Free surface and variable volume in the NEMO code

Historically, the NEMO system (Madec et al. 1998) was built for climate studies using strong hypothesis on the dynamics, such as the “rigid lid” approximation, which eliminates the fast gravity waves. A first improvement (Roullet and Madec 2000) was made by implementing a free surface while filtering the fast external gravity waves, which allows one to keep a large time step. Roullet and Madec (2000) compared a linear formulation (with fixed volume) with a non-linear one (with a variable first level thickness), and concluded that the linear formulation was the best compromise for climate (the linear formulation does not strictly conserve the ocean salt content unlike the non-linear formulation, but the differences were not large enough to play a large role in the experiments of Roullet and Madec (2000)).
People interested in regional and/or coastal studies must simulate rapidly phenomena with short spatial scales, such as tidal waves. With the filtering scheme of Roullet and Madec (2000), these phenomena are very rapidly damped, or not simulated at all (Talandier et al. 2003). That’s why a time-splitting scheme has recently been implemented, which allows the representation of the fast dynamics, while keeping a large time step (Bessières 2003). But this is not sufficient: although the free surface is implemented, the vertical grid of the model is fixed in time. This fact does not allow a good representation of tidal waves, and as mentioned above it precludes an exact conservation of the salt content. This is why the decision was made, as part of the MERSEA European project, to implement a variable volume in the NEMO system.
In this report, we first review the representation of the free surface in the NEMO system, with the different schemes available at the present time (chapter1). Then we introduce the equations of the free surface and the implementations induced by the variable volume (chapter 2). We present two kind of experiments in order to investigate the behaviour of the model with the variable volume implemented; chapter 3 focusses on the conservation of salt content, and chapter 4 on the representation of a gravity wave.