52 REDFIELD, KETCHUM AND RICHARDS [CHAP. 2 



deeper layers of the basin. It serves to indicate, however, how very slowly 

 exchange takes place in a stagnant basin of this sort. 



It is evident that accumulation of a constituent of sea-water can occur 

 locally only if the constituent circulates through the region more slowly than 

 does the water. If the constituent circulated at the same rate as the water, 

 there would be no change in its concentration. This consideration is over- 

 looked when estimates of the exchange of water are based on the accumulation 

 of nonconservative elements. 



The principle involved may be illustrated by a simplified model of a stagnant 

 basin in which a sharp transition zone at sill depth separates an upper layer of 

 water containing a nonconservative element in the concentration N u from the 

 stagnant lower layer having a concentration Nl- The process of eddy diffusion 

 is equivalent to the movement of equal quantities of water upward and down- 

 ward, each carrying with it quantities of the nonconservative element in pro- 

 portion to its concentration in the layer from which it comes. If dx/dt is the 

 rate at which water is exchanged, Nu dxjdt and Nl dx/dt are the rates at which 

 N is transported downward and upward respectively and (N 'l — N u) dxjdt is 

 the rate at which N is lost from the lower layer. Under steady-state conditions 

 the fraction of N lost from the lower layer in unit time is (Nl — Nu) dx/N L-h 

 while the fraction of water lost is dxlh. Consequently, the fraction of A T lost in 

 unit time equals (Nl—Nu)/Nl times the fraction of water lost. Since {Nl—Nu)I 

 Nl is less than one, the fraction of N lost in unit time is less than the fraction 

 of water lost. The half -life period, t, is inversely proportional to the fraction lost 

 in unit time. Therefore, 



_ N L -Nu 



Twater— T^ TN- 



In the case of the Cariaco Trench the concentration of phosphorus im- 

 mediately above sill depth is 1.2 mg atoms/m 3 while the mean concentration 

 below sill depth is 2.4 mg atoms/m 3 . If these values be taken for Nu and Nl 

 respectively, (Nl — Nu)/Nl = 0.5. tn has been estimated to be 142 years and 

 consequently r wa ter is 71 years. In other words, the water is circulating through 

 the basin twice as fast as is phosphorus. The estimate is not precise because of 

 the simplification of the model but serves to illustrate the principle that 

 accumulation occurs when a constituent circulates through a region more 

 slowly than does the water. 



c. The relation of stagnation to stability 



Equation (2) implies that for a given rate of regeneration, and under steady- 

 state conditions, the gradient in concentration, dN/dz, resulting from the 

 accumulation of a nonconservative element at depth, will be inversely propor- 

 tional to the coefficient of diffusivity, A. This coefficient in turn tends to vary 

 inversely with the stability of the water column, and consequently the 

 accumulation of the products of regeneration may be expected to be greater 

 where strong density gradients are present. 



