Step one is to multiply the power spectrum in deep water by 
the spectrum amplification function. Graphically this can be done 
by computing the value of the product point for point of (12.29) and 
(12.32). For any finite net over [A5p *(H on ]*, as in equation 
(9.22), the result of this operation is to predict the height of 
each elemental wave in the partial sum for the new point of obser- 
vation. 
Step two is to substitute equation (12.34) for 0,* everywhere 
it occurs. This converts the product given in (12.36) to the pro- 
duct given in (12.37). The result is some function of # and Ope 
For any partial sum the result is to assign the correct spectral 
directions to each elemental wave at the new point of observation. 
In general equation (12.36), is a continuous function and the effect 
of this operation is to squeeze (12.36) into a more compact function 
in the # 99, plane since elemental wave components with widely 
different directions in deep water have more nearly the same direction 
at the point of observation in the transition zone. 
Graphically this step can be accomplished by plotting the value 
of (12.36) at # =, and 6," = Orr in the BO," coordinate 
system at the point OR = @ (eH 7en7) and # = By in the new H 58, 
polar coordinate system. A line on which (12.36) is a constant 
is thus mapped into a new line in the pw 29, plane on which the same 
constant value is found. 
The third step is to multiply (12.37) by T (#,6,) as given 
by equation (12.35). The result is the desired power spectrum, 
[asee( sea l=, as a function of # and ©, at the point of obser- 
vation in the transition zone. This step is needed since the power 
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