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Degradation of Numerical Differencing Caused by Fourier Filtering at High Latitudes

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  • 1 Cooperative Institute for Meteorological Satellite Studies, University of Wisconsin, Madison, Wisconsin
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Abstract

In models with latitude-longitude grids it is common practice to filter the fields or their incremental values at high latitudes to remove structures of high zonal wavenumber that would otherwise necessitate excessively short timesteps in the forecast due to the advective stability criterion. The simplest filter to analyze is Fourier truncation, which retains all waves up to a critical zonal wavenumber but eliminates those of higher wavenumber. This critical wavenumber is typically a function of latitude and becomes very small at the subpolar latitude line. This paper presents an analysis of the effect of such filtering on the accuracy of estimated zonal derivatives. The method of analysis chosen enables an assessment of truncation error to be made as a function of the intrinsic spatial scales of the fields and is not compromised by the distortions of the numerical grid itself. A class of modified Fourier filters is proposed that approximately restore the higher zonal wavenumber structures on the innermost latitude circle by smoothly interpolating data from local surrounding circles of the grid. An analysis of the truncation errors of such modified schemes demonstrates that they yield a significant improvement in the attainable accuracy of zonal derivatives.

Abstract

In models with latitude-longitude grids it is common practice to filter the fields or their incremental values at high latitudes to remove structures of high zonal wavenumber that would otherwise necessitate excessively short timesteps in the forecast due to the advective stability criterion. The simplest filter to analyze is Fourier truncation, which retains all waves up to a critical zonal wavenumber but eliminates those of higher wavenumber. This critical wavenumber is typically a function of latitude and becomes very small at the subpolar latitude line. This paper presents an analysis of the effect of such filtering on the accuracy of estimated zonal derivatives. The method of analysis chosen enables an assessment of truncation error to be made as a function of the intrinsic spatial scales of the fields and is not compromised by the distortions of the numerical grid itself. A class of modified Fourier filters is proposed that approximately restore the higher zonal wavenumber structures on the innermost latitude circle by smoothly interpolating data from local surrounding circles of the grid. An analysis of the truncation errors of such modified schemes demonstrates that they yield a significant improvement in the attainable accuracy of zonal derivatives.

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