Using radiocarbon: an update.

Using radiocarbon: an update. A note in the 1990 ANTIQUITY volume dealt with four issues crucial tothe successful use of radiocarbon in archaeology (Bowman & Balaam1990): selection and characterization of material and context;determination of the radiocarbon result and error term; interpretationand publication; and strategic resourcing. Since then much has beenpublished, particularly on quality control of radiocarbon measurements('determination'), and on the calibration of radiocarbonresults ('interpretation'). Here is an update.Determination -- accuracy and precisionDiscussion of laboratory accuracy and precision in radiocarbondating, dull for reader and writer alike, is seemingly well rehearsed.Nevertheless, the difference between these two types of error is centralto any understanding of quality control in radiocarbon dating, and toany evaluation by the user of advice on how to use error terms. Accuracydetermines how close the experimental result is to the true value, andprecision determines the closeness of replicate measurements to eachother: accurate results can be imprecise and vice versa VICE VERSA. On the contrary; on opposite sides. (see, forexample, Bowman 1990: figure 15). The error quoted by a laboratory is,in theory, the precision (the uncertainty due to random variability);but most radiocarbon laboratories estimate their precision rather thandetermine it by replication because of the resources involved inrepeating measurements. In estimating there is the danger that not allpotential sources of random error are included.A proposed quality assurance protocol for radiocarbon (Long &Kalin 1990) covers all aspects of the dating procedure fromdocumentation of samples received to issue of results, but it may not beobvious to the user whether a radiocarbon laboratory is providingquality control as far as accuracy and precision are concerned. Anylaboratory should be able to provide information on its accuracy, eitheras evaluated in an intercomparison study with other laboratories oragainst known age samples. Much the most relevant samples of known agefor archaeological applications of radiocarbon are dendrochronologicallydated tree-rings from the same sequence as used for one of thehigh-precision calibration curves: laboratory accuracy demonstrated withsuch known age samples means users can be confident that theirradiocarbon results can be calibrated cal��i��brate?tr.v. cal��i��brat��ed, cal��i��brat��ing, cal��i��brates1. To check, adjust, or determine by comparison with a standard (the graduations of a quantitative measuring instrument): against accepted curves.Laboratory participation in an intercomparison, on the other hand, is'blind', i.e. the laboratory does not know the age of thesamples before it submits its results for scrutiny. Furthermore, withthe publication of the International Atomic Energy Agency International Atomic Energy Agency:see Atomic Energy Agency, International. International Atomic Energy Agency (IAEA)International organization officially founded in 1957 to promote the peaceful use of nuclear energy. (IAEA IAEAInternational Atomic Energy Agency. )intercomparison (Rozanski 1991) and Third International RadiocarbonIntercomparison ('TIRI', Scott et al. forthcoming) the resultsare no longer anonymous: users will be able to see for themselves howwell participating laboratories fared relative to the consensus resultsfrom these studies. Anonymity, not unnaturally, suggested thatlaboratories had something to hide, but it also, perhaps surprisingly,provided a potential safeguard of benefit to the user. A laboratory onfinding it has a systematic error (i.e. that it is producing inaccurateresults) can, and should, investigate and rectify the problem. Itsposition on a 'league table' at any given time is thereforenot immutable IMMUTABLE. What cannot be removed, what is unchangeable. The laws of God being perfect, are immutable, but no human law can be so considered. , and a correction made to the results of that laboratoryproduced at another time may well introduce, rather than remove, anerror. Only the laboratory itself can tell the user whether or not ithas, or has had, a systematic bias, and when.This is not to say that intercomparison studies are not useful --they are -- but largely to provide laboratories with independent checksof in-house procedures and, in the future, may well be requiredprocedures whereby laboratories can be 'quality certified' toenable them to tender at least for government funded contracts. Theyalso give the user a clear statement that the laboratory is committed toquality control: participation in an intercomparison study is no smalluse of limited resources.The need for results to be accurate is self-evident. Equallyimportant is the need to estimate realistically the precision, as this-- together with the shape of and error on the calibration curve In analytical chemistry, a calibration curve is a general method for determining the