A Transfer Function Analysis of Numerical Schemes Used to Simulate Geostrophic Adjustment

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Abstract
Traditional analysis of finite-difference and finite-element schemes used in numerical weather prediction has concentrated almost exclusively on an analysis of the accuracy with which the scheme simulates the phase speeds involved. In this paper we show, using the transfer function formulation common in the design of electrical filters, that these numerical schemes also have important amplitude distortion characteristics, which must be considered in any complete analysis. Our analysis leads to conclusions about the appropriateness of unstaggered arrangements of grid points to primitive equation models commonly used in weather prediction.

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