error reduction indicates a substantial advantage of the IMLE method. When 

 ensembles of 16 artificial cross spectra with random noise (to simulate field 

 data) were tested, the IMLE method was typically 4 to 20 times more accurate 

 than the MLE method. In no case were the general features of the true 

 spectrum misrepresented using the IMLE method. 



117. This is not formal proof that IMLE worlcs in all possible cases, 

 but the tests lend substantial confidence that the estimates obtained do 

 represent underlying true spectra faithfully. Since the FRF array has nine 

 gages (instead of five used in Pawka's tests) and measured spectra have more 

 than 150 deg of freedom (compared to 32 in the tests) , it is expected that the 

 quality of results reported here are better than the test results. 



118. One important property of IMLE is that results for spectra with 

 broad spreading are characterized by obvious but relatively minor fluctuations 

 about the true spectral distribution. This behavior means that all maxima and 

 minima in a measured directional spectrum are not meaningful separators of 

 individual wave trains. A deep minimum between two adjacent maxima is more 

 meaningful. This distinction is important in interpreting observations, 

 especially in analysis of modes (multiple peaks in directional distributions) 

 as discussed in Parts V and VI . 



Working Data Base 



119. Computational output from the IMLE algorithm is a discrete 

 directional spectrum of wave energy (sea surface variance) for each of the 



28 frequencies in the cross -spectral estimates. The direction increments vary 

 between frequencies because directional resolution is frequency dependent. 

 The higher frequency (shorter wavelength) waves are better resolved because 

 more of these wavelengths are represented by the length of the linear array. 

 Output direction increments vary from about 0.5 deg for 0.318 -Hz waves to 

 about 3.5 deg for 0.054-Hz waves. 



120. It is convenient to have direction increments the same for all 

 frequencies so that a regular array can be used to represent the full frequen- 

 cy-direction spectrum. As a trade-off between the two resolution extremes, 

 directional results were integrated over 2-deg arcs and renormalized with this 

 direction increment to create evenly spaced directional spectra at all 

 frequencies. This computation resulted in 90 direction arcs (91 arc center 



45 



