The use of the Schmidt transformation in a semi-implicit, semi-Lagrangian formulation for shallow water equations in spherical geometry gives the ability to focus resolution over one particular area of interest. The spectral transform computation is modified, to account for the grid transformation, by solving a linear system in spectral space. This paper will present a formlation for advection of vorticity and divergence that fits well with smooth grid transformations. Numerical results using this formulation for the shallow water test cases will be presented and generalizations to other types of grid transformations will be discussed.