TM No. 377 



A corresponding coefficient (V^ u orV^) c ^ n ^e defined for the pairs 

 lU-rijUs. /■)*;£> UJ ,(■>>':,).#. jo the obvious substitution can be made in 

 equation (Ill-ol). This function can now be interpreted as a spatial 

 correlation indicator, In other words, the "spatial coherence" of the 

 motions at points at various separations within the waves is indicated 

 by the magnitude of the coefficient. 



Miscellaneous Data Ana lysis — Aside from the spectrum analysis pro™ 

 grams, two other simple and useful computer programs were used to provide 

 information about the time series data by rendering it more suitable for 

 visual inspection of some of its more obvious statistical attributes. 

 These programs involved histogram construction and progressive vector 

 diagram calculation, 



1, Histogram Construction , This simple digital computer program makes 

 a frequency or population sort of N data points (sampled at equally spaced 

 time intervals AT) from a time series record. The data points are sorted 

 and placed into compartments associated with their individual magnitudes 

 (in equal increments) and, in the case of velocity values, with their signs. 

 From this sort of the tabulation and plotting of the e qui -time-spaced inter- 

 polated data., the shape of the skewness of the distribution can be assessed 

 to indicate how much the wave data deviate from the Gaussian, A few histo- 

 grams were prepared on samples of the wave data, and a brief discussion is 

 given in chapter IV, A listing of the histogram Fortran computer program 

 is given in appendix E, 



2, Progressive Vector Diagram Calculation , This program converts a 

 time-pair sequence of two orthogonal vector components into a new series 

 of data points, These points, if represented in the two dimensional plane, 

 delineate the consecutive "head-to-tail :l "positions of the sequence of vec- 

 tors represented by the time series. This program produces the vector 

 plotting data on punch-cards, which can then be used in conjunction with 

 an automatic plotting machine to produce a diagra& for visual study. The 

 plots portray roughly either the possible Lagrangian paths of the water 

 particles,, if the vector representation is in the horizontal plane XY; or 

 the possible orbital trajectories, if the vectors are representative of 

 motion occurring in a vertical plane XZ, Moreover, the plots show clearly 

 the amount of mean flow present, and any gross variation from the mean 

 (i,e,, any trend) occurring during the sampling period. This technique 

 was applied to data obtained from measurements of the horizontal current 

 at the Buzzards Bay Entrance Light Station over periods of several days. 

 Farther discussion of this analysis is included in chapter IV, The com- 

 puter program of this plotting data generation is given in appendix E, 



Sources of Error Introduction 



In the preceding summary of the data, reduction procedures, some of the 

 steps involved are quite critical to the quality of the processed data. 

 This section discusses the errors which may be introduced into the data 

 processing from the time the data are abstracted from the strip chart 



6k 



