74 EKDAHL AND KEELING 



After looking closely at the 14 C observations (Fig. 7), and at the predictions 

 given bv the one-reservoir model (Fig. 12) and the six-reservoir model (Figs. 10 

 and 1 1 of the next paper 1 ), we conclude that the tree-ring data for the period, 

 1700 to 1900, are not consistent enough to accept Stuiver's 15 correlation as 

 thoroughly proven. 



PARTITIONING OF INDUSTRIAL C0 2 



The transfer function is of use not only in predicting the attenuation and 

 phase shift of an oscillating source, but it also can be used to predict the 

 redistribution of inactive C0 2 injected into the lower atmosphere by the burning 

 of fossil fuels, if the rate of injection increases exponentially for a sufficient time 

 that exponential increases establish themselves in all reservoirs of the system. By 

 solving the system of model equations exactly, we have established that this 

 requires only the order of 100 years. The transfer function thus leads to quite 

 realistic results for current industrial C0 2 partitioning. 



To illustrate this use of the transfer function, we shall again first consider the 

 simple one-parameter model, in this case with a source term that is exponentially 

 growing. The perturbation equation (Eq. 7) is applicable if we replace the 

 oscillating source *j with an exponential source of the form 7(r)e r . Dropping 

 the asterisks so that the symbols in the equations now denote inactive carbon, 

 we obtain, in place of Eq. 7, 



^=-k e ffn a + 7(r)e rt (17) 



dt 



where r e ff (=k e ff -1 ) is the time constant for loss of inactive carbon to adjacent 

 reservoirs, 7(r) is a time-invariant factor, and 1/r is the time for an e-fold increase 

 in the production rate. Assuming zero as the initial value of the perturbation, 

 i.e., 



n a (0) = 



we integrate Eq. 17 to yield 



n a (t) = (r + k eff r 1 7(r)(e rt - e" kefft ) (18) 



For continued exponential growth until t>r e ff, the second term in the last 

 factor of Eq. 18 can be neglected. The perturbation grows in sympathy with the 

 source but reduced by a factor that has the same form as the transfer function 

 Z a (co) except that ico is replaced by r, i.e., 



n a (t) = Z a (r)7(r)e rt (19) 



