4. Data Reduction Methods . 



Laboratory data sorted on magnetic tape were analyzed on a CDC 6600 compute: 

 using a variety of data reduction schemes. The mean water level and the least 

 squares, best-fit linear trend in the data was first removed from each gage 

 record. A Fourier analysis was then performed on each gage record using a fast 

 Fourier transform (FFT) routine and cosine bell function that is part of the 

 CERC wave analysis package. 



Incident and reflected waves, which are mixed together in each of the gage 

 records, were separated using the method of Goda and Suzuki (1976) shown in 

 Figure 2. This technique gives an estimate of the incident and reflected wave 

 amplitudes, aj and a^, at each spectral line for each gage pair. Using 

 three gages in front of the structure gives three estimates of the incident and 

 reflected wave amplitude spectra. Calculations show that in this study the 

 three estimates of wave amplitudes seldom differed by more than 5 percent, so 

 the average incident and reflected wave amplitudes at each spectral line, j, 

 were taken as representative; i.e., (aj3j is the average incident wave ampli- 

 tude at spectral line, j. The wave amplitude at each of the spectral lines 

 was also determined for transmitted wave conditions; i.e., (ay)^- is the 

 average transmitted wave amplitude at spectral line, j. 



Incident Woves 



SWL 



K 



Li ■■ 125cm 



A 



Goges 



LZ ■- 90cm 



Ai : 35 cm 



Reflected Woves 



Tonk Bottom 



a^ - —, r v^A, - A, cos kA£ - B, sin kM)^ + (B, + A, sin kA£ - B, cos kAl)- 



■I 2 1 sin kt^l\ "'■ 2 1 1 --^21 1 



ao - /(A, - A, cos kA£ + B, sin khl)'^ * CB, - A, sin kA£ - B, cos kA£)' 



" 2|sin kU\ '21 1 ^^21 1 



A,B - spectral coefficients 

 k ■ wave number = j^ 

 A£ » gage spacing 



where 

 and 



0.05 < j— i 0.45 



gT^ /2ird\ 



L " - — tanh ( ) 



2ir \ L / 



where g equals acceleration due to gravity; d equals water depth; and 

 T equals wave period. 



Figure 2. Determination of incident and reflected waves using the 

 method of Goda and Suzuki (1976) . 



15 



