Radiocarbon calibration

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Radiocarbon dating measurements produce ages in "radiocarbon years", which must be converted to calendar ages by a process called calibration. Calibration is needed because the atmospheric 14
C/12
C ratio, which is a key element in calculating radiocarbon ages, has not been constant historically. [1]

Contents

Willard Libby, the inventor of radiocarbon dating, pointed out as early as 1955 the possibility that the ratio might have varied over time. Discrepancies began to be noted between measured ages and known historical dates for artefacts, and it became clear that a correction would need to be applied to radiocarbon ages to obtain calendar dates. [2] Uncalibrated dates may be stated as "radiocarbon years ago", abbreviated "14
Cya". [3]

The term Before Present (BP) is established for reporting dates derived from radiocarbon analysis, where "present" is 1950. Uncalibrated dates are stated as "uncal BP", [4] and calibrated (corrected) dates as "cal BP". Used alone, the term BP is ambiguous.

Construction of a curve

Intcal 13 calibration curve.png
Intcal 20 calibration curve.png
The Northern Hemisphere curves from INTCAL13 and INTCAL20. There are separate graphs for the Southern Hemisphere and for the calibration of marine data. [5] [6]

To produce a curve that can be used to relate calendar years to radiocarbon years, a sequence of securely-dated samples is needed, which can be tested to determine their radiocarbon age. Dendrochronology, or the study of tree rings, led to the first such sequence: tree rings from individual pieces of wood show characteristic sequences of rings that vary in thickness due to environmental factors such as the amount of rainfall in a given year. Those factors affect all trees in an area and so examining tree-ring sequences from old wood allows the identification of overlapping sequences. In that way, an uninterrupted sequence of tree rings can be extended far into the past. The first such published sequence, based on bristlecone pine tree rings, was created in the 1960s by Wesley Ferguson. [7] Hans Suess used the data to publish the first calibration curve for radiocarbon dating in 1967. [2] [8] [9] The curve showed two types of variation from the straight line: a long-term fluctuation with a period of about 9,000 years, and a shorter-term variation, often referred to as "wiggles", with a period of decades. Suess said that he drew the line showing the wiggles by "cosmic schwung", or freehand. It was unclear for some time whether the wiggles were real or not, but they are now well-established. [8] [9]

The calibration method also assumes that the temporal variation in 14
C level is global, such that a small number of samples from a specific year are sufficient for calibration, which was experimentally verified in the 1980s. [2]

Over the next 30 years, many calibration curves were published by using a variety of methods and statistical approaches. [10] They were superseded by the INTCAL series of curves, beginning with INTCAL98, published in 1998, and updated in 2004, 2009, 2013 and 2020. [11] The improvements to these curves are based on new data gathered from tree rings, varves, coral, and other studies. Significant additions to the datasets used for INTCAL13 include non-varved marine foraminifera data, and U-Th dated speleothems. The INTCAL13 data includes separate curves for the Northern and Southern Hemispheres, as they differ systematically because of the hemisphere effect; there is also a separate marine calibration curve. [12] The calibration curve for the southern hemisphere is known as the SHCal as opposed to the IntCal for the northern hemisphere. The most recent version being published in 2020. There is also a different curve for the period post 1955 due to atomic bomb testing creating higher levels of radiocarbon which vary based on latitude, known as bomb cal.

Methods

Probabilistic

The output of CALIB for input values of 1260-1280 BP, using the northern hemisphere INTCAL13 curve CALIB output example probabilistic radiocarbon date calibration.png
The output of CALIB for input values of 1260–1280 BP, using the northern hemisphere INTCAL13 curve

Modern methods of calibration take the original normal distribution of radiocarbon age ranges and use it to generate a histogram showing the relative probabilities for calendar ages. This has to be done by numerical methods rather than by a formula because the calibration curve is not describable as a formula. [10] Programs to perform these calculations include OxCal and CALIB. These can be accessed online; they allow the user to enter a date range at one standard deviation confidence for the radiocarbon ages, select a calibration curve, and produce probabilistic output both as tabular data and in graphical form. [13] [14]

In the example CALIB output shown at left, the input data is 1270 BP, with a standard deviation of 10 radiocarbon years. The curve selected is the northern hemisphere INTCAL13 curve, part of which is shown in the output; the vertical width of the curve corresponds to the width of the standard error in the calibration curve at that point. A normal distribution is shown at left; this is the input data, in radiocarbon years. The central darker part of the normal curve is the range within one standard deviation of the mean; the lighter grey area shows the range within two standard deviations of the mean. The output is along the bottom axis; it is a trimodal graph, with peaks at around 710 AD, 740 AD, and 760 AD. Again, the 1σ confidence ranges are in dark grey, and the 2σ confidence ranges are in light grey. [14]

Intercept

Before the widespread availability of personal computers made probabilistic calibration practical, a simpler "intercept" method was used.

