Decadal trends of the ocean carbon sink in Earth System Models in the past, present and future

The ocean and land biosphere are the two major natural sinks of carbon at present and the ocean is projected to become the dominant sink on centennial timescales when anthropogenic carbon emissions become zero and temperatures stabilize, and. Despite the ocean’s importance for the carbon cycle and climate, uncertainties of the decadal variability of this carbon sink and the underlying drivers of this decadal variability remain uncertain. The main tools to assess the ocean carbon sink over the last decades are global observation-based pCO₂ products that extrapolate sparse pCO₂ observations in space and time and global ocean biogeochemical models forced with atmospheric reanalysis data. However, these tools (i) are limited in time over the last 3 to 7 decades, which hinders statistical analyses of the drivers, (ii) are all based on the same internal climate state, and (iii) cannot assess the robustness of the drivers in the future, especially when carbon emissions decline or cease entirely. Here, I use an ensemble of 12 Earth System Models (ESMs) from phase 6 of the Coupled Model Intercomparison Project (CMIP6) to understand drivers of decadal trends in the past, present and future ocean carbon sink. The simulations by these ESMs span a period of 251 years and include 4 different future Shared Socioeconomic Pathways, from low emissions and high mitigation to high emissions and low mitigation. Using this ensemble, I show that 80% of decadal trends in the multi-model mean ocean carbon sink can be explained by changes in decadal trends of atmospheric CO₂ as long as the ocean carbon sink remains smaller than 4.5 Pg C yr^-1. The remaining 20% are due to internal climate variability and ocean heat uptake, which results in a loss of carbon from the ocean. When the carbon sink exceeds 4.5 Pg C yr^-1, atmospheric CO₂ rises faster, climate change accelerates, and decadal trends in the ocean carbon sink are substantially smaller than estimated based on changes in atmospheric CO₂ trends. The breakdown of this relationship under high emission scenarios, also implies that the increase in the ocean carbon sink is effectively limited, even if the trend in atmospheric CO₂ continues to increase. This limit of decadal trends in the ocean carbon sink is here estimated to be 1 Pg C yr^-1 dec^-1.Previously proposed drivers, such as the atmospheric CO₂ or the growth rate of atmospheric CO₂ can explain trends in the ocean carbon sink for specific time periods, for example during exponential atmospheric CO2 growth, but fail when emissions start to decrease again. The robust relationship over a large Earth System Model ensemble also suggests that very large  positive and negative decadal trends of the ocean carbon sink by some pCO₂ products are highly unlikely, and that the change in the decadal trends of the ocean carbon sink in 2000 is likely substantially smaller than estimated by these pCO₂ products.