Integrated Tree-Ring-Radiocarbon High-Resolution Timeframe to Resolve Earlier Second Millennium BCE Mesopotamian Chronology

500 years of ancient Near Eastern history from the earlier second millennium BCE, including such pivotal figures as Hammurabi of Babylon, Šamši-Adad I (who conquered Aššur) and Zimrilim of Mari, has long floated in calendar time subject to rival chronological schemes up to 150+ years apart. Texts preserved on clay tablets provide much information, including some astronomical references, but despite 100+ years of scholarly effort, chronological resolution has proved impossible. Documents linked with specific Assyrian officials and rulers have been found and associated with archaeological wood samples at Kültepe and Acemhöyük in Turkey, and offer the potential to resolve this long-running problem. Here we show that previous work using tree-ring dating to place these timbers in absolute time has fundamental problems with key dendrochronological crossdates due to small sample numbers in overlapping years and insufficient critical assessment. To address, we have integrated secure dendrochronological sequences directly with radiocarbon (14C) measurements to achieve tightly resolved absolute (calendar) chronological associations and identify the secure links of this tree-ring chronology with the archaeological-historical evidence. The revised tree-ring-sequenced 14C time-series for Kültepe and Acemhöyük is compatible only with the so-called Middle Chronology and not with the rival High, Low or New Chronologies. This finding provides a robust resolution to a century of uncertainty in Mesopotamian chronology and scholarship, and a secure basis for construction of a coherent timeframe and history across the Near East and East Mediterranean in the earlier second millennium BCE. Our re-dating also affects an unusual tree-ring growth anomaly in wood from Porsuk, Turkey, previously tentatively associated with the Minoan eruption of the Santorini volcano. This tree-ring growth anomaly is now directly dated ~1681–1673 BCE (68.2% highest posterior density range), ~20 years earlier than previous assessments, indicating that it likely has no association with the subsequent Santorini volcanic eruption.


Fig A. The separate elements which comprise the selected MBA (KUL-KBK-ACM), and Porsuk (POR) tree-ring chronologies, and the three Gordion (GOR) elements that overlap in approximate temporal terms with Porsuk (as
. These tree-ring samples (elements) are shown here placed as previously reported [23] -the work reported in this paper changes the placements for samples from POR and for the MBA chronology (see Fig 7 and Figure B in S1 File). Some additional samples in the ACM and KBK chronologies are also shown (dark shading) which were not employed in the crossdating analyses. For the individual site chronologies, and for identification of the individual samples in each chronology, see Figures C-G in S1 File, S1 Dataset, S2 Dataset, S3 Dataset, Tables A-C in S1 File. Figure A in S1 File revised according to the dendro-14 C placements reported in Table 2 (compare with Fig 7), and after removing the assumption of a crossdate between the Porsuk and Gordion chronologies and between the Porsuk and MBA chronologies. cambium, i.e., last ring before bark), +N = additional ring(s) incomplete and/or not measured, and v = outer ring close to bark (whose determination is somewhat subjective). Unmarked ends indicate samples with an unknown number of absent rings, which were removed in shaping timbers for construction, from deterioration, or other unknown causes. For crossdating information, see S1 Dataset, Table C in S1 File.  Table B in S1 File. S1 Dataset, S2 Dataset, S3 Dataset and Tables A-D in S1 File summarize the separate site chronologies comprised of selected robust elements for ACM, KBK, KUL, POR and GOR (note: we show in Table B in S1 File only those 3 GOR samples which potentially overlap in temporal terms with the POR chronology). Fig 3 shows the selected robust sample numbers for the MBA chronological grouping of KUL-KBK-ACM and a summary of the crossdating statistics for this MBA chronology (together) versus the Porsuk (POR) chronology and for POR against GORthe data cited in Fig 3 come from Table C in S1 File which shows the crossdating grid for the five individual site chronologies discussed and used in this paper (terminology as S1 Dataset, S2 Dataset, S3 Dataset, Tables A, B in S1 File). We see robust crossdates for KUL v. KBK and ACM v. KBK, especially; these combined site chronologies (KUL-KBK-ACM) form the basis of the MBA chronology. We note that KUL and ACM best crossdate in the same position also, but without the shared robust linkages with the KBK chronology, this crossdate would be less than clear-cut by itself. Whereas, altogether, the three sites form a secure chronology. The best available linkages of any of the MBA set elements with POR are less than secure, as is GOR with POR. There are only 1 or 2, or at most for a short period, 3 samples in the GOR chronology in these putative overlaps, which is too few for a secure crossdate, especially when there is not a strong statistical link nor good visual match (Fig 3, Tables C-E in S1 File).