Part of the INTCAL13 calibration curve, showing correct (t1) and incorrect (t2) methods of determining a calendar year range from a calibration curve with a given error Radiocarbon calibration error and measurement error.png
Part of the INTCAL13 calibration curve, showing correct (t1) and incorrect (t2) methods of determining a calendar year range from a calibration curve with a given error

Once testing has produced a sample age in radiocarbon years with an associated error range of plus or minus one standard deviation (usually written as ±σ), the calibration curve can be used to derive a range of calendar ages for the sample. The calibration curve itself has an associated error term, which can be seen on the graph labelled "Calibration error and measurement error". This graph shows INTCAL13 data for the calendar years 3100 BP to 3500 BP. The solid line is the INTCAL13 calibration curve, and the dotted lines show the standard error range, as with the sample error, this is one standard deviation. Simply reading off the range of radiocarbon years against the dotted lines, as is shown for sample t2, in red, gives too large a range of calendar years. The error term should be the root of the sum of the squares of the two errors: [15]

Example t1, in green on the graph, shows this procedure—the resulting error term, σtotal, is used for the range, and this range is used to read the result directly from the graph itself without reference to the lines showing the calibration error. [15]

Different radiocarbon dates, with similar standard errors, can give widely different resulting calendar year ranges, depending on the shape of the calibration curve at each point. Variations in calibration results.png
Different radiocarbon dates, with similar standard errors, can give widely different resulting calendar year ranges, depending on the shape of the calibration curve at each point.

Variations in the calibration curve can lead to very different resulting calendar year ranges for samples with different radiocarbon ages. The graph to the right shows the part of the INTCAL13 calibration curve from 1000 BP to 1400 BP, a range in which there are significant departures from a linear relationship between radiocarbon age and calendar age. In places where the calibration curve is steep, and does not change direction, as in example t1 in blue on the graph to the right, the resulting calendar year range is quite narrow. Where the curve varies significantly both up and down, a single radiocarbon date range may produce two or more separate calendar year ranges. Example t2, in red on the graph, shows this situation: a radiocarbon age range of about 1260 BP to 1280 BP converts to three separate ranges between about 1190 BP and 1260 BP. A third possibility is that the curve is flat for some range of calendar dates; in this case, illustrated by t3, in green on the graph, a range of about 30 radiocarbon years, from 1180 BP to 1210 BP, results in a calendar year range of about a century, from 1080 BP to 1180 BP. [10]

The intercept method is based solely on the position of the intercepts on the graph. These are taken to be the boundaries of the 68% confidence range, or one standard deviation. However, this method does not make use of the assumption that the original radiocarbon age range is a normally distributed variable: not all dates in the radiocarbon age range are equally likely, and so not all dates in the resulting calendar year age are equally likely. Deriving a calendar year range by means of intercepts does not take this into account. [10]

Wiggle-matching

For a set of samples with a known sequence and separation in time such as a sequence of tree rings, the samples' radiocarbon ages form a small subset of the calibration curve. The resulting curve can then be matched to the actual calibration curve by identifying where, in the range suggested by the radiocarbon dates, the wiggles in the calibration curve best match the wiggles in the curve of sample dates. This "wiggle-matching" technique can lead to more precise dating than is possible with individual radiocarbon dates. [16] Since the data points on the calibration curve are five years or more apart, and since at least five points are required for a match, there must be at least a 25-year span of tree ring (or similar) data for this match to be possible. Wiggle-matching can be used in places where there is a plateau on the calibration curve, and hence can provide a much more accurate date than the intercept or probability methods are able to produce. [17] The technique is not restricted to tree rings; for example, a stratified tephra sequence in New Zealand, known to predate human colonization of the islands, has been dated to 1314 AD ± 12 years by wiggle-matching. [18]

