Articles | Volume 7, issue 1
Geosci. Model Dev., 7, 407–417, 2014

Special issue: Isaac Newton Institute programme on multiscale numerics for...

Geosci. Model Dev., 7, 407–417, 2014

Development and technical paper 21 Feb 2014

Development and technical paper | 21 Feb 2014

Inherently mass-conservative version of the semi-Lagrangian absolute vorticity (SL-AV) atmospheric model dynamical core

V. V. Shashkin1,2 and M. A. Tolstykh1,2 V. V. Shashkin and M. A. Tolstykh
  • 1Institute of Numerical Mathematics, Russian Academy of Sciences, 8, Gubkina St., 119333 Moscow, Russia
  • 2Hydrometeorological Centre of Russia, 11–13, Bol. Predtechenskiy lane, 123242 Moscow, Russia

Abstract. The semi-Lagrangian absolute vorticity (SL-AV) atmospheric model is the global semi-Lagrangian hydrostatic model used for operational medium-range and seasonal forecasts at the Hydrometeorological Centre of Russia. The distinct feature of the SL-AV dynamical core is the semi-implicit, semi-Lagrangian vorticity-divergence formulation on the unstaggered grid. A semi-implicit, semi-Lagrangian approach allows for long time steps but violates the global and local mass conservation. In particular, the total mass in simulations with semi-Lagrangian models can drift significantly if no a posteriori mass-fixing algorithm is applied. However, the global mass-fixing algorithms degrade the local mass conservation.

The new inherently mass-conservative version of the SL-AV model dynamical core presented here ensures global and local mass conservation without mass-fixing algorithms. The mass conservation is achieved with the introduction of the finite-volume, semi-Lagrangian discretization for a continuity equation based on the 3-D extension of the conservative cascade semi-Lagrangian transport scheme (CCS). Numerical experiments show that the new version of the SL-AV dynamical core presented combines the accuracy and stability of the standard SL-AV dynamical core with the mass-conservation properties. The results of the mountain-induced Rossby-wave test and baroclinic instability test for the mass-conservative dynamical core are found to be in agreement with the results available in the literature.