Detecting Paleoclimate Transitions With Laplacian Eigenmaps of Recurrence Matrices (LERM)

Paleoclimate records can be considered low‐dimensional projections of the climate system that generated them. Understanding what these projections tell us about past climates, and changes in their dynamics, is a main goal of time series analysis on such records. Laplacian eigenmaps of recurrence matrices (LERM) is a novel technique using univariate paleoclimate time series data to indicate when notable shifts in dynamics have occurred. LERM leverages time delay embedding to construct a manifold that is mappable to the attractor of the climate system; this manifold can then be analyzed for significant dynamical transitions. Through numerical experiments with observed and synthetic data, LERM is applied to detect both gradual and abrupt regime transitions. Our paragon for gradual transitions is the Mid‐Pleistocene Transition (MPT). We show that LERM can robustly detect gradual MPT‐like transitions for sufficiently high signal‐to‐noise (S/N) ratios, though with a time lag related to the embedding process. Our paragon of abrupt transitions is the “8.2 ka” event; we find that LERM is generally robust at detecting 8.2 ka‐like transitions for sufficiently high S/N ratios, though edge effects become more influential. We conclude that LERM can usefully detect dynamical transitions in paleogeoscientific time series, with the caveat that false positive rates are high when dynamical transitions are not present, suggesting the importance of using multiple records to confirm the robustness of transitions. We share an open‐source Python package to facilitate the use of LERM in paleoclimatology and paleoceanography.