84 EKDAHL AND KEELING 



where the C;;' are constants (functions of the kjj'), and the factors \y are 

 nonnegative roots (eigenvalues) of the characteristic determinant Eq. A. 9 

 except that transfer coefficients, kj and /j, appropriate to the inactive carbon, 

 replace the *kj and */j, and U is set equal to r. For times long compared to the 

 longest of the characteristic time constants, Xy , the last, exponentially growing 

 term dominates, and, as was found for the one-reservoir case, the partitioning is 

 proportional to the transfer function, Z:(r). For the six-reservoir model, the 

 lower atmosphere (tropospheric) transfer function is 



, , , "l (r) (B.4) 



Z|<r) = CMri 



where 



D 6 (r) = r[(r + / 5 )(r 4 + Ar 3 + Br 2 + Cr + D) 



+ / 6 (r + / 3 )(r + / 1 )(r 2 +ar+ b)] (B.5) 



and 



i>l(r) = (r + / 5 )(r + / 3 )(r + /, )(r 2 + ar + b) (B.6) 



The coefficients A, B, C, D, and a and b are the same functions of the 

 (unstarred) transfer coefficients as are their starred counterparts listed in 

 Eqs. A. 12 and A.13. The transfer coefficients /; and kj for the inactive carbon 

 system are listed in Appendix C of part II with the exception that here, in order 

 to simplify the matrix (Fq. A. 9), we set / 7 = 0. This is equivalent to assuming 

 that the short-lived biota is governed by a transfer equation of exactly the same 

 form as for the long-lived biota, i.e., each reservoir assimilates CO2 at a rate 

 proportional to its own mass. The effect is a reduction of the magnitude of the 

 biota growth factor, j3 for a given uptake of industrial C0 2 by the biota as a 

 whole, but there is otherwise little influence on the predictions described here. 



For the five-reservoir model [which has the source 7(t) appearing in the same 

 reservoir as for the radiocarbon case] , 



where ^ a (r) and Ds(r) are of the same form as Eqs. A. 14 and A. 10. The 

 instantaneous and total partitionings for an exponential industrial C0 2 source 

 are equal to rZj(r) for the six-reservoir model, and rZ a (r) for the five-reservoir 

 model. 



