Global Wave Forecasts Using Spacecraft Data 



Fig. 8 - The locations on a Mercator projection of the triangles 

 that constitute the icosahedral-gnomonic projection 



points. While this is an important advantage of the system, it is not the only one. 

 The area represented by each point is hexagonal, as shown in Fig. 10, which 

 minimizes the maximum distance from the grid point to any point in the area. 

 Hence, the value of some parameter such as wind speed at the grid point may 

 be a better description of the entire area represented by the grid point than for, 

 say, square unit areas. Also, each grid point in the hexagonal system has six 

 natural directions associated with its neighbors. Twelve directions are exactly 

 defined within 1.7 grid units. This compares with only eight exact directions in 

 the square grid. And for the hexagonal system, the 12 can be increased to 24 if 

 we accept a reasonable approximation. To achieve the desired representation 

 for each grid point, each side of the triangle is divided into 48 intervals of 94.8 

 nautical miles by 49 grid points. Thus, an average grid point represents 6469 

 square nautical miles of the earth's surface. Extremes are therefore 6469/0.83 

 and 6469/1.66. 



Since the gnomonic projection is not conformal, the change in direction from 

 true geographical direction and the change in scale in the various directions be- 

 tween "radial" and "transverse" must be considered. For a general triangular 

 projection of this size Fig. 7 also illustrates the changes in scales and the 

 changes in directions at the vertices of the triangle compared with an infinitesi- 

 mal circle at true scale at the point of tangency. The circle is transformed to 

 an ellipse at any point other than the tangent point with the major axis in a radial 

 direction. 



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