A nonhydrostatic model with a generalized vertical coordinate

The advantages of a hybrid coordinate representation which is isentropic in the free atmosphere are that it dynamically provides high resolution near the tropopause and fronts, and that truncation error of vertical advection terms virtually vanishes in the adiabatic limit.A complete set of compressible and nonhydrostatic equations framed in generalized vertical coordinates are introduced. The hybrid coordinate is implemented by prescribing the vertical velocity in the coordinate space subject to the conditions that its associated grid locations generally follow isentropic surfaces, and that the grid locations always vary monotonically in z. In this respect, the current set of equations represents a nonhydrostatic generalization of the hybrid isentropic system used with success in hydrostatic models.The numerical system has been tested using a series of two-dimensional mountain wave simulations. In the case of steep and tall mountains; it is found that the system is flexible and robust enough to simulate nonlinear flow phenomena, such as rotors, which represent serious obstacles to traditional entropy-related coordinate models.In addition, a three-dimensional dry baroclinic simulation has been used to compare the hybrid coordinate model with a traditional z coordinate model. It is found that the hybrid coordinate model has slight advantages over the z coordinate model in prediction of upper-level PV gradient near the tropopause and fronts