Combination of calibrated dates

When several radiocarbon dates are obtained for samples which are known or suspected to be from the same object, it may be possible to combine the measurements to get a more accurate date. Unless the samples are definitely of the same age (for example, if they were both physically taken from a single item) a statistical test must be applied to determine if the dates do derive from the same object. This is done by calculating a combined error term for the radiocarbon dates for the samples in question, and then calculating a pooled mean age. It is then possible to apply a T test to determine if the samples have the same true mean. Once this is done the error for the pooled mean age can be calculated, giving a final answer of a single date and range, with a narrower probability distribution (i.e., greater accuracy) as a result of the combined measurements. [19]

Bayesian statistical techniques can be applied when there are several radiocarbon dates to be calibrated. For example, if a series of radiocarbon dates is taken from different levels in a given stratigraphic sequence, Bayesian analysis can help determine if some of the dates should be discarded as anomalies, and can use the information to improve the output probability distributions. [16]

Related Research Articles

<span class="mw-page-title-main">Radiocarbon dating</span> Method of determining the age of objects

Radiocarbon dating is a method for determining the age of an object containing organic material by using the properties of radiocarbon, a radioactive isotope of carbon.

<span class="mw-page-title-main">Dendrochronology</span> Method of dating based on the analysis of patterns of tree rings

Dendrochronology is the scientific method of dating tree rings to the exact year they were formed in a tree. As well as dating them, this can give data for dendroclimatology, the study of climate and atmospheric conditions during different periods in history from the wood of old trees. Dendrochronology derives from the Ancient Greek dendron, meaning "tree", khronos, meaning "time", and -logia, "the study of".

<span class="mw-page-title-main">Carbon-14</span> Radiosotope of carbon

Carbon-14, C-14, 14C or radiocarbon, is a radioactive isotope of carbon with an atomic nucleus containing 6 protons and 8 neutrons. Its presence in organic matter is the basis of the radiocarbon dating method pioneered by Willard Libby and colleagues (1949) to date archaeological, geological and hydrogeological samples. Carbon-14 was discovered on February 27, 1940, by Martin Kamen and Sam Ruben at the University of California Radiation Laboratory in Berkeley, California. Its existence had been suggested by Franz Kurie in 1934.

Before Present (BP) or "years before present (YBP)" is a time scale used mainly in archaeology, geology, and other scientific disciplines to specify when events occurred relative to the origin of practical radiocarbon dating in the 1950s. Because the "present" time changes, standard practice is to use 1 January 1950 as the commencement date (epoch) of the age scale, with 1950 being labelled as the "standard year". The abbreviation "BP" has been interpreted retrospectively as "Before Physics", which refers to the time before nuclear weapons testing artificially altered the proportion of the carbon isotopes in the atmosphere, which scientists must account for.

<span class="mw-page-title-main">Dendroarchaeology</span>

Dendroarchaeology is a term used for the study of vegetation remains, old buildings, artifacts, furniture, art and musical instruments using the techniques of dendrochronology. It refers to dendrochronological research of wood from the past regardless of its current physical context. This form of dating is the most accurate and precise absolute dating method available to archaeologists, as the last ring that grew is the first year the tree could have been incorporated into an archaeological structure.

Absolute dating is the process of determining an age on a specified chronology in archaeology and geology. Some scientists prefer the terms chronometric or calendar dating, as use of the word "absolute" implies an unwarranted certainty of accuracy. Absolute dating provides a numerical age or range, in contrast with relative dating, which places events in order without any measure of the age between events.

The Blytt–Sernander classification, or sequence, is a series of North European climatic periods or phases based on the study of Danish peat bogs by Axel Blytt (1876) and Rutger Sernander (1908). The classification was incorporated into a sequence of pollen zones later defined by Lennart von Post, one of the founders of palynology.

<span class="mw-page-title-main">Minoan eruption</span> Major volcanic eruption around 1600 BCE

The Minoan eruption was a catastrophic volcanic eruption that devastated the Aegean island of Thera circa 1600 BCE. It destroyed the Minoan settlement at Akrotiri, as well as communities and agricultural areas on nearby islands and the coast of Crete with subsequent earthquakes and paleotsunamis. With a Volcanic Explosivity Index (VEI) of 7, it resulted in the ejection of approximately 28–41 km3 (6.7–9.8 cu mi) of dense-rock equivalent (DRE), the eruption was one of the largest volcanic events in human history. Since tephra from the Minoan eruption serves as a marker horizon in nearly all archaeological sites in the Eastern Mediterranean, its precise date is of high importance and has been fiercely debated among archaeologists and volcanologists for decades, without coming to a definite conclusion.

