Qg*'Ci,j,n-l) + f At Q T ^(i,j,n-l) 



g At D 



vj(i'j F(i,j) AS^ 



H(i+l,j,n) - H(i+l,j,n) 



H(i-l,j,n) + H B ti-l,j,n) + 2 At x^ , 



(59) 



G 3 = Q T ^Ci,j,n-l) - f A Q s *(i,j,n-1) 



g At D 



v(j) F(i,jD AT* 



- H(i,j-l,n) + H_(i,i-l,n) 



H(i,j+l,n) - H B (i,j+l,n) 



2 At t_ , 



where 



D(i+l,j,n) + D(i-l,j,n) + D(i,j+l,n) + D(i,j-l,n) 



In order to maintain numerical stability, the time step must 

 satisfy the condition: 



At < 



Fyv AS* AT" 

 Gi 



/gD 



where 



G h = [(p AS*) 2 + (v AT*) : 



(60) 



(61) 



(62) 



(63) 



and the minimum value of the right-hand side of relation (26) is 

 implied. Thus, a search of the grid is required for a proper selection 

 of At . However, the conditions along the seaward boundary usually 

 limit the time step because of the deeper water. 



The values of p , v , F , and 6 given by equations (44) , (45) , 

 (46) and (49) , are required at the appropriate computational grid 

 points. A numerical spline under tension is employed to interpolate 

 E, given the IM values of S (S*) . The scale factor, y , is 

 determined by: 



P(i) 



5(1+1) - g(i-D 



2AS* 

 i = 1,2 • • - IM , 



(64) 



69 



