since there is a half time step between yc! and y. and a full time step 

 between yc. and yc! . In finite difference form, Equation 21 becomes: 



yc! = 2B 1 (Q! - Q! + 1 ) + yc. (22) 



A major goal has been achieved by arriving at Equation 22, because the seawall 

 constraint must be formulated in terms of yc-points. The implementation of 

 the constraint is similar to that for the explicit scheme, and only an outline 

 will be given. 

 Correction at a minus area 



68. As in the explicit scheme, transport adjustments start at a minus 

 cell and from there are performed in the direction of transport. For the mi- 

 nus cell itself, the adjustment resembles that expressed by Equation 6 and 

 reads as follows: 



yc - ys. 

 Q ! = 2(yc. - yf) Q i {23a) 



yc . - ys . 



Q' (23b) 



*i+-1 " 2(yc. - y|) x i+1 



Substitution of these corrected values into Equation 22, and using Equa- 

 tion 13, verifies that the desired result has been obtained, i.e., 



yc! = y Si (24) 



Finally, the corresponding corrected shoreline position is computed from Equa- 

 tion 13 as 



y°i 



(25) 



The corrected position is thus found to lie halfway between the previous ex- 

 tremal position, yc^ , and the seawall. 



Correction at a regular 

 cell, positive transport 



69. Corrections are made by moving in the positive x-direction. Since 



the transport rate into the cell has already been adjusted in connection with 



29 



