Vertical coordinate transformation is used in ocean modelling to provide good representation of the flow near bottom and free surface boundaries and to allow the concentration of grid points in regions of high gradient. A natural treatment of impermeability boundary conditions is achieved by considering transformations which fit the surface and bottom boundaries. This paper develops the governing equations of shallow sea hydrodynamics for a generalised vertical coordinate transformation, which embraces all formulations commonly used in ocean modelling, and allows greater freedom to concentrate grid points in regions of high gradient. In addition to the popular sigma coordinates, various hybrid "sigma-z" coordinate transformations, defined for ad hoc applications, are reviewed. Conservative formulations are proposed for the governing equations, including the pressure gradient and horizontal diffusion terms
