Introduction

Since Willard Libby won the Nobel prize in 19601, radiocarbon (14C) has played a revolutionary role in determining the timing and rates of key changes in Earth’s climate, our environment, and human society over the last 55,000 years2,3,4,5,6,7,8. However, as there have been substantial variations in atmospheric 14C/12C levels over time, all raw radiocarbon ages need to be calibrated in order to place them on the calendar scale9,10,11,12,13. Variations in atmospheric 14C/12C ratios, in the following reported as Δ14C, which denotes relative difference to 14C/12C at AD 1950 in permille, have occurred due to changes in the rate of 14C production in the upper atmosphere and/or shifts in the carbon cycle. To obtain an accurate and precise calendar age from a fossil sample, we need to know atmospheric Δ14C at its time of growth. Accurately estimating atmospheric 14C/12C variations over time is therefore essential to optimise our use of 14C. The more accurate our knowledge of past Δ14C levels, the more accurately we can calibrate a 14C measurement to obtain the sample’s calendar age.

Improvements in reconstructions of past Δ14C variations do not however only offer increased accuracy when calibrating radiocarbon determinations. They also provide wider insights into critical Earth and climate system processes. Since 14C production rates vary in response to changes in the strength of the geomagnetic and heliomagnetic fields, understanding past Δ14C levels and their variations allows reconstruction of the temporal variability of the Earth’s magnetic field and of past solar activity14,15,16. The subsequent transport of 14C via the carbon cycle also provides an opportunity to better understand the dynamics of the Earth system, through studying differences in Δ14C levels across the various carbon cycle reservoirs, from soils to the ocean interior. Carbon exchange between reservoirs and within the ocean affects marine and atmospheric Δ14C levels17,18,19.

Since 19939,10,11,12,13, the INTCAL working group has been responsible for providing internationally-agreed reconstructions of Δ14C levels in three principal reservoirs: the Northern Hemispheric (NH) atmosphere13; the Southern Hemispheric atmosphere (SH)20; and the surface oceans21. The most suitable data to produce atmospheric calibration curves are tree-ring 14C measurements dated by dendrochronology. IntCal20, the most recent reconstruction of past NH atmospheric Δ14Clevels, uses known-age dendrochronologically dated trees back to c.a. 12,300 cal yr BP22. These measurements are extended further using several highly-resolved overlapping 14C tree-ring sequences which, while not dendrochronologically dated, can be almost absolutely linked in terms of calendar age. This provides a highly precise and accurate estimate of Δ14C levels based upon only tree-ring 14C measurements back to c.a. 13,910 cal yr BP23.

Further back in time, however, between 14,000 and 55,000 cal yr BP, the IntCal20 estimate of Δ14C variation is less precise and high-frequency signals cannot currently be resolved. The recovery of NH trees during this glacial period has, to date, been extremely rare. In this critical period of glacial climate, the IntCal20 curve is therefore predominantly based upon combining measurements from a diverse range of additional archives such as speleothems, corals, and lake and marine sediments13. These archives have several complications: they are typically sparse, have complex calendar age uncertainties, and frequently do not directly record atmospheric Δ14C. Both speleothems and marine 14C records are depleted in 14C compared to the atmospheric levels via a dead carbon fraction and marine reservoir age, respectively. This depletion is likely to dampen atmospheric 14C variation and may also result in calibration datasets that diverge over time if not appropriately corrected.

