with a discrete process (50 storm events). Modeling more events would result 

 not only in a smoother curve but also in greater expense. For example, had 

 500 events been modeled, it would be highly unlikely that one height interval 

 would receive the probabilities of several events while the three intervals 

 below received none. Therefore, if an economically feasible number of events 

 were to be modeled, the raw output of the stage-frequency generation would 

 require smoothing to adequately represent a continuous curve. 



90. Smoothing was accomplished using linear regression of the stage- 

 frequency data when plotted on an appropriate probability paper. Equation 17 

 is a formula for the construction of Weibull probability paper. Where 



x new = [~ ln ( x old } ] 



(17) 



the variable * id i- s ^ ne inverse return period, x new is the transformed 

 abscissa value, and c is the variable to be adjusted to best represent the 

 data with a straight line. After numerous trials a c value of 0.80 was 

 chosen. Figure 35 contains a plot of both the raw and regressed stage- 

 frequency curves for the Fox Hill Drawbridge still-water location. 



14 





















12 





































_±^ — ~ 

















^F^ 







ID 

 Z 9 



ll B 



LJ 7 

 O 



If) 



S 



4 

 3 

 2 

























_— — « --=^=^~ 

































































































































































i.s a 



L£GEHD_ 



RETURN PERIOD, YRS 



STAGE-FREQUENCY 



STILL UATER LEUEL 



REGRESSION CHECK 



FOX HILL DRAWBRIDGE 



Figure 35. Example of raw and regressed stage-frequency curve 



67 