Fig B. Data in
See S1 Dataset, S2 Dataset, S3 Dataset, Tables A, B in S1 File.    (Fig 3) -and, critically, despite the long overlap, it cannot be considered as robust since: (i) the GOR chronology comprises only 1 or 2 (or for a short period) 3 samples across the relevant period (Fig 3, Figures A-B in S1 File); and (ii) because even this best available crossdate does not appear robust on the basis of a COFECHA analysis (Table E in S1 File).       There are other samples from the five sites (some examples are indicated, but not employed in this study, in Figures A-G in S1 File), and plausible site chronologies for this MBA set comprising some of these additional samples. However, in Fig 3, we show the selected most robust and clean (in terms of statistical and visual correlation) sets and samples from which we took 14 C dates for the tree-ring-14 C-wiggle-match analyses.
The individual tree-ring measurements for each of the samples in Fig 3 and S1 Dataset, S2 Dataset, S3 Dataset, and Tables A-C in S1 File have been submitted to the International Tree Ring Databank (ITRDB) (http://www.ncdc.noaa.gov/data-access/paleoclimatologydata/datasets/tree-ring) with ITRDB codes TURK044-TURK047, except for the select Gordion data which are already available (http://www1.ncdc.noaa.gov/pub/data/paleo/treering/measurements/europe/turk029.rwl). The Gordion juniper chronology (Figure G in S1 File) as a whole comprises many more samples over a long timespan reaching from the period shown in Fig 3 and Figures A-B in S1 File through to the earlier 1 st millennium BCE (Figure G in S1 File) [40,41]. However, for the time period relevant to this paper and for investigating the validity of the claimed dendrochronological crossdate with the Porsuk chronology, the total Gordion sample numbers in this time period are as shown in Fig 3 and Figures B and G in S1 File. The potential overlap of Gordion to Porsuk involves just 1 or 2 (or for only a short time) 3 samples.
Specific tree-ring sections (according to Relative Years, RY) were dissected by steel blade under a binocular microscope from selected samples for 14 C dating. As detailed for each sample in Table F in S1 File, these typically comprised either 10 or 9 tree-rings, but in a few cases a smaller stated number of tree-rings. Table F in S1 File lists all the specific tree-ring samples and the 14 C measurements which were then employed in the dating models (as summarized in Table  2). Figure H in S1 File indicates, as an example, the dissected and dated sections from the Porsuk tree-ring record. * The OxA δ 13 C data are stated as ±0.3‰ and from a separate stable isotope MS analysis. The VERA δ 13 C data are measurements from the AMS with the errors as stated in the table. The Heidelberg δ 13 C data are separate stable isotope MS measurements -the error is ~ 0.4‰. # OxA-30907 had a high offset between the δ 13 C measured on the AMS versus the stable isotope MS (suggesting fractionation at the level of 1.1%). Sometimes this indicates an issue with a sample and an age offset and this sample is also identified as an outlier in the model runs.
