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Normal mode initialization of a regional barotropic primitive model

Normal mode initialization algorithms of first and second order accuracy are formulated for a regional barotropic model. The initialization algorithms are implemented on the actual data of 500hPa level in different spatial resolutions using a potential enstrophy conserving Eulerian scheme due to Sadourney for time integration. If the linearized Potential vorticity qe, which is left unchanged during the normal mode initializations, is constructed based on the initial geopotential height Z only, and if the geostrophic wind associated with Z is used to define the boundary conditions needed to solve the modified Helmholtz equations involved, then the initialization algorithm will exhibit an undesirable sensitivity to spatial resolution. This sensitivity reflects different behavior of small and large scales as regards balance. But if q e is constructed based on the distribution of both Z and relative vorticity ^ of the initial wind field, and if the geostrophic wind associated with the q e thus constructed is used to define the boundary conditions, then consistent results at different spatial resolutions will be obtained. Qualitatively, the results of the first and second order algorithms are indistinguishable. By measuring the time variation of an Euclidean norm for the departure of actual states from their approximately balanced-state counterparts determined by the two initialization algorithms during 48 hours numerical integrations, the superiority of the second-order algorithm is demonstrated, particularly for the first 24 hours of integration.