easily resolved with a regular rectangular grid. Because of the second 

 problem, estimate on bottom flow and stress may be distorted. Although an 

 irregular grid spacing may be used at the bottom to better resolve the 

 topography, it makes the finite difference treatment of the bottom cells more 

 cumbersome. 



The second type of grid is a vertically-stretched grid, the so-called 

 o-stretching, which leads to a smooth representation of the topography and, 

 additionally, the same order of vertical resolution for the shallow and deeper 

 parts of the water body. Basically, the vertical coordinate z is transformed 

 into a new coordinate o: 



z-c(x.y.t) , „,, 



° " h(x.y)n(x,y.t) ^''"'^ 



Using this relationship, the water column at any location between z=c and 

 2=-h is transformed into a layer between a=0 and o=-l. (Figure 2.1). This 

 transformation introduces additional terms to the equation of motion 

 (Appendix A). However, most of the additional terms introduced by the 

 stretching are contained in the horizontal diffusion terms. Since horizontal 

 diffusion is generally small compared to the vertical diffusion and horizontal 

 advection, only the leading terms need to be retained in general. Significant 

 simplification of the equations may result if one assumes that i;<<h and hence 

 o=2/h. However, this assumption may lead to some error if one intends to 

 apply the model to shallow waters where flooding and drying of land may occur 

 during storm surges. 



28 



