Nonlinear Initialization on an Equatorial Beta-Plane

Joseph J. Tribbia National Center for Atmospheric Research, Boulder, CO 80307

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Abstract

The efficacy of the nonlinear initialization technique for use on global-scale numerical models is tested using a normal-mode, spectral model of the shallow-water equations on an equatorial beta-plane. Despite the nonexistence of strong, frequency separation for the ultralong, equatorially trapped modes, test integrations show that the nonlinear initialization scheme acts to smooth the most rapid oscillations in the system. Further integrations involving only spectral components associated with low-frequency, rotational modes show that the rotational mode trajectories are nearly unaffected by the presence of the balanced gravitational modes. The likely distortion of the divergence field obtained from a rotational-mode-only calculation makes this filtering-through-truncation technique appear unattractive, so an alternative scheme which uses both the truncation and nonlinear initialization schemes is proposed.

Abstract

The efficacy of the nonlinear initialization technique for use on global-scale numerical models is tested using a normal-mode, spectral model of the shallow-water equations on an equatorial beta-plane. Despite the nonexistence of strong, frequency separation for the ultralong, equatorially trapped modes, test integrations show that the nonlinear initialization scheme acts to smooth the most rapid oscillations in the system. Further integrations involving only spectral components associated with low-frequency, rotational modes show that the rotational mode trajectories are nearly unaffected by the presence of the balanced gravitational modes. The likely distortion of the divergence field obtained from a rotational-mode-only calculation makes this filtering-through-truncation technique appear unattractive, so an alternative scheme which uses both the truncation and nonlinear initialization schemes is proposed.

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