448 RILEY L CHAP - 20 



Riley, Stommel and Bumpus (1949) used the same method to estimate the 

 sinking rate and vertical eddy diffusivity simultaneously. Their estimates of 

 the sinking rate were essentially in agreement with Steele's. Most of the values 

 in both of these papers fell within a range of 1 to 5 m per day, which is well 

 within the rather large spread of measured values. 



Cushing (1958) discussed the difficulties of estimating grazing rates experi- 

 mentally and recommended the use of a simple model in which grazing is 

 derived from the difference between phytoplankton production and observed 

 changes in the standing crop. This presupposes that the effects of vertical 

 turbulence and sinking are negligible, but the method is a useful first approxima- 

 tion. The oversimplifications in his method were largely justified by successful 

 application to the spring growth period in the North Sea (Cushing, 1959). The 

 latter paper is particularly notable for a careful review of the various kinds of 

 information that can be brought to bear on problems of diatom growth and 

 zooplankton grazing and for the introduction of new methods for dealing with 

 these problems. 



3. Complex versus Simple Models 



The main purposes of most of the models that have been described are to 

 test physiological knowledge and ecological hypotheses ; hence they must be 

 as realistic as possible. However, useful purposes have been served by models 

 that are deliberately oversimplified in order to facilitate computation, so that 

 a wide range of variables can be examined without prohibitive labor. Fleming's 

 (1939) model was of this sort, as was an analytical solution of the relative 

 vertical distribution of phytoplankton described by Riley, Stommel and 

 Bumpus (1949). The latter postulated a two-layered system in which the surface 

 layer had a positive net production coefficient, coi, that was uniform with respect 

 to depth, and the lower layer had a negative coefficient, cl» 2 , i.e. 



oji = ph-r-gh, 



oil = r + gh. 



Vertical mixing and the phytoplankton sinking rate were postulated to be 

 uniform with respect to depth throughout both layers. The steady-state 

 solution for phytoplankton in the surface layer, pi, is 



Pl = E eaz-b.ii (£ cos p lZ + a s j n ^ ^ <,) 



and in the lower layer 



p 2 = E e(«-*2>2 (a sin fi x l + j8i cos fal), (20) 



where E is an integration constant, z is depth, and I is the depth of the boundary 

 between the two la vers. Further. 



a = rj2A . 



*--/&-)• *-yMf> 



