Global Wave Forecasts Using Spacecraft Data 



The discrete representation of the spectra allows a possibility of false 

 irregularities to develop in the variance fields, because truly continuous com- 

 ponents are forced to propagate at the mean velocity for the frequency interval. 

 Having a tight grid and many small components tends to minimize this effect. 

 Also, the smoother and larger scale the wind field and the field for the spectral 

 component is, the less the problem. But it must be allowed for in large area 

 forecasts. The solution might be the use of a smoothing function while consid- 

 ering the location of the component discontinuities. 



With experience it may also be found that the changing winds generate or 

 dissipate a significant number of real discontinuities. The discontinuity location 

 fields must therefore be updated. This is accomplished by testing the variance 

 fields often enough that newly generated discontinuities will not be smoothed out. 



The Combined Steps 



The computation procedure is to read in a wind field for a certain synoptic 

 time, and carry out the steps of growth and dissipation at each grid point. Then 

 the values of S (f j, (9. ) are propagated in their appropriate directions at their 

 appropriate group velocities, and the new spectra are reassembled, completing 

 a 2-hour time step. This is repeated twice more for the same wind field; then 

 the next wind field is read in and the process is continued. 



The usual starting point is a flat calm ocean, s (f . , e. ) = 0, for all fre- 

 quencies and directions, and it takes about one week for the North Atlantic to 

 begin to behave realistically. The initial condition for each time step is the 

 spectrum at each grid point, and the computations then proceed without inter- 

 ruption. Interesting effects have been observed in the results for the North 

 Atlantic obtained to date. At times, several bands of swell are present plus a 

 local sea. The swell off of North Africa is quite evident. Sometimes spectral 

 values are present for all 360° of wave direction. 



These procedures will be tested against data from the Weather Explorer, 

 from Argus Island, and from FLIP (1) as kindly provided by Dr. Walter Munk. 

 This will provide an independent check against the instrument used in measuring 

 the waves. 



PROGRAMMING AND COMPUTATIONS 



The flat earth approximation, the total number of data points (approximately 

 100,000), and the type of calculations being performed made the programming 

 problem for the North Atlantic case a fairly simple one. Since the computations 

 are of fairly low accuracy and the data are in a small range, it was possible to 

 deal with the 100,000 data points within the structure of a 32,000 machine by 

 packing four to a word. This packing and unpacking operation was efficient and 

 its cost is small. The propagation portion involves simply a translation of the 

 vector containing a frequency-direction field by some predetermined amount. 

 The language it was written in was a rather high quality FORTRAN. However, 

 the compiler which translated this does not produce a very efficient code. Even 



523 



