A Mass-conservative semi-implicit semi-Lagrangian limited-area shallow-water model on the sphere

The momentum equations are solved with the traditional semi-Lagrangian gridpoint form. The explicit continuity equation is solved using a cell-integrated semi-Lagrangian scheme, and the semi-implicit part is designed such that the resulting elliptic equation is on the same form as for the traditional semi-Lagrangian gridpoint system.

The accuracy of the model is assessed by running standard test cases adapted to a limited-area domain. The accuracy and efficiency of the new model is comparable to traditional semi-Lagrangian methods.