where 



Q = [Q c * + Qt!^ 2 



^S* Xr p* J » (->4) 



and K is a nondimensional drag coefficient taken as 2.5 x 10" 3 . 



3. Numerical Algorithm . 



The numerical analogs of equations (40), (41), and (42) are based 

 upon centered difference approximations of all terms (see App. F) . 

 The algorithm treats the time dependency explicitly and employs a 

 computing lattice as shown in Figure 36 in which the transports, Q 

 and Q-p* are computed at the same location but are staggered in 

 time and space with respect to the water level anomaly. This scheme 

 facilitates a simple representation of the Coriolis and bottom stress 

 terms in the difference equations. The surge model allows for vari- 

 able bathymetry and arbitrary coastlines which are represented as a 

 series of connecting straight line segments situated along lines of 

 constant S* or T* . For the simulation of the Hurricane Camille 

 storm surge, the arbitrary coastline feature of the algorithm is 

 mandatory to delineate the delta. However, in the more usual appli- 

 cation, the coast is a straight line in the computing grid. 



The difference equations for Qg*, Q T *, and H at interior 

 points of the computing grid are given by: 



Q s *(i,j,n+1) = (d G 2 + f At G 3 )/(cf + (f At) 2 ) , (55) 

 Q T Ji,j,n+l) = CGi G 3 - f At G 2 )/(Gi + (f At) 2 ) , (56) 



and 



H(i,j,n+1) = H(i,j,n-1) 



At 



F(i,j) : 



F(i+l,j) Q s# (i+l,j,n) - F(i-l,j) Q s *(i-l,j,n) 



y(i) AS* 



F(i,j+1) Q T *(i,j-H,n) - F(i,j-1) Q^(i,j-l,n) 

 v(j) AT* 



(57) 



where i , j , and n indices express the S* , T* , and time 

 coordinates, respectively, and At is the numerical time step. The 

 quantities G^ } G 2 , and G3 are given by: 



Gi = 1 + 2 K At Q(i,j,n-1)/D 2 , 



(58) 



67 



