A simple ocean and atmosphere box model illustrates the compensation of Ceq and C
which must hold for the global ocean. We define the global mean ocean C concentration
C (VdCd VthCth)/(Vd Vth) (see Fig. 3). From this and (1) we may relate C and
pCO2
at through mass balance. They must obey, MpCO2
at VC constant, where M is the
number of moles of gas in the atmosphere, and V Vd Vth is the total volume of the
ocean. Consider small perturbations in atmospheric pCO2 and mean ocean C concentration.
MpCO2
at VC 0. (27)
Following (6), a perturbation in C must be the sum of perturbations in Ceq and C in the
abiotic limit.
C Ceq C. (28)
Combining (28) with the definition of the Revelle or buffer factor (Bolin and Eriksson,
1959), (pCO2
at/pCO2
at)/(Ceq/Ceq) Bu O(10) we find an expression for the change
in global mean C:
C Ceq
BupCO2
atpCO2
at C. (29)
Combining (29) with the linearized mass balance (27) we can evaluate the sensitivity of the
ocean mean carbon concentration, C , to the saturation state, C:
C
C
1
1
1
MBupCO2
at
VCeq
0.2. (30)
This relationship tells us that, in the globally averaged, steady state, a change in saturation
state, C, must be largely compensated by a corresponding change in the saturation
carbon concentration, Ceq due to increasing atmospheric pCO2. Hence the resulting
change in C is moderate. C = 0.2C.