Multi-proxy crossdating extends the longest high-elevation tree-ring chronology from the Mediterranean

Annually precise dating is the cornerstone of dendrochronology. The accurate crossdating of relict wood is, however, frequently challenged during early chronology periods when sample replication is typically low. Here we present a multi-proxy approach in which stable carbon (δ¹³C) and radiocarbon (¹⁴C) isotope data are used to evaluate and correct dating errors in the early period of the longest high-elevation tree-ring chronology from the Mediterranean Basin. The record was initially developed using 878 tree-ring width (TRW) and 192 maximum latewood density (MXD) series from living and relict Bosnian pines (Pinus heldreichii) from Mt. Smolikas in Greece to reconstruct hydroclimate and temperature variability back to the 8th century. New annually resolved and non-pooled δ¹³C series now suggest a re-dating of first millennium relict pine samples during a period when sample replication was too low for proper TRW and/or MXD crossdating. The associated correction shifts the start of the Mt. Smolikas chronology from 575 back to 468 CE, a change independently confirmed by wiggle-matching annual ¹⁴C data along the 774/775 CE cosmic event. Our study demonstrates the importance of independent age validation for robust chronology development and shows how multi-proxy crossdating can improve dating success during periods of low sample replication.     

Tree-ring dating and radiocarbon wiggle matching of Buddhist arhat statues at Heungkuksa temple in Namyangju,South Korea

This paper reports the results of tree-ring dating and radiocarbon (AMS) wiggle matching of Buddhist statues stored at Heungkuksa Temple, Namyangju city, South Korea. A 121-yr composite chronology was made from the base panels of four Arhat statues, which were successfully dated using tree rings. The outermost ring was dated as A.D. 1538. The radiocarbon ages (measured by accelerator mass spectrometry, AMS) of eight single-year samples from a statue for wiggle matching fit the IntCal04 curve well, yielding a small error for the radiocarbon date (1528–1541 cal AD) of 14 years within the 2σ range, a 95.4% confidence interval. This range included the true dendro-date, A.D. 1538. The results suggested that there was no significant offset in radiocarbon in the 16th century between central Korea and the regions the IntCal04 curve was made from: Europe (Ireland) and the Pacific Northwest of the U.S.A. The date of the Arhat statues in Heungkuksa Temple (A.D. 1538), obtained in this study, becomes the earliest one for Arhat statues in Korea.     

甘肃省徐家城旧石器遗址的年代

庄浪县徐家城遗址是甘肃省新发现的含丰富旧石器文化遗物的遗址,主要埋藏于水洛河第二级阶地上覆的马兰黄土中。AMS14C测年及气候事件对比相结合的综合年代研究显示, 遗址主要文化层时代集中在距今4.6~2.3万年间, 属于晚更新世晚期。遗址所在的陇西盆地发现近50处晚更新世旧石器遗址, 测年、黄土地层学等的综合年代学研究利于建立该地区晚更新世完整的年代学框架, 为我们进一步讨论晚更新世人类行为演化、人类行为与环境变化的互动等重要学术问题提供了基础。     

Crossdating Juniperus procera from North Gondar, Ethiopia

The application of dendrochronology in (sub)tropical regions has been limited by the difficulty in finding trees with distinct annual rings that can be crossdated. Here, we report successful crossdating of Juniperus procera trees from North Gondar, Ethiopia. The trees form annual rings in response to a unimodal rainfall regime. The selection of mesic locations ensured that the trees did not respond to intra-seasonal weather anomalies. Crossdating was achieved by comparison of the wood anatomy directly on the surface of the core samples and purpose-adapted skeleton plotting. Wood-anatomical anomalies, such as false and indistinct rings, were regarded as potentially replicated features and used in crossdating. COFECHA yielded site-specific mean series inter-correlations between 0.52 and 0.59. AMS radiocarbon dating during the bomb era indicated that dating uncertainty is ±1 year.     

