A Note on the Integration of the Vorticity Equation for Quasi-Geostrophic Flow

By the transformation of integrals arising from the solution of the “quasi-geostrophic” equations for barotropic and simple types of baroclinic flow, it is shown that the isobaric height tendency can be expressed in terms of first derivatives of the heights of isobaric surfaces. This demonstrates that the procedure by which the equations are solved must tend to cancel or “average out” the large percentage errors in the geostrophic vorticity advection–i.e. errors in second and third order finite-differences. The height tendency may be computed by a simple graphical procedure, which is carried out directly on analyzed contour charts and which involves a minimum of multiplications.