Needed modifications of refraction diagrams _ 
The next step is to modify the usual refraction data so that 
they can be easily applied to [A (iaeg irs One of the quanti- 
ties evaluated in a study of refraction is the quantity Kie This 
quantity is a value related to the ratio of the distance between 
orthogonals at the point of observation to the distance between the 
Same orthogonals in deep water. Peocedates for obtaining the quantity 
are given by Johnson, O'Brien, and Isaacs [1948]. The value of Key 
must be multiplied by a factor D which depends on the depth below the 
point of observation and the period of the wave. It is essentially a 
correction for the group velocity effect in order to maintain a con-= 
stant energy flux between orthogonals. The product KD is usually then 
plotted as a function of the period and deep water direction of the 
wave. Such diagrams are given by Munk and Traylor [1947] and Pierson 
[1949]. The isopleths are lines of constant K,D on a polar diagram. 
To prepare such a diagram for application to the refraction of a Gaus- 
sian short crested wave system, it is necessary to invert the diagram 
and plot it as a function of / and 6," where H is the spectral fre-=- 
quency ard Op” is the direction toward which an elemental crest is 
moving just offshore in deep water (e,* is zero when the crest in deep 
water is parallel to the coast). The values on the diagram must also 
be squared point for point. The result is a considerably more rapid- 
ly varying function which will be defined to be the function 
[K,D(# y0_*) 1° as in equation (12.32) and which will be named the 
spectrum amplification function. The function must approach unit 
values as # approaches values of the spectral frequency such that 
the depth is greater than one half of 2mg/p °. 
a7 
