Tipping points and abrupt climate change: A comparison of advanced analysis methods for paleoclimate records

Paleoclimate proxy records are used to reconstruct past states of the Earth's climate. These records sometimes exhibit abrupt transitions that may serve as evidence of dramatic shifts in the Earths past climates. Such shifts, in turn, may be due to the climate system crossing a tipping point (TP). Identifying TPs in the Earth's past helps determine critical thresholds in present-day climate, where slow anthropogenic forcing may bring abrupt, and possibly irreversible, change to the physical climate system and impacted ecosystems. Information contained in paleoclimate proxy records is often ambiguous because of the complexity of the system, which includes both deterministic and stochastic processes. Furthermore, high levels of noise and a nonuniform resolution characterize paleoclimate time series. These combined sources of uncertainty highlight the need to develop methods for identifying and comparing TPs that address different aspects of change in paleoclimate time series. Here, we identify abrupt transitions and potential TPs for a selected set of high-quality paleoclimate records exhibiting centennial-to millennial-scale variability that make up the PaleoJump database. We apply different time series analysis methods, including an augmented Kolmogorov-Smirnov test, recurrence plot analysis, and singular spectrum analysis to identify abrupt transitions, regime shifts, and changes in periodicity in the records. We compare the different methodologies and discuss their respective advantages and disadvantages.