Probabilistic sequence alignment of stratigraphic records

The assessment of age uncertainty in stratigraphically aligned records is a pressing need in paleoceanographic research. The alignment of ocean sediment cores is used to develop mutually consistent age models for climate proxies and is often based on the O-18 of calcite from benthic foraminifera, which records a global ice volume and deep water temperature signal. To date, O-18 alignment has been performed by manual, qualitative comparison or by deterministic algorithms. Here we present a hidden Markov model (HMM) probabilistic algorithm to find 95% confidence bands for O-18 alignment. This model considers the probability of every possible alignment based on its fit to the O-18 data and transition probabilities for sedimentation rate changes obtained from radiocarbon-based estimates for 37 cores. Uncertainty is assessed using a stochastic back trace recursion to sample alignments in exact proportion to their probability. We applied the algorithm to align 35 late Pleistocene records to a global benthic O-18 stack and found that the mean width of 95% confidence intervals varies between 3 and 23 kyr depending on the resolution and noisiness of the record's O-18 signal. Confidence bands within individual cores also vary greatly, ranging from similar to 0 to >40 kyr. These alignment uncertainty estimates will allow researchers to examine the robustness of their conclusions, including the statistical evaluation of lead-lag relationships between events observed in different cores.