Carbon cycle

Carbon is exchanged among atmospheric, oceanic, biological and geological reservoirs. A model that only redistributes carbon among closed reservoirs cannot permanently remove its total excess burden.

Transfers of carbon among chemical forms and reservoirs.

Carbon held in organic matter, distinguished from carbonate and dissolved inorganic reservoirs.

A linear climate-carbon model with emissions $E$, concentration $C$, effective injection coefficient $b_1$, baseline $C_0$ and relaxation rate $b_0$. Constant emissions have equilibrium $C_0+b_{1}E/b_0$, and all transients about that equilibrium decay on time $b_0^{-1}$. Stopping emissions returns concentration to the baseline in this model. Real multiple reservoirs and long-lived carbon uptake tails prevent treating that one-time-constant assumption as universal.

Equal-capacity reservoirs exchanging carbon symmetrically preserve their total burden. Their difference decays at rate $2k$, so a pulse into one reservoir leaves one half there permanently unless an external sink is added. Coupling this response to a faster first-order thermal model produces an initial warming followed by relaxation to a nonzero asymptote.