Application of Tschebyscheff Functions to the Vertical Discretization of Atmospheric Models

Discussions are made on the vertical discretization of current global spectral atmospheric model. Based upon Tschebyscheff functions methods are given for integrating the hydrostatic equation and the continuity equation and for computing vertical advection and vertical diffusion. Furthermore, in the case that the vertical derivative of a meteorological element is discontinuous, the measures to be taken are discussed and suggested