## Abstract

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 model dynamics and model physics, and the semi-implicit time scheme is used both in dynamics and after physics computation.

Three configurations—sigma, sigma pressure, and sigma entropy—from the specific hybrid vertical coordinates with layer definition similar to NCEP operational GFS have been implemented in the NCEP GFS. Results from the sigma-isentropic coordinate show the largest anomaly correlation and the smallest root-mean-square error in tropical wind among all results at all layers, especially the upper layers. The scores from a period of daily forecast up to 5 days with the sigma-isentropic coordinate show the same level of skill as compared to the NCEP operational GFS. The results from the hurricane tracks for the fall of 2005 with sigma-isentropic coordinates show better scores compared with the operational GFS.

*Corresponding author address:*Dr. Hann-Ming Henry Juang, NOAA Science Center, Room 207, 5200 Auth Road, Camp Springs, MD 20746. E-mail: henry.juang@noaa.gov