Even the Lake Suigetsu record, which contains 14C measurements from terrestrial macrofossils and is used in IntCal20, is not absolutely calendar dated because its original, varve-counted, age scale must be adjusted by matching to 14C features in the Hulu Cave speleothem record24. Furthermore, due to their very small size the Lake Suigetsu samples often have large 14C uncertainties. In addition to the limitations of our current 14C archives, the IntCal20 curve prior to 14,000 cal yr BP is also not primarily intended for reconstruction of atmospheric Δ14C variations. Instead, it is designed for calibration. All the data beyond 14,000 cal yr BP used in IntCal20’s construction have uncertainties in their calendar ages. To ensure accurate calibration, this uncertainty needs to be incorporated into the curve. During construction, IntCal20 considers all the possible calendar age placements of its constituent archives and, for each hypothetical placement, creates individual curve realisations representing a plausible Δ14C history were that calendar age placement correct. While each Δ14C realisation is wiggly, the precise timing of these wiggles differs by realisation. To enable accurate calibration, IntCal20 must average over the possible calendar age placements of its records. It does this by averaging over all the individual realisations, summarising them by pointwise means and variances. Where calendar age uncertainty in the underlying records is substantial, this averaging results in a mean IntCal20 Δ14C curve which is smoother than any of its individual realisations25. As a consequence of all these factors, it is not possible to resolve high-frequency Δ14C variation from 14,000 to 55,000 cal yr BP in the IntCal20 NH curve. This currently limits our ability to rigorously test competing scenarios and hypotheses in both archaeological and climate science – particularly regarding the causes of atmospheric Δ14C variations26.

The discovery of subfossil trees suitable for the construction of further tree-ring 14C sequences would provide the ideal archives to improve the current lack of precision in the NH atmospheric Δ14C reconstruction from 14,000 to 55,000 cal yr BP. Due to their annually resolved internal structure, and the direct link between the Δ14C in tree-ring cellulose and the atmospheric Δ14C, such tree-ring sequences hold the key to resolve high-frequency atmospheric Δ14C variations and to provide chronologies for sequences involving just a few human generations. Currently, the tree-ring 14C sequences from glacial period that have been measured are known as floating. As they do not overlap with the absolutely dated tree-ring dendrochronologies, their absolute calendar ages are unknown25,27,28. However, their constituent rings can still be counted to create a relative internal chronology. Even if their absolute ages are not known, this known internal chronology provides important insight into the amplitude of Δ14C variations over time29,30.

Typically, these floating trees-ring sequences are incorporated into the IntCal calibration curves by splicing them in alongside other 14C data that have better absolute age controls25. However, as explained above, the published IntCal20 curve then averages over their potential absolute calendar age placements. Consequently the IntCal20 mean curve will not reproduce the amplitude of the internal Δ14C variation observed within any floating tree-ring sequence. This amplitude is critical if we wish to infer potential changes in 14C production rates or changes in the carbon cycle. To reliably estimate this, we must instead consider the Δ14C variation along the floating tree’s relative internal chronology (even if we are not exactly sure, in absolute age terms, when that variation occurred).

Our understanding of potential mechanisms for changes in 14C production rates and the carbon cycle is informed by comparison with other cosmogenic radionuclides, in particular 10Be and 36Cl records stored within ice cores31,32,33. Comparing observed 14C signals with these other cosmogenic radionuclides can be used to align the ice core with 14C timescales34; or to help distinguish between changes in the 14C production rate and shifts in the carbon cycle. One disadvantage is that the common production rate changes of 14C and 10Be vary in a quasi-cyclic fashion on decadal to centennial timescales due to periodic changes in solar activity. Thus, in order to establish a unique link, tree-ring chronologies need to provide relatively long (centennial) time series and possibly prior knowledge of the assumed absolute age window of the records. Another challenge is the different geochemistry of 14C and 10Be: while atmospheric Δ14C is affected by changes in the carbon cycle, 10Be is affected by deposition changes. Hence, even during strong production rate changes such as during the Laschamps geomagnetic field minimum, seemingly unique matches between ice-core 10Be and tree-ring 14C may be misleading due to apparently large and not well-understood changes in the carbon cycle35,36,37,38.

