Different splitting techniques are applied in the context of semi-Lagrangian semi-implicit approach to develop computationally efficient scheme. Vertical decoupling permits to apply simpler explicit calculations for slow vertical modes and transforms the 3D elliptic equation arising on each time step of the scheme to a set of 2D elliptic problems. By time splitting, the last are reduced to 1D problems, which admit an efficient direct solver. Finally, the space splitting diminishes the amount of operations due to approximation of the physically insignificant terms with lower order of accuracy. Application of these techniques results in an efficient scheme with time step chosen according to accuracy consideration and the amount of calculations proportional to the number of spatial grid points. Performed numerical experiments show good computational performance of the algorithm and accuracy of forecasting meteorological fields.