z-coordinates with surface layer insertion/removal for accurate representation of free-surface flows in ocean models

Ocean model performances are highly related to the vertical coordinate system implemented. We study geo-potential (or z-) coordinates and we focus on the numerical treatment of the moving free surface. Typically z-coordinate models are coded with a surface layer with varying but not-vanishing thickness, which limits the vertical resolution in areas with high tidal range. We propose a z-coordinate algorithm that, thanks to the insertion and removal of surface layers, can deal with an arbitrary large tidal oscillation independently of the vertical resolution. The algorithm is based on a classical two steps procedure used in numerical simulations with moving boundaries (grid movement followed by a grid topology change) which leads to a stable and accurate numerical discretization. With ad-hoc treatment of advection terms at non-conformal edges that may appear due to insertion/removal operations, mass conservation and tracer constancy are preserved. This algorithm can be reverted, in the particular case when all layers are moving, to other surface-following z-coordinates, such as z-star. With a simple truncation error analysis and realistic numerical experiments, we show the performances of z-coordinates with surface layer insertion/removal in coastal environments.