smoothed with a cosine bell data window. The spectmm is coisputed with 

 a fast Fourier transform (FFT) algorithm applied to 4,096 data points 

 (17-minute and 4-second record). 



The spectral analysis procedure assigns a fraction of the total var- 

 iance of the record to each of 1,024 frequencies, or frequency lines. 

 It is difficult to deal with such finely resolved spectra. To gain sta- 

 tistical stability, groins of 11 successive lines in each spectrum are 

 combined into bands. The resultant band width is 0.01074 hertz over the 

 full range of frequencies considered (0.03 to 1.00 hertz). The uniform 

 spectral resolution over the frequency range gives a nonuniform resolu- 

 tion in wave period. Significant height is estimated as four times the 

 square root of the total variance assigned to wave frequencies of inter- 

 est, usually 0.03 to 1.00 hertz. 



The frequency-dependent responses of some of the gage types required 

 some special treatment of the spectra. Accelerometer-buoy gage spectra 

 were terminated at the high-frequency end at 0.5 hertz. A special low- 

 frequency bound of about 0,065 hertz on the spectrum would have been 

 appropriate but was not used because energy at frequencies between that 

 and the low- frequency cutoff for other gage types (0.03 hertz) was in- 

 significant in the Great Lakes buoy records. 



Pressure-gage records were compensated for hydrodynamic attenuation 

 of the pressure signal with depth by multiplying the energy in each 

 spectral band by a frequency-dependent factor. The compensation factor 

 becomes very large at high frequencies where the small pressure signal 

 is often obscured by noise. Hence, it is necessary to terminate the 

 high-frequency end of pressure-gage spectra at a frequency below the 

 standard 1-hertz cutoff for staff gages. The high-frequency cutoff 

 used for the Michigan City and Presque Isle pressure gages is 0.33 

 hertz. The cutoff for the Pt. Mugu pressure gage is 0.31 hertz. All 

 spectral energy assigned to frequencies above the cutoffs was omitted 

 from both the spectrum and the significant height estimate. The neg- 

 lected energy is unimportant during high wave conditions, but it can 

 increase significant height by as much as 0.5 meter during low recorded 

 wave conditions. The latter effect is often partially balanced by slight 

 overcompensation of the high-frequency energy retained in the spectrum. 



b. Spectral Summarization . 



(1) Averaging . Individual shallow-water ocean wave energy 

 spectra are quite irregular and can change substantially and somewhat 

 erratically with time (see Fig. 5). Because of these problems, it is 

 difficult to identify typical spectra for each wave gage site. However, 

 it is desirable to condense the masses of individual spectra into a more 

 concise form. 



At this time, no completely satisfactory technique is in use for 

 isolating and summarizing general characteristics of field spectra. One 



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