Global Wave Forecasts Using Spacecraft Data 



The location of the discontinuity is remembered by keeping a field repre- 

 senting the fractional distance of any discontinuity to the next downstream grid 

 point in a parallel storage position to that of the spectral variance itself. This 

 simple system forces some assumptions that do not seem to have a significant 

 effect. 



Typically, the velocity-gradient propagation on grid points with a linear 

 assumption results in errors near maxima and minima. This has been at least 

 partially avoided in the present case at little expense by simply treating all 

 maxima and minima as discontinuities. 



It was pointed out previously that the 60° grid provides six primary direc- 

 tions, six secondary directions, and 12 tertiary directions. Propagation along 

 the six primary directions is relatively simple in that the energy moves from 

 grid point to adjacent grid point. However, in the other directions, the great 

 circle along which the energy propagates skips either one or two rows of grid 

 points. Thus, if the great circle path is taken too literally, winds a long way 

 from the grid point of interest will have an effect rather than just winds at the 

 adjoining grid points. Since both the wind and wave fields are relatively smooth, 

 and since the accuracy of the method cannot exceed the grid point spacing, and 

 to alleviate this proximity problem, we use a zigzag propagation scheme. 



This zigzag is accomplished by choosing the location from which the energy 

 travels by alternating between the grid points stradling the desired great circle 

 path at successive time steps as illustrated in Fig. 11. For the secondary direc- 

 tions the two intermediate grid points are used alternately. For the tertiary, 

 the grid point to one side is used thrice and the other once. This results in a 

 slight but unimportant error because of scale changes. 



In the above it is implicit that a system of grid directions are used in which 

 rhumb lines and great circles are the same within a subprojection. This is 

 similar to what was done for the North Atlantic computations. It thus becomes 

 necessary to translate between grid coordinates and true earth coordinates at 

 input and output and along the internal borders. 



There are discontinuities in the particular projection chosen along the three 

 internal triangle sides. As a great circle crosses these lines it changes direc- 

 tion dis continuously. These direction changes can most easily be seen by refer- 

 ence to the breaks in the latitude and longitude lines in Fig. 9. Near the center 

 of the triangle sides there is little or no effect, but near an apex there is up to a 

 30° change depending on the direction of the great circle. This change in direc- 

 tion must therefore be taken into account. 



At any grid point the spectral variance assigned to a particular frequency- 

 direction component represents the integrated value from the complete direc- 

 tional spectrum over the region represented by the component. Since the change 

 in grid direction which is required when a boundary is crossed is not usually an 

 integral change of components, an approximation is required. Further, the 

 angle representing a 15° grid increment on one projection will not always map 

 a 15° increment on the adjoining projection. 



521 