In order to improve the precision of radiocarbon calibration during the glacial period and to better understand the Δ14C variations, it is essential to build up further high-precision series of tree-ring-based 14C measurements. For IntCal20, the only NH trees from the deglaciation period, prior to the continuous Central Europe oak and pine dendrochronology, came from Northern Italy and were of a 700-year duration, between 14,000 and 14,700 cal yr BP31,34. In Europe, some sub-fossil trees of glacial age were deposited in sediments of river valleys, such as the Po plain and quarries in Italy, and in other glacial deposits. Here we demonstrate the potential of subfossil larch trees from North-East Italy at the Revine site (Venetian Prealps)39,40, to provide more detailed reconstructions of Δ14C further into the glacial. We present the first 1000-year-long section of tree-ring chronology segments, and corresponding sub-decadal 14C-series, covering the period from c.a. 18,475-17,350 cal yr BP in Heinrich Stadial 1 (HS-1) (Fig. 1). Our data provide a higher-resolution archive of Δ14C variations during HS-1 than achievable with IntCal20, with patterns associated with changes in solar activity41,42,43.

Fig. 1: Revine Trees, location and chronologies.
figure 1

A map showing the location of Revine (red square) (base map from GeoMappApp (www.geomapapp.org); B Revine trees collected in 1995 by B.K. field campaign (The photo is taken by B.K. co-author of the paper, and under his copyright); C Ring width index chronologies of Revine groups 1, 3, 2 and 4 on its relative Revine timescale. The relative positions resp. the approximately absolute ages of the tree-ring series are based on the Δ14C comparisons. Gr.1 and Gr.3 are matched dendrochronologically (tBaillie&Pilcher: 5,1). Gr. 2 and Gr. 4 overlap only very slightly and they do not show any obvious statistical significant match. Their tentative position is based on a multi-step argumentation line of Δ14C comparisons, 10Be-Δ14C comparisons and the statistically non-significant visual match of the tree-ring series.

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Results

Dendrochronological results

The dendrochronological analysis of 33 larch samples (Larix decidua Mill.) provided 25 tree-ring series, which could be combined into tree-ring chronologies. Based on the statistical and visual agreement (Supplementary Table 1a–d), 12 tree-ring series were combined to generate the Revine group 1 (Gr. 1) chronology (336 years; average tB&P: 8.54) (Supplementary Fig. 1). Three other tree-ring series were combined together to create the Revine Gr.3 chronology (296 years; average tB&P: 8.4) (Supplementary Fig. 2). Comparisons between chronologies Revine Gr.1 and Gr.3 revealed good visual and statistical correlations (TB&P: 5.6; Glk 63%; P > 99%) (Supplementary Fig. 3) that could be additionally affirmed by 14C-series comparisons on both groups. The combined chronology (Revine Gr.1/3) spans 429 years. Two tree-ring series were combined into the Revine Gr.4 chronology (260 years; average tB&P: 7,1) (Supplementary Fig. 4) and another four larch series were combined to form the Revine Gr.2 chronology (286 years; average tB&P: 7,1) (Supplementary Fig. 5).

In almost all cases, the trees consisted of trunks or stumps without branches and sapwood, and the outermost ring or bark was not preserved. Therefore, the exact year of death of the trees cannot be determined. The larch trees show an average ring width of 0.9 mm (Gr. 1), 0.98 mm (Gr. 2), 0.69 mm (Gr. 3), and 0.84 mm (Gr. 4), which is comparable to modern sites at the alpine altitudinal timberline at ca. 2000 m asl. The frequent occurrence of partial and total absent rings, especially in the Revine Gr. 1 chronology, is associated with the influence of larch moth infestation, which regularly leads to extremely low growth every 7–11 years in some trees. In Revine Gr. 1, 75% of the trees show locally absent rings. The procedure described for recent and late Holocene larch chronologies to identify larch budmoth years of infestation and conceivable totally absent tree rings using a non-host species chronology as a ref. 44 is not possible for this dataset. However, the successful cross-matching of the Revine Gr. 1 chronology with the Revine Gr. 3 chronology, whose trees are much less affected by the pest and do not show any absent rings, allows an additional validation of the chronologies, as it covers the full critical period (203 years) of Gr. 3. The influence of larch budmoth outbreaks is minor in Gr. 2, and totally absent in Gr. 4. Hence, the possibility of further unidentified tree rings in the chronologies is extremely unlikely. Chronologies Revine Gr. 1/3, Gr. 2, and Gr. 4 represent secure and robust floating tree-ring chronologies that are the solid basis for our high-resolution 14C series described in this work (Supplementary Table 2).

