In quantitative and qualitative assessment of the numerical algorithms for barotropic primitative equations, comparision with the real atmosphere can not be used as the main criterion to determine the accuracy of the algorithms. This holds particularly for limited-area applications when boundary conditions add to the difficulties of determining the true solution. The complexity comes from a combinations of the barotropic primitive model error, the numerical algorithm error, and errors in the way data are assimilated to the model. It is thus necessary to use ever increasingly our dynamical knowledge of the behavior of the solutions of the barotropic primitive, or shallow water, equations in the process of determining the accuracy of numerical algorithms. A useful approach here is to study balanced (vortical) and imbalanced (gravity waves) parts of the flows, and their interaction. In spite of the limitations faced when working with real-atmosphere data, such study can uncover some important information on the working of the algorithms. Having this objective in mind, the present paper is devoted to the study of spatio-temporal behavior of balanced and imbalanced parts in three numerical algorithms for the regional barotropic primitive equation. The algorithms are: the potential enstrophy conserving Eulerian algorithm of Sadoumy (1975), and two algorithms derived from Sadoumy’s algorithm by simply changing the prognostic variables from :momentum-geopotential height to (i) Rossby potential vorticity (PV), divergence, geopotential height, (ii) PV, divergence, and ageostrophic vorticity. In the latter two algorithms, PV is solved by a standard semi-Lagrangian method using piecewise bicubic interpolation and the other prognostic variables are solved by the proper use of Sadoumy’s algorithm for momentum components and geopotential height. Compared with the Eulerian algorithm of Sadourny, the PV-based algorithm shows a marked improvement in the representation of both balanced and imbalanced parts of the flow.
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