# Wiggle-match dating of tree-ring sequences of numbers

Radiocarbon dating measurements produce ages in "radiocarbon years", which must be converted to calendar ages by a process called calibration. Radiocarbon years ago may be abbreviated " 14 C ya" [3] years ago or "uncal BP" [4] and calibrated dates as "cal BP". To produce a curve that can be used to relate calendar years to radiocarbon Wiggle-match dating of tree-ring sequences of numbers, a Wiggle-match dating of tree-ring sequences of numbers

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: 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 in the s by Wesley Ferguson. Suess said he drew the line showing the wiggles by "cosmic schwung " — freehand, in other words. It was unclear for some time whether the wiggles were real or not, but they are now well-established. 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.

This was experimentally verified in the s. Over the next thirty years many calibration curves were published using a variety of methods and statistical approaches. Wiggle-match dating of tree-ring sequences of numbers

The improvements to these curves are based on new data gathered from tree rings, varvescoral, and other studies.

The INTCAL13 data includes separate curves for the northern and southern hemispheres, as they differ systematically Wiggle-match dating of tree-ring sequences of numbers of the hemisphere effect; there is also a separate marine calibration curve.

Wiggle-match dating of tree-ring sequences of numbers

calibration curve itself has an associated error term, which can be seen on the graph labelled "Calibration error and measurement error". 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 *Wiggle-match dating of tree-ring sequences of numbers* radiocarbon years against the dotted lines, as Wiggle-match dating of tree-ring sequences of numbers shown for sample t 2in 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: 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 BP to 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 t 1 in blue Wiggle-match dating of tree-ring sequences of numbers 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 t 2in red on the graph, shows this situation: A third possibility is that the curve is flat Wiggle-match dating of tree-ring sequences of numbers

some range of calendar dates; in this case, illustrated by t 3in green on the graph, a range of about 30 radiocarbon years, from BP to BP, results in a calendar year range of about a century, Wiggle-match dating of tree-ring sequences of numbers BP to BP.

The method of deriving a calendar year range described above depends solely on the position of the intercepts on the graph. However, this method does not make use of the assumption that the original radiocarbon age range is a *Wiggle-match dating of tree-ring sequences of numbers* distributed variable: Deriving a calendar year range by means of intercepts does not take this into account. The alternative is to take the original normal distribution of radiocarbon age ranges and use it Wiggle-match dating of tree-ring sequences of numbers 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. 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. 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.

This output can be compared with the output of the intercept method in the graph above for the same radiocarbon date range. 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 Wiggle-match dating of tree-ring sequences of numbers 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. 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 Wiggle-match dating of tree-ring sequences of numbers able to produce.

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 Wiggle-match dating of tree-ring sequences of numbers 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.

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, Wiggle-match dating of tree-ring sequences of numbers 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.

From Wikipedia, the free encyclopedia. Oxford Radiocarbon Accelerator Unit. Wiggle-match dating of tree-ring sequences of numbers 26 June Retrieved from " https: Views Read Edit View history.

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