Chapter 11 



Tracer Studies of the Sea and Atmosphere 



115 



Thus the average ages reported for the two 

 oceans are in almost exact agreement, and we 

 may consider the 400 year apparent age well 

 established as a world-wide phenomenon. 



The 400 year apparent age of mixed-layer 

 carbon is simply a less meaningful way of 

 stating that the radiocarbon activity of mixed- 

 layer carbon is 5 per cent lower than the ac- 

 tivity in modern wood, uncontaminated by the 

 Suess effect. Actually it is observed that the 

 activities in wood and in surface ocean carbon 

 are measured to be the same, but the measure- 

 ments must be corrected for natural isotopic 

 fractionation in the physical and chemical proc- 

 esses involved in the carbon cycle (see section 

 on carbon 13 variations). Marine shells con- 

 centrate carbon 13 by 2.5 per cent relative to 

 terrestrial wood, and must therefore concentrate 

 carbon 14 by 5 per cent; since this concentra- 

 tion factor is not observed, we see that the 

 activity of carbon in the mixed layer is, in fact, 

 5 per cent lower than expected. The relation- 

 ships between carbon 13 and carbon 14 varia- 

 tions expected on theoretical grounds, and on 

 the basis of laboratory measurements, were dis- 

 cussed in detail by Craig (1954) who showed 

 that the 5 per cent discrepancy must be the 

 result of slow transfer of carbon from the 

 atmosphere to the sea, and cannot be explained 

 by any other cause. Rafter (1955) verified the 

 conclusion that the carbon 14 difi'erence be- 

 tween atmospheric CO^ and wood must be twice 

 the carbon 1 3 difference, by direct measurement. 



The exchange rate of carbon dioxide between 

 atmosphere and sea may be deduced from con- 

 siderations of the steady state relationships be- 

 tween the exchange rate and the radioactive 

 decay rate; this type of evaluation is independ- 

 ent of considerations based on the magnitude 

 of the Suess effect and the kinetics of the 

 transient state. The general equations govern- 

 ing the transfer of a radioactive isotope between 

 its various exchange reservoirs have been given 

 by Craig (1957(a)) in terms of the rela- 

 tionship between the uniform activity which 

 would be observed if all of the sea and the 

 atmosphere were mixed together at a rate in- 

 finitely faster than the radioactive decay rate, 

 and the percentage deviations from this uni- 

 form activity which are actually observed in 

 the different reservoirs. Mixing rates are ex- 

 pressed in terms of the residence time of a 

 molecule in a particular reservoir, which cor- 



responds to the operational definition of flush- 

 ing time or replacement time, used by oceanog- 

 raphers, and, for the first order processes 

 with which we are concerned, to the reciprocal 

 of the exchange rate constant. 



The constant radioactive decay rate of carbon 

 14 furnishes a built-in clock which monitors 

 the transfer rate of carbon between its various 

 reservoirs. For example, if a barrier is inter- 

 posed between the atmosphere and sea, so that 

 the transfer rate of carbon between these reser- 

 voirs is slowed down, the radiocarbon atoms 

 formed in the atmosphere have less probability 

 of getting into the sea and thus of leaving the 

 atmosphere by physical removal. However, the 

 steady state requires that the total number of 

 C^* atoms leaving the atmosphere by all mech- 

 anisms be equal to the production of radio- 

 carbon atoms by the cosmic rays, and thus the 

 number undergoing radioactive decay in the 

 atmosphere must increase. The number of 

 radioactive atoms decaying per unit time is a 

 constant fraction of the total number present 

 (the exponential decay law), and therefore the 

 piling up of radiocarbon in the atmosphere 

 because of such an exchange barrier results in 

 an increase in the number decaying in just the 

 way required to maintain the steady state secu- 

 lar equilibrium with the production rate. The 

 percentage increase in the C^* activity of the 

 atmosphere is a function of the ratio between 

 the exchange rate and the decay rate, or, what 

 is the same thing, between the atmospheric 

 residence time and the radioactive mean life. 



Considering then, the percentage change in 

 the radiocarbon activity of atmospheric CO2 

 and terrestrial wood, relative to the activity 

 which would characterize these materials in the 

 hypothetical state of infinitely rapid mixing 

 between atmosphere and sea, it is found that 

 for each year of residence time of a CO, 

 molecule in the atmosphere as a result of slow 

 exchange, the atmospheric activity will increase 

 by 0.74 per cent. The activity in the sea would, 

 of course, decrease as a result of the slower 

 transfer of radiocarbon into the ocean, but since 

 there is some 60 times as much carbon in the 

 sea as in the atmosphere, the percentage de- 

 crease of activity in the sea will be only I/60 

 of the atmospheric increase, namely about 0.01 

 per cent, which is not observable. 



We can make a more detailed model of the 

 carbon exchange system by breaking the sea 



