AO index is derived from the height of the 1000mbar isobar.
High AO index means low sea level pressure in polar region.
A large proportion (almost all post 2000) of the deviation from 2 ppm/year rise in CO2 matches variations in the AO index.
The significant shift of AO index in 1989 also marks a change in the time lag between the two datasets.
the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.
Fick’s first law:
the flux is proportional to the negative of the gradient of the concentration.
Taking those two basic physical laws together relates the flux of CO2 entering or leaving surface waters to atmospheric pressure (as indicated by AO , for example).
The “constant” of Henry’s Law, a relationship in which other variables are held constant, is itself a function of temperature of the liquid.
The close correlation of the two series since 1997 is probably due to the lack of long term temperature trend in that period.