The solution of equation (316) is very dependent on a correct choice 

 of the roughness coefficient. Only very limited data are presently 

 available for estimating values of the roughness coefficient n. For 

 prototype conditions, the "roughness" may consist of groves of trees or 

 subdivisions of houses. Also, the roughness elements, e.g., trees and 

 houses, may be moved by the waves. 



Bretschneider and Wybro (1976) investigated the effect of bottom 

 friction on tsunami inundation by using the Manning n to describe the 

 roughness of the onshore slope. Although this is not entirely correct 

 (the Manning relationship was developed for uniform flow) , it provides 

 a simple means of investigating the effects of roughness on the limits 

 of inundation. It was shown that decreasing the Manning roughness coef- 

 ficient, n, from n = 0.025 (long grass with brush) to n = 0.015 (short, 

 cut grass and pavement) could increase the distance required for dissipa- 

 tion of the surge by 160 percent (from 670 to 1,770 meters or 2,200 to 

 5,800 feet in the example used, where h g = 10 meters or 33 feet). 

 Bretschneider and Wybro also demonstrated that a bore would be dissipated 

 faster than a tsunami acting as a rapidly rising tide. 



Chan, Street, and Strelkoff (1969) and Chan and Street (1970a, 1970b) 

 use a modified Marker and Cell (SUMMAC) numerical finite-difference tech- 

 nique for calculating the wave runup of solitary waves on a 45° slope and 

 on a vertical wall. Their results compared well with the experimental 

 results of Street and Camfield (1966), but their numerical method was 

 not applied to wave runup on the shoreline for flatter slopes. Heitner 

 (1969) developed a numerical method based on finite elements. However, 

 he provides only limited results for simulating waves in laboratory 

 channels, and the results depend on the choice of a bottom-friction fac- 

 tor and an artificial viscosity. 



Spielvogel (1975) developed a theoretical solution for tsunami runup 

 based on the wave or surge height at the shoreline, h g , and the wave 

 height, H, at the point where the leading edge of the wave is at the 

 shoreline. This relates the runup to the rate of shoaling just before 

 the wave reaches the shoreline, and effectively includes the influence 

 of the bottom slope and the wave period. Replotting Spielvogel' s results 

 into a more usable form gives the equation 



*- = 2 - 94 (317) 



h h 

 s JL _ 0.8 

 H 



Equation (317) indicates that^the higher values of relative runup, R/h s , 

 occur when the values of h s /H are the lowest. Spielvogel indicates that 

 equation (317) is correct for 3.74 > h g /H > 2.12, has limited application 

 where 2.12 > h /H > 1.76, and is invalid where h g /H < 1.76. This latter, 

 invalid case would be a nearshore bore or breaking wave. 



In addition to considering wave runup, it is necessary to consider 

 the drawdown of the water when the wave trough arrives at the shoreline. 



156 



