Global Wave Forecasts Using Spacecraft Data 



Fig. 7 - Areal and direction distortion for the icosahedral- 

 gnomic projection 



The orientation of the icosahedron relative to the earth sphere was opti- 

 mized for wave forecasting purposes by (a) having as many vertices as possible 

 on land, (b) having as many edges as possible along shore lines, (c) using as few 

 faces as possible for the ocean area, and (d) optimizing for the Northern oceans 

 where a choice is necessary. To accomplish this, a clear plastic icosahedron to 

 circumscribe a globe was prepared. For several interesting orientations thus 

 approximated, detailed computations were made and a "best" one chosen. The 

 final location of the 20 centers and orientations are listed in Table 2, and the 

 triangles are shown on a Mercator projection in Fig. 8. It must be remembered 

 that each triangular face represents the same area, since a presentation is sub- 

 ject to severe distortion. A further simplification is to put small extensions on 

 the few triangles which have edges only slightly offshore. This eliminates 

 bridging without significantly increasing distortion. Two possible arrangements 

 of the polynomonic projection on a plane are shown in Figs. 9a and 9b. An inset 

 in Fig. 9a shows how the map folds into an icosahedron, and Fig. 9b is the work- 

 ing projection that shows the coordinates of all grid points. 



A 60 -degree coordinate system was selected for use on the icosahedral- 

 gnomonic projection. In such a system the grid axes will coincide with two 

 sides of the triangles and the third side will fall precisely on a line of grid 



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