Probabilistic sequence alignment of stratigraphic records

Abstract

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 δ 18 O of calcite from benthic foraminifera, which records a global ice volume and deep water temperature signal. To date, δ 18 O 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 δ 18 O alignment. This model considers the probability of every possible alignment based on its fit to the δ 18 O 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 δ 18 O 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 δ 18 O signal. Confidence bands within individual cores also vary greatly, ranging from~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.

A Bayesian, multivariate calibration for Globigerinoides ruberMg/Ca

“…It can handle complex models with many parameters [ Gelman et al ., ]. Bayesian inference has been applied to several problems in climate research [e.g., Berliner et al ., , b; Blaauw and Christen , ; Haslett and Parnell , ; Haslett et al ., ; Jackson et al ., ; Lin et al ., ; Parnell et al ., ; Tebaldi et al ., ; Tingley and Huybers , ], including the calibration of the TEX86 paleothermometer [ Tierney and Tingley , ]. Bayesian statistics proceeds by drawing a set of samples from a prior probability distribution and updating the probability of these parameters in light of new data.…”

Deglacial carbon cycle changes observed in a compilation of 127 benthic <i>δ</i><sup>13</sup>C time series (20–6 ka)

“…For the time range of 6-20 kyr used in our δ 13 C compilation, the 95 % confidence interval widths of the regional age models range from 0.5-2.0 kyr. Although Match does not quantify alignment uncertainty, alignment uncertainties have been estimated using a similar algorithm, called HMM-Match (Lin et al, 2014). For age models generated either by δ 18 O alignment or radiocarbon dating, the amount of age uncertainty depends on the time resolution of the δ 18 O or 14 C data, respectively.…”

The Role of Uncertainty in Estimating Lead/Lag Relationships in Marine Sedimentary Archives: A Case Study From the Tropical Pacific

“…The age uncertainty resulting from the alignment to the LR04 curve through the HMM‐Match algorithm, expressed as the 95% confidence interval, varies from 0.9 kyr to 10 kyr at the glacial terminations. The large range of uncertainty found among the different records is mainly a function of the resolution of the data (supporting information; Lin et al, ). In fact, the correlation between the average resolution of a record and the mean age uncertainty is 0.71 ( p value < 0.01, Table ).…”

“…The age model for each of the records considered in this study was based on the alignment to the global benthic δ 18 O stack of Lisiecki and Raymo (, hereafter LR04) using a Hidden Markov model probabilistic alignment algorithm (HMM‐Match) (Lin et al, ). The advantage of this algorithm over the more traditional manual, qualitative comparison (Prell et al, ; Shackleton et al, ) or deterministic algorithms (e.g., Huybers & Wunsch, ; Lisiecki & Lisiecki, ; Martinson et al, ) is its ability to sample directly and exactly from the distribution of ages given the data and to use these samples to construct 95% confidence bands for the alignment by considering the probability of every possible alignment based on its fit to the δ 18 O data (the emission model, which is based on benthic δ 18 O residuals) and transition probabilities for sedimentation rate changes (Lin et al, ). Since the emission model and transition probabilities are modeled for marine sediment cores, alignment to ice core or speleothem chronologies is not possible at this time.…”

“…Here we seek to evaluate whether relative age dating can be used to assess phase relationships among various components of the climate system by testing the tropical Pacific hypothesis using a conceptual framework for the determination of phase relationships, and most importantly their significance, among time‐uncertain proxy SST records. This framework allows sampling renditions of the time series based on the uncertainty in age (Lin et al, ) and the temperature proxy (Khider et al, ). Although the use of Monte Carlo sampling is not a new concept in the estimation of uncertainty in paleoceanographic reconstructions, a probabilistic alignment algorithm was not available until recently.…”