Dendrochronology improves understanding of the charcoal production history

Charcoal piles have become a frequent subject of research in recent years as a better understanding of past human activities in forests is sought. The age of charcoal piles is usually determined by radiocarbon dating; dendrochronology is rarely used because of the small size of preserved charcoal remains and the insufficient number of visible tree rings. This paper presents the potential for dendrochronological and ¹⁴C method in research into charcoal piles. From 14 charcoal-burning sites in the Czech Republic, 214 pieces of charcoal were anatomically identified at the genus level and dendrochronologically analysed. Our results show that fir dominated in these charcoal remains, followed by oak, beech, spruce and pine. With an overall dendrochronological dating success of 24 %, fir charcoal was dated most often (65 %) with measurable tree rings ranging from 14 to 90. The oldest charcoals were dendrochronologically dated to summer 1682 CE; conversely, the youngest had end dates in the second half of the 19th century. The relatively poor dating success of oak charcoal very likely resulted from the use of branches for charcoal production rather than tree trunks. Based on an analysis of selected charcoal samples, we confirm that radiocarbon dating provided a very wide range of dates in the post-1650 CE period and the use of the wiggle-matching method was usually challenging because of short TRW series. Based on samples with preserved waney edges, we conclude that charcoal was more commonly made from wood felled in the summer than in the winter. Despite the relatively low level of success of dendrochronological dating, it seems more effective for dating charcoal than the ¹⁴C method, especially with samples from the last 350 years.     

Chronologie du Paléolithique supérieur dans le Nord-Est de la principale île du Japon

Palaeolithic archaeology in Tohoku region has long been discussed on constructing chronology, however it is difficult to build reliable chronological order because of poor stratigraphic excavations. In recent radiocarbon dating has advanced. In this paper I discuss the relation between chronology and radiocarbon dating in Tohoku region. At first, I categorize the Palaeolithic industries and establish the chronology by analyzing tool typology, lithic technology, and stratigraphic data. I correlate it with radiocarbon data from sites in Tohoku region. The result of analysis shows that Upper Palaeolithic industries are divided into 18 categories and 8 periods on chronology. The calibration curve IntCal 13 indicated that oldest Early Upper Palaeolithic site appeared around 37,000 cal BP, and late Upper Palaeolithic started about 27,000 cal BP. The pottery first appeared as far back as around 16,000 cal BP. Now we do not have enough radiocarbon data, so we have to gather and examine more ¹⁴C data.     

Missing link in Late Antiquity? A critical examination of Hollstein’s Central European Oak Chronology

In 1980 Ernst Hollstein published his Central European Oak Chronology, which covers a period from 724 BCE to 1974 CE. Besides a later correction of the end date of the sampling site chronologies Kirnsulzbach (Germany) and Gustavsburg (Germany) this master chronology has since not been changed and still remains one of the most important bases for dendrochronological dating in western Germany. It stands out in so far as it provides comprehensive graphical findspot series for each individual sampled site and year to year growth values for eight regional sub-chronologies in addition to the combined Central European reference curve.Particularly due to the fact of Hollstein’s chronology being publicly available, it has frequently been criticized for its insufficient data to bridge the Late Antiquity between 350 and 400 CE with only three sampling sites (tomb near Beerlegem, Belgium; tomb inside of Cologne Cathedral, Germany; subfossil trees near Broichweiden, Germany) and that these site chronologies cover those decades with inadequate correlation coefficients. With regard to recent statistical threshold values for crossdating, Hollstein’s Late Antiquity bridging needs to be reconsidered.Therefore, in a combined effort, the dendrochronological laboratories at Rheinisches Landesmuseum Trier (RLM), the University of Cologne and Albert-Ludwigs-University Freiburg re-evaluated Hollstein’s findings for Late Antiquity by including the respective dendrochronological examinations conducted in Rhineland-Palatinate, North Rhine-Westphalia and north-eastern France during the past 40 years. A total of 62 site chronologies were compiled to establish a new Late Antiquity chronology. Thirteen of these site chronologies could be used to support Hollstein’s original bridging series between 350 and 400 CE while the mean series for Broichweiden had to be corrected from end date 365 to 503 CE. Furthermore, this new bridging chronology could be validated by comparing it to an independent chronology from southern Germany. This study thus proves that the integrity of Hollstein’s Central European Oak Chronology is not compromised by a flawed Late Antiquity bridging and that therefore dating based on the Roman part of this chronology can still be considered as absolute.     

