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 HDTW-based 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.

古记录的连贯调查取决于对气候代理的多个时间序列的解释，这需要在单独的记录之间以及在单个记录内的不同代理测量中应用信号匹配技术。然而，当前的方法，例如相关矩阵或使用突出信号特征的手动调谐，导致相当大的信号操纵。在这里，我们扩展了动态时间规整（DTW）（一种广泛用于测量两个信号之间相似度的工具），以包括用于将DTW应用于两个以上输入信号的分层聚合（HDTW）。我们处理HDTW的方法不仅限于汇总层次结构，还为原始输入建立了统一的“路径矩阵”索引，从而强调了输入信号之间的非局部相似性并突出显示了非局部离群值，最终推断所有信号之间的最佳匹配。作为古重建的用例，我们将基于HDTW的峰发现算法应用于水源有限的环境（年生长周期不一致）的两个已发布的微米级鞘脂的测量中。通过HTDW对齐，然后堆叠平行代理测量的几个同时期时间轴（第一个测试样品的岩石学输入和第二个测试样品的元素测量），我们能够识别并排列样品上局部和非局部特征的突出程度。次年校准的结果与公开的年龄模型一致，并且在那些样本的已知年龄限制内。次年度校准的输出可提供对局部特征的洞察力，这些局部特征的等级不够高，无法包含在模型中。提出的年龄模型为研究人员提供了对信号一致性的深入理解，同时突出了针对领域特定分析的不一致性。未来的实现可能会探索不同规模（例如区域，全球）的相似地球科学应用，并且可能会使地球科学之外基于DTW的应用的一般情况受益。