50 REDFIELD, KETCHUM AND RICHARDS [CHAP. 2 



The dynamic equilibria obtaining in a series of situations of increasing 

 complexity will be discussed and illustrated in the following pages. These will 

 be (1) cases in one dimension in which the distribution of nonconservative 

 elements results from a balance between the effects of biological activity and 

 vertical diffusion; (2) cases in two dimensions in which advective motion in 

 one horizontal direction must also be considered ; and (3) cases in which motion 

 in all three dimensions is taken into account. 



A . Vertical Exchange under Steady-State Conditions 

 In many situations, the effect of horizontal motions on the composition of 

 sea-water is negligible. This is obviously true where the boundaries of a basin 

 prevent substantial advection, as in an enclosed basin. It happens frequently 

 that conditions are uniform over great horizontal distances, or that the horizon- 

 tal velocities are very small, in either of which case the influence of advection 

 is small and may be disregarded. If, in addition, conditions do not change with 

 the season so that a steady state exists, in which dN/dt = 0, the dynamic balance 

 on which the distribution of nonconservative elements depends is reduced to 

 the terms defining the rate of change in concentration due to the sinking and 

 regeneration of organic matter, and that due to the vertical diffusion of the 

 regenerated elements toward the surface. 



a. Stagnant basins 



Deep basins in which shallow sills limit the horizontal circulation to a layer 

 near the surface provide the simplest and the most extreme cases of the accumu- 

 lation of nonconservative elements under the influence of the vertical 

 circulation. 



The Cariaco Trench, described by Richards and Vaccaro (1956), is an example 

 of such a basin. It is a depression about 1400 m deep in the continental shelf off 

 Venezuela. The water of the Caribbean flows freely across this depression down 

 to the sill depth at 150 m and is not obviously influenced by the conditions 

 within the depression. Below 250 m the temperature and salinity are nearly 

 uniform and show that the water is isolated from the Caribbean water of 

 comparable depths and can exchange with its surroundings only by eddy 

 diffusion in the vertical across the transition zone separating it from the water 

 above sill depth. In the depths of the Cariaco Trench the total phosphorus 

 concentration is 2.6 mg atoms/m 3 ; at sill depth it is 1.4 mg atoms/m 3 . Con- 

 sequently 1.2 mg atoms/m 3 have accumulated in the deep water. Water at sill 

 depth, if carried downward by eddy diffusion, would contain only enough 

 oxygen to produce 0.4 mg atom/m 3 phosphorus of oxidative origin. Con- 

 sequently the oxygen has been completely exhausted by oxidation of the 

 excess of organic matter settling from the surface layer. The remaining organic 

 matter has been oxidized by oxygen derived from the reduction of nitrate and 

 sulfate as discussed on page 43. 



The accumulation of phosphorus in the depths of the basin may be con- 

 sidered to result from a balance between the gains from the regeneration of 



