Rescaled height coordinates for accurate representation of free-surface flows in ocean circulation models

Conventional height coordinate models have previously represented free-surface variations by a variable thickness upper layer. We present a rescaled height coordinate, which we call z∗, that treats the time-dependent free surface as a coordinate surface. This coordinate is isomorphic with the atmospheric η coordinate, sometimes known as the step-mountain coordinate. The z∗ coordinate has also been used in a coastal ocean model. However, unlike both these implementations, here we use the finite volume method within the z∗ coordinate framework, allowing an accurate representation of topography. The resulting scheme provides a very accurate representation of motions over steep topography in a three-dimensional general circulation model, even with fast and large amplitude free-surface variations.