Études du Paléolithique du Japon à partir des téphras

Many studies and discussions have been made on the problem of when the earliest human beings appeared in Japan. In general, hominid fossils in the latest Pleistocene are not preserved except for coralline limestone sequence in Ryukyu islands, but earlier Paleolithic tools were excavated from volcanic ash soil with a ¹⁴C age of about 30,000–35,000 yr. BP or younger at several archeological sites in almost all Japan. Recent studies, however, show a need for revision and refinement of these ages because calibration techniques have progressed from conventional to calendar ages and high-resolution oxygen isotope chronology has given a global standard sequence. Aïra-Tn tephra (AT), the most important time-marker of the Paleolithic age in Japan, was formerly dated at 21,000–22,000 yr ¹⁴C BP by conventional radiocarbon methods but was dated again at ca. 24,500 yr ¹⁴C BP by accelerated mass spectrometry radiocarbon methods. However, it has been further calibrated to a high-resolution calendar age of 30,000 cal yr. by varve chronology of lake sediments of Suigetsu of central Japan, well matched with combined date between oxygen isotope dates based and calibration from AMS radiocarbon dates. As the earliest Paleolithic tools in south Kanto are found in volcanic ash soil significantly below AT ash and above Sambe-Ikeda ash (SI, ca.46 ka), just above the oxygen isotopic stage 3.3, they are estimated to be dated slightly older than 40 ka. Palaeo-environment at that time is estimated mild to cool climate and relatively low sea level after the oxygen isotope stage 3.3. Sill land bridges between Japan islands and continents have not been formed at major straits. We have not yet obtained useful data for calibration older than ca. 45 ka. Also, correlation of oxygen isotopic fluctuation with the terrestrial sequences is incomplete in Stage 3.     

Radiocarbon and stable isotope investigations at the Central Rhineland sites of Gönnersdorf and Andernach-Martinsberg, Germany

The late glacial open-air sites of Gönnersdorf and Andernach-Martinsberg in the German Central Rhineland are well known for their Magdalenian occupation and activities. The latter site also produced evidence for a younger, Final Palaeolithic occupation of the locality by people of the Federmessergruppen. Both sites are particularly well preserved, largely due to their burial beneath volcanic deposits of the late glacial Laacher See eruption. We conducted a program of AMS radiocarbon dating and stable isotope analyses with the aim of improving understanding of the chronological history and ecological setting of the two sites.Previously published radiocarbon dates appeared to indicate that the earliest Magdalenian occupation at Gönnersdorf fell around 12,900 uncalibrated ¹⁴C yr BP, while the earliest occupation at Andernach may have been more than 500 radiocarbon years earlier. The AMS determinations presented here revise this impression and suggest that the onset of occupation at the two sites was in fact simultaneous and prior to the warming of Greenland Interstadial GI 1e. At Gönnersdorf, a chronological hiatus exists between the main Magdalenian faunal assemblage and mega-faunal remains interpreted as collected sub-fossil material. At Andernach-Martinsberg, there is a clear chronological hiatus between the Magdalenian occupation and subsequent Federmessergruppen activities at the site. However, an intermediate radiocarbon date on an atypically preserved horse bone is suggestive of ephemeral human visits to the site between these well demonstrated phases. A date of similar age on an elk bone from Gönnersdorf may indicate broadly contemporaneous human presence at Gönnersdorf too.Stable isotope analysis of faunal remains from Gönnersdorf and Andernach-Martinsberg was conducted with the aim of both reconstructing and comparing local environmental conditions at the two sites, and also potentially identifying subtle variations in the chronological development of the two sites not detectable at the level of precision of current radiocarbon dating techniques. No spatial trends in the faunal isotope signatures were observed within each site. In the case of samples with both radiocarbon and isotope data, no chronological pattern was observed for the isotope results. The Magdalenian faunal isotope signatures at the two sites resembled each other, suggesting comparable climatic and environmental conditions. The faunal δ¹³C signatures at Gönnersdorf and Andernach-Martinsberg were similar to those at contemporary European sites. While the faunal δ¹⁵N values were similar to those at contemporary sites in Germany, the UK, and Belgium, they were lower than those from the South of France. This difference in δ¹⁵N values is thought to relate to regional differences in the timing of changes in soil and plant nitrogen cycling in response to ameliorating climatic conditions.     

