Representation of Topography by Shaved Cells in a Height Coordinate Ocean Model

TLDR

Height coordinate ocean models typically represent topography as a staircase of discontinuous steps fitted to the grid. This study investigates the use of shaved cells to represent irregular topography. The authors formulate the problem with a finite‑volume method ensuring conservation, and compare partial‑step and piecewise‑linear topography representations against the staircase approach in standard tests such as the topographic β effect and flow over a Gaussian bump. Shaved cells outperform the conventional staircase representation; partial steps, while less accurate than piecewise linear, still surpass the staircase and can be easily implemented in existing models.

Abstract

Height coordinate ocean models commonly represent topography as a “staircase” of discontinuous steps that are fitted to the model grid. Here the ramifications of an alternative approach are studied in which “shaved cells” are used to represent irregular topography. The problem is formulated using the finite-volume method and care is taken to ensure that the discrete forms have appropriate conservation properties. Two representations of topography, “partial step” and “piecewise linear,” are considered and compared with the staircase approach in some standard problems such as the topographic β effect and flow over a Gaussian bump. It is shown that shaved cells are clearly more accurate than the conventional staircase representation. The use of partial steps, although not as accurate as the piecewise linear approach, is seen to be superior to the staircase approach. Moreover, partial steps can be readily implemented in existing height coordinate models.