SECT. 1] THE INFLUENCE OF ORGANISMS ON THE COMPOSITION OF SEA-WATER 49 



3. The Biochemical Circulation 



The selective absorption of certain elements by organisms, combined with 

 the movement of organized matter from one layer of water to another by 

 sinking or active migration, provides a mechanism for the fractionation of the 

 components of sea-water and the redistribution of these elements in charac- 

 teristic patterns. The circulation of nonconservative elements and the resulting 

 pattern of their distribution depends on biological as well as hydrographic 

 processes and they thus differ in detail from that of water and its inert solutes. 



The concentration of a conservative element at any point in the sea is deter- 

 mined by a dynamic equilibrium between the effects of eddy diffusion and 

 advection. In the case of nonconservative elements the effects of biological 

 processes on the equilibrium must also be taken into account. The theory of 

 this interaction, as developed by Sverdrup (1938), is essentially as follows. 



Consider the water in a unit cube of space within the sea in which the con- 

 centration of some nonconservative property is denoted by N. The value of N 

 is subject to change by biological processes, such as the assimilation or re- 

 generation of nutrients, the consumption of oxygen, etc., which change N at 

 a rate denoted by R. In addition, N will be altered by interchange of water 

 with adjacent cubes if they contain water with different concentrations of N. 

 These interchanges are of two sorts, eddy diffusion and advection. 



If the interchanges along the x-axis are considered, the effect of eddy diffusion 

 on the values of N is given by {A x jp) 8 2 N/dx 2 in which A x is the coefficient of 

 diffusion in the ar-axis and p is the specific gravity of sea-water. The effect of 

 advection is given by V x -cNjdx, in which V x is the component of current 

 velocity in the direction x. Similar expressions define the effect of water move- 

 ment in the y- and z-axes, and the complete expression is 



8N A x B 2 N A y 8W Aj, <PN_ <^__ v <^__ v ^ 



~dt ~ p'l^ + ~J'Jy~* + ~p~'lkz x ' dx '*' 8y z 'dz 



In its complete form the equation is too complicated to be readily usable. 

 With various assumptions it may be simplified and applied to the analysis of 

 oceanographic observations. Since oceanographic data commonly consist of 

 measurements at discrete points, practical application is most easily made by 

 expressing the relations in terms of Eulerian equations in finite difference form. 

 The papers of Riley (1951, 1956, 1956a) may be consulted for a discussion. of its 

 application. 



The utility of equations for the dynamic equilibrium affecting the concentra- 

 tion of nonconservative properties is of three sorts. When the physical terms 

 can be evaluated the expression may be used to determine the rates of the bio- 

 logical processes expressed by R. Conversely, if the value of R can be evaluated 

 from biological data, information on the physical terms may be obtained. When, 

 as is often the case, data are insufficiently numerous or precise to enable 

 quantitative estimates to be obtained, the equations provide a guide to the 

 intuitive reasoning with which observed conditions are interpreted. 