The three Revine chronologies (Gr. 1/3, Gr. 2, and Gr. 4) do not cross-date dendrochronologically, indicating that the trees likely grew during different time intervals, also confirmed by the later 14C analyses. From 14C data, a short overlap of 51 years between Gr. 4 and Gr. 2 is possible, which coincides with a visual tentative match of the tree-ring curves. This overlap cannot be statistically validated because of its short duration and low replication, but can be supported by the link to 10Be, as discussed below. We therefore further use the position of this tentative link, which lies well within the uncertainty range of the 14C-data. Comparison with existing 14C data from the speleothems of Hulu Cave36,45 and macrofossils of Lake Suigetsu24 indicate that the 3 chronologies cover a period of ca. 1200 calendar years (18,475–17,325 cal yr BP), albeit with a gap of c.a. 200 calendar years (from c.a. 18,050 to 17,850 cal yr BP) between the youngest ring of Gr. 1/3 and the oldest ring of Gr. 4.

14C results and link to IntCal20 raw data

One hundred and ten blocks (each consisting of three annual rings) at mostly decadal spacing were taken from the entire length of the Revine chronologies for radiocarbon age determination. The chronologies fall in a 14C age range between 15,250 and 14,180 14C BP (Supplementary Table 2). While the absolute calendar age of each distinct Revine chronology is unknown, the internal chronology within each of the three tree-ring groupings (Revine Gr. 1/3; Gr. 2; and Gr. 4) is due to dendrochronological ring counting. Reconstructing the atmospheric Δ14C levels seen within the Revine trees over the course of their exact internal chronologies allows us to obtain unique insight into the amplitude of Δ14C variation during HS-1. Furthermore, we can obtain relatively precise absolute calendar age positioning for each Revine Chronologies by comparison with existing 14C measurements from Hulu Cave36,45 and Lake Suigetsu24 for which independent estimates of calendar age have been obtained by the U-Th (uranium-thorium) method and varve counting respectively (see Methods for details). This comparison suggests that the most likely calendar dates (the posterior marginal mode) for the innermost ring of the tree-ring chronologies are 18,475 cal yr BP (±35 cal yrs) for Revine Gr. 1/3; 17,605 cal yr BP (±50 cal yrs) for Revine Gr. 2; and 17,830 (±55 cal yrs) for Revine Gr. 4. These calendar age placements are shown in Fig. 2 (alongside the Hulu and Suigetsu 14C measurements).

Fig. 2: Revine tree-ring 14C data.
figure 2

The 14C dates of Revine groups and their respective calendar ages in comparison with 14C measurements from Hulu Cave (purple open circle), Lake Suigetsu (orange open square), the marine foraminifera from Cariaco basin (black triangles) and the IntCal20 calibration curve (green dots)68, using the MCMC scheme. All the dates are plotted with 1σ error bars.

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Revine Gr. 1/3 documents in detail a strong decline in 14C ages (rise in \({\Delta }^{14}\)C) between 18,300 and 18,100 cal yr BP. This 14C age decline is seen more clearly within the Revine Gr. 1/3 tree-ring sequence than in the smoothed and indirect Hulu and Lake Suigetsu 14C data. The 14C age inversion apparent in IntCal20 around 18,400 cal yr BP appears to be artefact of systematic differences between the two raw data sets of IntCal20 rather than a genuine atmospheric feature. A similar discrepancy is evident between 17,600 and 17,300 cal yr BP in the IntCal20 raw data. In general, our tree-ring Revine data appear to confirm the sequence of the Hulu 14C data but with a resolution that is 10 times greater and with a reduced level of smoothing.

