The meridional barotropic transport can also be approximately expressed as 



V h — hvbPm- 



As noted in the discussion of the accuracy and precision of observations in section {d) 

 which follows, velocities are significant to within about 0.6 cm/sec. Representative 

 values of the depth, h, and the mean density, p,„, are 500,000 cm and 1 gm/cm 3 , respec- 

 tively, so the resulting difference in barotropic transport for a velocity difference of 0.6 

 cm/sec would be 



Vh ~ 3 ■ 10 5 gm cm -1 sec -1 , 



and terms on the right side of the expression for barotropic transport of order 10 4 gm cm -1 

 sec -1 and less could be neglected. Total transport and barotropic transport terms are of 

 the order 10 5 gm cm -1 sec -1 . The Ekman transport is of the order 10 4 or 10 5 gm cm -1 

 sec -1 . 



In examining the data from September 1961 (fig. 28), it is apparent that the most critical 

 combination of bottom velocity and bottom slope occurs at the Hawaiian Island Rise. 

 Between stations 25 and 26, the bottom velocity is about 2 cm/sec. The bottom slope of 

 2 • 10 -,i was computed from the smoothed isobaths on H.O. Chart 5486 and is in general 

 agreement with that computed from station soundings. The angle 6 which the stream 

 lines make with a line normal to the isobaths is uncertain because of the lack of detail 

 of bottom topography and the general character of the velocity determinations. It is ap- 

 parent, however, that the bottom water tends to flow along the bottom contours, a tendency 

 particularly evident in the northern and southwestern portions of the area observed (figs 

 27 and 28). Assuming a value of 9 of 85° (suggested in the present data by the close ap- 

 proach of the direction of the bottom currents to the isobaths), bottom velocity as 2 cm/sec, 



f 



j: as 3 X 10 K for 25° N, and p= 1 gm/cm 3 , the magnitude of the final term in the expres- 

 sion for barotropic transport is approximately 10 3 gm cm -1 sec -1 . This magnitude in a 

 depth of 5,000 meters results in a constant velocity of 0.2 cm/sec — one third the significant 

 value of 0.6 cm/sec (see below). 



[J) Since the ratios of the baroclinic to barotropic modes within the flow are computed 

 from oceanographic observations, the accuracy and the precision of these observations 

 must be examined for their influence on the velocity at any level. Velocity at the bottom 

 is of primary interest. If values of ±0.01°C and ±0.01"/oo are accepted as the precision 

 of temperature and salinity measurements and the difference between stations is such as to 

 give the maximum error in specific volume anomaly for the interval oi to 1.000 decibars, 

 an error of ±0.01 dynamic meter will arise. Wooster and Taft (1958), using a statistical 

 approach to this problem, found that the standard error of the difference in geopotential 

 anomaly (0 over 1,000 db) between two stations is 0.0056 dynamic meter and conclude that 

 the measurement error of this difference is ±0.011 dynamic meter (26). For a pair of 

 stations at 30° latitude separated by 250 km, the error in the computed geostrophic velocity 

 is ±0.6 cm/sec. These values of anomaly and velocity must be kept in mind when asses- 

 sing the significance of the horizontal velocities determined in this program. The method 

 used, equating baroclinic transport plus barotropic transport to wind-driven geostrophic 

 transport, partially compensates for errors in the observations. Any observational error 

 leading to a baroclinic transport too large will result in barotropic transport too small by 

 the same amount. Thus the barotropic velocity, constant with depth, will be slightly too 

 small. The error in total computed velocity at the depth of the observational error will be 

 slightly less than that in the baroclinic velocity and almost negligible at other depths. 



