For point vortex motion on a sphere, the stream function Q is a harmonic function except for logarithmic singularities at vortex locations. For n vortices of strengths Ki present at points Pi, the stream function is given by Q=Q0+sum(Ki*G) where Q0 is stream function of potential flow independent of Pi and Ki. Spherical harmonics are eigenfunctions for Laplace-Beltrami operator on a sphere and for study of atmospheric motion on the planetary scale, superpositional representation by spherical harmonic components of the stream function is often considered for flow over the sphere. Spherical harmonic representation of Q0 for point vortex motion on a sphere enables study of atmospheric vortices and insight into nature and properties of solutions from differential equations point of view. Integration of forecasting differential equations using example of cyclones embedded in such an atmosphere is considered. For low degree and order, the vortical trajectories are shown to be similar to particle advection by the velocity field of Rossby waves on barotropic beta-plane.