Analytical relationships between atmospheric carbon dioxide, carbon emissions, and ocean processes

[1] Carbon perturbations leading to an increase in atmospheric CO2 are partly offset by the carbon uptake by the oceans and the rest of the climate system. Atmospheric CO2 approaches a new equilibrium state, reached after ocean invasion ceases after typically 1000 years, given by PCO2 = P0exp(dIc/IB), where P0 and PCO2 are the initial and final partial pressures of atmospheric CO2, dIc is a CO2 perturbation, and IB is the buffered carbon inventory of the air-sea system. The perturbation, dIc, includes carbon emissions and changes in the terrestrial reservoir, as well as ocean changes in the surface carbon disequilibrium and fallout of organic soft tissue material. Changes in marine calcium carbonate, dICaCO3, lead to a more complex relationship with atmospheric CO2, where PCO2 is changed by the ratio PCO2 = P0{IO(A C)/(IO(A C) dICaCO3)} and then modified by a similar exponential relationship, where IO(A C) is the difference between the inventories of titration alkalinity and dissolved inorganic carbon. The overall atmospheric PCO2 response to a range of perturbations is sensitive to their nonlinear interactions, depending on the product of the separate amplification factors for each perturbation.