Monthly CO2 data from Mauno Loa Observatory. The monthly rate of change is filtered with a triple running mean filter to remove the annual variation.
Sea surface temperature from ICOADS (actual temp) and Hadley ISST (interpolated anomaly reconstruction) are scaled and offset to give best fit to long term variation. Temperature data is processed with the same filter.
It is noted that short term variations are more sensitive to temperature change. This may be hypothesised to be the faster response of shallower waters or other factors.
Here, SST has been scaled by eye to best match the long term variations. This approximate method gives ratios of 3.0 adn 3.1 for the two SST datasets. The ratio of short term variability is clearly greater.
A more accurate estimation can be made from higher derivatives:
Another variable strongly related to CO2 is atmospheric pressure in the Arctic, reflected in the AO index: