Rule of Plum: Comparison of lead-210 dates derived from Bayesian analysis and the Constant Rate of Supply model using simulated and real datasets

To understand changes in peat accumulation in response to recent and rapid climate or anthropogenic change, accurate ages for the last 100-200 years are essential. Dating this period is often complicated by poor resolution and large errors associated with calibrating radiocarbon (¹⁴C) ages. The use of lead-210 (²¹⁰Pb) is a popular method as it allows for the measurement of absolute and continuous dates for the last 150 years of peat accumulation.

In ombrotrophic peatlands, the ²¹⁰Pb dating method has traditionally relied on the Constant Rate of Supply (CRS) model which uses the radioactive decay equation to provide a logarithmic model to approximate dates, resulting in a restrictive model. Key limitations of the CRS model are: (1) the accurate estimation of the supported lead which varies between sites and can be problematic if sampling of the total inventory is not continuous (e.g. interval measurements, lack of samples); (2) the inconsistent assessment of uncertainties. The Plum model was developed in a statistical framework with a Bayesian approach, notably resulting in longer chronologies and more realistic uncertainty estimations, and has the advantage of not double-modelling dates for final age-depth models.

Here, we present two thorough tests of Plum. First, we created scenarios using simulated datasets with known age-depth functions in a range of shapes and with varying sampling resolution. These simulations are created using the physical behavior that most ²¹⁰Pb dating models are based on. Plum and CRS model outputs are compared under each scenario. We also take this opportunity to demonstrate the new Plum R package, for use by non-statisticians in palaeoecological studies. Second, we present a comparison of ²¹⁰Pb dates derived from CRS models and from Plum using real peat cores from Eastern Canada with additional independent dating controls. These cores represent a thorough test for Plum, as permafrost thaw during the last 50 years has drastically altered stratigraphy and peat type (e.g. shift from ligneous peat to Sphagnum moss) affecting ²¹⁰Pb retention within the peat. Recent decadal-scale changes are still poorly represented so accurate dating is now essential to quantify changes in carbon accumulation rates and predict future trends.