Figure 3 shows the reconstruction of \({\Delta }^{14}\)C based on the Revine trees alone (located at their most likely calendar ages according to the comparison with the Hulu and Suigetsu 14C data). This reconstruction uses the same spline methodology as for the dendrodated tree-ring section of IntCal2021. Knots have been placed every 5 cal yrs. The amplitude of the \({\Delta }^{14}\)C variations within the Revine trees appear to be of greater magnitude (δΔ14C 45‰) than those observed within the Holocene (δΔ14C 20 to 35‰– see Supplementary Fig. 6 which presents the three periods in the Holocene with the greatest Δ14C variation). This increase in Δ14Cvariation during HS-1 is perhaps due to differences in the carbon cycle (e.g., rate of exchange between ocean and atmosphere, internal mixing of Southern Atlantic Ocean)42,43.

Fig. 3: Reconstruction of Δ14C.
figure 3

Atmospheric 14C reconstruction based on Revine 14C tree-ring sequences located at their most likely (marginal posterior mode) calendar ages compared to IntCal20 estimate (green shape). The Revine observations are plotted with 1σ error bars, while the IntCal and Revine curves show 95% (or 2σ) probability intervals.

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10Be link to ice core scale GICC05

We compare our Revine 14C-data, placed at their posterior modal calendar ages, to ice-core 10Be records. In the case of Revine, the tree-ring records are relatively short and record the quasi-cyclic 14C-variations caused by the solar DeVries (~200 years) and Gleissberg (~90 years) cycles which occur throughout large parts of the Last Glacial Maximum46. This leads to many acceptably good matches between the ice-core and tree-ring data but limits the possibility to use the Revine trees to constrain the ice core timescale. In addition, the Greenland ice core timescale GICC0547 has been shown to systematically deviate from the radiocarbon timescale during the glacial over long periods, with the greatest change in the inferred difference between the ice core and 14C timescale occurring between Greenland Interstadial 1 and ~22,000 cal yr BP48. Linearly interpolating between the latest estimate of the timescale difference of approx. zero years around 13,000 cal yr BP and 375 years at 22,000 cal yr BP48,49 implies an offset of around 190 years at 18,000 cal yr BP. We note, however, that the older tie-point is particularly uncertain (68.2% probability interval from 75 to 625 years). Once we include the ice-core layer counting errors in between the tie-points of 211 years between 13,000 and 18,000 cal yr BP, and 180 years between 18,000 and 22,000 cal yr BP, it becomes clear that the ice cores cannot be used to provide strong (independent) constraints on the precise calendar ages of the Revine trees during this period.

Nonetheless, the 10Be record is still able to provide useful inferential support. Figure 4 shows the comparison between ice-core 10Be and the Revine tree-ring 14C data. We modelled Δ14C-variations from 10Be using a box-diffusion carbon cycle model50 under a constant carbon cycle with reduced air-sea gas-exchange and ocean internal mixing compared to preindustrial48. As discussed above, we shifted the ice-core timescale by +190 years to account for the previously inferred differences between the ice core timescales GICC05 and IntCal48,49. Especially for Gr. 2 (blue symbols in Fig. 4), there is a good match between ice-core 10Be and tree-ring 14C, lending support to the proposed ages for the tree-ring chronology and the ice-core timescale adjustment. Gr. 4 agrees with the 10Be best when shifted 50 calendar years younger than the posterior marginal modal calendar age (17,830 cal yr BP) that is obtained when using the Hulu cave and Lake Suigetsu 14C data. This revised calendar age placement of Gr. 4 is, however, well within the calendar uncertainty (±55 yr) of the match and also supported by a tentative dendrochronological match between Gr. 4 and Gr. 2. The combined Gr. 1/3 data show co-variability between 18,200 and 18,400 cal yr BP lending support to their relative alignment. However, the tree-ring 14C-data exhibits Δ14C variations of greater amplitude than those inferred from ice-core 10Be. This is possibly due to the lower resolution of the 10Be-data, which, in this period, is an average of around 25 cal yrs. This means that it cannot capture some of the high-frequency changes resolved by the tree-ring data. Higher-resolution 10Be-data could help to resolve this and enable a more robust link between tree-rings and ice cores. Nonetheless, this comparison lends support to the proposed difference between ice-core and radiocarbon timescales during the glacial, as well as to the inferred calendar ages for the tree-rings.

