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The deep-atmosphere Euler equations in a non-approximated shallow-atmosphere-alike form
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    The deep-atmosphere Euler equation set has been derived into a form similar to the shallow-atmosphere Euler equation set without any approximation, which makes it more convenient to evolve any existing shallow-atmosphere dynamics model to deep-atmosphere dynamics.The deep atmospheric dynamics system is a fully non-approximated Euler equation set, which includes all-dimensional Coriolis force, vertically expanded cells (r=a+z), and geocentric gravitational force with height. The deep-atmosphere Euler equation in spherical height coordinates was transferred into spherical generalized vertical coordinates with pseudo horizontal wind in NCEP Office Note 477 (Juang 2014). The deep-atmosphere continuity equation in generalized vertical coordinates can be easily converted into a shallow-atmosphere-alike form by introducing scaled horizontal winds and scaled height with a hydrostatic relationship in generalized coordinates to represent density. The relationship provides a coordinate pressure change with respect to scaled height for a given density. From this relationship we can use geopotential height to define scaled vertical motion, thus all the three-dimensional winds in deep-atmosphere dynamics can be replaced by scaled winds. Since all winds are using a scaled form, the momentum equations are converted into scaled momentum equations with scaled terms plus some add-on terms. [doi:/10.7289/V5/ON-NCEP-488: http://doi.org/10.7289/V5/ON-NCEP-488]

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