For the present numerical scheme, the values of wind stress, seabed 

 depths below the undisturbed level, and coriplis effects are presumed 

 supplied at all discjete positions of i, while S, D, and V are evaluated 

 at i + 1/2. On this basis the numerical analogs of Equations 012], (13], 

 and (14) can be written as follows: 



(AS )"}'} =-^—T CA. - A.^j"*l (16) 



(AS )"^^ = -^^ (f. -H f . J V":,^ (17) 



y l+*5 -^ rsH+l 1 1+1 1+*S 



28^i.^ 



^n 



n+1 



,,^r(B. + B. J (B. + B. J 1 At + V. 1 

 n+1 _ l/2[ri i+l-* + ^ 1 1+1^ ■* i+h Qg-) 



i*^^ [l+K] V", |At(D-2) n+lj 



where the overbar signifies the spatial average of B at the specified time 

 levels and A and B are defined as 



2 

 A = k W cos e 



B = k W^ sin e 



The ordinal number n represents the previous time level and n+1 

 represents the new time level. The values of D can be regarded as the 

 total water depth at a position centered between x. and x.^^. The total 



water depth at any specified position not only depends upon the mean water 

 depth and storm- induced setUp, but also on the effects of setup due to 

 pressure, astronomical forces, and the initial sea level - provided there 

 is a departure from the normal level. Thus, the total water depth at a 

 time midway between two time levels is given by 



, d. + d. , S, + S, 

 n+i-a^ 1 1+1 ^ ^ A A 5 . S )" , 

 i+h 2 e 2 ^ X y"^i+% 



where S = initial setup 



S = setup due to astronomical forces 

 S. = atmospheric pressure setup. 



Specification or determination of these setups will be discussed in more 

 detail later. The total water depth at the new time level is given by 



17 