concentration of a substance in an unknown sample by comparing the unknown to a set of standard samples of known concentration. --determines the calendar age range(s). Given that precision is estimated,the concern is that all sources of variability are taken into account,and not just those associated with counting statistics. A laboratory candemonstrate that its estimated precision is valid via replication: ifall sources of error have been taken into account, the scatter of theserepeat measurements should be the same as the estimated precision.Alternatively, but less satisfactorily, it may compare its estimatedprecision with the scatter of its results about the consensus data in anintercomparison (note that inaccurate, i.e. biassed, results will tendto be systematically higher or lower than the consensus data rather thanrandomly scattered relative to them). An error multiplier is an ad hoc For this purpose. Meaning "to this" in Latin, it refers to dealing with special situations as they occur rather than functions that are repeated on a regular basis. See ad hoc query and ad hoc mode. device for modifying estimated precision so that the estimate is morerealistic, i.e. more in line with the true variability in the resultsassessed in one of the two ways outlined. Such a multiplier is specificto a given laboratory and can, with changes in measurement procedures,change with time. This is the problem of using intercomparison data toevaluate error multipliers, as they necessarily represent a'snapshot' in time. The only valid error multiplier is thatissued by a laboratory when it issues the radiocarbon result; even then,if the laboratory believes it needs a multiplier it ought to quote theerror with that multiplier included, clearly stating that it has doneso: this inclusive error is, in fact, the laboratory's bestestimate of its precision.Occasionally advice has been given to users to apply a blanket errormultiplier (for example, International Study Group 1982) dependent onlyon the size of error quoted by a laboratory, whichever that laboratorymay be. As an alternative, it has also been suggested (Stuiver &Reimer 1993: 227, modified, but regrettably not withdrawn, by Reimer1994) that an additional error term (variance) be incorporated, its sizedepending only on whether the radiocarbon result is older or youngerthan 2700 b.p. This suggestion, following Clark (1975), is based on datanow at least 20 years old. These are not approaches to be recommended.Whilst it may seem better to underestimate the precision (i.e. toincrease the size of the error term) rather than to overestimate o��ver��es��ti��mate?tr.v. o��ver��es��ti��mat��ed, o��ver��es��ti��mat��ing, o��ver��es��ti��mates1. To estimate too highly.2. To esteem too greatly. it, infact this may not be erring on the side of caution: for example, a[[Chi].sup.2]-test (Ward & Wilson 1978: 'Case I') couldgive an entirely erroneous confirmation of assumed contemporaneity con��tem��po��ra��ne��ous?adj.Originating, existing, or happening during the same period of time: the contemporaneous reigns of two monarchs.See Synonyms at contemporary. . Onlythe laboratory itself can demonstrate the validity of its precision andshould be required to do so.The user has the ultimate weapon if the laboratory consistently failsto demonstrate accuracy and realistic precision -- to take his/hersamples elsewhere.InterpretationBowman & Balaam (1990) ranged, albeit briefly, over severalissues of interpretation. Here comment will be confined to the currentsituation regarding calibration, both calibration data and methodology.Calibration curvesAfter it was recognized that radiocarbon results are not the same ascalendrical ages (de Vries de Vries.For some persons thus named use Vries.1958), the first continuous calibration curvewas published by Suess (1970). Intensive dendrochronological andradiocarbon research followed, with intermittent attempts to reconcilethe published data and provide a consensus calibration curve (e.g. Clark1975; Klein et al. 1982). The publication in 1986 of an internationallyagreed calibration curve back to 2500 BC (Mook mook?n. SlangAn insignificant or contemptible person.[Probably alteration of moke.] 1986) was a majormilestone in the long saga of radiocarbon calibration. This was aconsiderable achievement, not only because it was based onhigh-precision radiocarbon results, with error terms of [+ or -] 20years or less ([+ or -]1[Sigma]) but because two laboratories, Belfastand Seattle, using wood from different dendrochronological sequences,had produced results in agreement (within quoted errors) over the entireperiod (Pearson & Stuiver 1986; Stuiver & Pearson 1986): noreconciliation of data was required. The Belfast data were largely onIrish oaks The Irish Oaks is a Group 1 flat horse race in the Republic of Ireland for three-year-old thoroughbred fillies. It is run over a distance of 1 mile and 4 furlongs (2,414 metres) at the Curragh in July. , whereas Seattle data for years ad