SECT. 2] LARGE-SCALE INTERACTIONS 113 



where the constants were obtained from (18) and (19) taking p = l,2x 10^3 g 

 cm""^ Cj, = 0.24 cal g~i deg~i and Cd= 1-4 x 10^3 (mean wind speed ~ 14 knots 

 from Fig. 6), where all units are c.g.s. and the measurables may be mean values 

 for the period considered. 



The problem of arriving at momentum flux using a formula of the type (17) 

 and climatological mean data is much more difficult and uncertain. Since each 

 component of shearing stress is a directed quantity, the formulation analogous 

 to (18 a-d) is more complex and since the wind speed squared appears, the 

 errors in the climatological approach are almost certain to be larger than those 

 for heat and moisture. Such calculations, their limitations and results are 

 described in more detail in Section 6 on Large-Scale Momentum Relations 

 (p. 180). 



A method of testing results of computations from these exchange equations 

 by direct flux measurements has recently come into existence with the develop- 

 ment of the instrumented and calibrated research aircraft (Bunker, 1955). 

 While direct comparisons of the two methods are still very limited, the results 

 to date are encouraging. The aircraft method is based on measuring the actual 

 vertical transports of the property involved, using the definitions 



T = -puW, (22) 



Fh = pCpT'w', (23) 



and 



Fe = pq'W, (24) 



where r is the vertical momentum flux, Fh the vertical heat flux, and Fe the 

 vertical water- vapor flux through the level in question. The aircraft is flown 

 horizontally at 50-100 ft above the sea and a continuous record is made of 

 wind speed, u, temperature, T, specific humidity, q, and vertical velocity, w, 

 throughout the run. The primes denote the departure from the mean values of 

 these quantities. The method is presently able to include fiuxes accomplished 

 by elements in the size range from about 10 m to 10 km, cutting off at the small 

 end due to limitations in speed of response of instruments and aircraft, and at 

 the large end due to limitations in run length and aircraft calibration to deter- 

 mine w'. Recent calculations by Bunker (1960) of heat fiuxes from (23) and (20) 

 in comparison show that the direct method gives values proportional to ship- 

 board determinations of the product of property difference and wind speed, but 

 about 25% lower numerically. It appears likely, however, that the discrepancy 

 is due to height difference and to the limitations of size spectrum coverage by 

 the aircraft method. 



Although many more such careful comparisons are required, and will be forth- 

 coming, it appears that the exchange formulas are on a sufficiently sound footing 

 at present to enable useful fiux computations to be made from simply obtained 

 and relatively plentiful shipboard observations, particularly the accurate ones 

 provided by weather ships and research vessels. That we are able in this way 



5 — s. I 