Fig. 4: Absolute ages of the tree-ring data.
figure 4

Comparison of the 3 floating tree-ring chronologies (coloured symbols, plotted with 1σ error bars) to modelled Δ14C based on 10Be-fluxes from the GRIP ice core (yellow line)46. The absolute ages of the tree-ring data are inferred by14C/12C comparison. The Δ14C is shown as the anomaly from the mean of each chronology. The ice-core data are shown on the GICC05 timescale shifted by +190 years48,49 and high-pass filtered with a cutoff-period of 1000 years.

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Generally, 14C and 10Be are covariant in the solar variability time spectrum, except for about one century around 18,100 cal yr BP. Here, 14C is increasing in the atmosphere, most probably caused by a reduction in 14C uptake of the Atlantic Ocean mixed layer at the onset of HS-1. A reduction of AMOC strength at the onset of HS-1 is indicated by an increase of 231Pa/230Th ratio in ocean sediments of the western deep Atlantic51. Also, a sedimentary terrestrial high-resolution record from Southern Iberia reveals centennial subphases of HS-1, starting cold and arid at ca. 18,400 cal yr BP52. However, only the tree-ring record can provide decadal resolution in 14C to study the effect of a weakening AMOC on the carbon cycle on decadal time scales.

Discussion and conclusion

The temporal alignment suggested by comparison to other absolutely-dated 14C records and 10Be links, resulting in a sequence without major gaps, confirms the existence of a well-established larch forest in the Alpine region during HS-1, i.e., by the initial Revine site study39. In the southern Alpine region, other fossil wood dated back to 18,300 cal yr BP is found in Lago Piccolo di Avigliana (353 m a.s.l). Together with pollen evidence (e.g., Lago di Viverone, 220 m a.s.l., Torfsee, 270 m a.s.l.,53), it suggests that larch was already present in the lowlands when deglaciation started53,54,55. The larch tree finds at Revine together with abundant macrofossils and pollen findings in different regions of northern Italy56,57 indicate that larch pioneer forests may have been widespread in the southern alpine region during HS-1 and that larch forest-steppe persisted throughout GS-258.

The onset and the duration of the larch forest documented at Revine is synchronous with the end of the Alpine Late Glacial Maximum and the Alpine ice retreat at 19,000-17,500 cal yr BP. This is consistent with global climate warming59 and increased drought in the Mediterranean60,61. Here we have demonstrated the advantage of tree-ring 14C data sets, where the decadal temporal resolution is three to ten times higher than that of the Suigetsu and Hulu archives, and the 14C uncertainty is reduced by a factor of two to three. We also note that in the period covered by our trees, the Hulu and Suigetsu 14C data often appear somewhat offset from one another with the IntCal20 curve falling in between. Our 14C data set appears to follow the Hulu data more closely than Suigetsu. Hence, we see an important role for our data in future IntCal calibration data during this time range as well as a possible need for minor revisions to the Suigetsu calendar timescale.

This work clearly shows the strength of the combined studies of dendrochronology, radiocarbon dating, and 10Be to develop new floating tree-ring width chronologies and high-resolution 14C-data sequences from sub-fossil trees grown during the most recent glacial period. As already outlined above, fieldwork is ongoing in the Mediterranean area. Newly found trees, together with those already existing, will provide 14C data sets of sub-decadal temporal resolution and high 14C precision in various time intervals. The findings document intervals of favourable conditions of forest growth, contributing strongly to local paleoclimate reconstruction during the last glacial period.

