We describe a method to improve both the accuracy and computational
efficiency of a given finite difference scheme used to simulate a
geophysical flow. The resulting modified scheme is at least as
accurate as the original, has the same time step, and often uses the
same spatial stencil. However, in certain parameter regimes it is
higher order. As examples we apply the method to the shallow water
equations, the Navier-Stokes equations, and to a sea breeze model.