Ocean Currents in a Non-homogeneous Ocean 507 



open sea it is either entirely impossible, or possible only with great loss of time, to 

 place a station in exactly the same position as in a previous survey. The assumption in 

 the figure, that the stations of survey B are halfway between those of survey A, is 

 probably exaggerating matters a little. Since the conditions have apparently not 

 essentially changed, it seems to be justifiable in spite of the rather wide distance between 

 the stations to combine the data from both surveys as has been done below. However, 

 the conclusions drawn from this section are obviously erroneous. For a large station 

 network conditions may be the same, even in the absence of variations in time, when 

 deahng with a single oceanic area where large local differences are present (stationary 

 vortices, strong deflections of the current and others). In such cases (macro-turbulence 

 of the flov/) only a dense network of more or less synoptic character would then result 

 in a correct picture of the oceanographic conditions. 



There are an additional number of sources for errors in the calculation of topo- 

 graphies that should be mentioned here. In the usual calculation of dynamic depths at 

 fixed standard pressures one proceeds according to equation (IX.9), so that the values 

 of the specific volume a found at certain depths (given in metres) were actually found 

 at depth (given in decibars). At the same time the integral values of/? are put equal to 

 the depths given in ordinary metres. The integral expressions for the dynamic depths 

 D will thus be about 1% (or at the most 2%) too small. A further error results from 

 the uncertainty in the a-values, especially in the upper layers, due to errors in depth in 

 series measurements when there is a large vertical gradient in a. Proof can be given 

 that an error €„ in a at a depth //„ will give rise to an error h,^ in D which can be 

 calculated from the equation 



. _ K+i — /?»-! 



where A„+i and /?„_i are the observed depths immediately above and below Z/^; if the 

 error at all depths is equal to e then the total error in D will be 3„ = eh, where h is 

 the total depth of D. In general, these errors are not large, and they can be avoided by 

 calculation of a second approximation but this is rarely done. Parr (1936, 1938 b) has 

 given an emphatic warning against uncritical use of the dynamic methods and has 

 pointed out that no more can be expected of these than their simple assumptions 

 permit. The calculations are seldom so accurate that the stream lines obtained can 

 be regarded as actual trajectories as should be the case for steady currents. The 

 stream, lines determined by the dynamic method are connected only with a single 

 isobaric surface and this may also give rise to erroneous conclusions. In reality they 

 are not subject to this constraint. Vertical displacements are also possible. This plays 

 probably a role in areas of upwelling water. 



Another circumstance is of much greater importance. The oceanic structure at 

 stations where there are strong vertical density gradients depends on the occurrence 

 of internal waves. With these the water masses in a water column are displaced in a 

 periodic way and these periodic variations in oceanic structure will show in the 

 dynamic evaluations made for that station. The magnitude of such effects can be 

 judged upon at anchor stations, where repetitions of series observations at short 

 intervals are made. Dietrich has calculated an example of this type (Table 1 37, "Meteor" 

 anchor station no. 197, series 9). During the period of the measurements the physical 



