TM No. 377 



frequency scale, as shown by equation (III-2). But at the deeper depths, 

 where the low particle velocities supply a low density of data points, 

 the rapid fluctuations are filtered out anyhow, leaving the effects of 

 the low frequency swells to dominate the variance contribution. Thus, 

 the relatively high sampling rate may still he used to portray the ambient 

 oscillations at this depth without biasing the spectral character of the 

 swell or longer wind wave motions. 



There is, however, a subtle form of potential 'biasing inherent in 

 the linear interpolation which is associated with low variance velocity 

 records. This is illustrated in figure III-9, which represents a 25 second 

 segment of the vertical velocity record of (040) BBELS-11 (3.5 m l). The 

 lower graph is a plot of the uninterpolated velocity values obtained by 

 conversion from the raw data tapes. The upper curve represents the linearly 

 interpolated, equally time spaced, data points obtained from the bottom curve. 

 The upper curve displays the same slight smoothing effect as in figure III-3. 

 However, note that the amplitudes of the velocity function are relatively 

 small; i.e., the peaks occur at less than 30 cm sec" 1 . As was discussed in 

 chapter II, the threshold velocity of OMDUM III and LIMDTJM I is between 

 5 and 7 cm sec" 1 . Hence, when the instrument is recording oscillatory 

 motions with relatively small variance (as displayed in figure III-8), 

 there is a certain fraction of time when the instrument produces no output. 

 This fraction increases as the oscillatory motions grow weaker. 



The linear interpolation method introduces an obvious error into the 

 final record (upper curve) as demonstrated for the time interval AB„ Although 

 only one point occurs between A and B (in the lower curve), the interpolation 

 places 13 points of approximately equal velocity value. It is obvious that, 

 with a threshold of sensitivity of .5-7 cm sec" 1 , the 13 points are not very 

 representative of the actual flow. In fact, it is probable that the velocity 

 value became negative between A and B. If a zero crossing is indicated by 

 a sign reversal of consecutive velocity values, the interpolation error is 

 much less, since a more probable portrayal of the velocity function would be 

 obtained. 



The biasing effect between points A and B only occurs when the data 

 points are of low density. It would not occur with high velocity fluctu- 

 ations (i.e., when there is a large variance), since the ducted meters pro- 

 duce a higher data point density (average number of points per unit time) 

 the higher the variance of the sample. This is readily seen by comparing 

 the uninterpolated traces of figures III-8 and III-9. This biasing would 

 probably affect the mean values of the records, since the mean is calculated 

 from the equally spaced interpolated data. This error in the mean should be 

 small, however, since it should average out algebraically over the record. 

 Also not that these biased values are always of the order of 5=7 cm sec" 1 

 or less. 



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