PART III: ANALYSIS OF DATA AND DEVELOPMENT 

 OF RUNUP FORMULAS 



11. The biggest difficulty with analyzing the data from the NCE study 

 was making accurate estimates of the zero-moment wave height FL at the toe 

 of the structure. In the NCE study the wave heights were measured offshore in 

 a water depth 25 cm greater than at the toe of the structure. Due to shoaling 

 and breaking, a wide range of offshore wave conditions can yield the same 

 zero-moment wave height in shallow water. Therefore, the offshore wave height 

 is not as useful as the wave height at the toe of the riprap structure. The 

 wave conditions near the structure correlate well with the runup and often can 

 be estimated accurately by depth-limited considerations. Originally in the 

 NCE study the wave heights at the toe were estimated by using the method of 

 Goda (1975) which accounts for shoaling and breaking of irregular waves. 

 However, after scrutinizing the information generated by Goda's model, it was 

 observed that for some situations the method yielded values of H^/dg 

 greater than 0.8 which is higher than has been observed in any of CERC's wave 

 tank calibration tests. Because of this limitation, it was decided to try and 

 develop another method to estimate FL at the toe of the structure. 



12. Several methods were tested to account for the wave shoaling and 

 breaking between the offshore gages and the toe of the structure. The method 

 that worked best was a hybrid method which combined linear-wave shoaling with 

 the relation given by Hughes (1984) as 



H 

 mo 



sr 



ji 



H 

 mo 



(S) 



\3/4 



(1) 

 JO 



where 



L = Airy wave length calculated at those depths for the period of 

 peak energy density T 



I and = inshore and offshore water depths, respectively 



From wave-tank calibration tests it has been found that the approximate 

 limiting value for the zero-moment wave height is given by 



'2ird 

 = 0.10 tanh ( -j- 1 ) 



