The CMC–MRB Global Environmental Multiscale (GEM) Model. Part III: Nonhydrostatic Formulation

Abstract

An integrated forecasting and data assimilation system has been and is continuing to be developed by the Meteorological Research Branch (MRB) in partnership with the Canadian Meteorological Centre (CMC) of Environment Canada. Part III of this series of papers presents the nonhydrostatic formulation and some sample results. The nonhydrostatic formulation uses Laprise's hydrostatic pressure as the basis for its vertical coordinate. This allows the departure from the hydrostatic formulation to be incorporated in an efficient switch-controlled perturbative manner. The time discretization of the model dynamics is (almost) fully implicit semi-Lagrangian, where all terms including the nonlinear terms are (quasi-) centered in time. The spatial discretization for the adjustment step employs a staggered Arakawa C grid that is spatially offset by half a mesh length in the meridional direction with respect to that employed in previous model formulations. It is accurate to second order, whereas the interpolations for the semi-Lagrangian advection are of fourth-order accuracy except for the trajectory estimation. The resulting set of nonlinear equations is solved iteratively using a motionless isothermal reference state that gives the usual semi-implicit problem as a preconditioner. The Helmholtz problem that needs to be solved at each iteration is vertically separable, the impact of nonhydrostatic terms being simply a renormalization of the separation constants. The convergence of this iterative scheme is not greatly modified by the nonhydrostatic perturbation. Three numerical experiments are presented to illustrate the model's performance. The first is a test to show that hydrostatic balance at low resolution is well maintained. The second one is a mild orographic windstorm case, where the flow should remain hydrostatic, to test that hydrostatic balance at high resolution is also well maintained. The third one is a convective case taken from the Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX). Although these results are encouraging, rigorous testing of the model's performance for strongly nonhydrostatic flows still remains to be done.