A conservative leapfrog time stepping method

This paper addresses the issue of the non conservation of tracer that occurs when a leapfrog time stepping scheme is used in association with a Robert-Asselin time filter within the framework of a time varying vertical coordinate system. A re-formulation of both the forcing and filtering terms that provides a globally conservative scheme is presented. Local conservation is then achieved when the model levels and subsequently the sea surface height satisfy a local compatibility condition. The properties of the resulting scheme are illustrated by a global coupled ocean–sea ice model based on the Nucleus for European Modelling of the Ocean (NEMO).