Wiggle matching, also known as carbon–14 wiggle-match dating (WMD) is a dating method that uses the non-linear relationship between 14C age and calendar age to match the shape of a series of closely sequentially spaced 14C dates with the 14C calibration curve. A numerical approach to WMD allows one to assess the precision of WMD chronologies. The method has both advantages and limitations vis-a-vis the calibration of individual dates. High-precision chronologies are needed for studies of rapid climate changes. Andrew Millard refers to wiggle matching as a way of dealing with the flat portion of the carbon 14 calibration graph that is known as the Hallstatt plateau, named after the Hallstatt culture period in central Europe with which it coincides.

<span class="mw-page-title-main">Avellino eruption</span> Plinian eruption of the Somma-Vesuvius complex

The Avellino eruption of Mount Vesuvius occurred in c. 1995 BC. It is estimated to have had a VEI of 6, making it larger and more catastrophic than Vesuvius's more famous and well-documented 79 AD eruption. It is the source of the Avellino pumice deposits extensively found in the comune of Avellino in Campania.

<span class="mw-page-title-main">Hatepe eruption</span> Major eruption of Taupō volcano

The Hatepe eruption, named for the Hatepe Plinian pumice tephra layer, sometimes referred to as the Taupō eruption or Horomatangi Reef Unit Y eruption, is dated to 232 CE ± 10 and was Taupō Volcano's most recent major eruption. It is thought to be New Zealand's largest eruption within the last 20,000 years. The eruption ejected some 45–105 km3 (11–25 cu mi) of bulk tephra, of which just over 30 km3 (7.2 cu mi) was ejected in approximately 6–7 minutes. This makes it one of the largest eruptions in the last 5,000 years, comparable to the Minoan eruption in the 2nd millennium BCE, the 946 eruption of Paektu Mountain, the 1257 eruption of Mount Samalas, and the 1815 eruption of Mount Tambora.

Yuchanyan is an early Neolithic cave site in Dao County (Daoxian), Hunan, China. The site yielded sherds of ceramic vessels and other artifacts which were dated by analysis of charcoal and bone collagen, giving a date range of 17,500 to 18,300 years old for the pottery. The pottery specimens may be the oldest known examples of pottery.

Carbon dating the Dead Sea Scrolls refers to a series of radiocarbon dating tests performed on the Dead Sea Scrolls, first by the AMS lab of the Zurich Institute of Technology in 1991 and then by the AMS Facility at the University of Arizona in Tucson in 1994–95. There was also a historical test of a piece of linen performed in 1946 by Willard Libby, the inventor of the dating method.

<span class="mw-page-title-main">Chronology of the ancient Near East</span>

The chronology of the ancient Near East is a framework of dates for various events, rulers and dynasties. Historical inscriptions and texts customarily record events in terms of a succession of officials or rulers: "in the year X of king Y". Comparing many records pieces together a relative chronology relating dates in cities over a wide area.

The Hallstatt plateau or the first millennium BC radiocarbon disaster, as it is called by some archaeologists and chronologists, is a term used in archaeology that refers to a consistently flat area on graphs that plot radiocarbon dating against calendar dates. When applied to the Scythian epoch in Eurasia, radiocarbon dates of around 2450 BP, so c. 500 BC, always calibrate to c. 800–400 BC, no matter the measurement precision. The radiocarbon dating method is hampered by this large plateau on the calibration curve in a critical period of human technological development. Just before and after the plateau, radiocarbon calibration gives precise dates. However, during the plateau the calendar date estimates obtained when calibrating single radiocarbon measurements are very broad and cover the entire duration of the plateau. Only techniques like wiggle matching can yield more precise calendar dates during this period. The plateau is named after the Hallstatt culture period in central Europe with which it coincides.

<span class="mw-page-title-main">Lake Suigetsu</span> Lake in Wakasa, Japan

Lake Suigetsu is a lake in the Hokuriku region of Honshu, Japan, which is one of the Mikata Five Lakes located in Mihama and Wakasa, Fukui Prefecture, close to the coast of the Wakasa Bay in the Sea of Japan. Since 1993, it has been attracting the attention of scientists because of the undisturbed nature of the water for many thousands of years. It is possible to identify the annual deposits of silt in a similar manner that tree rings are identified.

Wesley Ferguson was an American academic at the Tree-Ring Research Laboratory at the University of Arizona at Tucson who studied tree-rings. He built a tree-ring sequence from bristlecone pines which was used by Hans Suess to create a calibration curve for radiocarbon dating.

