are 180 rings until the formation of the ring for AD 286. In this case, the model calculated using IntCal13 (lower), the model calculated using IntCal20 (middle), and the model calculated using IntCal20 allowing for a potential systematic offset (upper), all clearly provide dating that is incompatible with the dendrochronological age for the formation of the ring for AD 286. The date estimate provided using IntCal13 is too early, and those provided using IntCal20 are too late.

Figure 3. Probability distributions of dates from AD 76–106. Each distribution represents the relative probability that an event occurs at a particular time. For each of the dates two distributions have been plotted: one in outline, which is the result of simple radiocarbon calibration, and a solid one, based on the wiggle-match sequence. Distributions other than those relating to particular samples, correspond to aspects of the model. For example, the distribution “AD 286” is the estimated date when the ring for AD 286 formed. The model has been calculated using IntCal13 (lower), IntCal20 (middle), and IntCal20 with an allowance for a potential systematic offset (upper).

The highest posterior density intervals for the ring for AD 286 from all 43 models, calculated using the three calibration approaches are provided in Appendix 2. The true value lies outside these intervals more often than expected (Table 1). The posterior distributions for the ring for AD 286 are illustrated in Figure 4. Those where the true date lies outside the Highest Posterior Density intervals at 95% probability are shown in magenta-pink. Again, it is clear that the wiggle-match results produced using IntCal13 are biased towards older ages, and that those produced using IntCal20 are biased towards younger ages. The use of the ΔR approach to allow for a potential systematic offset between the new data and the calibration curve marginally mitigates, but does not resolve, the younger bias in the dating produced using IntCal20.

Table 1. Number of models where the known-age of AD 286 is not included in the Highest Posterior Density intervals (rounded outwards to the nearest year)

Figure 4. Posterior density estimates for the ring formed in AD 286, from wiggle-matching measurements from seven rings spanning successive 31-year blocks between AD 46–76 and AD 256–286 (Acomb > An: 26.7, n: 7 for all), calculated using IntCal13 (lower), IntCal20 (middle), and IntCal20 with an allowance for a potential systematic offset (upper). Five of the models calculated using IntCal20 allowing a potential systematic offset (ΔR) have poor overall agreement (see Appendix 2). Distribution where the true date lies within the Highest Posterior Density intervals at 95% probability are shown in black, those where it is outside these intervals in magenta-pink.

Discussion

The greater quantity of data in IntCal20 means that it is usually more robust than IntCal13, although this case study demonstrates that producing accurate dating in the period between ca. AD 60 and ca. AD 230 is challenging using either calibration curve. Replication shows that the new data produced in Groningen and Zürich are consistent within the quoted uncertainties, which are of a similar scale to those reported for the calibration datasets (averages GrM: ±19 BP, ETH: ±19 BP; Table 2).

Table 2. Summary of calibration data included in IntCal13 and IntCal20 AD 46–286 (* average uncertainty includes reported error multiplier)

The reason that IntCal20 diverges from IntCal13 in this period is that it includes additional data from two Japanese trees (HKN-1, Japanese cedar, and NNMSM-TR1, Japanese cypress), which produce older ages than the data we have from North American trees (RC and SR, Giant Redwood) and European trees (Q451, Q455, Q218, and Q9887, oak), which were included in both IntCal13 and IntCal20, only during the late first and second centuries AD. The datasets are more compatible at later times, including with the single-year data on European trees measured in Mannheim (MAMS-; Figure 1 [upper]).

Systematic offsets can arise from laboratory biases, but also from geographic offsets. In this case, significant systematic laboratory bias is perhaps less likely since the data have been measured in more than one laboratory, and the data from the same trees measured in those same laboratories are in good agreement in the third and fourth centuries AD (Figure 1 [upper]). The Global Circulation Model of Braziunas et al. (1995) predicted a decline in atmospheric ¹⁴C of ca. 8 BP per 10° of latitude, but such a meridional trend has proved difficult to demonstrate in practice (but see Büntgen et al. 2018, fig 3; Pearson et al. 2020, table 1). In this case a simple latitudinal trend seems unlikely, because IntCal13 in this period is dominated by measurements on Giant Redwoods (from 36°N) and IntCal20 is dominated by measurements on Japanese trees (from 35°N). These datasets differ as much from each other as they do from the data on the Irish oak (from 52°N−54°N) (Figure 1 [lower]).

The offsets between the datasets included in IntCal20 anyway appear to vary through time. This is also apparent in the new dataset on Irish oak (Figure 5), which is significantly older than IntCal13 in the late first and second century AD, and significantly younger than IntCal20 in the second and earlier third century AD. Nakamura et al. (2013) have previously suggested that there may be a time-variable offset in Japanese trees, perhaps arising from variations in the East Asian monsoon, and Miyake et al. (2014, 1192) similarly observe that data on Japanese trees were older than IntCal13, but this would not explain the differences observed between IntCal13 and our new dataset.

Figure 5. Offsets between the data presented in Appendix 1 and IntCal13 (magenta-pink) and IntCal20 (black) (ETH = triangles, GrM = circles). Weighted mean offsets shown in bold are statistically significant at the 5% significance level.

It is also possible that there is annual variation in ¹⁴C which is currently not captured by the calibration curves as they are not visible in the blocked data that are currently available (Table 2). This may be the reason why some of the models calculated using IntCal20 and allowing for a systematic offset between the new dataset and the calibration curve have poor overall agreement (Table 2). If so, this may suggest that more year-to-year variation in atmospheric ¹⁴C content may be expected in the decades around AD 100. Generally, detailed understanding of the short-term variations in the shape of the calibration curve is critical for providing precise and accurate chronologies in situations where an archaeological site, or the available archaeological sequence, spans only a few decades.

Conclusions

This study suggests that there may be considerable difficulties in providing accurate calendar age estimates in the period between ca. AD 60 and ca. AD 230 using the radiocarbon calibration datasets that are currently available. It is possible that there may be locational differences in atmospheric radiocarbon that are important for archaeological interpretation at this time, although further work is clearly required to understand the observed variation. Incorporating the potential for systematic offsets between the measured data and the calibration curve using the ΔR approach suggested by Hogg et al. (2019), only marginally mitigates the biases in calendar date estimates observed (and it should be noted that this approach was not actually adopted in the statistical methodology used for constructing IntCal20 [Heaton et al. 2020]).

At present, it clearly behoves researchers in this period to “caveat emptor” and validate the accuracy of their calibrated radiocarbon dates and chronological models against other sources of dating information, such as the termini post quos provided by coins issued by known historical figures and documentary evidence where this is available.