energy averaged over y and t are the new point of observation 
is only one fourth of what it was at the closer point. The wave 
height which is (crudely) proportional to the square root of the 
average potential energy therefore decreases like 1/Rk. 
In particular, for waves observed on the x axis, at large 
values of x, Ap= gD,/2x and Ao = W./x. The effect of the 
short crestedness of the sea surface at the source is then of 
the same order of magnitude as the effect of dispersion, and the 
average potential energy decreases like 1/x°. Consequently, the 
actual short crestedness of waves from a storm at sea cannot be 
neglected in an adequate wave forecasting theory. 
At this point, reference is made to H.O. Publication No. 604, 
Techniques for Forecasting Wind Waves and Swell. This book contains 
the lates theory for forecasting significant waves as developed 
by Sverdrup and Munk. Consider, in particular, Plate VI of the 
above publication. It can also be found as figure 3 in Forecasting 
Ocean Waves by Munk and Arthur [1951]. It gives values of Hp/Hp as 
functions of T,. For T, in the plate, equal to 10 seconds, Hp/Hp 
is 0.8 at 200 nautical miles, 0.63 at 400 nautical miles, 
0.43 at 800 nautical miles, and 0.26 at 1600 nautical miles. The 
numbers squared are given by 0.64 at 200 nautical miles, 0.40 at 400 
nautical miles, 0.17 at 800 nautical miles and 0.07 at 1600 nauti- 
cal miles. Roughly these values decrease by a little more than 
one half as the decay distance is doubled. 
The theory discussed above in this paper says that at great 
distances the values should decrease by one fourth as the decay 
distance is doubled. The methods employed in the derivation of 
the theory on which the figure in H.0O. Pub. No. 604 is based, 
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