Detection of Adriamycin–DNA adducts by accelerator mass spectrometry at clinically relevant Adriamycin concentrations

Limited sensitivity of existing assays has prevented investigation of whether Adriamycin–DNA adducts are involved in the anti-tumour potential of Adriamycin. Previous detection has achieved a sensitivity of a few Adriamycin–DNA adducts/10⁴ bp DNA, but has required the use of supra-clinical drug concentrations. This work sought to measure Adriamycin–DNA adducts at sub-micromolar doses using accelerator mass spectrometry (AMS), a technique with origins in geochemistry for radiocarbon dating. We have used conditions previously validated (by less sensitive decay counting) to extract [¹⁴C]Adriamycin–DNA adducts from cells and adapted the methodology to AMS detection. Here we show the first direct evidence of Adriamycin–DNA adducts at clinically-relevant Adriamycin concentrations. [¹⁴C]Adriamycin treatment (25 nM) resulted in 4.4 ± 1.0 adducts/10⁷ bp (~1300 adducts/cell) in MCF-7 breast cancer cells, representing the best sensitivity and precision reported to date for the covalent binding of Adriamycin to DNA. The exceedingly sensitive nature of AMS has enabled over three orders of magnitude increased sensitivity of Adriamycin–DNA adduct detection and revealed adduct formation within an hour of drug treatment. This method has been shown to be highly reproducible for the measurement of Adriamycin–DNA adducts in tumour cells in culture and can now be applied to the detection of these adducts in human tissues.     

Developing tree ring chronologies from New Zealand matai (Prumnopitys taxifolia (D.Don) Laub.) for archaeological dating: Stable isotope dendrochronology

Aotearoa New Zealand has a rich cultural heritage but dating wooden objects using classic dendrochronology is challenging due to a paucity of master tree-ring width chronologies for species commonly identified in the archaeological record. This paper explores the potential for using a stable isotopic approach to dendrochronology for matai (Prumnopitys taxifolia (D.Don) Laub.). A total of six annual stable oxygen isotope (δ¹⁸O) series for matai growing in the Pureora Forest Reserve, were analysed and their oxygen isotopes found to exhibit a level of coherence that enabled cross-dating. A provisional chronology covering the period 1930–2018 CE was developed and tested against a sample of matai from the Kauaeranga Valley (200 km to the north of Pureora) and a sample of miro (Prumnopitys ferruginea (D.Don) Laub.). Miro is another species common in the cultural archive, but also difficult to date using ring-width dendrochronology. Both the Kaueranga matai and Pureora miro samples cross matched against the site chronology at the correct position, but with weaker dating statistics (Student’s t: 4.26 and 4.11 respectively) compared to the results obtained for two (non-2019) sampled Pureora matai analysed in this study (Student's t: 6.80 and 5.66). These results nevertheless demonstrate the presence of a regional-scale dating signal which may be developed for future use as a precision dating tool.     

Changes in the Radiocarbon Reservoir Age in Lake Xingyun,Southwestern China during the Holocene

Chronology is a necessary component of paleoclimatology. Radiocarbon dating plays a central role in determining the ages of geological samples younger than ca. 50 ka BP. However, there are many limitations for its application, including radiocarbon reservoir effects, which may cause incorrect chronology in many lakes. Here we demonstrate temporal changes in the radiocarbon reservoir age of Lake Xingyun, Southwestern China, where radiocarbon ages based on bulk organic matter have been reported in previous studies. Our new radiocarbon ages, determined from terrestrial plant macrofossils suggest that the radiocarbon reservoir age changed from 960 to 2200 years during the last 8500 cal a BP years. These changes to the reservoir effect were associated with inputs from either pre-aged organic carbon or ¹⁴C-depleted hard water in Lake Xingyun caused by hydrological change in the lake system. The radiocarbon reservoir age may in return be a good indicator for the carbon source in lake ecosystems and depositional environment.     

Prehistoric salt mining in Hallstatt,Austria. New chronologies out of small wooden fragments

The prehistoric salt mine of Hallstatt together with its burial ground is one of the most prominent archaeological sites in the world, and has given its name to the “Hallstatt period”, an epoch of European prehistory (800 to 400 BCE). Due to the perfect conservation in rock salt a high number of organic materials have been found, including mostly wooden artefacts and structural timber.More than 2000 samples were taken from various archaeological sites in the mines as well as at the surface. It was possible to date 763 samples by the means of dendrochronology and by ¹⁴C wiggle matching. The dendrochronological dating was possible due to crossdating with various available chronologies (like Villingen-Magdalenenberg or Dachstein/Schwarzer See). The fir (Abies alba Mill.) chronologies span the periods: -1232 to -1063; -819 to -425 and -371 to-129. The spruce (Picea abies L. Karst.) chronologies span the periods: -1228 to -1063; -813 to -669 and -342 to -123. The larch (Larix decidua Mill.) chronologies span the periods: -1393 ± 18 to-1286 ± 18 based on wiggle matching data and -252 to -164. A beech (Fagus sylvatica L.) chronology span the time -1182 to -1062.     

