Southern Ocean heat burp in a cooling world

The ocean accumulates carbon and heat under anthropogenic CO₂ emissions and global warming. In net-negative emissions scenarios, where more CO₂ is extracted from the atmosphere than emitted, we expect global cooling. Little is known about how the ocean will release heat and carbon under such a scenario. Here we use an Earth system model of intermediate complexity and show results of an idealized climate change scenario that, following global warming forced by an atmospheric CO₂ increase of 1% per year and CO₂ doubling at year 70, subsequently features decreasing atmospheric CO₂ at a rate of -0.1% per year, implying sustained net-negative emissions. After four hundred years of net-negative emissions and gradual global cooling, abrupt reemergence of heat from the ocean interior leads to a global mean surface temperature increase of several tenths of degrees that lasts for more than a century. The ocean heat "burp" originates in heat that has previously accumulated under global warming in the Southern Ocean at depths and emerges to the ocean surface via deep convection. Surprisingly, this heat burp is largely devoid of CO₂. This is because changes in ocean circulation affect heat more than carbon, with an additional muting effect of CO₂ loss due to particularities of sea water carbon chemistry. As the ocean heat loss causes a global mean surface temperature increase that is independent of atmospheric CO₂ concentrations or emissions, it  presents a mechanism that introduces a break down of the quasi-linear relationship of the TCRE.