TM No. 377 



range from to about 125 cm sec"- 1 ;, The relative error for the upper value is 

 about + 6 percent and. drops off rapidly with decreasing speedy e.g^, at 50 

 cm sec~2- the error is about + 2 percent. 



Thus there is a certain amount of subjectivity involved in abstracting the 

 velocities from the raw data tapes. For better or worse 9 much of the respon- 

 sibility for successful data abstraction rests with the man operating the film 

 reader. It proved, beneficial to attempt to convey to him the nature of the 

 measurements and the data. With this background he was able to anticipate the 

 critical areas (such as keeping the data pairs exactly on the same time base). 



The repeatability of the data-reading step was checked by re-reading a raw 

 •lata tape. To ensure an unbiased experiment ;, the person re-reading the tape 

 was unaware of the purpose of the experiment „ The re -evaluation was made on 

 the lj,3^1 data pairs from (023) 3B2LS-9 (0»5 m l)„ (Tae Reman numeral after 

 the depth refers to the number of the observation at that depth,, ) This sample 

 was obtained near the surface j hence s it displayed a maximum number of high 

 frequency surface fluctuations „ It also contained a generous number of data 

 points o The aim was to compare the gross velocity values.? but ; even more 

 important^, to compare the variances^, covariances, and spectra. 



The results of the data-reading check were s in general 5 very encouraging 

 Table 111=2 lists the pertinent parameters and compares the read and re-read 

 velocity series. The variances, covariances (at zero lag); and correlation 

 coefficients are all within a few percent of each other.-. Likewise n the peak 

 auto-spectra and cross-spectra values occur at about the same frequencies, A 

 direct comparison of the two pairs of auto-spectra, c£>y_ and Cp>uo , is show" in 

 figures III-7A and III-7B0 The ordinate is the spectral density (cm 2 sec =1 )j 

 the abscissa is given in millicycles per second (meps) for frequency and in 

 seconds for period* 



Examine first the C^V, curves (figure 7A)-> The low frequency regions 

 (below 1500 meps) are almost identical., whereas in the higher ranges the curves 

 are somewhat divergent. The Biajor peak at 100 meps and a lesser peak occuring 

 at 65O meps are clearly delineated 'oj both curves,, 'The cp^, spectrum displays 

 remarkable similarity over the whole frequency range, displaying the identical 

 peaks at 100, 6 SO, and 1200 meps, and similar profiles through 2500 meps,, 

 Thus, with conscientious use of the Teiereader, the recorded data can be quite 

 faithfully reproduced from the original tapes , 



The :ity data,- after being preliminarily processed (including inter- 

 polation arid corrections), are examined in terms of their auto -co variance 

 and covariance functions. From these functions the corresponding auto-spectra 

 and cross-spectra are estimated* It should be emphasized that computations 

 dealing with the estimates of the covariance function and the covariance spectra 

 between two simultaneously recorded variables demand a maximum amount of 

 accuracy in the determination of the two functions relative to the same time 

 basec Errors such as spurious single values, which may be few in number com- 

 pared to the total sample, can be easily tolerated in the estimates of the auto- 

 covariance function and the auto-covariance spectra,. However s in the estimates 



