Representation of topography by shaved cells in a height coordinate ocean model

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.