An Energy Conserving Restoration Scheme for the Shallow Water Equations.
Quarterly Journal of the Royal Meteorological Society
This article is protected by copyright. All rights reserved.
Reason for embargo
The numericalmethods that solve the governing equations in an atmospheric dynamical core are designed to dissipate potential enstrophy and prevent the buildup of kinetic energy at the grid scale. A side effect of this is the dissipation of total energy which should be conserved. Energy fixers are used in climate models to replace the dissipated energy by modifying the temperature in the thermodynamic equation, and stochastic backscatter schemes have also been developed for use in weather prediction models. Here, we present the first steps towards designing a deterministic energy conserving restoration scheme that considers the conversion of kinetic energy to heat, replacing kinetic energy lost due to model error, and the backscatter of kinetic energy. The energy conserving restoration scheme (ECRS) is presented in the context of the shallow water equations on the sphere. It is designed to be used with any existing shallow water equation scheme (called the preliminary scheme) which can adequately dissipate potential enstrophy, and in this paper we use a semi-implicit semi-Lagrangian (SISL) scheme. For each prognostic variable a spatial pattern is chosen; this is added to the preliminary scheme solution, and the amount added is calculated to ensure energy conservation. Results from short-termtest cases show that ECRS and SISL have very similar error norms. For long-term simulations ECRS conserves energy to a good approximation whereas SISL dissipates energy.
Office of Science, U.S. Department of Energy
This is the peer reviewed version of the article, which has been published in final form at DOI 10.1002/qj.2713. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
Quarterly Journal of the Royal Meteorological Society, 2015