The forecasting problem for a sea level surface represented by 
short crested waves, a Gaussian Lebesgue Power Integral, and 
ee ES SS SS ES ST 
the disturbance exists everywhere and has the same character every- 
where, once E,(# ,®) is fixed. If the disturbance were observed 
as a function of y and t at x = 0, it would be represented by 
equation (9.53). The limit of the partial sum given in equation 
(9.54) is again a representation for equation (9.53). 
In order to produce a localized storm, instead of a disturb- 
ance everywhere, the representation given by equation (9.54) can 
be multiplied by a slowly varying function of y and t as given 
by F(y,t). For a particular example, F(y,t) can be represented 
by equation (9.55). Other functional forms for F(y,t) with smooth- 
er sides might be employed for somewhat more realistic results, 
but the form given in equation (9.55) at least has the property 
that the area covered by the waves has a finite width and that 
the waves are of finite duration at the source. Waves produced 
by storms in nature are not so sharply defined as this model. 
The argument now follows the same line as the one which was 
used in equation (7.39). If F(y,t) as given in equation (9.55) 
is applied to 7(0,y,t) as given in equation (9.54), the disturb- 
ance which results is observed at the source only over a distance 
of length Wy and only for a time Doe If the disturbance is ob- 
served within the time interval indicated, it will be indistinguish- 
able from a similar short observation at any time and place in 
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