APPENDIX C 



A FORTRAN PROGRAM FOR ITERATIVE WAVE TRAIN ANALYSIS 



The FORTRAN listing of a Burroughs B-5500 program for the itera- 

 tive least square multiple wave train analysis of a spectral matrix 

 is presented. The mathematics is an iterative utilization of the 

 single wave train analysis described in the body of this report. 

 Following the single wave train analysis of the measured spectral 

 matrix the resulting values of single wave train power, A, and wave 

 bearing, 0, are used to find the spectral matrix that would occur for 

 such a wave. Details for this are given in Section 5 of this report. 

 From the above, a residual measured spectral matrix is formed by sub- 

 tracting a fractional portion of the single wave spectral matrix from 

 the previously used spectral matrix. The residual spectral matrix is 

 then single wave train analyzed. The above procedure is continued 

 iteratively until a specified number of iterations have been com- 

 pleted or the residual spectral matrix total power gets smaller than 

 a specified value. Table CI shows numerical results for several fre- 

 quencies. Figure CI is a plot of the bearing, 6, and the ratio of A 

 to the total power available in the original measure spectral matrix 

 for the frequency band 0.00833 to 0.24187 Hz. The iteration parameters 

 were set for a maximum of five iterations, a residual power ratio of 

 0.1, and a fractional portion value of 0.1. Both results are for data 

 collected for task SWOC at Stage II between 1220 and 1249 hours on 

 4 June 1965. The wind speed was 12 knots from a bearing of 280 degrees. 

 In Table CI A, H, and bearing are as previously defined. AVE P is the 

 average ^±±(0 for the residual spectral matrix and P is the AVE P for 

 the first iteration; i.e., the original measured average power. The HI 

 and H2 values are measures of the isotropicity of the energy represented 

 by the residual spectral matrix. HI compares the least square value of H 

 with the value H' that would have been obtained if the wave energy were 

 isotropic: 



HI = 1 - (H/H') . 



H2 compares the power A of a single wave fit to the total power, AVE P, 

 and the value A' that would have been obtained for isotropic energy: 



H2 = (A-A')/(AVE P-A'). 



Both HI and H2 are between and 1, the lower limit is for the isotropic 

 case and the upper for a plane wave from a single direction. 



C-1 



