Abstract
In studies of environmental change of the past few centuries, ^{210}Pb dating is often used to obtain chronologies for sedimentary sequences. One of the most commonly used approaches to estimate the age of material at different depths in a sequence is to assume a constant rate of supply (CRS) or influx of ‘unsupported’ ^{210}Pb from the atmosphere, together with a constant or varying amount of ‘supported’ ^{210}Pb. Current ^{210}Pb dating models do not use a proper statistical framework and provide poor estimates of the uncertainties. Here, we develop a new model for ^{210}Pb dating, where ages and values of supported and unsupported ^{210}Pb form part of the parameters. We apply our model to a case study from Canada as well as to some simulated examples. Our model can extend beyond the current CRS approach, deal with asymmetric errors and mix ^{210}Pb with other types of dating, thus obtaining more robust, realistic and statistically better defined age estimates.
Highlights
210Pb is a radioactive isotope which forms part of the 238U decay series. 238U is contained within most rocks, and over time it decays into 226Ra, which decays into 222Rn
To allow for faster convergence of the MCMC, a limit to the chronology is considered. This chronology limit is inspired by the 210Pb dating horizon, which is the age at which 210Pb samples lack any measurable unsupported 210Pb
Our approach to 210Pb dating creates a structure in which the data are the result of a physical model, which allows us to have a more realistic measurement of the chronology uncertainty
Summary
The CRS model was not developed within a satisfactory statistical framework This resulted in a series of uncertainty approximations (Binford 1990; Appleby 2001; Sanchez-Cabeza et al 2014), which use error propagation and assume normality around the estimated ages. Since the original method uses the radioactive decay equation (N (t) = N0e−λt , where N (t) is the quantity of a radioactive element left in the sample at age t, N0 is the initial quantity, and λ is the element’s radioactive decay constant) to infer the ages, it results in a logarithmic approximation to a series of dates This logarithmic approximation heavily restricts the age-depth model. Details about the CRS model and the modelling of supported and unsupported 210Pb can be found in Appendices A and B, respectively
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