were on North American North Americannamed after North America.North American blastomycosissee North American blastomycosis.North American cattle ticksee boophilusannulatus. species and most of the BC data used German oak. An extension of thiscurve seemed imminent, since the Belfast data already stretched back to5210 BC (Pearson et al. 1986). The criterion to be satisfied was thatthese and any future data be 'sufficiently double-checked'(Mook 1986) if they were to be accepted as extensions to theinternationally recommended calibration data.In 1993, Radiocarbon produced a special Calibration Issue (Vol. 35,no. 1). Of the Belfast and Seattle data published in it, those for theperiod AD 1840--5000 BC are in statistical agreement and, as above, arebased on substantially different dendrochronological sequences (Stuiver& Pearson 1993; Pearson & Stuiver 1993). These references alsoinclude a further 1000 years of calibration based solely on German oakchronology (Bowman & Leese (in press) summarizes the date-rangescovered and resolution of the data presented in the 1993 CalibrationIssue).Provided with the 1993 Calibration Issue was a new version of theUniversity of Washington's calibration program, CALIB 3.0 (Stuiver& Reimer 1993), incorporating data published in the Issue by a rangeof laboratories. These data have not been discussed widely, nor has anysubset of them been internationally agreed. This lack of discussion isparticularly surprising given that the triennial tri��en��ni��al?adj.1. Occurring every third year.2. Lasting three years.n.1. A third anniversary.2. A ceremony or celebration occurring every three years. internationalradiocarbon conference, held in Glasgow in August 1994, was the logicaloccasion on which to affirm all or parts of the data sets.For users the uncertainties lie in which calibration data to use andwhether the use of other data might have given rise to significantlydifferent archaeological interpretations. To summarize the data (seealso Bowman & Leese in press), those in the 1993 Calibration Issuenot only extend the data published in 1986, but also amend them. Whileone might wish that calibration data were immutable, such amendments aretestimony to the continuing and considerable care and quality controlinvested by the high-precision laboratories. The Seattle data are someof those that have been re-evaluated. A correction for previouslyunsuspected incorporation of radon, a radioactive gas, in the carbondioxide carbon dioxide,chemical compound, CO2, a colorless, odorless, tasteless gas that is about one and one-half times as dense as air under ordinary conditions of temperature and pressure. samples has led to an age increase of between 10 and 30 years(Stuiver & Becket beck��et?n. NauticalA device, such as a looped rope, hook and eye, strap, or grommet, used to hold or fasten loose ropes, spars, or oars in position.[Origin unknown.]Noun 1. 1993). The Belfast data were also corrected for acounting efficiency The counting efficiency is the ratio between the number of particles or photons counted with a radiation counter and the number of particles or photons of the same type and energy emitted by the radiation source (IUPAC Compendium of Chemical Terminology 2nd Edition, 1997). problem (Pearson & Qua 1993), retaining goodagreement between the two data sets over the majority of the time-rangecovered by both. The implication therefore is that the 1986internationally agreed data-set has been superseded. However, McCormacet al. (forthcoming) have recently made radiocarbon measurements oncontemporaneous con��tem��po��ra��ne��ous?adj.Originating, existing, or happening during the same period of time: the contemporaneous reigns of two monarchs.See Synonyms at contemporary. Irish oak and bristlecone pine samples. This, the firsttime the two types of wood have been measured quasi-simultaneously byone high-precision laboratory (Belfast), shows that the bristlecone pineis depleted in the isotope 14C relative to the Irish oak; so it willappear older on the radiocarbon time-scale. Further, they have beenunable to trace any efficiency problems in Pearson et al.'soriginal data (1986). Together these findings show that the 1986 Seattleand Belfast results should not in fact have agreed so well; the'double check' criterion would appear invalid for wood fromdifferent regions.Furthermore, the difference between the radiocarbon ages far Irishoaks and American Douglas Fir found by McCormac et al. (forthcoming)varies with calendar (dendrochronological) age in a manner thatcorresponds with a possible solar activity cycle. A difference in thecalibration, curves for the northern and southern hemispheres has longbeen recognized (for a given calendar date, the southern date is some 40radiocarbon years older (Vogel et al. 1993): calibration curves for thesouthern hemisphere are being produced (for example, Barbetti et al.forthcoming; McCormac & Hogg hoggcastrated male sheep usually 10 to 14 months old. Also used to describe