correction factor. The roughness and porosity correction factor, r, is 

 the ratio of the runup on a rough permeable or rough impermeable slope 

 divided by the runup on a smooth impermeable slope; i.e., 



R_ (rough slope) 



r = -§ (1) 



R (smooth slope) 



A compilation of r values used for selecting r is shown in a 

 Table from Battjes (1974). The table includes an entry by McCartney and 

 Ahrens (1975) . The values of r as determined by these sources are 

 relatively consistent. 



III. ESTIMATING THE RUNUP DISTRIBUTION 



The approach assumes that the individual wave runup elevations have a 

 Rayleigh distribution of the type commonly associated with the distribu- 

 tion of wave heights at sea. Saville (1962), Saville, McClendon, and 

 Cochran (1962), van Oorschot and d'Angremond (1968), and Battjes (1971, 

 1974), suggest that a Rayleigh distribution for runup is plausible and 

 probably conservative for runup caused by naturally occurring wave condi- 

 tions. The runup distribution is then given by: 



(iZLil/Ei) 1 - 



5> /in (1/p) \ 1/2 

 R 



where R p is the runup associated with a particular probability of exceed- 

 ance, p. For example, assume a desire to know the 1-percent runup, i.e., 

 the elevation exceeded by 1 percent of the runups, then p = 0.01 and 

 equation (2) yields: 



In 



01 



Rs 



m 



1/2 



= 1.517 



This indicates that the 1 -percent runup would be about 52 percent greater 



than R s . A graph of equation (2) showing R p / R s versus p is given in 



a Figure. Note that the percent runup (or wave height) means the percent 



exceedance and not the average value for the given percent as used in 



many sources. The figure or equation (2) can also be used to determine 



the percent exceedance for wave heights (i.e., Hp/H s ) having a Rayleigh 

 distribution. 



IV. EXAMPLE DESIGN PROBLEMS 

 **************** EXAMPLE 1**************** 



To illustrate the application of this approach to irregular wave run- 

 up prediction, consider the example given in SPM (p. 7-24). 



