ATMOSPHERIC CARBON DIOXIDE AND RADIOCARBON: I 81 



than with 10% diffuse radiation even though total solar radiation was about 25% 

 less. 



APPENDIX A: CALCULATION OF TRANSFER FUNCTIONS FOR 

 ATTENUATION OF RADIOCARBON SOURCE OSCILLATIONS 



Transfer functions for the five- and six-reservoir models may be 

 determined in much the same manner as was employed for the one-reservoir 

 model described in the text. Each of the *N;, denoting the mass of C in each 

 reservoir j, is decomposed into steady-state and perturbation terms, as is the 

 stratospheric l C source term, *T: 



*Nj = *Nj + *nj(t), j = 1, 2, . . ., 5 or 6 (A.l) 



*r=*r + *7(t) (A. 2) 



Substitution of Eqs. A.l and A. 2 into the governing equations (see Appendix A 

 of part II) yields a decomposition into a set of steady-state equations: 



J %L XT 



__rf!=0= £ <*kj'j*Nj' -- *k jj '*N jo >- *X*N j0 + *Fjo (A.3) 



and a set of perturbation equations 



_p= £ (*k j 'j*n j '-*k jj '*n j )-*X*n j + *7j (A.4) 



'M 



where the *!<;;' and *k;'j are transfer coefficients, *X is the C decay constant 

 (= 1/8267 years), and the source terms are nonzero only for the stratosphere. 



Again, harmonic variations are assumed for the C mass and source 

 perturbations: 



*nj(t) = *nj(co)e iwt (A. 5) 



*7(t) = *7(co)e iwt (A- 6) 



and the resulting linear algebraic equations are solved simultaneously for the 

 variables *n;(co). In the five-reservoir model, the atmospheric transfer function, 

 Z a (co), is computed as the ratio of two determinants 



* Za (C0)= *y a (U)/*D 5 (U) (A.7) 



