Pierson, Tick, and Baer 



Fig. 10 - The hexagonal unit 

 areas and the 60° grid system 

 (from Ref. 25) 



Each frequency-direction component propagates along a great circle tangent 

 to its principal direction at a speed depending on its frequency, in accordance 

 with linear wave theory. These tangent great circles connect nearby grid points 

 in the chosen grid system. Further, this is relatively simple because great cir- 

 cles are straight lines within each triangular subprojection. There are, how- 

 ever, complications which occur because of scale and direction variations, 

 bridging between subprojections, spatial discontinuities in the spectral compo- 

 nents, and the discrete representation for the spectra. 



Neither wave nor wave component fields representing the spatial distribution 

 are continuous to first order. For example, regions of zero spectral variance 

 are adjacent to regions where waves exist. Allowance for these possible dis- 

 continuities is a serious problem. As shown by Baer (2), propagation by multi- 

 plying the linear gradient as computed from grid points by the velocity to get the 

 change at the grid point is inadequate for such discontinuities when repeated 

 many times. Use of higher order gradients can cause other more serious er- 

 rors. Allowance for discontinuities was accomplished in the previous North 

 Atlantic work by assuming that all values were discontinuous. This was possi- 

 ble because in the region of the projection that was used the scale did not vary 

 significantly throughout the field. It was thus possible to "jump" the values 

 from all grid points in the field to the adjoining ones simultaneously after, of 

 course, waiting the required time for the wave components to travel that dis- 

 tance. This caused some temporary irregularities in the component fields. 



In the present case, using the icosahedral-gnomonic projection, variations 

 in true distance between grid points are slightly over 50%, which is too much for 

 such a simple system. A system has therefore been established which keeps 

 track of the location of each discontinuity and uses the velocity gradient method 

 within continuous regions. 



520 



