^{14}C Age Calibration in Matlab

The ^{14}C) age calibration in Matlab using the Bayesian highest posterior density (HPD). The function produces a probability distribution function (PDF) of calibrated ages, as well as 1 sigma (68.27%) and 2 sigma (95.45%) probability calibrated age credible intervals, calculated using HPD. Publication ready calibration plots are also produced, with the option to save to disk. Calibration output can be in either Cal BP or BCE/CE (BC/AD), and a reservoir age can be specified if necessary. The user can choose from a number of calibration curves, including the latest version of IntCal.

^{14}C

Radiocarbon (^{14}C) age calibration is a necessary process for estimating the true age range of a ^{14}C determination. Atmospheric ^{14}C activity (Δ^{14}C) has not been constant throughout history, due to changes in the rate of ^{14}C production in the upper atmosphere, as well as changes in the Earth’s carbon cycle. Simply knowing the ^{14}C activity of a given sample and applying the half-life of ^{14}C is, therefore, in itself not sufficient to determine the true age range; one must also have knowledge of past Δ^{14}C.

Reconstructions of past Δ^{14}C have been carried out using independently dated terrestrial archives, including tree-ring, speleothem and lake records. Additionally, independently dated marine archives have also been used to indirectly reconstruct past Δ^{14}C. The aforementioned Δ^{14}C records can be combined to produce what is known as a ^{14}C activity. The most commonly used calibration curves are produced by the ^{14}C ages (^{14}C yr BP) corresponding to a certain true age, or calibrated age (Cal yr BP).

^{14}C age determinations produced by radiocarbon laboratories are given in the form of a normal (Gaussian) distribution, whereby mean and 1 sigma values for the ^{14}C age are reported. The age calibration process involves using the shape of the calibration curve and its associated 1 sigma value to produce a probable calibrated age range for the ^{14}C age determination. A number of software tools offering ^{14}C calibration functionality have been authored and are widely used by researchers. Two of the most widely used such tools are the standalone calibration programs Calib [^{14}C calibration routines are built into the R-based, open source age modelling software packages Clam [^{14}C age calibration script (IOSACal) has also been written [

Many researchers within geosciences and archaeology make use of Matlab when analysing data. Some of these researchers also carry out ^{14}C determinations as part of their work. ^{14}C calibration function that can easily be implemented into a Matlab-based workflow.

The first methods used for ^{14}C age calibration, including in the earliest versions of Calib, involved using the so called ‘intercept method’, where one essentially uses the calibration curve as a lookup table to find the calibration curve values directly associated with median, 1 sigma and 2 sigma values of the normal distribution of the ^{14}C age determination. Later, OxCal [^{14}C age calibration by using the normal distribution of the ^{14}C age determination and the 1 sigma range of the calibration curve to calculate a probability density function (PDF) of calibrated ages, which is subsequently analysed using the Bayesian highest posterior density (HPD) method, resulting in a superior calibrated age range determination [

The ^{14}C age determination is represented by _{D}^{14}C age for each calibrated year (_{f}^{14}C data and the user inputted ^{14}C data are converted to F14C space when calculating

A resulting

An example of a ^{14}C calibration output plot from MatCal. The red shaded area indicates the ^{14}C age normal distribution. The darker and lighter blue shading respectively indicates the 1 sigma and 2 sigma credible intervals of the calibrated age PDF. The darker and lighter grey shaded areas indicate the calibration curve 1 sigma and 2 sigma confidence intervals, respectively. The green error bars (only shown in the case of ^{14}C data used to construct the calibration curve.

It is also possible to include a reservoir age (_{R}^{14}C determination, using the input variables ^{14}C determination (_{D}_{r}_{r}

MatCal has been tested against the two most commonly used ^{14}C calibration tools, the aforementioned Calib and Oxcal (Table

^{14}C age calibration in MatCal 2.0, Calib 7.0.0 and OxCal 4.2 and using IntCal13. Calibration results shown are the 1σ calibrated age ranges in Cal yr BP.

^{14}C age |
MatCal 2.0 | Calib 7.0.0 | OxCal 4.2 |
---|---|---|---|

500 ± 30 | 536 – 514 | 536 – 514 | 537 – 513 |

10000 ± 60 | 11610 – 11520 |
11610 – 11519 |
11610 – 11519 |

15000 ± 80 | 18346 – 18109 | 18345 – 18109 | 18346 – 18110 |

25000 ± 100 | 29177 – 28861 | 29175 – 28859 | 29178 – 28860 |

35000 ± 120 | 39758 – 39342 | 39757 – 39339 | 39760 – 39341 |

45000 ± 250 | 48801 – 47953 | 48792 – 47944 | 48801 – 47953 |

Further quality control has been carried out for Matlab in the form of user testing, which has led to the implementation of a number of error and warning messages. For example, if the user attempts to calibrate a ^{14}C age which produces a calibrated age PDF partially exceeding the range of the chosen calibration curve (e.g. <0 cal yr BP or >50000 cal yr BP in the case of

Any system capable of running Matlab R2012a or higher.

Tested as working in Matlab R2012a, likely to work in earlier versions also.

Unknown.

The MatLab plotting toolbox is required if the user decides to make use of the plotting functions.

Bryan C. Lougheed (wrote ^{14}C calibration routine, plotting module and manuscript)

Stephen P. Obrochta (wrote input parser and rewrote parts of code to increase compatibility across multiple Matlab versions)

English

The ^{14}C ages using multiple calibration curves or multiple reservoir ages. Previously, researchers may have had to implement calibration in an external software package, but now it is possible to implement the ^{14}C calibration into a Matlab workflow. For example, one may wish to batch calibrate multiple ^{14}C ages, which can be easily done by calling the

The calibrated age probability density function (

Brett Metcalfe is thanked for user testing. The authors acknowledge Maarten Blaauw’s informative webpage at Queen’s University Belfast.

The authors declare that they have no competing interests.