An inherently mass-conserving semi-implicit semi-Lagrangian discretisation of the shallow-water equations on the sphere

For the shallow-water equations on the sphere, an inherently mass-conserving semi-Lagrangian discretisation (SLICE) of the continuity equation is coupled with a semi-implicit semi-Lagrangian discretisation of the momentum equations. Various tests from the literature (two with analytical nonlinear solutions) are used to assess the model's performance and also to compare it with that of a variant model that instead employs a standard non-conserving semi-implicit semi-Lagrangian discretisation of the continuity equation. The mass-conserving version gives results that are overall somewhat better than the non-conserving one.