D (f n ,Q m ) 

 and then finding a new directional distribution function estimate D r (f n ,Q m ) from 



^c/„,e m )|0 + 1 



£,(/„, 6j = D' r (f n ,Q m ) 



i + 



Y^<X,.ej 



(15) 



The parameters P and y in Equation 15 control the rate of convergence of the 

 estimator. As used by Pawka (1983), the values P = 1 and y = 5 were used for 

 all estimates discussed in this report. 



In each iterative loop, a convergence check e r is computed as the sum of the 



squares of the magnitudes of the differences of elements of the estimated cross 

 spectrum of Equation 1 2 and the measured cross spectrum of Equation 1 . This 

 takes the form 



^E£r*W)-Aw n) |> 06) 



i=i , = 1 



Iteration continues as long as e r decreases between successive iterations, or until 

 an upper limit R of iterations has been completed. In computations reported here- 

 in, R =30. 



Equations 9 to 16 form the basis of the IMLE technique. For the iteration r 

 that satisfies the convergence check, the frequency-direction spectrum at frequen- 

 cy f n is formed from 



S(f n ,Q m ) = S(f„) D r {f n , 9 m ) (17) 



The complete frequency-direction spectrum is formed when Equations 9 through 

 17 are evaluated for all frequencies. 



An example of such a spectrum is illustrated in Figure 3. The upper graph is a 

 three-dimensional plot of 5(/ n , 6 m ) , and the lower right graph is a contour plot of 

 the spectrum. The right panel in the three-dimensional plot is a linear graph of the 

 discrete frequency spectrum S(f n ), which is related to the frequency-direction 



spectrum through Equations 7 and 8 by 



Sif n ) = E S(f„,Q m )dQ (18) 



12 



Chapter 3 Primary Data Analysis 



