14 



PROCESSING OCEAKOGRAPHIC DATA 



Methods for computing the dependent quan- 

 tities used for describing tlie field of mass are 

 presented below, and methoils for determining 

 relative currents arc discussed at the end of the 

 section. 



SPECIFIC VOLUME AND SPECIFIC VOL- 

 UME ANOMALY 



Specific volume (or volume per unit rnassj in 

 situ in the sea is expressed by the symbol 

 «s,(,p. where the subscripts indicate the salinity, 

 temperature, and pressure of the sample. 



Specific volume in situ can be computed 

 directly bj^ the following equations developed 

 by V. W. Ekman (190S) (30). 



*•.(. p = «i. I. o — P«. .1.0 10 ' 



4S86 



1 + 0.0000183 p 

 -(227 + 28.33 (-0.551 <2 + o.004 fi] 

 + plO-* [!05.5 + 9.50(-0.158(2]-1.5p''/ lO"' 

 <T„-28, 



10 



[147.3-2.72( + 0.04(2-pi0-*(32.4-0.87< 



+ 0.0i2(2)] + (^?^^yi4.5-0.1/-p 10-'(1.8 



-o.oeoil 



The above equation can be evaluated from 

 values of temperature, t (° C.) ; salinity, s (°/oo), 

 or chlorinity, CI (°/oo); and pressure, p (deci- 

 bars), by means of the following expressions 

 (Knudsen, 1901) (13): 



8 = 0.030+1.8050 CI 



<7„= -0.069 + 1.4708CT-0.001570CT + 0.0000398CT 

 <r....o = S,+ (,r„ + 0.1324)[l-^, + B,(<r ,,-0.1324)], 



where, 



^ r«-3.98)n r <+283 1 



' L 503.570 J b + 67.26 J 



^, = ((4.7867-0.098185 ( + 0. 0010843 (') 10-3 

 B, = ((18.030-0. 8164« + 0. 01667 P) 10^" 



and 



1 



1 



p. .1.0 1 + 10 'a,,(,, 



The error in the specific volume calculated from 

 the above expressions is believed to be ±0.00001 

 for pressures of 1,000 decibars^ and ±0.0001 

 for 10,000 decibars. 



The more practical method of computing 

 specific volume is by expressing it as a known 

 specific volume under given conditions, plus 

 a series of correction terms for the dependent 

 variables of temperature, salinity, and pressure. 

 These terms may be grouped, computed, and 

 added as follows to give specific volume wi situ: 



a.,(.p = (a35. 0. o + 5p) + (5, + 5, + S,.,) + 5,.p + Ji,p + (5, .!,„). 



In the first two terms, aas.o.o is a constant 

 (0.97264) and 6p represents the effect of pres- 

 sure at standard salinity and temperature 

 (35%o and 0° C). The sum of the two terms 

 gives a standard specific volume: 



«35. O.0 + Sd = "35,0.p. 



The values of the standard term 035, o,» are given 

 in table IV, page 40. 



The next three terms of the expansion depend 

 only upon salinity and temperature, and are 

 combined to form the single term Aj, ,; that 

 is, 5s + S, + 6j, , = As, ,. This temperature-salinity 

 term of the anomaly of specific volume (dis- 

 cussed below) is found from values of tempera- 

 ture and salinity by means of tables or graphs, 

 as will be illustrated presently (Sverdrup, 1933) 

 (13). If c, (see p. 16 of this section) has 

 already been computed, Aj. , may be found from 



the formula, A,,, = 0.02736 - 



10- 



1 + 10-V, 



or by 



the table IX, page 88. 



The salinity-pressure term, 5j,p, and temper- 

 ature-pressure term, 5,,,,, of the anomaly of 

 specific volume are found from tables or graphs. 

 The final term, 5s,t.p, is so small that it may 

 be neglected. 



The sum of the terms A,,„ 5,,p, and 6,, p, con- 

 stitute the anomaly of specific volume from the 

 standard, 035, o,p, and are designated by the single 

 symbol 5. Thus, 



5. + Si + 5,., + 5,.p + «,.p = A,., + 5,.p + J,.p = a. 



For current calculations, the variation in 

 specific volume along an isobaric surface is 

 required. Since pressure is constant along any 

 given isobaric surface, the term 5p is a constant 

 as well as ajs. 0, o- It is sufficient, therefore, to 

 calculate the specific volume anomaly, 5, since 

 the standard term contributes nothmg to varia- 

 tion in specific volume along an isobaric surface. 



