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A new vertical discretization used in the atmospheric dynamics of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) is illustrated, with enthalpy as the thermodynamic prognostic variable to reduce computation in thermodynamic equations while concerning all gas tracers in the model. Mass, energy, entropy, and angular momentum conservations are utilized as constraints to discretize the vertical integration with a finite-difference scheme. A specific definition of a generalized hybrid vertical coordinate, including sigma, isobaric, and isentropic surfaces, is introduced to define pressure at the model levels. Vertical fluxes are obtained by the equation of local changes in variables defined for vertical coordinates at all model layers. The forward-weighting semi-implicit time scheme is utilized to eliminate computational noise for stable integration. Because of time splitting between the dynamic and physics processes, the vertical advection is required both in the ...

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A Multiconserving Discretization with Enthalpy as a Thermodynamic Prognostic Variable in Generalized Hybrid Vertical Coordinates for the NCEP Global Forecast System