On the computational noise of finite-difference schemes used in ocean models

Open Access
Publisher Website
Google Scholar
Abstract
As a guide for the choice of finite-difference schemes for use in ocean modeling, different distributions of variables over the horizontal array of grid points in an ocean circulation model are investigated using the shallow water equations. Numerical and analytical techniques are used to study the types of computational noise present in each grid system. It is shown that the B-scheme (in which the horizontal velocity is carried at the center and the height field is carried at each corner of a rectangular grid) with diffusive dissipation successively suppresses numerical noise in a coarse grid (> 100 km) ocean model. For fine-scale resolution (<50 km), as in mesoscale ocean eddy models, it is shown that the C-scheme (in which the zonal velocity is carried at points to the east and west of the point of a rectangular grid where the height is carried, with the meridional velocity carried to the north and south of the height point) can be free of noise for the gravest mode (as in a two-layer model). DOI: 10.1111/j.2153-3490.1981.tb01761.x