an uncastrated male pig. pers. comm.). Also, specificenvironments can have localized effects on atmospheric 14C concentration(for example, in the immediate vicinity of volcanic vents (for example,Bruns et al. 1980) or due to localized anthropogenic an��thro��po��gen��ic?adj.1. Of or relating to anthropogenesis.2. Caused by humans: anthropogenic degradation of the environment. activity (Levin1985)). The recent Belfast research, however, proves more generallocation-dependent 14C variations, and this raises the spectre, within agiven hemisphere, of location-dependent calibration curves. Are thesevariations likely to be important? The answer is undoubtedly'yes' for the geophysicist or geochemist studying solaractivity, the carbon cycle, ocean mixing etc. For calibrating mostradiocarbon results for archaeological samples, the effect will benegligible. Likewise the differences between the 1986 and 1993 sets ofcalibration data are unlikely to give noticeably different calibrateddate-range(s) for most radiocarbon results. For Hiberno-Britisharchaeology, at least, the appropriate course is clear: use the 1986Belfast calibration data based on Irish (and very occasional British)oaks (Pearson et al. 1986), rather than the 1993 data.A key concern is the proliferation of calibration curves togetherwith the confusion these are causing. At the Glasgow meeting in August1994, the Belfast group together with a number of users of radiocarboncalibration data (including the author) proposed the establishment of aworking group to discuss this.Calibration methodsArchaeologists, a small user group in the radiocarbon world, arerelatively unusual in hoping to produce fairly refined chronologies.Since problems associated with calibrating radiocarbon results are morepressing in archaeology than elsewhere -- indeed, some user groups areyet to acknowledge consistently the need to calibrate To adjust or bring into balance. Scanners, CRTs and similar peripherals may require periodic adjustment. Unlike digital devices, the electronic components within these analog devices may change from their original specification. See color calibration and tweak. ! -- the greatmajority of recently published papers on methods of calibration, notleast in ANTIQUITY, have been focused on archaeological applications.There is a growing consensus that calibrated dates can only befaithfully represented by probability distributions which fully takeaccount of both the error term on the radiocarbon results and the effectof wiggles wiggles - [scientific computation] In solving partial differential equations by finite difference and similar methods, wiggles are sawtooth (up-down-up-down) oscillations at the shortest wavelength representable on the grid. in the calibration curves. The 'intercept' method(Pearson 1987), while easy to use, cannot do this. To generateprobability distributions requires the use of a computer program,several of which exist for calibrating individual results (e.g. Van derPlicht 1993; Nicklaus et al. 1992; Stuiver & Reimer 1993). Theseparticular programs all implicitly use Bayesian methodology with theeminently reasonable a priori assumption a priori assumption(ah pree ory) n. from Latin, an assumption that is true without further proof or need to prove it. It is assumed the sun will come up tomorrow. that, in the absence of anyother information to the contrary, all calendar ages for the event beingdated are equally likely.For the resulting calendar date-range(s), the degree to which it isvalid to ignore short gaps between ranges, or indeed low probabilityranges, is yet to be explored adequately. Given that it is advisable toquote the calibration curve(s) and calibration program used (and derigueur de ri��gueur?adj.Required by the current fashion or custom; socially obligatory.[French : de, of + rigueur, rigor, strictness. the raw radiocarbon result), arbitrarily and subjectively toignore output from the program seems gratuitous Bestowed or granted without consideration or exchange for something of value.The term gratuitous is applied to deeds, bailments, and other contractual agreements. , currently at least, andmight even mislead in future re-evaluation of the data.Representation of groups of calibrated dates can simply be graphical,using charts of confidence bars or probability distributions for theindividual calibrated results, ideal for some applications (e.g. Amberset al. 1992). Often it would also be useful to include archaeologicaldata. Bayesian methodology allows this to be done. Fundamental to thisapproach are the archaeologist's knowledge about the chronologybefore radiocarbon dating, explicitly stated, and thestatistician's ability to model the measurement and calibrationprocess together with that archaeological knowledge. The resultingmodel, combined with the radiocarbon results, leads to a probabilitydistribution Probability distributionA function that describes all the values a random variable can take and the probability associated with each. Also called a probability function.probability distributionfor the calendar dates which reflects all the availableinformation (Buck et al. 1991), for example incorporating anarchaeological or historical terminus into the calibration of anindividual radiocarbon result, or dealing with results from samples ofknown stratigraphic stra��tig��ra��phy?n.The study of rock strata, especially the distribution, deposition, and age of sedimentary rocks.strat ordering (Buck et al. 1991; 1992).