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Xingliang Li, Chungang Chen, Xueshun Shen, and Feng Xiao

1. Introduction The nonhydrostatic effects are found to be very important in the meso- and synoptic-scale atmospheric dynamics and have been included in regional models for several decades. Among others, some examples of regional nonhydrostatic dynamical models are the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5; Dudhia 1993 ), Environment Canada’s mesoscale compressible model, version 2 (MC2; Benoit et al. 1997

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Masuo Nakano, Hisashi Yashiro, Chihiro Kodama, and Hirofumi Tomita

global nonhydrostatic model with the finite-volume method is one of the promising tools for achieving the mesh simulation of a few kilometers (or even less; e.g., Miyamoto et al. 2013 ). Using a global nonhydrostatic model with an icosahedral grid system, Yashiro et al. (2016) proposed a new framework for high-resolution large-ensemble data assimilation. In the proposed framework, the simulated grid data are relocated as it is suitable for ensemble data assimilation; owing to this relocation, each

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Robert L. Walko and Roni Avissar

spatial and temporal discretization of the compressible nonhydrostatic Navier–Stokes equations, which we describe in detail. Some aspects of the discretization are unique, while certain others have appeared elsewhere but have not previously been tested in atmospheric model applications. This paper also describes how topography is represented in OLAM, which is by means of shaved grid cells (e.g., Adcroft et al. 1997 ; Marshall et al. 1997 ) on a height–coordinate grid with horizontal surfaces. We

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M. L. Yu, F. X. Giraldo, M. Peng, and Z. J. Wang

1. Introduction Numerical weather prediction (NWP) models have been profoundly influenced by the paradigm shift in high performance computing (HPC). On the one hand, the ever increasing computing power allows researchers to run nonhydrostatic (NH) models at resolutions finer than 10 km ( Steppeler et al. 2003 ; Lynch 2008 ; Marras et al. 2015 ); on the other, both HPC and the intrinsic complex physical processes in NH modeling pose many challenges to the development of numerical methods (e

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Miodrag Rančić, R. James Purser, Dušan Jović, Ratko Vasic, and Thomas Black

1. Introduction This paper describes a cubed-sphere version of a global, nonhydrostatic model of the atmosphere, the Nonhydrostatic Multiscale Model on the B grid (NMMB) (e.g., Janjić et al. 2001 ; Janjić 2003 ; Janjić and Gall 2012 ), developed at the Environmental Modeling Center (EMC) of the National Centers for Environmental Prediction (NCEP). The NMMB was developed in both regional and global modes, the latter using the standard longitude–latitude (or geographical) grid, with polar

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Günther Zängl

found that the hybrid coordinate reduces the cold bias in the polar stratosphere, which is a widespread problem of GCMs. A disadvantage of classical σ – θ hybrid systems making a transition toward strictly isentropic coordinates at some vertical distance from the ground is their limited suitability for nonhydrostatic models. Such models resolve atmospheric motions in which the potential temperature may attain local extrema (e.g., breaking gravity waves), violating the requirement of strict

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Jihyeon Jang and Song-You Hong

1. Introduction Hydrostatic approximation has been used for numerical weather prediction models for several decades in order to allow a longer time step by filtering out vertically propagating sound waves. However, nonhydrostatic models have become necessary, as the resolvable grid spacing in numerical weather prediction increases with continuously improving computing resources. Advancement of new numerical treatments to handle the sound waves, such as the semi-implicit ( Tapp and White 1976

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Lei Bao, Robert Klöfkorn, and Ramachandran D. Nair

1. Introduction With an increased amount of supercomputing resources available to present-day modelers, it is possible to develop global atmospheric models with horizontal grid resolution of the order of a few kilometers. At this fine resolution, the models require a set of nonhydrostatic (NH) governing equations in order to resolve clouds at a global scale ( Tomita et al. 2008 ). However, this necessitates the development of spatial and temporal discretization schemes that are capable of

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William C. Skamarock, Joseph B. Klemp, Michael G. Duda, Laura D. Fowler, Sang-Hun Park, and Todd D. Ringler

1. Introduction Computational capabilities that are expected to be generally available in the near future will enable global atmospheric model applications permitting explicitly resolved nonhydrostatic motions that will require the solution of the nonhydrostatic equations. The applications will likely include both variable-resolution mesh modeling with limited areas allowing nonhydrostatic motions, such as the exploratory efforts in the global nonhydrostatic variable-resolution modeling of Yeh

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Junya Uchida, Masato Mori, Masayuki Hara, Masaki Satoh, Daisuke Goto, Takahito Kataoka, Kentaroh Suzuki, and Teruyuki Nakajima

1. Introduction In regional climate studies, nonhydrostatic, limited-area atmospheric models are used to simulate short- and long-range numerical forecasts and detailed features of local meteorology ( Skamarock et al. 2008 ; Lo et al. 2008 ; Sasaki et al. 2008 ); in those cases, high resolution is normally required to reproduce mesoscale flows and small-scale phenomena that are as important as large-scale flows in local climates. Such limited-area climate models (LAMs) often have resolutions

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