Airborne Fraction of CO2 is the ratio of the amount observed in the atmosphere to the amount emitted. I have been writing (here and here) about how it seems to be extraordinarily stable. In saying this I define and plot it in a different way to the usual, in which it appears more variable, leading to speculation about trend. I'll say more about this different way below. But I think I have worked out the explanation for the stability, and it isn't obvious.
People tend to think first of Henry's Law, which suggests a fixed partition of a solute (including gas) between two phases. This is a material property, and refers to equilibrium, which does not apply to CO2 in air/sea. It applies even less to the land sink, which is quite important.
In this note, I will show that the constancy, perversely, depends on the dynamics, and is a result of the near exponential increase in CO2 emissions. This effect is mostly independent of the actual mechanism for the sinks. It is really a consequence of linearity with exponential increase.
Since this post is something of a math proof, here is a TOC:
Quantitative continuity estimates
7 hours ago