Semi-Lagrangian semi-implicit regional atmospheric model with multigrid solver

In the last decade the semi-Lagrangian semi-implicit numerical integration schemes are being used in increasing range of atmospheric models. We present a finite difference semi-Lagrangian semi-implicit scheme applied to adiabatic baroclinic regional model of atmosphere. To achieve a computationally economic scheme we apply a vertical decoupling linear transformation and calculate the fastest vertical mode tendencies by semi-implicit semi-Lagrangian scheme and the lowest mode tendencies by simple explicit semi-Lagrangian scheme. The vertical decoupling permits also to reduce the 3D elliptic problem of the semi-implicit part to set of 2D ones. The latter are solved by efficient multigrid methods. The criteria of stability of multilevel fully discretized scheme is derived to demonstrate the possibility of using the increased time steps. The efficiency of proposed variant of semi-Lagrangian semi-implicit scheme is evaluated. Numerical experiments on South region of Brazil are carried out and some estimations are presented.