ATMOSPHERIC CARBON DIOXIDE AND RADIOCARBON: I 75 



where 



Z a (r) = (r+ k e ff) _1 (20) 



To obtain the instantaneous partitioning (i.e., the rate of accumulation of 

 C0 2 in the atmosphere divided by the rate of industrial production), we 

 differentiate Eq. 19. This leads to 



dn a /dt 



T(r)e - - rZ a <r) (21) 



To obtain the total partitioning, i.e., the mass of industrial CO2 that has 

 accumulated in the atmosphere during the industrial era divided by the total 

 production of industrial CO2, M, we first divide Eq. 19 by 



M= r 7(r)e ru du = r _1 7(r)(e rt - 1) ~ r" 1 7(r)e rt (22) 



J 



where u is a "dummy" variable of integration. For times substantially greater 



than 1/r, the latter equality holds approximately, and 



n a (t) 

 M 



= rZ a (r) (23) 



i.e., for times long compared to both 1/r and r e ff, the instantaneous and total 

 partitioning approach the same value. 



To investigate the importance of the various model parameters in de- 

 termining the long-term partitioning of industrial carbon in the cvcle, we have 

 derived atmospheric transfer functions for five- and six-reservoir models with an 

 exponentially growing atmospheric source (Appendix B). A value of 1/22 

 years was chosen for the exponential factor, r, to reflect the average rate of 

 increase in industrial C0 2 production during the past decades. 



The fraction of inactive industrial C0 2 remaining in the lower atmosphere 

 (Figs. 19 to 21) is somewhat more sensitive to variations in the transfers within 

 the oceans than was the attenuation of oscillations in the 14 C production rate in 

 the same reservoir. The fraction also depends on possible increase in carbon of 

 the land biota (Fig. 22), a change not significant in the 14 C model calculations. 



(The possible growth of the land biota is parameterized in the model by a 

 growth factor, (3, such that if the concentration of atmospheric C0 2 increases bv 

 x%, the rate of assimilation of C0 2 increases by (3x°o per unit mass of land 

 plants.) Of special interest is that the inclusion or neglect of the stratosphere as a 

 separate reservoir has very little influence on the partitioning of industrial C0 2 

 (Fig. 23). For realistic values of the oceanic transfer coefficients and reservoir 

 sizes, the fraction remaining in the lower atmosphere agrees with our current 



