510 Ocean Currents in a Non-homogeneous Ocean 



volume transport of the density current can be determined from (XV. 1 8) , if the vertical 

 mass distribution is known. One obtains 



S. = -^ \ -^-dz and Sy=--.\ -^ dz (XV.21) 



10 f'^ dAD 



7 



Using the equation defining D (equation IX.9) a quantity 



n: 



Q=\ hdpdz {XN21) 



can be introduced in equations (XV.21) giving 



^^ = 7 -dy ^^^ ^^^-Jd^- ^^^-^^^ 



Since the anomalies of the dynamic depths of the isobaric surfaces are always calcu- 

 lated when evaluating observational data, it is always possible to obtain the volume 

 transport of the density current without difficulty. 



A determination of the mass transport of the density current is considerably more 

 difficult. The first theoretical calculations of this type were made by Ekman (1929) 

 who has given later (1939) a detailed and extensive account of this and of the related 

 problems. He obtained also formulae similar to (XV.22) but rather more difficult to 

 evaluate; it involves the pressures at given dynamic depths which are usually not 

 calculated during the dynamic preparation of observational data. Since the mass 

 transport can be obtained with sufficient accuracy from the volume transport by multi- 

 plication with the mean density, it is not necessary to calculate it independently. 

 Calculations of the volume transport and the introduction of the quantity Q have been 

 done by Jakhelin (1936). For the practical application of the equations (XV.21 and 

 22), p has to be taken in decibars and the depth d in metres which both can be expressed 

 approximately in the usual way by the same figures. This inaccuracy leads to values of 

 Q which, as was shown by Jakhelin, are systematically about 1 % too low. Although 

 the errors are small, it is nevertheless desirable to apply a correction for this to the 

 calculated values. The volume transport between two stations A and B [B to the right 

 of ^ at a distance L) is thus finally 



S = L\ V dz = y 



(ADA-ADB)dz. (XV.24) 



It depends only on the dynamic depth anomaly at the two stations and is independent 

 of the distance between them. In this way it is also independent of the mass distribution 

 within this space. Lines of equal Q can be drawn for any larger area. Their direction 

 gives the direction of the volume transport and their spacing at any point is propor- 

 tional to the volume transport. This proportionality factor, however, depends on the 

 latitude. The same "current amount" does not flow everywhere between each pair of 

 Q-lines ; for a current towards the north and south the transport in the flow direction 

 will decrease and increase respectively. 



For more extensive oceanic areas this dependence on the latitude cannot be neglected. 

 Attempts to show the changes in transport with latitude directly on a transport chart, 



