424. In calculation of the wave height distribution across shore at a 

 specific time-step, the beach profile from the previous time-step is used, and 

 the transport rates are calculated explicitly. The mass conservation is 

 written in difference form as 



1 



At 2 



k+i k+i k k 



4i+l Hi Ri+l Mi 



Ax Ax 



(41) 



where k denotes the time level and i the cell number over which the 

 discretization is carried out. 



425. The equation of mass conservation is discretized over two time 

 levels using transport rates evaluated at the present and previous time -step. 

 To obtain a realistic description of the wave height distribution across 

 highly irregular profiles exhibiting bar formations, a moving average is used 

 to obtain representative depth values. Averaging of the profile depth, 

 carried out over a distance of three breaking wave heights as determined from 

 Equation 25, was found to make the model numerically more stable. If the wave 

 calculations are not based on a beach profile which has been filtered to some 

 degree, the wave height will respond in an unrealistic manner to small changes 

 in the profile. The beach profile generated with the moving average scheme is 

 used only for calculation of the wave height distribution, and no changes in 

 the profile itself are made. 



426. Since the transport rate distribution is determined using various 

 relationships in various regions of the profile, the derivative of the 

 transport rate may be discontinuous at inter-region boundaries. To obtain a 

 smoother transport rate, a three-point weighted filter is applied to the 

 calculated transport rates. The wave height distribution is calculated 

 explicitly in a manner similar to that of Dally (1980), proceeding from the 

 most seaward cell onshore until the end of the surf zone is detected. The 

 advantage of using an explicit solution scheme is that it easily allows 

 description of initiation of breaking, switching to the breaker decay model, 

 and reformation of broken waves. Use of an implicit solution scheme would 

 considerably complicate the calculation and require an iterative procedure 



174 