* Until recentlythe Bayesian methodology required considerable computing power and wastherefore not readily accessible. Bronk Ramsey (forthcoming) hasperformed a great service by developing PC programs which will enablethem to become widely available. His programs also allow the user todecide which calibration curves to use (which is an advantage over CALIB3.0). If there is any disadvantage in them, it is perhaps their userfriendliness -- possibly too friendly, with the concomitant dangers thismay hold for over-and inappropriate interpretation of data.Strategic resourcingThe national use of resources for radiocarbon dating is an issue asyet rarely considered (but see Bowman & Balaam 1990). Mostarchaeologists continue to be taxed by site-specific strategies andresourcing, in particular whether or not radiocarbon can solve aparticular chronological problem, if so how many samples are needed, andthen how much it might cost (and only then whether it is worth it!).Simulation of the potential of radiocarbon dating is a valuable aidwhich many archaeologists unwittingly use on a simple level at least. Bycalibrating feasible results and errors based on educated guesswork, itis possible to judge the likely success of the strategy, and indeed ofradiocarbon dating after calibration, in resolving the chronologicalproblem. Take, as a simple example, an archaeologist digging an EarlyIron Age site in Britain; by 'simulation' he/she would knowthat any calendar event dating to 800-400 BC would be indistinguishableby radiocarbon because of the shape of the calibration curve over thatperiod, and thus that any radiocarbon sampling strategy would be ofextremely limited, if any, value. Similarly, if an archaeologist hasgood reason to believe two events were very closely spaced in time,then, intuitively, poor precision on the radiocarbon results will be amajor limitation in determining the time difference. Using simulationand Bayesian statistics, Buck et al. (1994) demonstrate how theseintuitive approaches to the shape of the calibration curve andradiocarbon precision can be modelled together with any archaeologicalpremisses as an aid in deciding a sampling strategy. In particular, theysimulate the difference between dating an event which in archaeologicalterms would be considered to be 'single' (but may have afinite if short time-span) and contemporaneity of samples in radiocarbonterms; the different archaeological inferences that can arise areillustrated graphically. Bayesian approaches to simulation such as thiscan now be tried using Bronk Ramsey's programs (forthcoming: seeReferences for contact address).Sample selection -- and laboratory selection Although nothing hasbeen said here about specific selection and characterization of materialand context for dating (see Bowman & Balaam 1990), their importanceremains paramount. The most accurate and precise laboratory cannotproduce sensible radiocarbon results on samples such as bulked woodcharcoal from long-lived species.Many laboratories scrutinize scru��ti��nize?tr.v. scru��ti��nized, scru��ti��niz��ing, scru��ti��niz��esTo examine or observe with great care; inspect critically.scru the samples submitted to them byarchaeologists, and -- vice versa -- archaeologists wanting accurate andprecise radiocarbon results should scrutinize the laboratory.The potential effect of calibration of radiocarbon results oninterpretation must be considered well before the samples are dated. Thesampling strategy will determine the type and complexity ofchronological model that can be considered (whether or not Bayesianmethodology is used). Increasingly the use of simulation will aid indeciding a sampling strategy, and it will have the additional benefit ofpromoting early collaboration between archaeologists, statisticians Statisticians or people who made notable contributions to the theories of statistics, or related aspects of probability, or machine learning: A to EOdd Olai Aalen (1947–) Gottfried Achenwall (1719–1772) Abraham Manie Adelstein (1916–1992) andradiocarbon scientists.Acknowledgements. I wish to thank Janet Ambers, Morven Leese, GerryMcCormac, Stuart Needham, Jonathan Pilcher and Christopher Bronk Ramseyfor reading and commenting on this paper.ReferencesAMBERS, J., S. BOWMAN, A. GIBSON & I. KINNES. 1992. 14C resultsfor the British Beakers, Radiocarbon 34(3): 916-27.BARBETTI, M., T. BIRD, G. DOLEZAL, G. TAYLOR, R. FRANCEY, E. COOK& M. PETERSON. Forthcoming. 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