aid of the upper part of figure 23. Another important direction 
namely the direction to the point x,,y,, is given by equation (9.61). 
The # -band cutoff points 
The second term in equation (9.56) can be studied as a function 
of # and © for a fixed value of x and tobe The upper and lower 
ranges of integration when set equal to zero, yield the information 
that when # /cos © is less than g(top - D)/2x, the disturbing ele- 
ment in the partial sum will already have passed, and that when 
P/eos © is greater than gt ,/2x the disturbance will not yet have 
arrived. When the © band width is small, the variation of cos ® 
is small and the range of the values determines the range of p 
essentially. 
The square filter for the Gaussian case of a short crested sea 
surface in a disturbance which lasts Do seconds at the edge of 
a storm of width, Ws 
Under the assumption that the Fresnel fringes will cancel out 
because of the finite time of observation, the square cutoff filter 
for this model wave system can be given by equation (9.62). Since 
0,< 8p <0,, and if ©, - 9; is small, the value of H/cos © can be 
approximated by M/eos 8p- 8p is the angular direction of the 
point X59¥,, from the point x = 0, y = 0. The second inequality 
in equation (9.62) can then be multiplied through by cos 6p, and 
the result is a factor of the form (cos Op )/x- The factor, (cos Op )/x 
is simply equal to the reciprocal of the distance a given elemental 
disturbance must travel to reach the point (499) and consequently 
it is equal to 1/R. The value of R is measured from the center of 
the forward edge of the storm to the point of forecast. With this 
= Dee 
