ATMOSPHERIC CARBON DIOXIDE AND RADIOCARBON: I 83 



(A. 13) 



*a = *k 4 + *k 5 + *k 6 

 *b = *k 4 *k 6 



The numerators of *Z a (co) and *Z\{co) are given by the expressions 



X(U) = (U + */ 3 )(U + */, )(U 2 + *aU + *b) (A. 14) 



*i;,(U) = */ 5 (U + */ 3 )(U + */,)(U 2 + *aU + *b) (A. 15) 



The transfer functions evaluated at zero angular frequency are obtained 

 by setting co = 0, i.e., U = *X in Z a (co) and Z[(co), and the fractional response in 

 the designated reservoir to a fractional perturbation in the source is given (for 

 the five- and six-reservoir cases, respectively) by 



*n a (co) Z.,(cj) *7(co) 



(A.16) 



*N a0 z a (o) *r 



n,(co) Z^co) *7(co) 



(A. 17) 



*N l0 Z,(0) *r 

 analogous to the one-reservoir model (Eq. 12). 



APPENDIX B: TRANSFER FUNCTIONS FOR PARTITIONING 

 OF INDUSTRIAL C0 2 



The perturbation of inactive carbon in each reservoir, n;, owing to the 

 injection of fossil fuel into the lower atmosphere, is described by an equation 

 analogous to Eq. A. 4, i.e., 



dm 

 dt 



£ (kj'jnj'-kjj'nj) + 7j(t), j = 1, 2, . . ., 5 or 6 (B.l) 



where the source terms 7j(t) are zero for all except the lower atmospheric 

 reservoir. For an exponentially growing source 



-y(t) = <y(r)e» (B.2) 



the exact solution to Eq. B.l is expressed as a sum of terms that decay 

 exponentialh' plus one that grows in sympathy with the source: 



nj (t)= £ Cjj'e^j' 1 + Zj(r)7(r)e» (B.3) 



j'-l 



