A New Method for Solving the Quasi-Geostrophic Omega Equation by Incorporating Surface Pressure Tendency Data

Abstract

A new method for numerically solving the classical quasi-geostrophic omega equation is proposed. The method, in effect, integrates the omega equation upward using two bottom boundary conditions at the top of the boundary layer: ? and ??/?p. The former can be specified by using methods that use only surface data while the latter is calculated using information contained in the horizontal Laplacian of the surface pressure tendency field. As opposed to traditional solutions, the proposed method requires no explicit horizontal boundary condition, requires no data above the level at which ? is desired, nor constrains the static stability. When integrated to the level near the top of the atmosphere where ? is normally taken to be zero, the equation becomes a development equation that is similar to (and is shown to be more complete than) the Petterssen-Sutcliffe development equation. The new method to calculate omega is tested in a simple, analytic atmosphere and the solution is found to satisfy the classical omega equation. Variations on the static stability were found to have important effects in the amplitude of ? as well as the development term. Assuming that the Laplacian of the pressure tendency field can be made free of nonquasi-geostrophic effects, applications are suggested that could improve omega diagnostics in operational meteorology.