d. + d. , , 



d"\i = -1 111 . s . s^^ 



1+% 2 e A 



1/2 [(S, ). + (S, ). ,] 

 "-^ Ap-^i Ap'^i + 1-' 



(S + S ) '/ , 



n+1 



Ap^ 



(20) 



The components o£ storm setup, S and S , 



S = y (AS ). 



s = y (AS ). 



(21) 

 (22) 



In other words, the total wind setup for any discrete position along the 

 traverse is the setup in that reach and the accumulation of setups in all 

 reaches seaward of that reach. It should be noted that in Equations (19) 

 and (20) , an error is introduced each time D is evaluated since the term 

 (_S-^ + Sy) is taken at the previous time level and should be the value at 



time level n+^ for Equation (19) and at n+1 for Equation (20). This is, 

 of course, due to the fact that the correct values are unknown at those 

 time levels and an approximation is taken. This error, however, is small 

 provided that increments in time and space are not taken too large. 



For problems of this sort it is customary to assume for initial con- 

 ditions that the system at t = to is at equilibrium state which infers 

 that the current velocities are zero and the water surface is uniform. 

 For the present case, this implies that V is zero and S is uniform for 

 the system. Although for actual conditions the system seldom, if ever, 

 would be in a complete state of equilibrium. After a suitable lapse of 

 time, this is usually of little consequence, since eventually the response 

 of the system reflects only the effects of the forcing functions. 



Calculations are initiated at the seaward boundary, and then stepped 

 forward through all prescribed spatial positions to the boundary at the 

 shore. The same process is repeated by commencing again at the seaward 

 boundary. This procedure is continued for the entire temporal range. For 

 any discrete position along the traverse line, V, at the new time level is 

 first evaluated based on V at the previous time level as well as B and D 

 as the average value in the domain of x + ^x and t + At . A knowledge of 

 V at the new time level (Equation (18)) allows determination of x and y 

 components of setup (Equations (16) and (17)). The total water level 

 rise at the coast can then be evaluated by a summation of the components - 

 those related directly to the meteorological storm and those unrelated - 

 as follows: 



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

 y Ap e A W I 



C23) 



