The NCAR spectral element climate dynamical core: Semi-implicit Eulerian formulation

A prototype dynamical core for the Community Atmospheric Model ( CAM) component of the Community Climate System Model ( CCSM) is presented. The 3D governing primitive equations are specified in curvilinear coordinates on the cubed-sphere combined with a hybrid pressure. vertical coordinate. The horizontal space discretisation is based on a P-N - P-N spectral element variational formulation. A semi-implicit time integration scheme is derived in order to circumvent the severe time step restrictions associated with gravity waves. Eigen-mode decomposition of the vertical structure matrix results in a set of decoupled 2D modified Helmholtz problems which are solved using a preconditioned conjugate gradient iteration. An idealized climate simulation is presented, where the semi-implicit scheme permits a much larger time step.