Radiocarbon dating the late Middle Paleolithic and the Aurignacian of the Swabian Jura

Many lines of evidence point to the period between roughly 40 and 30 ka BP as the period in which modern humans arrived in Europe and displaced the indigenous Neandertal populations. At the same time, many innovations associated with the Upper Paleolithic--including new stone and organic technologies, use of personal ornaments, figurative art, and musical instruments--are first documented in the European archaeological record. Dating the events of this period is challenging for several reasons. In the period about six to seven radiocarbon half-lives ago, variable preservation, pre-treatment, and sample preparation can easily lead to a lack of reproducibility between samples and laboratories. A range of biological, cultural, and geological processes can lead to mixing of archaeological strata and their contents. Additionally, some data sets point to this period as a time of significant spikes in levels of atmospheric radiocarbon. This paper assesses these questions in the context of the well-excavated and intensively studied caves of Geissenkl?sterle and Hohle Fels in the Swabian Jura of southwestern Germany. We conclude that variable atmospheric radiocarbon production contributes to the problems of dating the late Middle Paleolithic and the early Upper Paleolithic. To help establish a reliable chronology for the Swabian Aurignacian, we are beginning to focus our dating program on short-lived, stratigraphically secure features to see if they yield reproducible results. This approach may help to test competing explanations for the noisy and often non-reproducible results that arise when trying to date the transition from the Middle to the Upper Paleolithic.     

A 14C age calibration curve for the last 60 ka: the Greenland-Hulu U/Th timescale and its impact on understanding the Middle to Upper Paleolithic transition in Western Eurasia

This paper combines the data sets available today for ¹⁴C-age calibration of the last 60 ka. By stepwise synchronization of paleoclimate signatures, each of these sets of ¹⁴C-ages is compared with the U/Th-dated Chinese Hulu Cave speleothem records, which shows global paleoclimate change in high temporal resolution. By this synchronization we have established an absolute-dated Greenland-Hulu chronological framework, against which global paleoclimate data can be referenced, extending the ¹⁴C-age calibration curve back to the limits of the radiocarbon method. Based on this new, U/Th-based Greenland_Hulu chronology, we confirm that the radiocarbon timescale underestimates calendar ages by several thousand years during most of Oxygen Isotope Stage 3. Major atmospheric ¹⁴C variations are observed for the period of the Middle to Upper Paleolithic transition, which has significant implications for dating the demise of the last Neandertals. The early part of “the transition” (with ¹⁴C ages > 35.0 ka ¹⁴C BP) coincides with the Laschamp geomagnetic excursion. This period is characterized by highly-elevated atmospheric ¹⁴C levels. The following period ca. 35.0-32.5 ka ¹⁴C BP shows a series of distinct large-scale ¹⁴C age inversions and extended plateaus. In consequence, individual archaeological ¹⁴C dates older than 35.0 ka ¹⁴C BP can be age-calibrated with relatively high precision, while individual dates in the interval 35.0-32.5 ka ¹⁴C BP are subject to large systematic age-‘distortions,’ and chronologies based on large data sets will show apparent age-overlaps of up to ca. 5,000 cal years. Nevertheless, the observed variations in past ¹⁴C levels are not as extreme as previously proposed (“Middle to Upper Paleolithic dating anomaly”), and the new chronological framework leaves ample room for application of radiocarbon dating in the age-range 45.0-25.0 ka ¹⁴C BP at high temporal resolution.     