** The two 14 C measurements for ACM RY677-685 are not compatible with being the same 14 C age at the 5% level (T = 5.14 > 3.8) [60]. These two dates are not combined as a weighted average in the models (see Tables G-J in S1 File). $ Sample with VERA standard ABA treatment + Sample dated comprises the humic acid extract from the same numbered A_2 sample [56]. @ Sample received soxhlet, AB and bleaching pretreatment & Sample received soxhlet and ABA pretreatment Figure H. The tree-ring growth record for samples POR-26 and POR-2 and the locations (in terms of the relative chronology) from where samples for 14 C dating were dissected.

B. 14 C known age checks (Oxford) and laboratory inter-comparisons
A routine known-age sample testing program is run at the Oxford Laboratory to assess on-going dating accuracy (for examples, see [50] at SOM Section 2.2 and Fig.S1, [Reference D in S1 File]). During the period when the samples dated in this project were run at Oxford (03/06/2011 to 02/04/2015), a total of 433 measurements were made on samples of known age wood and these indicate that 97.7% of dates were within 2σ with a systematic bias of 1.6±1.3 yr (older).
As shown in Fig 4, three samples were dated -and several times and employing different approaches -both at Oxford and Vienna and all measurements produced compatible 14 C ages within 95% confidence limits [60]. Figure I in S1 File provides further details on the comparison by lab and sample pretreatment regime. Previous comparisons or known age tests for the Oxford, Vienna and Heidelberg radiocarbon laboratories have yielded good and comparable data [40,50,57,65,91]. Small contributions from correlated uncertainties, which may arise when data obtained by the same laboratory are combined, were not considered in the uncertainty of the combined final, weighted mean values employed [60]. To indicate the scale of this minor issue, we note with regard to the VERA dates, where we have most data, that the differences between the weighted average values used (i), and the values trying to allow for correlated uncertainty (ii), are: VERA-5750 (i) 3359±12 versus (ii) 3358±13; VERA-5751 (i) 3374±13 versus (ii) 3373±14 and VERA-5752 (i) 3392±13 versus (ii) 3390±14. Such very small differences are not significant to the analysis. The Oxford KUL and ACM dates and Heidelberg KBK dates were run on juniper wood from different sites, but in those instances where the data are similarly placed in calendar terms (similar RY ranges within <5 years) all the 14 C ages are similar and overlap within their 95% ranges.  Table F in S1 File with 2σ (95.4%) errors shown -all measurements for each set of the identical tree-rings are compatible with being estimates of the same 14 C age [60].

C. Chronological modelling and analysis -further details
Four examples of the Bayesian dendro-14 C-wiggle-match code used, for Models 3, 6b, 8a and 8b, are listed in Tables G-J in S1 File and examples of outputs are shown in Table 2, Figs 5, 6, and Figures J-M in S1 File. For details on the modelling, see the methods discussion in the main text. For some further discussion, see below in this section.  One point of detail to note is that in previous work it was argued that use of only the earlier (older, in calendar terms) section of the Gordion series gave a likely better calendar age placement [22,40]. The situation is less clear-cut with IntCal13 [61], although it remains the case that there is more noise in the later (more recent) part of the series -21.8% of data after Relative Year (RY) 1145.5 are outliers in Model 1 (all data) versus 14% of data for the earlier section RY 776.5 to 1145.5 in Model 4 (earlier data only): Table 2. We consider both the whole and reduced earlier Gordion datasets (see Fig 5 inset), and the difference in respective calendar placement is now small: ~6 years including outliers and ~4 years once outliers are excluded (Table 2). We observe that the various fits reported all appear good, but we note that some of the apparent outliers in these analyses result from their comparison against the smoothed IntCal13 record -whereas the data nearly all fit comfortably versus the underlying non-modelled (raw) IntCal13 dataset (Fig 5). Regardless of whether we prefer the use of the entire Gordion dataset, or the reduced earlier section (the options shown in Fig 5 and quantified in Table 2), the 14 C placement of the Porsuk chronology leaves it as incompatible with the previously stated (and now withdrawn) dendrochronological crossdate.
