= Two-reservoir carbon adjustment
{title2=$t_p\ll t_C$}
A coupled atmosphere–ocean <mass conservation> model can have a fast atmospheric <exponential relaxation time> and a much slower ocean-carbon time. For atmospheric inventory coefficient $I$, exchange coefficient $h$, ocean <water> mass $M_o$, removal coefficient $b$ and linear surface-<pressure> relation $p_s=C/K$, atmospheric balance gives $p\simeq C/K+(v-A_LW)/h$. Substitution into the ocean equation cancels the weathering and exchange terms, giving $(M_o/b)\dot C=v/(M_{\mathrm{CO}_2}b)-C$. Sustained extra emissions therefore first raise <pressure> at nearly fixed ocean <concentration> and then increase both reservoirs over the ocean removal time.
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