Note, only CO2 concentration is shown at the simplest complexity level.
Note: fossil emissions are the same as the total in the regional emissions plot, but the timescale here is longer
The annual change in CO2 concentration is simply the sum of the emissions, minus the sinks. So, if the brown curve is above the cyan curve then the concentration will rise, or vice versa.
Note that controls to stabilise CO2 emissions may be found on the regional emissions plot
It is easier to understand see this effect in a "forward" calculation, applying the no-policy SRES scenarios or the "stabilise emissions" option (mitigation menu).
Then, if you increase one of the sinks by adjusting the model parameters, the atmospheric CO2 falls slightly, and so the other sink drops.
However, when you run the model in inverse mode, adjusting the sink parameters will cause the emissions to change, in order to continue to reach the target concentration or temperature curve.
Later, the biosphere sink begins to "saturate", as other factors such as water, sunlight and nutrients become more rate-limiting than CO2 for photosynthesis.
Only one parameter, the eddy diffusivity factor (blue arrow), is shown at the "basic" complexity level. This controls the rate at which CO2 mixes vertically in the bulk of the ocean.
If you select "expert" from the complexity menu, you can see more controls, and can compare the relative importance of processes. The mixing is dominated by the vertical diffusion and horizontal advection. The upwelling loop makes only a small difference. The effect of the gas-exchange rate is also small (unless you cut it altogether), since the mixed surface layer quickly catches up with the atmosphere.
Note that the upwelling is more important in the climate model which has no horizontal advection. There is some physical sense in this difference structure, since mixing depends on density gradients which depend on temperature, so this effect supresses mixing of heat in a way that does not affect CO2.
CO2 + H2O <=> HCO3- + H+
This conversion reduces the partial pressure of CO2 in seawater, giving the ocean has a vast capacity to store CO2. Currently the ocean holds about 50 times more inorganic carbon than the atmosphere, 99% of it in the form of HCO3-.
However adding CO2 to seawater makes it more acidic, which reduces this "buffer capacity". Increasing the temperature also affects the chemical equilibria and reduces the solubility of CO2 in seawater. Both these feedbacks (acidification and temperature) act to decrease the future ocean sink.
If you select "linear" from the "carbchem" menu (expert level) you will switch off the acidification effect.
If you disable the "CF" option, you will switch off the feedback from temperature. You may observe that this removes the spikes in the historical ocean sink, which are caused by equivalent spikes in radiative forcing, especially volcanos.