Tracking δ13C and δ18O fluctuations uncovers stable modes and key patterns of paleoclimate

The examination of fluctuations in the correlations between ${\delta }^{13}$C and ${\delta }^{18}$O is of significant importance for the reconstruction of the Earth’s climate history. A key challenge in paleoclimatology is finding a suitable method to represent the correlated fluctuation system between ${\delta }^{13}$C and ${\delta }^{18}$O. The method must be able to handle data sets with missing or inaccurate values, while still retaining the full range of dynamic information about the system. The non-linear and complex correlations between ${\delta }^{13}$C and ${\delta }^{18}$O poses a challenge in developing reliable and interpretable approaches. The transition network, which involves embedding the ${\delta }^{13}$C and ${\delta }^{18}$O sequence into the network using phase space reconstruction, is a coarse-grained based approach. This approach is well-suited to nonlinear, complex dynamic systems, and is particularly adept at emerging knowledge from low-quality datasets. We have effectively represented the fluctuations in the correlation between ${\delta }^{13}$C and ${\delta }^{18}$O since $66$ million years ago (Ma) using a system of complex network. This system, which has topological dynamical structures, is able to uncover the stable modes and key patterns in Cenozoic climate dynamics. Our findings could help to improve climate models and predictions of future climate change.