A non-hydrostatic global spectral dynamical core using a height-based vertical coordinate

Most of the dynamical cores of operational global models can be broadly classified according to the spatial discretisation into two categories: spectral models with mass-based vertical coordinate and grid point models with height-based vertical coordinate. This article describes a new non-hydrostatic dynamical core for a global model that uses the spectral transform method for the horizontal directions and a height-based vertical coordinate. Velocity is expressed in the contravariant basis (instead of the geographical orthonormal basis pointing to the East, North and Zenith directions) so that the expressions of the boundary conditions and the divergence of the velocity are simpler. Prognostic variables in our model are the contravariant components of the velocity, the logarithm of pressure and the logarithm of temperature. Covariant tensor analysis is used to derive the differential operators of the prognostic equations, such as the curl, gradient, divergence and covariant derivative of the contravariant velocity. A Lorenz type grid is used in the vertical direction, with the vertical contravariant velocity staggered with respect to the other prognostic variables. High-order vertical operators are constructed following the finite difference technique. Time stepping is semi-implicit because it allows for long time steps that compensates the cost of the spectral transformations. A set of experiments reported in the literature is implemented so as to confirm the accuracy and efficiency of the new dynamical core.