ATMOSPHERIC CARBON DIOXIDE AND RADIOCARBON: I 



67 



u 



15 



5 — 



i I M M I I I I II I I I I I M i I i I I I | I I I I I i i | i i | i i | ii i I i | i | i I i ii it 



• i J \> \ 



■15 



30 I i i i i i i i i i I i i i i i i i i i I i i i i i i i i i I i i i I i i i i i i i i i 



1700 1750 1800 DATE 1850 1900 1950 



Fig. 12 Comparison of measured ' 4 C content (A 1 4 C) of tree rings (full curve) 

 and that predicted by Grey and Damon 2 s using a single reservoir model with 

 an effective exchange time of r e ff =100 years. 



1 4, 



equations stepwise in 1-year increments to obtain a prediction of C in the 

 atmosphere. They varied the effective time constant, *T e ff, and, for >40 years, 

 obtained substantial agreement between the model prediction and the observed 

 C record for times prior to the 20th century, i.e., before dilution by 

 inactive industrial CO2 began to disturb the C distribution significantly 

 (Fig. 12). In spite of the apparently excellent prediction given by Grey and 

 Damon's "' model, there are objections to using such a simple model unless it 

 can be shown that it actually approximates the behavior of atmospheric C. 

 Especially questionable is the use of a single adjustable time constant for which, 

 as Grey states, the correct value is "not immediately apparent from 

 experimental observations." 



To obtain a useful comparative index of the behavior of the one-parameter 

 model, we will now express its basic properties in terms of a transfer- function 

 ratio that describes, as a complex number, the attenuation and phase lag 

 imposed on a sinusoidal variation in the ' C production *7(t) for any given 

 oscillation frequency. This ratio may be derived either from the Fourier 

 transform of Eq. 7 or more directly by setting the time-varying perturbations 

 equal to complex harmonic variations: 



'7(0 = *7(<^)e 



iwt 



(8) 



n a (t) = *n a (oj)e 



lCJt 



(9) 