Material and methods

The subfossil larch trees of Revine

The paleoenvironmental context of the deposits with subfossil wood stems in the clay quarry of Revine was initially studied between 1972 and 197639,40. At that time, 70 subfossil larch (Larix decidua Mill.) tree stumps and trunks were found ‘in situ’ and described. The trees grew during the deglaciation at the edge of the Glacial main moraine rim at a glacial lake and were gradually covered by fine-grained colluvial deposits, which allowed for excellent preservation. By our own fieldwork and investigations at museums, universities and private collections since 1994, 34 individual larch (Larix decidua Mill.) and two individual elder trees (Alnus spec.) of the same site in Revine were collected. Sixteen of these trees could be reliably assigned to the original logs sampled in 1976 and thus embedded in the stratigraphy established by Casadoro39. Five logs were documented and resampled during our own fieldwork in the no longer used clay pit. The dendrochronological analyses were carried out at the University of Hohenheim, and 3 chronologies of 429, 296, and 286 rings (which were not connected to one another dendrochronologically) could be constructed. Initial radiocarbon analysis on some single tree sections gave the first insight into the variation of 14C in the period of Heinrich Stadial-1 (HS-1)41. Then high-resolution (sub-decadal) 14C data sets were obtained covering in total almost one millennium. Subsequently, these results were compared to 10Be in Greenland Ice cores.

Dendrochronological analysis

The clean cross section at surfaces of the subfossil trees were cut with razor blades to enable precise visual identification of the ring boundaries using a microscope. Measurements of the annual growth widths on multiple radii per tree were made using a LINTAB measurement device of RinnTech (Heidelberg, Germany) with an accuracy of 0.01 mm and the software TSAPWin (Version 4.87)62. Cross-dating, chronology building and data verification were performed with software program TSAPWin62. Cross-dating measurements were compared using standard dendrochronological cross-dating statistics: Student’s t-values based on cross-correlation coefficients (r) between the detrended measurement series (tB&P)63 and a sign test (GLK %) with its significance level (p)64. Programs that support chronology building (COFECHA63,65) were not useful here, as they give very contradictory results for larch trees with rhythmically occurring narrow rings, which are typical when tree are affected by the larch bud moth. In order to ensure the identification of all rings, even the partially absent ones, we prepared the entire surface on several discs per tree and measured a large number of radii, including in areas of reaction wood or root attachments, where remnants of partially absent rings are often still detectable.

Revine samples preparation and 14C dating

From the four tree-ring chronologies of Revine, we selected tree specimens with well-preserved wood. A series of sub-samples of 3 rings each (25 to 500 mg) was cut in the Hohenheim tree-ring laboratory and sent to the BRAVHO radiocarbon laboratory at the University of Bologna, Italy, for extraction of cellulose. For 14C measurements, every third 3-ring sample (every 9 years) were selected. Most of the samples were pretreated using the BABAB method66. Samples of low preservation, resp. very low initial dry weight had to be pretreated by ABAB66. Until the end of 2021, the cellulose samples were graphitized at the Radiocarbon laboratory of ETH Zurich. From then on, they were graphitized at BRAVHO, using an AGE 3 system. All samples were measured by AMS at ETH Zurich. The results are listed in Supplementary Table 2.

