Abstract
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.
Highlights
1.1 Motivation for the researchThe modern atmospheric models used for long-range forecasting or climate change modeling should treat concentrations of the greenhouse gases and certain other atmospheric constituents as prognostic variables
The SL-AV dynamical core (SLAV-MC) dynamical core conserves the global mass up to machine precision, whereas the standard SLAV dynamical core with the mass fixer turned off produces the monotonic global mass decrease that amounts to 0.02 % of the total atmosphere mass during the month integration of the test case initial conditions on the 640 × 400 grid
The quantitative assessment of the similarity and difference between the SLAV-MC solution and reference solution from the T340 spectral SL dynamical core of the CAM3 atmospheric model is available via the l1, l2, and l∞ surface pressure difference norms defined in Jablonowski and Williamson (2006a)
Summary
The modern atmospheric models used for long-range forecasting or climate change modeling should treat concentrations of the greenhouse gases and certain other atmospheric constituents as prognostic variables. The mass field of such constituents is characterized by the local and global mass conservation in the absence of sources and sinks and chemical transformations. Treatment of the atmospheric constituent concentrations as the prognostic variables is a difficulty for the semiLagrangian (SL) models that is well known to violate both local and global mass conservation. The approach for consistent coupling between the discrete tracer transport and continuity equations in the SISL shallowwater model is implemented by Wong et al (2013). Lauritzen et al (2008) developed the inherently mass-conservative, limited-area SL dynamical core for HIRLAM model using floating Lagrangian vertical levels. This article presents the cell-integrated, mass-conservative discretization of the continuity equation in the SISL framework for the semi-Lagrangian absolute vorticity (SL-AV) global atmospheric dynamical core. We consider this research as a first step towards the hydrostatic SL dynamical core with mass-conservative and consistent tracer transport (as discussed in Wong et al, 2013), the tracer transport problems are beyond the scope of the article
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