Hierarchical Dynamic Time Warping methodology for aggregating multiple geological time series

Coherent investigation of paleo-records relies on the interpretation of multiple time series of climate proxies which requires the application of signal matching techniques between separate records and within different proxy measurements inside a single record. However, current methodologies, such as correlation matrices or manual tuning using prominent signal features, result in considerable signal manipulation. Here, we extend Dynamic Time Warping (DTW), a widely used tool for measuring similarity between two signals, to include a Hierarchical aggregation (HDTW) for applying DTW on more than two input signals. Our approach to HDTW is not limited to aggregating up the hierarchies but also indexes a unified ?path matrix? for the original inputs, thus emphasising non-local similarities between the input signals and highlighting non-local outliers, eventually extrapolating the optimal match between all signals. As a use case for paleo-reconstructions, we apply an HDTWbased peak finding algorithm on two published micron-scale measurements of speleothems from water-limited environments, where annual growth cycles are inconsistent. By HTDW-aligning and then stacking several coeval time axes of parallel proxy measurements (petrographic input for the first test sample and elemental measurements for the second) we were able to identify and rank prominence of local and non-local features on the sample. The results of the sub-annual calibrations agree with published age models and are within known age constraints of those samples. The output of the sub-annual calibration provides insights into local features which were not ranked high enough to be included in the model. The presented age model provides the researcher with an in-depth understanding of signal conformity while highlighting unconformities for domain-specific analysis. Future implementations may explore similar geoscience applications in different scales (e.g. regional, global), and may benefit the general case of DTW-based applications outside of geosciences.