A Nonparametric Hierarchical Stack Construction Algorithm for Benthic Oxygen Isotope Ratios based on the Gaussian Process Regression

Abstract:

The δ¹⁸O of benthic foraminiferal calcite is a proxy that responds to changes in global ice volume as well as deep water temperature and salinity. Because temperature and salinity have relatively little spatial variability in deep water and glacial ice volume is a major driver of benthic δ¹⁸O change, it has been extensively employed to infer synchronous ages. In addition, multiple records are often aligned to produce a high-resolution reference in the form of a “stack,” which can be used as both a summary of the observations and an alignment target for new records. However, local variability in benthic δ¹⁸O between sites can also provide spatial information about climate and circular changes. One approach to capture local variability in benthic δ¹⁸O is to construct regional (local) stacks of cores assumed to have similar (homogeneous) signals based on ocean circulation patterns (e.g., Stern and Lisiecki, 2014). Although these local stacks have been an important advance for capturing lags between Atlantic regions quantitatively, they are based on only a limited number of records within each region and, thus, fail to fully capitalize on the global characteristic of benthic δ¹⁸O from those in the other regions. Here we develop a hierarchical stack construction method that considers both global and local characteristics of benthic δ¹⁸O based on a Bayesian statistical method that links input records. The model improves inferences for every local record by borrowing information from all the other records while weighting their expected similarity based on core location and models of deep-water mass distribution. In this way, our hierarchical stack not only captures local differences but also capitalizes on the global nature of benthic δ¹⁸O. The model in addition uses radiocarbon data to capture the lags between homogeneous subsets of benthic δ¹⁸O that occurred in the last glacial termination. Stacks are constructed using Gaussian process regression, which is a nonparametric regression that does not require any parametric structure, such as polynomial models, in benthic δ¹⁸O. We present the results of our hierarchical model applied to the data from 54 Atlantic cores that yields clusters of homogeneous records to form local stacks without expert assessment.