defined to be [a5 (@ ,0)1° as in equation (12.26). The angle 6 is 
defined as zero along the x axis defined in relation to the storm 
in connection with the forecasting problem. At B, the forecasted 
power spectrum can be found from the results of Chapter 9. A new 
angular variable can then be found, which will be called Ope In 
terms of the forecasted power spectrum, by equation (12.28), the 
power spectrum at B is given by [Bop ( H yO) 16 The direction 6, 
equals zero is usually the dominant apparent direction of the short 
crested waves at B. The line, ©, equal to zero, is shown on the 
coordinate system labeled B, in figure 32. 
The variable, 6,;, must be transformed to the variable, 6p *; in 
order to align the forecasted power spectrum with the refraction 
diagrams for the point C. The angle, On*; can best be picked to 
be zero when the angle coincides with the Xp axis chosen perpendi- 
cular to the coast through the point C. The angle £8, which defines 
6," in terms of ep is the angle between the continuation of R through 
B and the line xp equal to zero. The function [Aon *(# ,6n*)]°, is 
thus the forecasted power spectrum at B aligned properly to the 
Xp = O and xp = O axis. The line, On* equal to zero, is shown on 
the polar diagram marked By in figure 32. 
If now, (BE (Pare) is is defined to be the power spectrum at 
the point, C, (that is, in the vicinity of the point Xp = 0, Yp = 0) 
how can it be determined from [Ane (1 0p *) 1° given the usual re- 
fraction data? It can be found by applying operations to the con- 
tinuous spectrum which are analogous to those operations applied to 
pure sine waves in the theory of wave refraction. The reader can 
check each step of what follows and assure himself that each step applied 
to a sum such as in equation (8.5) would yield correct results for 
each discrete component. 
46 
