A temperature-dependent positive feedback on the magnitude of carbon isotope excursions

The decrease in the average magnitude of carbon isotope excursions in marine carbonates over Phanerozoic time is a longstanding unresolved problem. In addition, carbon isotope excursions commonly co-occur with oxygen isotope excursions of the same sign, implying the existence of a longstanding link between organic carbon burial fluxes and temperature. It was proposed that this connection was provided by the thermodynamic relationship between temperature and microbial respiration rates - changes in temperature drive changes in organic carbon remineralization rate and organic carbon burial efficiency. Such a mechanism provides the logic for a positive feedback affecting the magnitude of both climate changes and carbon isotope excursions. Here, we employ feedback analysis to quantify the strength of this mechanism with modifications to a simple carbon isotope mass balance framework. We demonstrate that the potential strength of this feedback is large (perhaps several permil) for plausible ranges of historical climate change. Furthermore, our results highlight the importance of the surface temperature boundary condition on the magnitude of the expected carbon isotope excursion. Comparisons of our model predictions with data from the terminal Eocene and Late Ordovician (Hirnantian) greenhouse- icehouse climate transitions suggest that these excursions might be substantially explained by such a thermodynamic microbial respiration feedback. Consequently, we hypothesize that the observed pattern of decreasing excursion magnitude toward the present might be explained at least, in part, by a decrease in the mean temperature of environments of organic carbon burial driven by long-term climate and paleogeographic trends.