A mass-conservative version of the semi-implicit semi-Lagrangian HIRLAM

A mass-conservative version of the semi-implicit semi-Lagrangian High-Resolution Limited-Area Model (HIRLAM) is presented. The explicit continuity equation is solved with the so-called cell-integrated semi-Lagrangian (CISL) method. To allow for long time steps, the CISL scheme is coupled with a recently developed semi-implicit time-stepping scheme that involves the same non-complicated elliptic equation as in HIRLAM. Contrarily to the traditional semi-Lagrangian method, the trajectories are backward in the horizontal and forward in the vertical, i.e. cells moving with the flow depart from model layers and arrive in a regular column, and their vertical displacements are computed from continuity of mass and hydrostatic balance in the arrival column. This involves just two-dimensional upstream integrals and allows for a Lagrangian discretization of the energy conversion term in the thermodynamic equation. Preliminary validation of the new model version is performed using an idealized baroclinic wave test case. The accuracy of the new formulation of HIRLAM is comparable to the reference version though it is slightly more diffusive. A main finding is that the new discretization of the energy conversion term leads to more accurate simulations compared to the traditional 'Eulerian' treatment.