# Correlating Paleoclimate Time Series: Sources of Uncertainty and Potential Pitfalls

## TL;DR

This paper evaluates methods for correlating irregular, uncertain paleoclimate time series, finding that interpolation-based approaches generally outperform downsampling, with the specific series features being more influential than the method choice.

## Contribution

It compares the performance of different correlation estimation methods for paleoclimate records, highlighting the importance of series features over method selection.

## Key findings

- Interpolation methods yield better accuracy and precision.
- Series features like observation count and persistence are more influential.
- Observation time uncertainty adds less error than sampling irregularities.

## Abstract

Comparing paleoclimate time series is complicated by a variety of typical features, including irregular sampling, age model uncertainty (e.g., errors due to interpolation between radiocarbon sampling points) and time uncertainty (uncertainty in calibration), which, taken together, result in unequal and uncertain observation times of the individual time series to be correlated. Several methods have been proposed to approximate the joint probability distribution needed to estimate correlations, most of which rely either on interpolation or temporal downsampling. Here, we compare the performance of some popular approximation methods using synthetic data resembling common properties of real world marine sediment records. Correlations are determined by estimating the parameters of a bivariate Gaussian model from the data using Markov Chain Monte Carlo sampling. We complement our pseudoproxy experiments by applying the same methodology to a pair of marine benthic oxygen records from the Atlantic Ocean. We find that methods based upon interpolation yield better results in terms of precision and accuracy than those which reduce the number of observations. In all cases, the specific characteristics of the studied time series are, however, more important than the choice of a particular interpolation method. Relevant features include the number of observations, the persistence of each record, and the imposed coupling strength between the paired series. In most of our pseudoproxy experiments, uncertainty in observation times introduces less additional uncertainty than unequal sampling and errors in observation times do. Thus, it can be reasonable to rely on published time scales as long as calibration uncertainties are not known.