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Ludwig Umscheid and Peter R. Bannon

Abstract

Three finite-difference global grids [the original Kurihara (OK), a modified Kurihara (MK) and latitude- longitude (LL)] are tested by comparing numerical solutions with a barotrpic free-surface model to a high-resolution control run and by comparing forecasts with a general circulation model to observations.

With the free surface model, 30-day integrations are made for three different resolutions of each grid and with three initial conditions two mathematical patterns and one 500 mb observed field. The LL grid performed well on the mathematical patterns, especially the case with zonal wavenumber 4. The numerical solutions with the high resolution MK grid also performed satisfactorily for both mathematical patterns. The OK grid did not perform as well, particularly on the case with zonal wavenumber 1. For the observed case, the LL grid in general had lower rms errors although the solutions did not depend as strongly on the three different grid types as the solutions for the mathematical patterns.

For the three-dimensional cases, the GFDL nine-level model was used for 14-day forecasts for observed conditions in March and 3-day forecasts in November. Forecast sensitivity to the different grids is low for short range. The MK grid had the lowest 500 mb rms errors for the duration of both forecasts. Both the MK and LL grids were free of the problem of anomalously high geopotential heights over the North Pole that occurred with the OK grid.

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Jonathan W. Smith and Peter R. Bannon

Abstract

The response to an instantaneous diabatic warming and the resulting hydrostatic and geostrophic adjustment in compressible and anelastic models is examined. The comparison of the models includes examining the initial conditions, time evolution, potential vorticity, and both the traditional and available energetics. Between the two models, the buoyancy flow fields and potential vorticity perturbations are qualitatively and quantitatively similar. Traditional and available energetics can both be accurately conserved within the models. There are some short-lived (e.g., several minutes) differences in the model solutions as the compressible model undergoes an acoustic adjustment that contains vertically propagating acoustic waves and horizontally propagating Lamb waves. The acoustic waves are effectively eliminated in an upper-level numerical sponge layer using Rayleigh damping. Moreover, the relative computational efficiency and accuracy of the two models are assessed.

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Peter R. Bannon, Jeffrey M. Chagnon, and Richard P. James

Abstract

Numerical anelastic models solve a diagnostic elliptic equation for the pressure field using derivative boundary conditions. The pressure is therefore determined to within a function proportional to the base-state density field with arbitrary amplitude. This ambiguity is removed by requiring that the total mass be conserved in the model. This approach enables one to determine the correct temperature field that is required for the microphysical calculations. This correct, mass-conserving anelastic model predicts a temperature field that is an accurate approximation to that of a compressible atmosphere that has undergone a hydrostatic adjustment in response to a horizontally homogeneous heating or moistening. The procedure is demonstrated analytically and numerically for a one-dimensional, idealized heat source and moisture sink associated with moist convection. Two-dimensional anelastic simulations compare the effect of the new formulation on the evolution of the flow fields in a simulation of the ascent of a warm bubble in a conditionally unstable model atmosphere.

In the Boussinesq case, the temperature field is determined uniquely from the heat equation despite the fact that the pressure field can only be determined to within an arbitrary constant. Boussinesq air parcels conserve their volume, not their mass.

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