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Numerical models are important tools for understanding the processes and feedbacks in the Earth system, including those involving changes in atmospheric CO2 (CO2,atm) concentrations. Here, we compile 55 published model studies (consisting of 778 individual simulations) that assess the impact of six forcing mechanisms on millennial-scale CO2,atm variations: changes in freshwater supply to the North Atlantic and Southern Ocean, the strength and position of the southern-hemisphere westerlies, Antarctic sea ice extent, and aeolian dust fluxes. We generally find agreement on the direction of simulated CO2,atm change across simulations, but the amplitude of change is inconsistent, primarily due to the different complexities of the model representation of Earth system processes. When freshwater is added to the North Atlantic, a reduced Atlantic Meridional Overturning Circulation (AMOC) is generally accompanied by an increase in Southern Ocean- and Pacific overturning, reduced Antarctic sea ice extent, spatially varying export production, and changes in carbon storage in the Atlantic (rising), in other ocean basins (generally decreasing) and on land (more varied). Positive or negative CO2,atm changes are simulated during AMOC minima due to a spatially and temporally varying dominance of individual terrestrial and oceanic drivers (and compensating effects between them) across the different models. In contrast, AMOC recoveries are often accompanied by rising CO2,atm levels, which are mostly driven by ocean carbon release (albeit from different regions). The magnitude of simulated CO2,atm rise broadly scales with the duration of the AMOC perturbation (i.e., the stadial length). When freshwater is added to the Southern Ocean, reduced deep-ocean ventilation drives a CO2,atm drop via reduced carbon release from the Southern Ocean. Although the impacts of shifted southern-hemisphere westerlies are inconsistent across model simulations, their intensification raises CO2,atm via enhanced Southern Ocean Ekman pumping. Increased supply of aeolian dust to the ocean, and thus iron fertilisation of marine productivity, consistently lowers modelled CO2,atm concentrations via more efficient nutrient utilisation. The magnitude of CO2,atm change in response to dust flux variations, however, largely depends on the complexity of models' marine ecosystem and iron cycle. This especially applies to simulations forced by Antarctic sea ice changes, in which the direction of simulated CO2,atm change varies greatly across model hierarchies. Our compilation highlights that no single (forcing) mechanism can explain observed past millennial-scale CO2,atm variability, and identifies important future needs in coupled carbon cycle-climate modelling to better understand the mechanisms governing CO2,atm changes in the past.

© 2018 The Publisher. Over the past 3.5 million years, there have been several intervals when climate conditions were warmer than during the pre-industrial Holocene. Although past intervals of warming were forced differently than future anthropogenic change, such periods can provide insights into potential future climate impacts and ecosystem feedbacks, especially over centennial-to-millennial timescales that are often not covered by climate model simulations. Our observation-based synthesis of the understanding of past intervals with temperatures within the range of projected future warming suggests that there is a low risk of runaway greenhouse gas feedbacks for global warming of no more than 2 °C. However, substantial regional environmental impacts can occur. A global average warming of 1-2 °C with strong polar amplification has, in the past, been accompanied by significant shifts in climate zones and the spatial distribution of land and ocean ecosystems. Sustained warming at this level has also led to substantial reductions of the Greenland and Antarctic ice sheets, with sea-level increases of at least several metres on millennial timescales. Comparison of palaeo observations with climate model results suggests that, due to the lack of certain feedback processes, model-based climate projections may underestimate long-term warming in response to future radiative forcing by as much as a factor of two, and thus may also underestimate centennial-to-millennial-scale sea-level rise.