Integrating the rate of change relationship provides the change in CO2 over the entire interval. Given temperature anomaly, we can reconstruct CO2 fairly accurately. Anthropogenic inputs are not needed.

You can make it yourself. The data are all at the woodfortrees website and you can select options from the menu. The options I chose for this plot at shown in the plot. woodfortrees.org/plot/

A surface temperature offset throttles downward transport, thus causing a change in the rate of accumulation or dissipation at the surface. The atmosphere is a flea on the ocean elephant’s back. Anthropogenic inputs are like piddling into a massive river. It has little impact.

How does it happen? My hypothesis is that CO2 laden waters are continuously upwelling at the equator, so there is a constant influx of CO2 to the surface system. Downwelling waters at the poles continuously remove it.