210Pb-dating of recent sediments with the χ-mapping CF and CSAR models. On the attractors.

Conventional 210Pb-dating models use assumptions on sedimentary conditions that allow for analytical formulations. The novel χ-mapping models use numerical methods to generate and test a large number (∼106) of potential solvers. Empirical data (excess 210Pb vs. mass depth profile) serve to attract the solver that minimizes the χ function (the attractor), and it has been assumed that it also defines the most likely chronology. This work aims to test this assumption in a deep way. In synthetic and varved sediments, the performance of each solver can be quantified through a parameter ξa accounting for the deviation of the model and the true ages. This work studies the complex relationships between χ and ξa using the constant flux (χ-CF) and the constant sediment accumulation rate (CSAR) models, which operate in a parametric 3D space. The full mapping of the 3D χ function serves to find the absolute minimum, for the graphical representation of the complex topology of the attractors, which is model-specific, and for plotting clouds of chronological lines from solvers with varying χ values. The minimum value of ξa (the best chronology) is achieved for a wide range of χ values, including the region of the absolute minimum. In complex cases, tiny changes in χ can result in quite different chronologies. Alternative attractors that include a reference date and an objective function are studied. The results provide guidelines for strengthening the 210Pb-based chronologies.

210Pb-based dating of recent sediments with the χ-mapping version of the Constant Sediment Accumulation Rate (CSAR) model.

The 210Pb-based method aims at determining the absolute age of recent sediments on the centennial scale. A family of models assumes that at the sediment-water interface the flux of unsupported 210Pb (210Pbexc), F, relates to its initial activity concentration, Ao, and the mass sedimentation rate, w, as: F=Aow. Additional specific assumptions that allow for analytical formulations of the models are: i) constant Ao (CIC), constant F (CF), and constant F with constant w (CFCS). A model with constant w (CSAR) was suggested for completeness but never used because of the lack of a suitable analytical formulation. The TERESA model assumes random and independent variability for Ao and w, described by normal distributions. It systematically generates a large number (∼105) of potential solutions, whose performance for fitting the empirical 210Pbexc profile is quantified through the χ-function. This work aims to adapt the above methodology to formulate the χ-mapping version of the CSAR model. The performance of the model is evaluated with a set of synthetic and real cores for which an independent chronology is available. CSAR is able to capture the mean sedimentation rate from the 210Pbexc data and provides reliable chronologies and paleorecords of Ao, useful for tracking past changes in sedimentary conditions. CSAR provides an interesting different perspective for researchers working with 210Pb-based dating of recent sediments.