are used to denote discrete points in space and time, respectively. The 

 quantities Ax and At are allowed to be nonuniform spacings along the 

 traverse line and time increments, respectively. The finite difference 

 forms of Equations 3-61, 3-62, and 3-63 are then given as follows: 



Ax 





n + l 



(As,)r.v! 



^^^- If +f \ v"""^ 





1 



B.- + B.>i)" + (B.- + B.^,) 



n + l 



At + V 



+ 'A 



l + K|V«,^JAt(D-)-^^ 



(3-65) 

 (3-66) 



(3-67) 



where A and B are the kinematic forms of the wind stress given by: 



A = k W cos 



B == k W^ sin 



(3-68) 

 (3-69) 



The time step specified by the ordinal number n represents a time 



level at which AS^, AS^, and V are known, while n+l represents the 



new time level for which the quantities AS^, ^Sy and V are to be 

 determined. 



The total water depth at the mid-interval between two time steps is 

 given by: 



i + Js 2 ^ 



„n „n + l 



^A ■*■ ^A 



+ (s. + s),;,^ 



<^ 



(3-70) 



(%),• + {^Ap)i + l]" + [(%).■ + {^Ap)i + lY^'] 



where 



Sg = initial setup 



S^ = astronomical tide 



S^p — atmospheric pressure setup. 



3-105 



