Pierson, Tick, and Baer 



A 



PRIMARY 



USE DIRECTLI. 



USE LOCATIONS 1 AND 2 ALTERNATELY 

 TO GET EQUIVALHiT OF PATH FROM 

 LOCATION 3. 



SECONDARY 



USE LOCATION 1 THRICE AND 2 ONCE 

 ALTERNATELY TO GET EQUIVALENT OF 

 PATH FROM LOCATION 3. 



TERTIARY 



Fig. 



1 1 - Propagation scheme for the 

 24 different directions 



To facilitate solution of this problem a set of grid points has been chosen 

 such that they fall exactly along the borders. The 24 direction increments are 

 then split into two parts so that 12 are in the coordinates associated with each 

 of the adjacent projections. Specifically, the 180 components representing out- 

 going directions are in the coordinates of the projection. This is simplified, 

 because the two directions along the discontinuity are common to both projec- 

 tions. Before allowing energy to enter the region of the projection the incoming 

 spectral components are curve-fitted (piecewise) and integrated over the appro- 

 priate directional limits found from the ±7.5° limits within the projection. This 

 introduces some smoothing and error which would be significant if repeated 

 many times. However, for the entire North Pacific only a maximum of three 

 such corrections are required. 



For some situations with discontinuities, forward interpolation is required. 

 Important here is that if a discontinuity is associated with an incoming direction 

 at a border point and passes the next adjacent internal grid point in the time 

 step, information must be provided in the adjoining projection to allow this for- 

 ward interpolation. That is to say, instead of working with a triangle of only 49 

 grid points on a side there must be 51 grid points including a one-grid-point 

 overlap of the adjoiningprojections. This overlap is integrated in much the same 

 manner as the interpolation to allow for the changed location of the desired point. 



522 



