Time scale evaluation and the quantification of obliquity forcing

The geologic time scale serves as an essential instrument for reconstructing Earth history. Astrochronology, linking regular sedimentary alternations to theoretical quasi-periodic astronomical rhythms, often provides the highest resolution age models for strata that underlie the time scale. Although various methods for testing astronomically-tuned time scales exist, they often present challenges, such as the problem of circularity. Here, we introduce an approach to extract a reliable obliquity envelope from astronomically tuned data, avoiding the effects of frequency modulations that can artificially introduce astronomical beats. This approach includes (1) the application of a broad obliquity filter followed by (2) a Hilbert transform and (3) a low-pass filter of the amplitude envelope to (4) test the significance of correlation between amplitude envelope and astronomical solution. These data amplitudes provide a robust means to evaluate the climate response to obliquity forcing and, more specifically, to test the significance of correlation with the theoretical astronomical solution, in a manner similar to the phase-randomized surrogate approach previously introduced for the evaluation of precession tuning. Synthetic astronomical/ice-sheet models and several Quaternary climate proxy records – where obliquity can be a dominant component of astronomically driven climate variability – are used to demonstrate the feasibility of the proposed method and yield new insight into climate system evolution.