Computationally efficient schemes and boundary conditions for a fine-mesh barotropic model based on the shallow-water equations

Two types of computationally efficient semi-implicit and leap-frog schemes for integrating the shallow-water equations are presented. Their accuracy and stability are investigated, both for the pure initial value problem and for limited-area forecasts. The proper formulation of boundary conditions for the latter case is also discussed. Two sets of stable and sufficiently accurate boundary conditions are given. The practical usefulness of these conditions is also supported by computer experiments.