seaward boundary conditions for high-resolution, limited-area models such as 

 ours. 



The water level response for a given tidal constituent is usually 

 expressed in the following form (Shureman, 1941) in terms of the surface 

 displacement 5: 



C = F(t) A(A,<^) cos [ a)t + X - G (X,^,)] (5.1) 



where X is the longitude, (j) is the latitude, A is the mean amplitude over 18.6 

 years and G the Greenwich phase or epoch at given position (X,<|)), m is tidal 

 frequency, x "is the astronomical argument, while F is the nodal factor, a 

 slowly varying function of time. Tides at particular stations are 

 characterized by A and G for individual constituents. In our study, A's and 

 G's for 5 constituents (01, Kl, PI, S2 and M2) along the open boundaries of 

 our grid are supplied from Reid and Whitaker's model. Surface displacements 

 at the open boundary stations are determined from a linear combination of 

 those due to the five tidal constituents. 



Surface Displacement during a 5-day Simulation (9/20/80 to 9/25/80) 



As a first example, tides during 20 Sept. to 25 Sept. 1980 (GMT) are 

 computed with our three-dimensional model. The surface displacements at four 

 stations (see Figure 5.1 for locations) within the Mississippi Sound are 

 compared with measured data in Figure 5.4. Notice that the measured data have 

 been filtered such that variations due to short-period oscillations on the 

 order of a few hours or less are not included. In the beginning, diurnal 

 tides dominate over the semi-diurnal tides. Towards the end of the five-day 

 period, the diurnal tides become somewhat less predominant while the 

 semi-diurnal tides became gradually more apparent. Good agreement is found at 

 all stations. 



Surface displacement over the coastal area at the end of the third day of 

 simulation is shown in Figure 5.5. The results exhibit variation in surface 

 displacement from nearly zero along the open boundary to -7 cm within the 

 Mississippi Sound, indicating the phase difference in tide. 



76 



