With these definitions the coherence Ri2("f) and the phase difference 

 (|)l2("f) between time series I and 2 become: 



^f^l2(f)P - 1,(f) ■ s'(f) ^'^^ 



and 



012(f) 

 tan [(l)i2(f)] = p^^(jy (14) 



where S^ and S2 are the power spectra of time series I and 2, respectively, 

 as defined by equation (6), and where positive values of (l)i2 represent a 

 phase lead of series 2 relative to series 1. 



The coherency and phase difference between the records from two 

 stations can be interpreted as follows: If any two time series (1,2) 

 are "played" through a narrow filter peaked at some frequency f, and the 

 filtered I series lagged relative to the filtered 2 series by a variable 

 phase (j), the plotted angle is that value of (f) for which the correlation 

 is a maximum; and the plotted coherence R is the value of this maximum 

 correlation. It should be noted that the phase relation between records 

 is meaningful only where there is good coherency between records. 



The spectra and the coherence and phase between two digital wave 

 staffs mounted near the surf zone are shown in Figure 15. Note that for 

 frequencies near the major spectral peaks, there is good coherence between 

 staffs and that the phase shift is uniformly progressive for changing 

 frequency. The phase shift between staffs gives a measure of the direction 

 of energy flux associated with the passage of - these waves. 



3. Adaption to BOMl^ Program 



Standard punch cards have proven to be most useful for instructing 

 the computer in processing the data. Once a program is established, it 

 may be used as often as desired. I^inor changes to the program are easily 

 accomplished by removing or adding cards to the "deck". 



A prel iminary computer program has been written for the output of the 

 data acquisition system (DAS) to facilitate its further programming by BOMM. 

 The preliminary program has two purposes: ( I ) to add' "record gaps" to the 

 tape record and (2) to convert the information in the data frames from a 

 binary to a binary-coded-decimal (BCD) system. Record gaps are necessary 

 to provide places for the computer tape-reading equipment to pause while 

 the information in each record is electronically registered in proper 

 memory banks within the computer. Record gaps are not generated by the 

 DAS because this would permit data to be lost during the time the gap is 

 put on the tape. The conversion to BCD is required by the BOMM program 

 to enable it to locate errors in the record. DAS writes data in straight 

 binary form to reduce the amount of logic equipment and the length of 

 magnetic tape needed to record a given amount of data. 



27 



