16 



PROCESSING OCEANOGRAPHIC DATA 



of the preceding pages and then taking the 

 reciprocal. For example, if at a given salinity, 

 temperature, and pressure the specific vol- 

 ume is 0.96996, the density P>.'.j' = frqcqqc = 



1.03097. 



Another way to express the density is by 

 the symbol <t,, ,.p. By definition, o-,, , „=10' 

 ip,,,,^-l). Thus, if p,.,.p = 1.03097, a,,,,^ = 

 30.97. This expression has the advantage that 

 the numerical value contains fewer digits and 

 consequently is easier to handle. 



It is common practice to abbreviate the 

 expression <T,,t.o to only o-,, which represents 

 the density of water of given salinity and 

 temperature at surface pressure. "Sigma-T" 

 is widely used to describe the sea and has the 

 significance that motion along a, surfaces in- 

 volves little change in energy, and therefore 

 mixing of water masses tends to take place 

 along these surfaces. By definition, 



Thus, if p,,,, 0=1. 02727, (t, = 27.27. In like 

 manner, (r„=10nPs.o,o— 1). 



0-, depends only upon salinity and temper- 

 ature, and may be found directly from values of 

 these variables, either graphically or by means 

 of tables. If A,,, has been calculated, o-, may 

 be read directly from table VIII, page 86. 

 Other aids in the determination of c, are 

 graphs such as shown in figure 18*, and 

 nomograms as shown in figure 19. 



If the temperature is 4.55° C. and salinity is 

 34.40%o, <r, will equal 27.27. 



Several tables for a,, in addition to table X, 

 page 91, have been compiled by various 

 people including McEwen (1929) (17), Mat- 

 thews (1932) (18), Fleming (1939) (19), Ennis 

 (1944) (20), and Bumpus and Martineau (1948) 

 (21). These tables are based on Knudsen's 

 equations given on the preceding pages. 



RELATIVE CURRENTS 



As indicated previously, the current along an 

 isobaric surface is essentially a function of the 

 geopotential (or dynamic) slope of the isobaric 

 surface. If, at some depth, motion may be 

 assumed negligible and an isobaric surface essen- 

 tially level, the dynamic slope of an upper 



•Such 0-1 charts have been published by the Hydrographic Department, 

 British Admiralty, 'under the title "Density (Sigma-T) from Salinity 

 and Temperature," Misc. 354, 354A, and 354B, 1942. 



SALINITY. 7co S= 34.40 



340 341 34 20 34 30 34!40 34 50 34.60 34 70 

 jr— , 1 ^ , -^-^ ^ „ . . 



Figure 18. — Portion of a graph for datermining "Sigma-T," 

 (T,, from temperature and salinity. 



isobaric surface may be found from the varia- 

 tion of specific volume along the isobaric layer. 

 Thus the current at the upper surface relative 

 to any possible current at the lower surface is 

 determined. 



For each oceanographic station of a network 

 of stations, the dynamic thickness of the iso- 

 baric layer may be calculated by means of the 



J'P2 

 a dp, where, 

 Pi 



Z?2 — Z?i = dynamic thickness of the isobaric 

 layer, 

 a=specific volume, 

 rfp = pressure interval. 



Since a=a35.o, p + 5, the total dynamic thick- 

 ness of the layer may be considered composed 

 of the dynamic thickness of the layer of stand- 

 ard specific volume plus the increment in 

 dynamic thickness due to the anomaly of 

 specific volume from standard. Thus, 



J'P2 CP2 



«35,0.P<^P+ 5 dp 



Pi J Pi 



= (Z?2-Z>i).t.„d.rd + AZ?. 



The dynamic thickness of the standard 

 layer is the same at every station. Therefore 

 the differences in djoiamic height between sta- 

 tions are completely given by the differences 

 in the increments, aD, and it is only necessary 

 to calculate AD at each station, using the for- 



mula AD = 



= I ^' 5 dp. 

 Jpi 



In practice, meters of depth are substituted 

 for decibars of pressure in the equation. The 



