Semi-Lagrangian semi-implicit locally one-dimensional scheme for hydrostatic atmospheric model

A semi-Lagrangian semi-implicit locally one-dimensional scheme is considered for a regional atmospheric model. Vertical decoupling allows to separate the principal fastest physical components approximated by the semi-implicit method of the second order accuracy from the secondary slowest modes integrated explicitly with the first order of accuracy. Horizontal splitting is applied to the principal vertical modes in order to reduce the implicit part of equations to one-dimensional elliptic problems solved efficiently by the direct solver. This approach allows to reduce the computational cost of a single time step when compared to traditional schemes. Numerical experiments with actual atmospheric fields showed that the developed scheme is efficient and supplies the accurate forecast fields using time steps up to 40 min.