2.2 Assumptions and Approximations 



The validity of results from the approach used here is dependent on the assumptions 

 (a) that the wind-driven geostrophic transport tabulated by Fofonoff (1960) is accurate 

 in the region of interest: (b) that acceleration terms, bottom friction terms and horizontal 

 friction terms can be neglected in developing the expressions for wind-driven transport 

 (p. 21, appendix I); and (c) that convergence due to the effect of bottom topography can 

 be neglected. The results will also depend on (d) the accuracy, precision, number and 

 distribution of the oceanographic observations. 



(a) Fofonoff (1960, p. 3). in considering the applicability of his computations of wind 

 stress at the surface, stated, "It should be remembered that the transports are very sen- 

 sitive to the proportionality factors used in relating geostrophic to surface wind and 

 surface wind to wind stress. Numerical equivalence of computed and observed transports 

 is not anticipated." His calculations of surface stress are based on the equation 



T s = PaC[)W 2 , 



where t„ is the surface stress, p„ is the air density, Co is the drag coefficient, and w is the 

 wind speed. It is assumed that the wind speed and stress magnitude are functions of 

 the pressure difference, Ap, between positions so that 



Ts^ w 2 ^(Ap) 2 . 



Additional error is introduced in Fofonoff s computed stresses by using the square of 

 monthly means of pressure differences, (Ap) 2 , rather than computing the mean stress from 

 the actual pressure (that is, satisfying the relationship t., x Ap 2 ). The error arising from 

 calculation of stresses from a monthly mean of pressure differences rather than using 

 the monthly mean of stresses estimated from continuou s re ports of pressure is propor- 

 tional to the variance of the pressure differences. Since Ap 2 is larger than (Ap) 2 , the less 

 rigorous relationship leads to stresses that are too small. 



Fofonoff (1960) used a value of 0.0026 for the drag coefficient in his tabulation of 

 wind-driven transport. Deacon and Webb (1962) have summarized recent determinations 

 and find a range of values from about 0.0010 to 0.0015. Because of the linear relation- 

 ships between the drag coefficient and Ekman and total transport, this discrepancy in- 

 creases Fofonoff s values by a factor of about 2. 



Graphic comparisons have been made to assess the effects of these two discrepancies. 

 Figure 18 shows the alternate determinations for the variation with latitude of integrated 

 geostrophic transport in September 1962 (Section 3). The three determinations are 

 based on: 



" (i) stresses obtained by using a drag coefficient of 0.0026 and monthly means of 

 pressure differences; 

 (ii) a drag coefficient of 0.0026 and a monthly mean of values estimated from twice- 

 daily pressure reports; and, 

 (iii) a drag coefficient of 0.0012 and a monthly mean of the values estimated from 

 twice-daily pressure reports. 

 The use of the higher drag coefficient (of 0.0026) rather than the more nearly correct 

 value of 0.0012 leads to high transport values: but the use of monthly mean pressures 

 (rather than means from twice-daily values) gives low transports. Accordingly, errors in 

 method (i) are partly compensated and the results obtained agreed well with method (iii); 

 whereas method (ii) gives erroneously high results in all cases. Figures 38, 39 and 41 

 show for the 5,000 meter level the dynamic topography resulting from the September 1962. 

 observations adjusted to these three techniques of wind-driven transport computation. 



