as well as 



r , 2 C/„) = r 43 c/;) 4> 12 (/ B ) = 4, 43 c/ n ) (5) 



and 



r i 5 c/„) = r 46 (/ B ) (j) 15 c/ n ) = K(/ n ) (6) 



Figure 4 is an example of coherence and phase comparisons, showing graphs of 

 the functions named in Equations 4, 5, and 6 (upper, middle, and lower sets of 

 graphs in Figure 4, respectively). This type of error checking is useful for isolat- 

 ing cases where a data point is dropped during telephone transmission from the 

 data buffer, resulting in an apparent temporal shift of data from one gauge relative 

 to data from the other gauges. Such a shift causes a significant phase error in 

 cross spectra, and is readily apparent in a graphic display like Figure 4. 



The combined effects of intercomparing frequency autospectra and coherence 

 and phase functions for the pressure gauge array on Harvest Platform provide 

 clear indications of faulty or suspect data. When such conditions are detected in a 

 collection, frequency-direction spectra are not computed. Such rigorous examina- 

 tion of the data ensures that only high-quality time series are used in directional 

 estimation. 



Frequency-Direction Spectra 



Estimates of frequency-direction spectra are made using the iterative maximum 

 likelihood estimator (IMLE) developed by Pawka (1983). Estimates are made by 

 iterative approximations of directional distribution functions D(f n ,Q m ), which are 



related to corresponding frequency-direction spectra S(f n ,Q m ) by 

 5(/,0 ) 



£></„, e m ) = " (7) 



" S(f n ) 



where 9 m is a discrete angle indicating the direction from which wave energy ar- 

 rives, measured counterclockwise from true north (Figure 2), and S(f n ) is the 

 (surface-corrected) frequency spectrum. The direction index m ranges from 

 m =1 torn = M = 181 , while direction ranges from 0, = -180 deg to 

 6, 81 = 180 deg in steps of dQ = 2 deg. The directional distribution function has 

 the property 



M 



T,D(/ n ,e m )de = i (8) 



m=l 



which must be satisfied in all estimates. 



Chapter 3 Primary Data Analysis 



