Two modulated vortex methods for the study of large scale atmospheric or oceanic flow are presented. In particular the methods discussed are based on the equations for the conservation of potential vorticity. The point vortex method is shown to be first order accurate in frequency and second order accurate in group velocity. The blob method presented is shown to be second order accurate in frequency and group velocity. Although the blob method is more accurate it is less efficient than the point vortex method. Currently fast methods exist for the point vortex method but not for the blob vortex method. A methodology for choosing the blob radius is given. These methods are used to calculate the behavior of a modon.