T = 



ds 

 7^= . (38) 



S n (n) o 



where S n is the distance along the isoline of E, , D is the 

 local depth relative to mean sea level, and g is the acceleration 

 due to gravity. The relation between n and T* is given by: 



T* = T*(T(S n (n))) , (39) 



The incremental values of T* are determined from equation (38) 

 subject to the (arbitrary) expansion relationship of T*(T). This 

 relationship is a convenience which permits an additional degree of 

 freedom in adjusting the relative spacing between isolines of n . 

 However, if T* = T , the value of AT* is that which divides the 

 total long wave travel time by an integer number of lines of n • 

 The selection of the final AT* is based upon a compromise for pro- 

 viding adequate resolution for the wind field and the resulting surge 

 with a minimum number of points. The form chosen for the expansion 

 is T = A + B(T*) C where A , B , and C are constants. 



The stretched shelf coordinate system provides a grid system 

 with a finer resolution near the coast than at the 180-meter iso- 

 bath. The expansion curve, S*(Sp) , stretches the horizontal reach 

 of the grid while maintaining a finer grid in the area of landfall 

 of the hurricane. In this manner an economy is achieved in terms of 

 the number of grid points required by the surge program. However, 

 because the preferred expansion curves dictate the locations (in 

 x,y space) of the depths required for the surge calculations, the 

 depth field must be redefined for different pairs of stretching 

 functions. Application of this procedure has been accomplished for 

 the simulation of the storm surges caused by Hurricanes Carla, 

 Camille, and Gracie. Figure 24 shows the trans form- generated coast- 

 line and seaward boundary curves for the western gulf coast area. 

 Also shown is the shelf coordinate system (£,n) which was employed 

 in the Hurricane Carla surge simulation. The track of the hurricane 

 is the dashline. The grid system extends over approximately 750 

 kilometers of coastline. The stretched shelf coordinate system 

 (Figure 25) is attained through the functional relationships speci- 

 fied in Figure 26 for the S* axis and Figure 27 for the T* axis. 

 The shelf coordinate system, the stretched shelf coordinate system, 

 and similar transformation relationships are shown in Figures 28 

 through 31, for the grid used to simulate the storm surge caused by 

 Hurricane Camille, and in Figures 32 through 35 for the grid asso- 

 ciated with the Hurricane Gracie storm surge. 



52 