Dating archaeobotanical remains: a cautionary tale from Port au Choix,Newfoundland

In this paper we report on the first ¹⁴C dated archaeological seeds from the island of Newfoundland, Canada. Ninety-three archaeobotanical specimens were recovered from a midden deposit adjacent to a small dwelling at Point Riche (EeBi-20), a large Dorset Palaeoeskimo site near Port au Choix, northwestern Newfoundland. These remains were collected from a seemingly secure context within the midden, but AMS ¹⁴C testing of a sample of specimens produced modern ¹⁴C dates, indicating that the remains are intrusive to the Dorset occupation. While the majority of Newfoundland-based research assumes antiquity of archaeobotanical remains, we recommend using AMS ¹⁴C dating and other proxy data in future archaeobotanical studies to confirm antiquity prior to making interpretations regarding human–plant interactions.     

Radiocarbon age of carbonate in fruits of Lithospermum from the early Bronze Age settlement of Hirbet ez-Zeraqōn (Jordan)

Uncarbonized fruits of the Boraginaceae occur widely in cultural layers of archaeological sites in the Mediterranean and the Near East. To date, interpreting their origin remains problematic. It is difficult for archaeobotanists to tell whether such fruits were deposited as part of the cultural layer or were introduced post-depositionally. In an attempt to answer this question for the early Bronze Age site of Hirbet ez-Zeraqon (Jordan), we used direct ¹⁴C dating of biogenic carbonate from calcareous fruits of Lithospermum. The radiocarbon ages of seven fossil samples of the fruits suggest that they originate from plants that grew during or around the time of occupation.     

Ancient juniper trees growing on cliffs: toward a long Mediterranean tree-ring chronology

Juniperus phoenicea is a tree that can grow on vertical cliff faces in dry and warm Mediterranean climate conditions. These trees are adapted to extreme growing conditions where the main constraints are verticality, compact hard limestone, and low water supply. They respond to these constraints via various specific features and high longevity. The objective of this study is to confirm whether or not their tree-rings are annual in order to specify growth strategies and accurately date these trees. Trunk morphology, anatomical wood anomalies and radial growth were analyzed on 53 trees in the Ardèche canyon. Crossdating of the ring widths using traditional dendrochronological techniques was unsuccessful, so radiocarbon dating of tree pith was used to assess tree age, and wiggle-match dating was used to test for differences between number of rings counted and radiocarbon dates. Radiocarbon dates span the period 2520–685 BP. Minimal difference between radiocarbon dates and ring counts was apparently small—missing rings occur, but not in large numbers. Tree-ring formation is annual and radial growth is low, which creates stunted old trees. Such old living trees are uncommon in the Mediterranean basin, especially at low elevation. They can provide long tree-ring chronologies back to 792–524 cal BC. Results from the radiocarbon dating indicate that accurate annual dating of these rings may be possible by crossdating. J. phoenicea growing on cliffs offer a valuable model to better understand cliff population ecology and the functional responses of trees that can live in harsh environmental conditions.     

Occurrence of the Stripe Field Mouse lineage (Apodemus agrarius Pallas 1771; Rodentia; Mammalia) in the Late Pleistocene of southwestern France

The Stripe Field Mouse lineage (Apodemus agrarius) was present in the Late Pleistocene in southwestern France (locality of Bouziès-Q, Quercy), according to the age of ca. 17,417–17,044 BC of the collected sample (AMS ¹⁴C dating of collagen extracted from small mammal bones). This occurrence demonstrates that a much western expansion of the Stripe Field Mouse lineage than believed occurred at the end of the last cold phase of the Pleistocene, the few fossil populations up to now known being both younger and located inside the present-day distribution area of the lineage. The AMS ¹⁴C date supports the hypothesis of the late migration of this species into Europe. If tooth morphology indicates clear differences with respect to Apodemus sylvaticus or A. flavicollis, there are appreciable ones between the Bouziès-Q population and the present-day Apodemus agrarius of western Europe, likely indicating evolution at the sub-specific level despite the short time period involved.     

Radiocarbon and dendrochronology

The radiocarbon dating method relies on calibration through an independent dating method. Dendrochronology is an ideal partner of radiocarbon, because tree-rings are close-to-perfect archives of the atmospheric ¹⁴C level, and the tree-ring time scale can be built beyond doubt with high replication. Over the past 30 years, several stages of ¹⁴C calibration data sets have been constructed from the work of tree-ring laboratories in Europe and North America. This process is outlined and the present state is documented. In turn, ¹⁴C age fluctuations, caused mainly by helio-magnetic changes, can be used to anchor floating tree-ring sections to the calendar scale with a precision of a few decades.