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

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 P-CO2 = P(0)exp(delta I-chi/I-B), where P-0 and P-CO2 are the initial and final partial pressures of atmospheric CO2, delta I-chi is a CO2 perturbation, and I-B is the buffered carbon inventory of the air- sea system. The perturbation, delta I-chi, 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, delta I-CaCO3, lead to a more complex relationship with atmospheric CO2, where P-CO2 is changed by the ratio P-CO2 = P-0{IO(A - (C))/( I-O(A (- C)) - delta I-CaCO3)} 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 P-CO2 response to a range of perturbations is sensitive to their nonlinear interactions, depending on the product of the separate amplification factors for each perturbation.