The Use of Linear Filtering as a Parameterization of Atmospheric Diffusion

TLDR: In this article, a simple linear filter of order n is adapted for use in numerical models of the large-scale circulation to act in place of an explicit horizontal diffusion term in the equations.

Abstract: A simple linear filter is adapted for use in numerical models of the large-scale circulation to act in place of an explicit horizontal diffusion term in the equations. The filter can be shown to be ideally suited for this purpose in the sense that it can be made increasingly scale-dependent as the order of the filter is increased. The one-dimensional filter of order n is constructed from n three-point symmetrical operators and involves 2n/1 grid points. It is capable of eliminating two-grid-interval waves completely, yet allowing little or no damping of longer waves. In one space dimension, the use of the n = 1 order filter can be shown to be equivalent to the incorporation of a one-dimensional Fickian diffusion term in the differential equation. For any order n, the use of the one-dimensional filter is equivalent to the incorporation of a one-dimensional linear diffusion of order 2n. It is therefore apparent that as n increases, the ability of the filter to discriminate in its response to short-...