Figures J-M in S1 File show the modelled best placements (μ±σ is shown) for the dendrosequenced 14 C data for Models 3, 5, 6 and 8a from Table 2. In Bayesian Chronological Modelling with large or complex datasets, small variations occur between different runs (usually very minimal when employing fixed dendro-sequenced models as in this project).  Figure N in S1 File shows the modelled calendar probability distributions and most likely (highest probability density, hpd) 68.2% and 95.4% calendar age ranges, and μ±σ and median calendar ages for the placement of RY776 from Models 3, 5, 6 and 8a (as in Table 2, and Figures J-M in S1 File). Note: the tree-ring series do not all include an RY776 -this year is extrapolated in such cases to enable the comparison in terms of a single year. As noted in the main text, we also considered, as a comparison with the OxCal Bayesian modelling approach, the best fit of the Model 7b data (  Figure O in S1 File is only 6 years different (older) than the mean of the best fit probability distribution for Model 7b (Table 2). This comparison, as in previous studies (e.g. [22,43]), highlights that the calendar best fits calculated for the dendro-14 C wiggle-matches in Table 2 by OxCal are robust, and do not rely only on use of Bayesian statistical methods or any particular implementation. In addition, display of this least squares fit versus the IntCal13 modelled curve in Figure O in S1 File allows the chance to visualize the dendro-sequenced 14 C data from the MBA chronology data versus not only the modelled IntCal13 curve but also against the constituent data behind the IntCal13 model. We see the MBA data fitting well within the cloud of IntCal13 raw data. Three of the MBA data points are subjectively observed as particular outliers -more than 3 standard deviations (SD) from the mean IntCal13 value (indicated by orange arrows in Figure O in S1 File). Figure P in S1 File shows the analysis re-run excluding these three data points when calculating the least squares best fit function. The best fit is very similar, but 4 years more recent and only 4 calendar years different (older) than the mean of the best fit probability distribution for Model 8a in Table 2. The data visually offers a good fit in Figure P in S1 File with only a couple of the MBA dates (data points centered at RY 661 and 671) perhaps looking like possible outliers -although here it is relevant to note that there is in fact a relative dearth of constituent IntCal13 data points in this particular area, and so, were there additional data available, the MBA data might not seem so far then from the IntCal13 trend. . All data from the MBA chronology (shown in blue) are employed (except OxA-30907 for RY607-615, which had divergent δ 13 C values recorded by the AMS versus those independently measured on an MS, and so is considered inherently less than entirely reliable) with dates on the (exactly) contemporary tree-rings (even if from different sites) combined. Three data stand out, subjectively, as outliers and are more than 3 SD from the relevant IntCal13 modelled mean age and are indicated by the orange arrows. The constituent data employed to model the IntCal13 curve are shown by the magenta data points. All error bars are ±1SD. The inset shows the fit function of the least squares analysis with the best fit point, expressed in terms of the mid-point of the last dated sample = RY 701. As a final robustness test, the models after outliers were removed (Models 3, 6, 8a) were run again considering a possible 0±10 ΔR offset test [62]: see Table 2 (Models 3a, 6a, 8c). This was to consider whether there might be a small regional (e.g., growing season related) offset in contemporary 14 C levels between the trees growing in Anatolia over this time period versus the trees employed in building the IntCal13 dataset for this time period (which are from southern Germany and Ireland). Although small regional offsets have been observed in the East Mediterranean region at certain specific periods (in particular associated with major solar minima or other climate change episodes) (e.g. [57, Reference E in S1 File]), we find, as in previous work examining this issue more widely in Anatolia and the East Mediterranean (outside of Egypt -and we might hypothesize some parts of the southern Levant) that for most periods including the second millennium BCE [40, Reference F in S1 File], no substantive offset is evident -instead there is either only a very small offset and/or an offset found that is potentially compatible with a 0-year offset. Hence the data reported in Table 2 appear to be robust.