heights are assumed to have a Rayleigh distribution in deep water and this dis- 

 tribution is used to characterize wave heights as the waves move into shallower 

 water until a depth is reached where the waves begin breaking. Goda's approach 

 allows the broken waves to reform at a lower height, so that the wave height 

 distribution is no longer described by the Rayleigh distribution. As the waves 

 move into shallower water the nonlinear method developed by Shuto (1974) is 

 used to estimate wave shoaling coefficients. Shuto' s method of calculating 

 shoaling coefficients usually gives somewhat higher waves than would be pre- 

 dicted using the conventional linear shoaling method. Nonlinear shoaling is 

 consistent with the observed behavior of waves in shallow water and is conserv- 

 ative when compared to linear shoaling. 



The offshore beach profile is assumed to be represented by a straight plane 

 surface. Dissipation of wave energy by bottom friction is usually very small 

 for typical sand beaches; therefore, bottom dissipation is neglected. 



Wave setup or setdown and surf beat are related to the wave breaking process 

 and are accounted for in the model. The radiation stress (i.e., wave-induced 

 transport or momentum) of the waves progressing toward the shore causes wave 

 setup which can either increase or decrease the local water depth; a decrease 

 is often referred to as setdown. Setdown occurs seaward of the breaker zone 

 and setup occurs shoreward from the point where a significant number of the 

 waves break. Surf beat is the longer period component of water level oscillation 

 (periods from 20 seconds to several minutes) due to longer period irregularities 

 in wave action. The magnitude of the surf beat is amplified in shallow water. 

 Figure 2 shows the conditions used in this model. 



Deep Water 



Effective Water 

 Level 



Setup, S* 



Point of Interest 

 m, Average bottom slope 

 one -half to one wavelength 

 seaward of the point of interest 



Non- Rayleigh 



^ Rayleigh 



Wave Height 

 Local Wove Height Distribution 



Figure 2. Definition sketch. 



Wave Height 



Deepwater Wave Height 



Distribution 



14 



