40 



Atomic Radiation and Oceanography and Fisheries 



particular model in the paper by Craig. From 

 these discussions, we choose for the present 

 calculations a value Td=300 years as perhaps 

 the best guess. As discussed by the writer in a 

 separate chapter of this report, radio carbon data 

 indicate a residence time for water of about 

 1000 years, as a world-wide average. Mixing 

 in the Atlantic is probably a good deal faster 

 than in the Pacific, and 300 years is probably a 

 safe lower limit estimate for the Atlantic, con- 

 sidering the material to be deposited on the 

 bottom. Thus the mixed-layer activities we cal- 

 culate should be upper limits, which would be 

 approached more closely in the Atlantic than in 

 the Pacific. 



The average world-wide depth of the mixed 

 layer, w, is taken as 100 meters, and the average 

 depth of the sea is taken as 3800 meters. The 

 volume of the sea is 1.4xl02i liters; thus the 

 volume of the mixed layer is taken as 1/38 of 

 this or 3.7x10" liters. Putting these nu- 

 merical values into (16), and noting that ^ = 

 Ag, we have for the activity of any fission prod- 

 uct per unit volume of sea water in the mixed 

 layer: 



10-3 A 

 a^= ^^ dps/liter (17) 



'" 300A+38 ^ ' ^ ' 



in disintegrations per second per liter, where 

 Ag is in megacuries, as tabulated in column 5 

 of Table 1, and A is in years^^ From this 

 equation the values tabulated in column 8 of 

 Table 1 were calculated, and were converted 

 to microcuries per liter for column 9. 



From the relation aa/a„^= {A^Vm/^mVd) = 

 (Aa/A,„) (m/D-m) we obtain: 



— =At,h-1-1 



where Tm> the residence time of a water mole- 

 cule in the mixed layer, is given by (12) as 

 1/37 of Td = S.l years. We thus write: 



-^=8.1A+1: 



(18) 



from which, given the values of a^n computed 

 above, the values of a^ tabulated in column 7 

 of Table 1 were computed. We call a the 

 "oceanographic partition factor." It is a func- 

 tion of the mixing rate of the sea and the decay 

 constant of the individual isotope, and is a 

 measure of the effectiveness of the cross-thermo- 

 cline exchange rate in buffering the mixed 

 layer from the fission products introduced into 



the deep sea. Values of a are tabulated in 

 column 6 of the table, and range from about 

 1 for the longest lived isotopes to about 250 

 for an isotope with a half-life of 8 days. For 

 stable isotopes A is 0, a is 1, and (18) reduces 

 to simple statistical partitioning. 



From (17) we see that as A, the decay con- 

 stant of an isotope, increases, the activity in 

 the mixed layer decreases; i.e., if more of the 

 isotope can be removed from the deep sea by 

 decay, less needs to be transferred to the mixed 

 layer to preserve the steady state. If the half- 

 life were so long that the radioactivity did not 

 affect the distribution between the mixed layer 

 and the deep sea, we would have simply a sta- 

 tistical partitioning of the isotope between these 

 reservoirs, such that the activity per unit volume 

 in each reservoir would be the same. From the 

 above equations we can derive the ratio of the 

 activity in the mixed layer for an isotope to the 

 activity per unit volume which would be ob- 

 served if the partitioning were statistical: 



/ X -- (19) 



a^{stat) aTa+Tm a 



and we see that a~^ is approximately the frac- 

 tion of the statistical activity per unit volume 

 attained by a fission product in the mixed layer. 

 Equation (19) can be written exactly as: 



_ ^1/ 



a^(stat) /1/2 + 5.5 



(20) 



where /^/o is the half-life of the isotope in years. 

 The ratio a„J a^-y^{stat) is plotted in Figure 1 

 as a function of the half -life, and one reads, 

 for example, that an isotope with a 5 year half- 

 life attains about 48 per cent of the activity 

 per unit volume in the mixed layer which it 

 would have if its half-life were so long, relative 

 to the mixing rate in the sea, that its radio- 

 activity had no effect on its distribution. 



The values of a^^, a^, and a are tabulated in 

 Table 1, in which the isotopes are arranged in 

 order of their activity in the deep sea. For 

 comparison, the activities of potassium 40 and 

 rubidium 87, which provide essentially all the 

 radioactivity in the sea, are also listed. In the 

 deep sea, the predicted fission product activity 

 is 19.3 disintegrations per second per liter, as 

 compared with the natural activity of 12.2 dps/ 

 liter; thus the fission products in steady state 

 with the 1000 ton fission rate would almost 

 triple the deep-sea activity. 



