fk-iJhfk+i - (k-iyth, k'th, and (&+l)'th HARBD computational frequencies, 

 with f k .,<f k <f k+1 



Though not shown in the equation, the weighting factor also includes fractional 

 energy interpolated across JONSWAP frequencies bracketing the two end points 

 of each HARBD band. 



Directional spread is also calculated over 1,000 points, covering a range 

 oi-idl to +;z/2. The midpoints between HARBD wave directions are used to 

 define directional bands. The weighting factor for each HARBD-defined 

 directional band becomes: 



(16) 



E D ( ,) 



w = - 



" 1,000 



E 0(6,) 



;=1 



where 



w n = weighting factor for rith HARBD computational direction 



fl +fl 

 N nl = index of lowest spreading direction 6 i satisfying 0. > - 



N„2 - index of highest spreading direction $ satisfying 0. < 



2 



On-i> Q* Q n +i = (n-l)'th, n'th, («+l)'th HARBD computational directions, 

 with 0„_!<0 n <0 n+1 



The width of the lowest HARBD-defined directional band is assumed to be twice 

 the difference between the HARBD direction and the first midpoint. The width 

 of the highest HARBD-defined directional band is defined similarly. 



The effective amplification factor at each node can then be computed as 



2 

 0+0 



(A ) _ 



x amp' eff 



Hi W n ™ k AL(fM (17) 



where 



( A amp)eff = effective, or spectral, amplification factor at a node 



Chapter 4 Numerical Model 5-] 