Estimation of absolute calendar ages for the three Revine 14C chronologies

Each of the three Revine tree-ring groupings was considered to have an unknown calendar age for its oldest measured ring (denoted \({S}_{1/3}\), \({S}_{2}\), and \({S}_{4}\) respectively). These values were estimated via a Bayesian errors-in-variables Markov Chain Monte Carlo (MCMC) scheme based upon the approach used to incorporate the floating tree-ring sequences into IntCal2025. The Revine 14C measurements were combined with 14C observations from between 19,000 and 17,000 cal yr BP provided by the H82 and MSL Hulu Cave speleothems, and the 14C observations from the macrofossils from Lake Suigetsu. While the absolute calendar ages \({\theta }_{i}\) of the Hulu and Lake Suigetsu 14C measurements are themselves uncertain, estimates \({T}_{i}\) are available via U/Th and an adjusted varve count respectively. Given the age of the oldest ring in a Revine tree-ring group, the entire chronology for that particular grouping becomes known precisely due to the internal ring-counts. Within our MCMC scheme, the common atmospheric level of \({\Delta }^{14}\)C was modelled as a Bayesian cubic spline (placing knots every 5 cal yrs) with unknown coefficients \(\beta\) and an unknown smoothing parameter \(\lambda\). Fit to the 14C data was assessed in the \({F}^{14}\)C domain where observational uncertainties are symmetric.

Intuitively, the MCMC scheme aimed to find plausible calendar age placements for all the 14C measurements within the Revine, Hulu and Suigetsu records simultaneously (while respecting the complex calendar age covariance structure within the Hulu and Suigetsu observations, and the known internal ring counts of the three Revine groupings). These calendar age placements are obtained based on the principle that the 14C measurements from all the records arise from a common and shared atmosphere, albeit in the case of the Hulu speleothem, the observed Δ14C is offset from the atmosphere by its dead carbon fraction (DCF). It is critical to locate all the Revine groupings on the calendar scale simultaneously (rather than to wiggle match each Revine sequence separately) since every group provides information on the atmospheric levels of 14C/12C (and on the DCF of Hulu), and hence, informs the placement of each other.

Metropolis-within-Gibbs was implemented to alternate between updates to the spline coefficients \(\beta\) (that represent the joint atmospheric estimate of Δ14C)67, updates to the smoothing parameter \(\lambda\), and updates to the true calendar ages of the various 14C measurements – both for the comparison Hulu and Lake Suigetsu observations; and the three Revine groupings. We modelled the mean DCF within the Hulu Cave speleothems as unknown, with a prior value of \(N(480,\,{8}^{2})\) 14C yrs. This was selected based upon investigation into the observed offset between Hulu Cave 14C measurements and contemporaneous 14C measurements from dendro-dated trees25 between 14,000 and 10,000 cal yr BP. This means DCF value was also updated within our MCMC scheme. Additionally, we placed a further level of independent variation of 50 14C yrs on the Hulu DCF (at 1\(\sigma\)) to model any temporal DCF variation around the mean level. This choice of ±50 14C yrs was again based on investigation into the variability of Hulu’s 14C offset to dendro-dated tree-ring measurements. Uninformative priors were placed on both the smoothing parameter \(\lambda\), and on the starting calendar ages (\({S}_{1/3}\), \({S}_{2}\), and \({S}_{4}\)) of the Revine groupings.

The sampler was run for 250,000 iterations with the addition of parallel tempering to improve chain mixing. The first 125,000 iterations were discarded as burn-in. This provided complete posterior calendar age estimates for each of \({S}_{1/3}\), \({S}_{2}\), and \({S}_{4}\). The posterior mean for the calendar age of the oldest ring in Revine Gr. 1/3 was 18,450 ± 34 cal yrs (1σ); for Gr. 2 it was 17,588 ± 49 cal yrs; for Gr. 4 it was 17,849 ± 54 cal yrs. However, rather than using the mean values, for our investigation into the amplitude of the atmospheric 14C/12C we chose to fix each Revine chronology at its marginal posterior mode calendar age. These modal ages represent the most-likely individual calendar ages for the sequences according to our modelling above using the Hulu and Lake Suigetsu 14C records. For Revine Gr. 1/3 this was 18,475 cal yr BP; for Gr. 2 it was 17,605 cal yr BP; and for Gr. 4 it was 17,830 cal yr BP. These calendar age placements are shown in Figs. 2 and 3. For Gr. 4 a shift by 51 years to younger ages appears possible, as discussed below, and used when creating the Revine-only atmospheric \({\Delta }^{14}\)C curve in Fig. 3.