Minze Stuiver was a Dutch geochemist who was at the forefront of geoscience research from the 1960s until his retirement in 1998. He helped transform radiocarbon dating from a simple tool for archaeology and geology to a precise technique with applications in solar physics, oceanography, geochemistry, and carbon dynamics. Minze Stuiver's research encompassed the use of radiocarbon (14C) to understand solar cycles and radiocarbon production, ocean circulation, lake carbon dynamics and archaeology as well as the use of stable isotopes to document past climate changes.

The variation in the 14
C/12
C ratio in different parts of the carbon exchange reservoir means that a straightforward calculation of the age of a sample based on the amount of 14
C it contains will often give an incorrect result. There are several other possible sources of error that need to be considered. The errors are of four general types:

<span class="mw-page-title-main">Paula Reimer</span> Earth scientist and scientific archaeologist

Paula Jo Reimer is a radiocarbon and archaeological scientist. Reimer is the former director of the 14Chrono Centre for Climate, the Environment, and Chronology at Queen's University Belfast.

References

  1. ↑ Taylor (1987), p. 133.
  2. 1 2 3 Aitken (1990), p. 66–67.
  3. ↑ Enk, J.; Devault, A.; Debruyne, R.; King, C. E.; Treangen, T.; O'Rourke, D.; Salzberg, S. L. l; Fisher, D.; MacPhee, R.; Poinar, H. (2011). "Complete Columbian mammoth mitogenome suggests interbreeding with woolly mammoths". Genome Biology. 12 (5): R51. doi: 10.1186/gb-2011-12-5-r51 . PMC   3219973 . PMID   21627792.
  4. ↑ P. Semal; A. Hauzeur; H. Rougier; I. Crevecoeur; M. Germonpré; S. Pirson; P. Haesaerts; C. Jungels; D. Flas; M. Toussaint; B. Maureille; H. Bocherens; T. Higham; J. van der Pflicht (2013). "Radiocarbon dating of human remains and associated archaeological material". Anthropologica et Præhistorica. 123/2012: 331–356.
  5. 1 2 Reimer, Paula J.; et al. (2013). "IntCal13 and Marine13 radiocarbon age calibration curves 0–50,000 years cal BP". Radiocarbon. 55 (4): 1869–1887. doi: 10.2458/azu_js_rc.55.16947 . hdl: 10289/8955 .
  6. ↑ Heaton, Timothy J.; Blaauw, Maarten; Blackwell, Paul G.; Ramsey, Christopher Bronk; Reimer, Paula J.; Scott, E. Marian (August 2020). "The IntCal20 Approach to Radiocarbon Calibration Curve Construction: A New Methodology Using Bayesian Splines and Errors-in-Variables". Radiocarbon. 62 (4): 821–863. doi: 10.1017/RDC.2020.46 . ISSN   0033-8222.
  7. ↑ Taylor (1987), pp. 19–21.
  8. 1 2 Bowman (1995), pp. 16–20.
  9. 1 2 Suess (1970), p. 303.
  10. 1 2 3 4 Bowman (1995), pp. 43–49.
  11. ↑ Reimer, Paula J (2020). "The IntCal20 Northern Hemisphere Radiocarbon Age Calibration Curve (0–55 cal kBP)". Radiocarbon. 62 (4): 725–757. doi: 10.1017/RDC.2020.41 . hdl: 11585/770531 .
  12. ↑ Stuiver, M.; Braziunas, T.F. (1993). "Modelling atmospheric 14
    C     influences and 14
    C     ages of marine samples to 10,000 BC"    . Radiocarbon. 35 (1): 137–189. doi: 10.1017/S0033822200013874 .
  13. ↑ "OxCal". Oxford Radiocarbon Accelerator Unit. Oxford University. 23 May 2014. Retrieved 26 June 2014.
  14. 1 2 Stuiver, M.; Reimer, P.J. Reimer; Reimer, R. (2013). "CALIB Radiocarbon Calibration". CALIB 14C Calibration Program. Queen's University, Belfast. Retrieved 26 June 2014.
  15. 1 2 Aitken (1990), p. 101.
  16. 1 2 Walker (2005), pp. 35−37.
  17. ↑ Aitken (1990), pp. 103−105.
  18. ↑ Walker (2005), pp. 207−209.
  19. ↑ Gillespie (1986), pp. 30−32.

Bibliography

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