SECT. 2] LARGE-SCALE INTERACTIONS 179 



A . Methods and Difficulties of Ocean-Surface Stress Determinations 



Direct measurement of surface wind stress over the open sea is for all 

 practical purposes impossible. While several indirect methods of computation 

 exist, all from meteorological observations, the only one which has to date 

 proved suitable for extensive and systematic determinations is that based on 

 the exchange formula set forward in Section 3 of this chapter (page 109), 

 namely : 



TO = pCoUa^. (17) 



This formulation has the great advantage that surface ship wind measurements 

 alone are required to arrive at shearing stress. It has, in fact, been used in all 

 stress-curl calculations and in many meteorological studies of circulation 

 dynamics, where as we shall see later its implications are vast concerning the 

 constraints upon and efficiency of thermally driven air motions. It is, therefore, 

 of the utmost importance to inquire carefully into its usage and range of 

 validity. 



Regrettably, shearing-stress computations from (17) are considerably less 

 satisfactory and less certain than those of heat and moisture flow from (18) 

 and (19), discussed in Sections 3-5 of this chapter. The reasons are numerous 

 and fall into two main categories, the first concerning the very foundations of 

 equation (17) and the second relating to its operational usage with existing 

 data. 



As was pointed out earlier, far and away the largest exchanges of heat and 

 moisture take place in those parts of the oceans (tropics and western basins) 

 where the foundations of the exchange formulas are most solid. Unhappily, this 

 cannot be true of momentum exchange, which is of necessity about evenly 

 divided between tropical and temperate latitudes. The atmosphere gains 

 westerly momentum from — and loses easterly momentum to — its lower 

 boundary in tropical latitudes, while on the average it must put back the same 

 amount to the earth's surface in high latitudes. As we shall see, it is in the latter 

 regions that the real difficulties in assessing stress distribution arise. 



When the air temperature structure in the lowest few meters departs sig- 

 nificantly from neutral stability, as it frequently does in temperate regions, 

 the conditions for the logarithmic increase of wind speed as a function of 

 height are not met. Therefore errors would arise in applying (17), the derivation 

 of which depends upon the logarithmic profile, using the Cd of the solid line of 

 Fig. 6, which was determined experimentally under neutral conditions. Estima- 

 tion of the magnitudes of these errors may be made using a beautiful 

 observational study of oceanic stress and wind profiles by Deacon, Sheppard 

 and Webb (1956), from which Fig. 6 was taken. They measured wind-profiles 

 from a research vessel, carefully corrected for ship roll and flow disturbance, 

 obtaining stresses and Cd under varying conditions of stability, some of which 

 departed appreciably from neutral on both sides. The basis of their computa- 

 tions in non-neutral cases was the Rossby-Montgomery (1935) formulation of 



