On a simplified solution of climate-carbon dynamics in idealized flat10MIP simulations

Idealized experiments with coupled climate-carbon Earth system models (ESMs) provide a basis for understanding the response of the carbon cycle to external forcing and for quantifying climate-carbon feedbacks. Here, we analyze globally-averaged results from idealized esm-flat10 experiments and show that most models exhibit a quasi-linear relationship between cumulative carbon uptake on land and in the ocean during a period of constant fossil fuel emissions of 10 Pg C yr⁻¹. We hypothesize that this relationship does not depend on emission pathways. Further, as a simplification, we quantify the relationship between cumulative ocean carbon uptake and changes in ocean heat content using a linear approximation. In this way, changes in oceanic heat content and atmospheric CO₂ concentration become interdependent variables, reducing the coupled temperature-CO₂ system to just one differential equation. The equation can be solved analytically or numerically for the atmospheric CO₂ concentration as a function of fossil fuel emissions. This approach leads to a simplified description of global carbon and climate dynamics, which could be used for applications beyond existing analytical frameworks.