122 BACASTOW AND KEELING 



N a o 



*F| m =a am Rik am -^— Ni 



Nio 



t 



*Fmd = R m k m dN m + a mg RmFgo 



> (Eq. A. 11 continued) 



* 



F dm = Rd^dmNd 



where R; = *Nj/N| = isotopie ratio of radioactive to inactive carbon in reservoir 

 i 

 Rj = isotopie ratio of radioactive inorganic carbon to inactive inorganic 

 carbon in the surface ocean layer 



R m = similar ratio for combined inorganic and organic carbon in the 

 surface ocean layer 



a ab> a ba = isotopie fractionation factors associated with uptake and release of 

 radiocarbon by the land biota (fractionation of long- and short-lived 

 land biota are not differentiated) 



a am> tt ma = isotopie fractionation factors for ocean invasion and evasion of 

 radiocarbon at ocean— atmosphere boundary 



d m g = isotopie fractionation factor for formation of particulate carbon in 

 ocean surface layer 

 (All isotopie fractionation factors are assumed to be time invariant.) 



In expressing the flux *F m i, we have neglected the very small variation in 

 isotopie fractionation factor a am with changes in the distribution of inorganic 

 carbon species in surface water. This variation is discussed by Keeling. 5 



APPENDIX B: PREIiMDUSTRIAL 14 C EQUATIONS 



Equations for preindustrial 14 C can be derived from Eq. A. 9, the time- 

 dependent equations, by setting the derivatives to zero and masses of carbon to 

 their preindustrial values. The sum of these six equations, one for each reservoir, 

 is 



*r = *A(*N u0 + *N b0 + *N e0 + *N, +*N m0 + *N do )=*AE*Nio (B.l) 



i 



where *T is the l4 C production rate in the upper atmosphere. This equation 

 can be used to eliminate *T from the equation for the upper atmosphere 



(*\ + k ul )*N u0 -k ul ^ *N, = *r = *A E *N i0 (B.2) 



Nio i 





