Using hierarchical dynamic time warping to synchronize age-uncertain (proxy) time series
Authors: Burstyn Yuval , Gazit Asaf 
Published: March 2020

&lt;p&gt;Climate- and environmental-proxy time series obtained from different archives, such as speleothems, allowed for major leaps in the understanding of past climate and environmental dynamics. However, age uncertainties that arise from the applied dating techniques and from the proxy sampling methodologies, respectively, are often neglected. These age uncertainties are important when leads and lags between different proxy time series are examined or if the relationship to climate-forcing is investigated. This is most pronounced when examining data that detail events of sub-centennial down sub-annual resolution, where noise is not smoothed by a low resolution sampling (e.g. conventional dental drill), or in records karst systems where the noise is inherently high (e.g. water-limited environments).&lt;/p&gt;&lt;p&gt;We explore the use of dynamic time warping with a hierarchical aggregation layer (or HDTW) on multiple trajectories to generate an indexing table for the input samples. We hypothesize that this aggregation process results a temporally aligned references table (of the original trajectories) and allows for an analytical space to investigate and distinguish between local and non-local phenomena. We aim to compare sample derived features, such as peaks in trace element, organic fluorescence analyses and potentially &amp;#948;&lt;sup&gt;18&lt;/sup&gt;O (not tested here), on the derived analytical space, for the purpose of enabling a robust and simplified approach to multi-sample age modelling.&lt;/p&gt;&lt;p&gt;We show HDTW compatibility to existing peak-counting methodologies applied on laser-ablation trace element analysis and confocal fluoresce laser microscopy. As a case study, we use HDTW on three published micron-scale elemental measurements of samples from Mediterranean climates with strong dry summer &amp;#8211; wet winter seasonality - two from south-western Australia (Nagra et al., 2017) and one from the Soreq Cave in the Eastern Mediterranean (Orland et al., 2014). The HDTW continuous space for these samples yields results that are within the published age constraints, without the need to stack multiple traverses and manually account for double or missing peaks.&lt;/p&gt;&lt;p&gt;HDTW is an important new tool for locating and identifying local and non-local phenomena in micron scale measurements (e.g. parallel laser ablation trace element traverses) by automatically aligning several coeval time axes of similar proxies. In the future HDTW could be applied for regional scale investigation (e.g. a coeval speleothems from a single cave or the same region, multiple cores from a single lake) allowing the unbiased fine-tuning between different environmental archives registering similar forcing mechanisms.&lt;/p&gt;&lt;p&gt;Nagra, G., Treble, P.C., Andersen, M.S., Bajo, P., Hellstrom, J.C., Baker, A., 2017. Dating stalagmites in Mediterranean climates using annual trace element cycles. Sci. Rep. 7, 621.&lt;/p&gt;&lt;p&gt;Orland, I.J., Burstyn, Y., Bar-Matthews, M., Kozdon, R., Ayalon, A., Matthews, A., Valley, J.W., 2014. Seasonal climate signals (1990&amp;#8211;2008) in a modern Soreq Cave stalagmite as revealed by high-resolution geochemical analysis. Chem. Geol. 363, 322&amp;#8211;333.&lt;/p&gt;