The generalized vertical coordinates has been developed in NCEP GFS, it is designed in the way to have possibility to run model in sigma, sigma-pressure, sigma-theta, and sigma-theta-pressure combining coordinates. Since the model equation set changed from specific sigma coordinates to generalized coordinate, the discretization of the model prediction equations have to redo. The conservations of mass, momentum, total energy and potential temperature existed in the differential equations are considered in the differencing form of the equations.
The performance of the first version of generalized vertical coordinates showed that the results from sigma-theta coordinates have better performance as compared to those from sigma and sigma-pressure coordinates. Half year of parallel tests from generalized vertical coordinates GFS in sigma-theta indicated consistently less root mean square error over tropical areas. Also the performance of hurricane season on 2005 showed better track prediction as compared to operational and ready-to-implemented parallel versions of GFS.
However, there existed negative thickness once or twice per month, which ruined the prediction.
In order to solve the negative model layer thickness, positive-definited advection was considered with semi-Lagrangian advection. Some results will be presented.