Editing Radiocarbon dating (section)

===Calibration<!--'Calibrated years' redirects here-->===
{{Main|Radiocarbon calibration}}
[[File:Prometheus tree1.jpg|left|thumb|The stump of a very old bristlecone pine. Tree rings from these trees (among others) are used in building calibration curves.]]
The calculations given above produce dates in radiocarbon years: i.e. dates that represent the age the sample would be if the {{chem|14|C}}/{{chem|12|C}} ratio had been constant historically.<ref>Taylor & Bar-Yosef (2014), p. 155.</ref> Although Libby had pointed out as early as 1955 the possibility that this assumption was incorrect, it was not until discrepancies began to accumulate between measured ages and known historical dates for artefacts that it became clear that a correction would need to be applied to radiocarbon ages to obtain calendar dates.<ref name=Aitken_66>Aitken (1990), p.&nbsp;66–67.</ref>

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. The study of tree rings led to the first such sequence: individual pieces of wood show characteristic sequences of rings that vary in thickness because of environmental factors such as the amount of rainfall in a given year. These factors affect all trees in an area, so examining tree-ring sequences from old wood allows the identification of overlapping sequences. In this 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 by [[Wesley Ferguson]].<ref name=Taylor2014/> Hans Suess used this data to publish the first calibration curve for radiocarbon dating in 1967.<ref name=Bowman_16/><ref name=Suess_1970/><ref name=Aitken_66/> 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 he drew the line showing the wiggles by "cosmic ''schwung''", by which he meant that the variations were caused by extraterrestrial forces. It was unclear for some time whether the wiggles were real or not, but they are now well-established.<ref name=Bowman_16/><ref name=Suess_1970/><ref>Taylor & Bar-Yosef (2014), p. 59.</ref> These short term fluctuations in the calibration curve are now known as de Vries effects, after [[Hessel de Vries]].<ref>Taylor & Bar-Yosef (2014), pp. 53–54.</ref>

