The Relative Importance of Resolution, Accuracy and Diffusion in Short-Range Forecasts with the NCAR Global Circulation Model

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  • 1 National Center for Atmospheric Research, Boulder, Colo. 80307
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Abstract

A series of 5-day forecasts is made with the National Center for Atmospheric Research (NCAR) Global Circulation Model (GCM) starting from the National Meteorological Center (NMC) analysis of 0000 GMT 11 January 1973. The six-layer model, formulated with height as a vertical coordinate, is integrated without mountains. Hemispheric forecasts are made with 5°, 2½° and 1¼° horizontal resolution and second- and fourth-order horizontal, centered finite-difference approximations. Integrations are also carried out with two types of horizontal diffusion. The first, similar to that usually used in the NCAR GCM, has the form ∇ṁK∇, where K is a nonlinear coefficient dependent on the deformation. The second, more scale selective, is of the form ∇2K2, where the nonlinear coefficient K is the same as in the first type.

The eddy kinetic energy and 6 km pressure patterns of the forecasts are examined in detail. The fourth-order approximations result in the same general kinetic energy characteristics as the second-order, with slightly more aliasing. The ∇ṁK∇ diffusion produces excessive damping of all scales especially with the 5° grid, whereas the more scale-selective ∇2K2 diffusion controls the small scales with less damping of the baroclinic scales. The 6 km pressure patterns are examined in terms of root-mean-square errors in spherical harmonic spectral bands with the contributions from both phase and amplitude errors separated. Fourth-order accuracy results in improvements in the phases of the shorter waves (wavenumber 10–18), but not in the largest waves where the second-order approximations have sufficient accuracy. The improvement in the amplitude of the largest scales (wavenumbers 1–3) with the finer resolution can be attributed to the accompanying decreased diffusion rather than more accurate approximations. This amplitude improvement in the largest scales is also seen in 5° forecasts which use a smaller diffusion coefficient, or more scale-selective diffusion, and is accompanied by improvement in the phase of the small scales through more accurate advection.

Abstract

A series of 5-day forecasts is made with the National Center for Atmospheric Research (NCAR) Global Circulation Model (GCM) starting from the National Meteorological Center (NMC) analysis of 0000 GMT 11 January 1973. The six-layer model, formulated with height as a vertical coordinate, is integrated without mountains. Hemispheric forecasts are made with 5°, 2½° and 1¼° horizontal resolution and second- and fourth-order horizontal, centered finite-difference approximations. Integrations are also carried out with two types of horizontal diffusion. The first, similar to that usually used in the NCAR GCM, has the form ∇ṁK∇, where K is a nonlinear coefficient dependent on the deformation. The second, more scale selective, is of the form ∇2K2, where the nonlinear coefficient K is the same as in the first type.

The eddy kinetic energy and 6 km pressure patterns of the forecasts are examined in detail. The fourth-order approximations result in the same general kinetic energy characteristics as the second-order, with slightly more aliasing. The ∇ṁK∇ diffusion produces excessive damping of all scales especially with the 5° grid, whereas the more scale-selective ∇2K2 diffusion controls the small scales with less damping of the baroclinic scales. The 6 km pressure patterns are examined in terms of root-mean-square errors in spherical harmonic spectral bands with the contributions from both phase and amplitude errors separated. Fourth-order accuracy results in improvements in the phases of the shorter waves (wavenumber 10–18), but not in the largest waves where the second-order approximations have sufficient accuracy. The improvement in the amplitude of the largest scales (wavenumbers 1–3) with the finer resolution can be attributed to the accompanying decreased diffusion rather than more accurate approximations. This amplitude improvement in the largest scales is also seen in 5° forecasts which use a smaller diffusion coefficient, or more scale-selective diffusion, and is accompanied by improvement in the phase of the small scales through more accurate advection.

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