Surprised by Simplicity: Model Experiments Reveal Rule of Thumb for Carbon-Climate Dynamics

Studying climate change is a very complex challenge, but sometimes simplicity unexpectedly emerges. Researchers have used idealized experiments with Earth system models to derive an approximation that allows them to estimate how the atmospheric carbon content will develop under different emission scenarios and what this means for the climate.

Together, the land vegetation and the ocean take up approximately half of anthropogenic carbon emissions, thereby keeping that fraction out of the atmosphere and mitigating human-induced climate change. But how much longer will this invaluable service be provided, and how much warmer will it get when their ability to absorb carbon declines? Scientists use complex Earth system models to answer these questions. A team of researchers led by the Max Planck Institute for Meteorology (MPI-M) has derived useful, easy-to-use approximations from such model experiments that can be evaluated with paper and pencil. These approximations help draw general conclusions about how atmospheric carbon dioxide evolves with further increasing carbon emissions and about the implications for global warming.

The team used idealized model experiments that examined what would happen if fossil fuel emissions remained at 10 PgC/year—the current emission level—over 100 years and then slowly reversed to 10 PgC/year carbon removal from atmosphere within the next 200 years. By analyzing the results, MPI-M researchers Victor Brovkin, Noel Brizuela, Tatiana Ilyina and Hongmei Li, in collaboration with colleagues from several international climate modeling groups, found that accumulated carbon uptake on land and in the ocean increase proportionally for most Earth system models analyzed.

“This was surprising, as carbon uptake on land and in the ocean are driven by very different processes. On land, carbon uptake is governed by biological processes such as photosynthesis and microbial respiration, while in the ocean, the chemical uptake of carbon dominates”, explained lead author Victor Brovkin.

Reducing dynamics to a single equation

Another surprising finding was that the proportionality persisted even when emissions decreased. This striking empirical relationship is therefore quite robust and helps simplify the dynamics of the Earth system for certain purposes. Based on the observation that ocean carbon uptake is proportional to its heat uptake, another simplification can be made, reducing the complex carbon-climate dynamics to a single equation that can be solved analytically or numerically. The result is the atmospheric carbon dioxide concentration as a function of fossil fuel emissions.

The scientists point out that once atmospheric carbon dioxide concentrations reach double the pre-industrial value, the approximations begin to fail as carbon uptake on land slows down. Brovkin: “Ultimately, of course, we need complex Earth system models. However, we now also have a useful tool to estimate the extent to which humankind can rely on the ocean and the land for carbon uptake in the medium term, and what this means for atmospheric carbon dioxide concentrations and the warming associated with them.”

Original publication

Brovkin, V., Sanderson, B. M., Brizuela, N. G., Hajima, T., Ilyina, T., Jones, C. D., Koven, C., Lawrence, D., Lawrence, P., Li, H., Liddcoat, S., Romanou, A., Séférian, R., Sentman, L. T., Swann, A. L. S., Tjiputra, J., Ziehn, T., and Winkler, A. J. (2025) On a simplified solution of climate-carbon dynamics in idealized flat10MIP simulations, Earth Syst. Dynam., 16, 2021–2034, DOI: 10.5194/esd-16-2021-2025.

Contact

Prof. Dr. Victor Brovkin
Max Planck Institute for Meteorology
victor.brovkin@we dont want spammpimet.mpg.de