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Spectral Budget Analysis of the Short-Range Forecast Error of the NMC Medium-Range Forecast Model

Masao KanamitsuDevelopment Division, National Meteorological Center, Washington, D.C.

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Suranjana SahaDevelopment Division, National Meteorological Center, Washington, D.C.

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Abstract

The budget of the systematic component of the short-range forecast error in the National Meteorological Center's Medium-Range Forecast Model (NMC MRF) is examined. The budget is computed for the spectral coefficients and the variances of vorticity, divergence, virtual temperature, and specific humility at every time step during the 24-h model integration. Two months in winter and three months in summer, totaling 150 cases, were integrated with the budget diagnostics. The results of the budget of the spectral coefficients—that is, the budget of mean error—showed compensation among large terms except near the model boundary; therefore, it is difficult to point to a significant source of the systematic error in the free atmosphere. Near the model lower boundaries, dynamics cannot fully compensate physical forcing, and estimation of some physical processes responsible for the mean errors is possible. In contrast, the budget of the variance of the coefficients—that is, the energy budget—is more interesting and informative. The most apparent problem found in the model is a loss of rotational kinetic energy in the medium (total wavenumber n = 11–40) and small (n = 41–80) scales in the free atmosphere. About 50% of the loss is explained by the excessive horizontal and vertical diffusion. There is a strong indication that the rest of the loss of kinetic energy is related to the insufficient generation of available potential energy in the medium scale.

To isolate further the cause of the error in the energetics, several forecasts with budget diagnostics were performed. The experiments showed complex interactions between the physics and dynamics and among the different physical processes. Particularly noteworthy are (a) the compensation between horizontal and vertical diffusion and (b) the balance among horizontal/vertical diffusion, the barotropic scale interaction, and the baroclinic conversion terms in the rotational kinetic energy equation. The results of this study guided the design and implementation of changes in the NMC model in the horizontal diffusion and the cumulus parameterization.

Abstract

The budget of the systematic component of the short-range forecast error in the National Meteorological Center's Medium-Range Forecast Model (NMC MRF) is examined. The budget is computed for the spectral coefficients and the variances of vorticity, divergence, virtual temperature, and specific humility at every time step during the 24-h model integration. Two months in winter and three months in summer, totaling 150 cases, were integrated with the budget diagnostics. The results of the budget of the spectral coefficients—that is, the budget of mean error—showed compensation among large terms except near the model boundary; therefore, it is difficult to point to a significant source of the systematic error in the free atmosphere. Near the model lower boundaries, dynamics cannot fully compensate physical forcing, and estimation of some physical processes responsible for the mean errors is possible. In contrast, the budget of the variance of the coefficients—that is, the energy budget—is more interesting and informative. The most apparent problem found in the model is a loss of rotational kinetic energy in the medium (total wavenumber n = 11–40) and small (n = 41–80) scales in the free atmosphere. About 50% of the loss is explained by the excessive horizontal and vertical diffusion. There is a strong indication that the rest of the loss of kinetic energy is related to the insufficient generation of available potential energy in the medium scale.

To isolate further the cause of the error in the energetics, several forecasts with budget diagnostics were performed. The experiments showed complex interactions between the physics and dynamics and among the different physical processes. Particularly noteworthy are (a) the compensation between horizontal and vertical diffusion and (b) the balance among horizontal/vertical diffusion, the barotropic scale interaction, and the baroclinic conversion terms in the rotational kinetic energy equation. The results of this study guided the design and implementation of changes in the NMC model in the horizontal diffusion and the cumulus parameterization.

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