Orbital Signals in Carbon Isotopes: Phase Distortion as a Signature of the Carbon Cycle

Isotopic mass balance models are employed here to study the response of carbon isotope composition (δ13C) of the ocean-atmosphere system to amplitude-modulated perturbations on Milankovitch time scales. We identify a systematic phase distortion, which is inherent to a leakage of power from the carrier precessional signal to the modulating eccentricity terms in the global carbon cycle. The origin is partly analogous to the simple cumulative effect in sinusoidal signals, reflecting the residence time of carbon in the ocean-atmosphere reservoir. The details of origin and practical implications are, however, different. In amplitude-modulated signals, the deformation is manifested as a lag of the 405 kyr eccentricity cycle behind amplitude modulation (AM) of the short (~100 kyr) eccentricity cycle. Importantly, the phase of AM remains stable during the carbon cycle transfer, thus providing a reference framework against which to evaluate distortion of the 405 kyr term. The phase relationships can help to (1) identify depositional and diagenetic signatures in δ13C and (2) interpret the pathways of astronomical signal through the climate system. The approach is illustrated by case studies of Albian and Oligocene records using a new computational tool EPNOSE (Evaluation of Phase in uNcertain and nOisy SEries). Analogous phase distortions occur in other components of the carbon cycle including atmospheric CO2 levels; hence, to fully understand the causal relationships on astronomical time scales, paleoclimate models may need to incorporate realistic, amplitude-modulated insolation instead of monochromatic sinusoidal approximations. Finally, detection of the lagged δ13C response can help to reduce uncertainties in astrochronological age models that are tuned to the 405 kyr cycle.