The Geostrophic Relationship 19 



Were the velocity known for any one value of z it would be possible to 

 determine the velocity at all z by numerical integration with respect to z. 

 In this way one calculates the geostrophic currents (often called, in oceano- 

 graphic parlance, by the unfortunate solecism 'dynamic currents') from 

 the density field. Meteorologists use the same principles for computing 

 winds aloft from observed density fields, but they have the inestimable 

 advantage of knowing the true pressure distribution at the earth's surface, 

 and thus there is no uncertainty in the constant of integration. Every- 

 thing hinges on a proper determination of the constant of integration. In 

 oceanography we speak of a 'level of no motion', that is, a value of z at 

 which we can believe the velocity is zero, and from which we can carry 

 out the vertical integration of differential equations (4) and (5) for the 

 velocity field. The fact that this all-important level of no motion, or 

 reference level, is still, to all intents and purposes, undetermined, is one of 

 the most disconcerting features of physical oceanography. Some methods 

 for estimating this reference level are given in Sverdrup's textbook 

 (Sverdrup eial., 1942, pp. 456-457). One school of thought simply reHes on 

 placing the reference level sufficiently deep to be below the most intense 

 horizontal gradients of density. Thus Isehn's (1940, p. 24) transport calcu- 

 lations of the Gulf Stream are based upon an arbitrary choice of 2000 m. 

 as the reference level, or level of no motion. ^ Were the chosen level signifi- 

 cantly lower, say at the bottom, the resulting transports would be at least 

 50 per cent greater; however, the velocities in the very surface layers of 

 the Gulf Stream would not be changed much. Fortunately, the choice of 

 the reference level has less effect upon velocities of surface water than on 

 those of deep water. It is very important to remember that the 2000 m. 

 reference level is completely arbitrary. Defant (1941) has proposed that 

 the level of no motion coincides with the level of no vertical gradient of 

 geostrophic velocity. Since he has been able to find levels of no vertical 

 gradient in most of the ocean, he has drawn up charts of velocity based on 

 this completely intuitive criterion. Finally, the use of continuity of mass 

 and of conservation of various properties such as salt and heat content 

 has been proposed in special cases in which a section covers all possible 

 entrances and exits for water in a closed arm of the sea. Fuglister and I 

 have tried such calculations. They place a very severe load upon the 

 accuracy of the observations and upon the assumption that there is no 

 time variabiUty or mixing in the structure of the deep water. They involve 



2 The depth of an observation level, or reference level, is sometimes given in terms 

 of hydrostatic pressure rather than in linear measure. The decibar is nearly equivalent 

 to the meter. I have used meters even when referring to works which use the decibar 

 unit. Also, in the past oceanographers usually neglected the transports below the 

 reference level. 



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