Numerical Investigations with a Hybrid Isentropic–Sigma Model. Part I: Normal-Mode Characteristics

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  • 1 University of Wisconsin—Madison, Space Science and Engineering Center, Madison, Wisconsin
  • | 2 University of Wisconsin—Madison, Space Science and Engineering Center, Madison, Wisconsin
  • | 3 University of Wisconsin—Madison, Department of Meteorology, Madison, Wisconsin
  • | 4 University of Wisconsin—Madison, Department of Meteorology, Madison, Wisconsin
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Abstract

In a validation experiment of a hybrid isentropic–sigma coordinate primitive equation model developed at the University of Wisconsin (the UW θσ model), an initial value technique is used to investigate numerically the normal-mode characteristics of baroclinically amplifying disturbances over a spectrum of meteorologically significant wavelength. The experiments are designed to determine the impact of coupling an isentropic-coordinate free atmospheric domain to a sigma-coordinate planetary boundary layer (PBL) on the normal-mode characteristics. The growth rate and phase speed spectra of the most unstable normal modes are obtained for an analytically prescribed zonal flow field. The evolution and vertical structure of the kinetic energy, energy conversions, growth rates, and geopotential fields are investigated.

Several modifications have been made to earlier versions of the UW θσ model to overcome noise introduced by adjustments associated with emerging and submerging grid volumes at the sigma–isentropic interface. With these modifications, the hybrid model accurately simulates the evolution and structure of normal-mode baroclinic disturbances for all wavenumbers considered except for wavenumber two. The normal-mode growth rate and phase speed spectra compare well with previous studies using standard sigma coordinate models. There is no evidence of aliasing the baroclinic normal-mode characteristics due to the coupling of isentropic and sigma domains.

Abstract

In a validation experiment of a hybrid isentropic–sigma coordinate primitive equation model developed at the University of Wisconsin (the UW θσ model), an initial value technique is used to investigate numerically the normal-mode characteristics of baroclinically amplifying disturbances over a spectrum of meteorologically significant wavelength. The experiments are designed to determine the impact of coupling an isentropic-coordinate free atmospheric domain to a sigma-coordinate planetary boundary layer (PBL) on the normal-mode characteristics. The growth rate and phase speed spectra of the most unstable normal modes are obtained for an analytically prescribed zonal flow field. The evolution and vertical structure of the kinetic energy, energy conversions, growth rates, and geopotential fields are investigated.

Several modifications have been made to earlier versions of the UW θσ model to overcome noise introduced by adjustments associated with emerging and submerging grid volumes at the sigma–isentropic interface. With these modifications, the hybrid model accurately simulates the evolution and structure of normal-mode baroclinic disturbances for all wavenumbers considered except for wavenumber two. The normal-mode growth rate and phase speed spectra compare well with previous studies using standard sigma coordinate models. There is no evidence of aliasing the baroclinic normal-mode characteristics due to the coupling of isentropic and sigma domains.

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