cm i"! - I Afi.j) * Afi+l,j) 

 1 '- J 2 AS* AT* u(i) v(j) 



(70) 



1,2 



IM . 



The angle, 6 , relating the orientation of the stretched shelf 

 coordinate system to the x,y plane is determined at grid points, 

 excluding j = 1 and JM , by the following smoothing procedure: 



8(1, j) 



6 + (i-l,j) + 6 + (i,j-l) + 9 + (i + l,j) + e + (i,j + i) + 4 e T ( i , j ) 



1.2 • • • IM , 



2.3 ■ • • JM- 1 , 



(71) 



,t . 



where 6' is given by equation (44). Along the sea and coastline 

 boundaries we have 



(i,l) = 



(i-1,1) + 26 1 (i,2) 



) + (i+l,l) + 40 + (i,l) 



(72) 



and 



0(i,JM) = 



i = 1,2 • • • IM , 



+ (i-l,JM) + 26'(i,JM-l) + e'(i+l,JM) + 4e'(i,JM) 

 i = 1,2 • • • IM . 



(73) 



4 . Boundary Conditions . 



A wall condition is employed in the surge simulation along the 

 coast while the surface elevation anomaly is placed in equilibrium 

 with the atmospheric pressure along the seaward boundary. Vanishing 

 normal derivatives of transport are specified on the lateral open 

 boundaries. This condition is used by Jelesnianski (1965, 1966) and 

 Forristall (1974), although it may not be the most desirable (Reid, 

 1975). 



In the x,y plane the coast is curved making the wall (coast) 

 and lateral boundary conditions difficult to apply in a rectilinear 

 grid system. However, the stretched shelf coordinate system repre- 

 sents the coast as: 



= 



(74) 



or, the analog is simply, 



71 



