the # ,® plane which determines the 9 cutoff values. Note that 
the @ cutoff values do not depend upon time, and that for a given 
storm and a given point of forecast, they are fixed once and for 
all for all forecasts. Note the complete symmetry upon reflection 
in the © equals zero axis of the coordinate system as given by 
the equation. Only the first quadrant is shown in figure 24 for 
this reason. 
Determination of the F cutoff values 
In equation (9.62), the ratio, H/cos 6, mast lie between 
two fixed numbers, once top? Do and x are fixed. An equation of 
the form, -H/cos @ = const, is an equation of a circle in the 
#,@ polar coordinate system which passes through the two points 
(PH = 0,0 = 7/2, and # = const/cos @),9 = 6p). The circle has 
a center on the line © = 0. The intersection of the two curves 
H/cos 0 = const, and M/cos © = const, and the two lines, 
© = Op + Ae, and © = ©) - Aé,, then determines an area in the 
/@,® plane bounded by segments of two straight lines and two 
ecimedesye 
In equation (9.63) in which cos 6) has replaced cos 0, 
H., is given by t.)/2R and #, by g(t,, - D,)/2R. Figure 15 can 
then be employed, upon reading R for x, to find the band width 
and the upper and lower cutoff values for the point and the time 
of the forecast. In the M,® plane the area bounded by pm = Ha 
b= Hy, © = Op + A®, and © = 6) - Ae, then determines the 
edges of the filter given by equation (9.63) once x, y, Wso tops 
and D, are given. (D, is ten hours for figure 15, but the 
extension to any value of D, is simple. ) 
Sah 
