11. In a design situation, H' , F , and g are assumed or known, 

 and R is the vertical distance the monochromatic wave would run up the 

 structure if the slope were built high enough to prevent overtopping 

 (Figure 1). 



-LIMIT OF WA VE RUNUP 



Figure 1 . Wave runup definition sketch 



Chapter 7 of the SPM describes how to estimate R . Weggel calculated the 

 empirical coefficients, Q* and a , for the situations tested by Saville. 

 These empirical coefficients are presented in the SPM (1984), Figures 7-24 

 through 7-32. The 

 Figure 2. 



12. To apply Weggel 's equation to a sea of irregular waves, Ahrens 

 (1977a) assumes that the distribution of runups (R's) caused by an irregular 

 sea will follow a Rayleigh distribution. Ahrens estimates the overtopping 

 rate by summing the overtopping contributions from the individual runups, 



Q* - a figure for 1:3 smooth slopes is reproduced here in 



199 



"SPM 



= iqq X. Q i 



i=1 



(3) 



where 



^SPM = vol 1 ™ 6 fate of overtopping caused by irregular waves, L /T 

 Q,- = volume rate of oyer topping caused by one runup in the runup 



j. = volume rate of overtopping 

 distribution, L /T , or 



Qi = 



e Q o( H s) 



1/2 



exp 



0.217 . . -1 

 tanh 



(4) 



