A Mass-Conservative Semi-Implicit Semi-Lagrangian Limited-Area Shallow-Water Model on the Sphere

A locally mass conservative shallow-water model using a two-time-level, semi-implicit, semi-Lagrangian integration scheme is presented. 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.