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Jonathan W. Smith and Peter R. Bannon

1. Introduction Atmospheric convection is nonhydrostatic. For example, for deep convective phenomena such as thunderstorms, the vertical pressure gradient, and buoyancy forces are not in balance. Because the depth scale of deep convection is comparable to the density-scale height, the use of compressible and/or anelastic models is warranted. The compressible model contains the acoustic, Lamb, and buoyancy waves; the anelastic model retains only the buoyancy waves. The presence of acoustic and

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Joon-Hee Jung and Akio Arakawa

; Clark 1979 ; Takahashi 1981 ; Lipps and Hemler 1986 ; Redelsperger and Sommeria 1986 ; Tao and Soong 1986 ; Kogan 1991 ; Khairoutdinov and Randall 2003 ; and many others). The three-dimensional cloud models developed so far can be classified into two families: one based on the anelastic system of equations and the other on the fully compressible system of equations. Whether they are anelastic or fully compressible, most of the three-dimensional cloud models formulate the dynamics of convection

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Jun-Ichi Yano, Pierre Bénard, Fleur Couvreux, and Alain Lahellec

environment; but can be generalized for various different processes such as convective downdrafts, or even various mesoscale subcomponents such as stratiform clouds. The goal of the present paper is to present a model that is simply constructed by subdividing the gridbox domain into subcomponents. Unlike the standard mass-flux parameterization, this model however introduces no further approximations nor hypotheses. For this goal, the present study adopts a nonhydrostatic anelastic model (NAM) as a full

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Marcin J. Kurowski, Damian K. Wojcik, Michal Z. Ziemianski, Bogdan Rosa, and Zbigniew P. Piotrowski

motivation of developing a robust high-resolution limited-area nonhydrostatic model. According to the COSMO Science Plan ( Baldauf 2010b , 16–20; Baldauf 2015 , 25–31) it is required that a dynamical core has basic conservative properties, which allows for a robust treatment of discontinuities and strong gradients ( LeVeque 2002 ). One of the project branches involves the implementation and testing of an anelastic dynamical core of the Euler–Lagrangian (EULAG) model ( Prusa et al. 2008 ; www2.mmm

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Rupert Klein, Ulrich Achatz, Didier Bresch, Omar M. Knio, and Piotr K. Smolarkiewicz

1. Introduction Ogura and Phillips (1962) derived the original anelastic model through systematic formal asymptotics using the flow Mach number as the expansion parameter. Their goal was to derive a set of model equations that would simultaneously represent internal gravity waves and the effects of advection while suppressing any sound modes. Such a model would not only cast the notion that compressibility plays only a subordinate role in the majority of atmospheric flow phenomena in

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Rupert Klein and Olivier Pauluis

–Stokes equations have been developed with the specific goal of filtering out specific types of motions. The Boussinesq approximation ( Boussinesq 1903 ) is probably the best known of these. It filters out sound waves by replacing the continuity equation by an incompressibility condition. The anelastic and pseudoincompressible approximations have further expanded the mathematical framework to account for large vertical variations of pressure and density and are the basis for a wide range of numerical models

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Daniel Hodyss and David S. Nolan

: 1) the disturbance time scale is set by the buoyancy frequency, and 2) the perturbations of potential temperature are small and about an isentropic reference state. Wilhelmson and Ogura (1972) extended this model by incorporation of vertical variations in the potential temperature of the reference state. This allowed for the application of the anelastic system to environments that are not isentropic, but at the cost of losing energy conservation. Lipps and Hemler (1982) revisited the

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

is over the closed fluid volume V . Substituting from the anelastic version of Poisson’s relation, yields the required constraint on the pressure: where the vapor mixing ratio r υ and virtual potential temperature are derived prognostically and H ρ is the density scale height. We note that the constants in (1.6) and (1.8) would have to be generalized to be functions of time if open boundaries are employed in limited area models. Section 2 presents an analytic study of the problem of

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Olivier Pauluis

results implies that this anelastic model simultaneously obey the first and second laws of thermodynamics. Sections 4 and 5 address some implications of this result. For example, analysis of the entropy and energy budgets such as that in Pauluis and Held (2002) can provide an estimate of the work produced by the atmosphere. In section 4 , it is shown that, under the anelastic approximation, the same considerations yield a constraint on the vertically integrated buoyancy flux. This is illustrated

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Akio Arakawa and Celal S. Konor

1. Introduction The nonhydrostatic anelastic system of equations (called the anelastic system in this paper) is widely used in theoretical and numerical studies of small-scale nonacoustic motions, such as turbulence and convection, while most large-scale models use the compressible quasi-hydrostatic system (the “primitive equations,” called the quasi-hydrostatic system in this paper) as the dynamics core. Both of these systems filter vertically propagating sound waves, but they do so in quite

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