116 



Atomic RadJatio7i and Oceanography and Fisheries 



up into a two-layer ocean, taking the upper layer 

 to be about 75 meters deep corresponding to 

 the average mixed layer as actually observed 

 in the sea. (The 75 meter estimate was made 

 by Dr. Warren Wooster, who kindly studied 

 the question of the average depth of the mixed 

 layer over the year in the various areas of the 

 oceans.) The lower layer, extending to a depth 

 of 4000 meters on the average, is termed for 

 convenience the "deep sea," though it is of 

 course obvious that such a uniform layer has 

 little resemblance to the actual structure of the 

 sea below the thermocline. Nevertheless, it is 

 found that the consequences of such an assump- 

 tion about the nature of the deep sea are not 

 serious insofar as affecting the validity of the 

 calculations on the atmospheric residence time, 

 and the treatment of the relationships existing 

 between the atmosphere, mixed layer, and main 

 body of the sea, is of course improved im- 

 mensely by assuming such a model. If we then 

 add a barrier between the mixed layer and the 

 deep sea, representing slow mixing across the 

 thermocline, the radiocarbon is further piled 

 up in both the atmosphere and the mixed layer, 

 in the same manner as previously described. 

 Calculation shows that the activities in the 

 atmosphere and mixed layer are both increased 

 by about 1.2 per cent, relative to the case of a 

 rapidly mixed, uniform sea, for each 100 years 

 of residence time in the deep sea, or, what is 

 almost the same thing, for each 100 years of 

 "age" of the deep water. The activity in the 

 deep sea is reduced by 0.05 per cent for each 

 100 years of deep-sea residence time. 



For deep-sea residence times up to several 

 thousand years, the interpolation of a mixing 

 barrier at the thermocline in the sea causes very 

 close to the same activity increase in both the 

 atmosphere and the mixed layer, and thus the 

 activity difference observed between the atmos- 

 phere and mixed layer is sensitive only to the 

 atmosphere-sea exchange rate for internal mix- 

 ing times of the sea of the order of a few 

 thousand years or less. The physical evidence 

 discussed by Wooster and Ketchum in a sep- 

 arate paper in this report, and the tritium cal- 

 culations cited previously in this paper, clearly 

 show that the average mixing time of the sea 

 is at least within this range. 



Thus the figure cited above of a 0.74 per cent 

 increase in atmospheric activity for each year 

 of atmospheric residence time, indicates that 



the residence time of a COg molecule in the 

 atmosphere, before entering the sea, is about 

 7 years, corresponding to the 5 per cent activity 

 difference between carbon in the atmosphere 

 and in the mixed layer of the sea. 



An independent calculation of the atmos- 

 pheric residence time can be made by consider- 

 ing only the steady-state material balance in the 

 atmosphere as a function of the production 

 rate of radiocarbon, taken as (2 ± .5)0* atoms/ 

 cm^ sec, and the rate at which carbon enters the 

 sea. This calculation gives an atmospheric resi- 

 dence time of about 6 years. Considering the 

 errors to be assigned the numerical values in 

 both these calculations, it appears that the best 

 value of the atmospheric residence time of car- 

 bon dioxide may be taken as 7±3 years, cor- 

 responding to a rate constant >^(j-m = 0-l4, where 

 k is the fraction of the carbon in the atmosphere 

 transferred to the mixed layer per year (Craig, 

 1957 (a)). 



The average annual exchange flux of carbon 

 dioxide, into and out of the sea each year, is 

 thus found to be about 2x10'^ mioles per 

 square centimeter of sea surface. This rate is 

 lower by a factor of 10,000 than the rate re- 

 cently obtained by Dingle (1954) from consid- 

 eration of the various rate constants involved, 

 and the discrepancy thus serves to emphasize 

 the power of natural isotopic studies to yield 

 quantitative data, as compared with more tra- 

 ditional methods. 



An entirely independent calculation of the 

 atmospheric residence time, not based on steady- 

 state considerations, may be made from the 

 magnitude of the so-called Suess effect described 

 previously. It is known that since the begin- 

 ning of the industrial revolution, man has added 

 an amount of carbon dioxide to the atmosphere 

 by fuel combustion equivalent to about 12 per 

 cent of the amount originally present. The 

 degree of dilution of radiocarbon activity in 

 contemporaneous wood by incorporation of C^*- 

 free COo, measured relative to the activity of 

 19th century wood, is then a measure of the 

 rate at which the dead CO2 has been removed 

 from the atmosphere into the sea. The first 

 measurements of this effect, made by Suess 

 (1953), indicated a dilution of about 3 per 

 cent, and from these data Suess deduced an 

 atmospheric CO^ residence time of 20-50 years. 



More recent and extensive measurements by 

 Suess (1955) have shown that the figure of 