A calibration curve is used by taking the radiocarbon date reported by a laboratory and reading across from that date on the vertical axis of the graph. The point where this horizontal line intersects the curve will give the calendar age of the sample on the horizontal axis. This is the reverse of the way the curve is constructed: a point on the graph is derived from a sample of known age, such as a tree ring; when it is tested, the resulting radiocarbon age gives a data point for the graph.<ref name=renamed_from_18_on_20200701175743/>
[[File:Intcal 20 calibration curve.png|alt=|thumb|The Northern hemisphere curve from IntCal20. As of 2020, this is the most recent version of the standard calibration curve. The diagonal line shows where the curve would lie if radiocarbon ages and calendar ages were the same.<ref name=":0"/>]]
Over the next thirty years many calibration curves were published using a variety of methods and statistical approaches.<ref name=renamed_from_18_on_20200701175743/> These were superseded by the IntCal series of curves, beginning with IntCal98, published in 1998, and updated in 2004, 2009, 2013, and 2020.<ref name=":0">{{Cite journal | last1=Reimer | first1=P.J. | display-authors=etal  | date=2020 | title=The IntCal20 Northern Hemisphere Radiocarbon Age Calibration Curve (0–55 cal kBP) | journal=Radiocarbon | volume=62 | issue=4 | pages=725–757 | doi=10.1017/RDC.2020.41 | bibcode=2020Radcb..62..725R | doi-access=free | hdl=11585/770531 | hdl-access=free }}</ref> The improvements to these curves are based on new data gathered from tree rings, [[varve]]s, [[coral]], plant [[macrofossil]]s, [[speleothem]]s, and [[foraminifera]]. There are separate curves for the northern hemisphere (IntCal20) and southern hemisphere (SHCal20), as they differ systematically because of the hemisphere effect. The continuous sequence of tree-ring dates for the northern hemisphere goes back to 13,910 BP as of 2020, and this provides close to annual dating for IntCal20 much of the period, reduced where there are calibration plateaus, and increased when short term {{sup|14}}C spikes due to [[Miyake event]]s provide additional correlation. Radiocarbon dating earlier than the continuous tree ring sequence relies on correlation with more approximate records.<ref>{{cite journal| last=van der Plicht |first=J|display-authors=etal | journal=Radiocarbon |title=Recent Developments in Calibration for Archaeological and Environmental Samples|volume=62 |number=  4|year= 2020|page=1095|doi=10.1017/RDC.2020.22|bibcode=2020Radcb..62.1095V|s2cid=219087775|url=https://www.cambridge.org/core/journals/radiocarbon/article/recent-developments-in-calibration-for-archaeological-and-environmental-samples/671DCC8A4A38ACF57786EFC659E5D8F6 |hdl=11585/770537|hdl-access=free}}</ref> SHCal20 is based on independent data where possible and derived from the northern curve by adding the average offset for the southern hemisphere where no direct data was available. There is also a separate marine calibration curve, MARINE20.<ref name=INTCAL13/><ref>{{cite journal|last1=Stuiver|first1=M.|last2=Braziunas|first2=T.F.|year=1993|title=Modelling atmospheric {{chem|14|C}} influences and {{chem|14|C}} ages of marine samples to 10,000 BC|url=https://journals.uair.arizona.edu/index.php/radiocarbon/article/view/1558/1562|journal=Radiocarbon|volume=35|issue=1|pages=137–189|doi=10.1017/s0033822200013874|doi-access=free}}</ref><ref>{{Cite journal|last1=Hogg|first1=Alan G.|last2=Heaton|first2=Timothy J.|last3=Hua|first3=Quan|last4=Palmer|first4=Jonathan G.|last5=Turney|first5=Chris SM|last6=Southon|first6=John|last7=Bayliss|first7=Alex|last8=Blackwell|first8=Paul G.|last9=Boswijk|first9=Gretel|last10=Ramsey|first10=Christopher Bronk|last11=Pearson|first11=Charlotte|date=August 2020|title=SHCal20 Southern Hemisphere Calibration, 0–55,000 Years cal BP|journal=Radiocarbon|language=en|volume=62|issue=4|pages=759–778|doi=10.1017/RDC.2020.59|issn=0033-8222|doi-access=free|bibcode=2020Radcb..62..759H |hdl=1893/31560|hdl-access=free}}</ref><ref>{{Cite journal|last1=Heaton|first1=Timothy J.|last2=Köhler|first2=Peter|last3=Butzin|first3=Martin|last4=Bard|first4=Edouard|last5=Reimer|first5=Ron W.|last6=Austin|first6=William E. N.|last7=Ramsey|first7=Christopher Bronk|last8=Grootes|first8=Pieter M.|last9=Hughen|first9=Konrad A.|last10=Kromer|first10=Bernd|last11=Reimer|first11=Paula J.|date=August 2020|title=Marine20—The Marine Radiocarbon Age Calibration Curve (0–55,000 cal BP)|journal=Radiocarbon|language=en|volume=62|issue=4|pages=779–820|doi=10.1017/RDC.2020.68|issn=0033-8222|doi-access=free|bibcode=2020Radcb..62..779H |hdl=1912/26513|hdl-access=free}}</ref> For a set of samples forming a sequence with a known separation in time, these samples form a subset of the calibration curve. The sequence can be compared to the calibration curve and the best match to the sequence established. This "wiggle-matching" technique can lead to more precise dating than is possible with individual radiocarbon dates.<ref name=Walker2005>Walker (2005), pp. 35–37.</ref> Wiggle-matching can be used in places where there is a plateau on the calibration curve,{{#tag:ref|A plateau in the calibration curve occurs when the ratio of {{chem|14|C}}/{{chem|12|C}} in the atmosphere decreases at the same rate as the reduction due to radiocarbon decay in the sample. For example, there was a plateau between around 750 and 400 BCE, which makes radiocarbon dates less accurate for samples dating to this period.<ref>{{cite journal|url=https://www.jstor.org/stable/3840039|first1=Tom|last1=Guilderson|first2=Paula |last2= Reimer |first3= Tom |last3= Brown|title=The Boon and Bane of Radiocarbon Dating|journal=Science|date=21 January 2005|volume=307|number=5708|page=363|doi=10.1126/science.1104164 |jstor=3840039 |pmid=15661996 |s2cid=128466798 }}</ref> |group=note}} and hence can provide a much more accurate date than the intercept or probability methods are able to produce.<ref>Aitken (1990), pp. 103–105.</ref> The technique is not restricted to tree rings; for example, a stratified [[tephra]] sequence in New Zealand, believed to predate human colonization of the islands, has been dated to 1314&nbsp;AD ± 12 years by wiggle-matching.<ref>Walker (2005), pp. 207–209.</ref> The wiggles also mean that reading a date from a calibration curve can give more than one answer: this occurs when the curve wiggles up and down enough that the radiocarbon age intercepts the curve in more than one place, which may lead to a radiocarbon result being reported as two separate age ranges, corresponding to the two parts of the curve that the radiocarbon age intercepted.<ref name=renamed_from_18_on_20200701175743/>

[[Bayesian inference|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 stratigraphic sequence, Bayesian analysis can be used to evaluate dates which are outliers and can calculate improved probability distributions, based on the prior information that the sequence should be ordered in time.<ref name=Walker2005/> When Bayesian analysis was introduced, its use was limited by the need to use mainframe computers to perform the calculations, but the technique has since been implemented on programs available for personal computers, such as OxCal.<ref>Taylor & Bar-Yosef (2014), pp. 148–149.</ref>