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Filter Properties of Spectral transformations

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  • 1 Meteorologisches Institut der Universität München, München, Germany
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Abstract

Recently, a special group of global spherical coordinate transformations has been introduced in order to focus attention on the interactions of an enlarged spectral band of only one selected area, while de-focusing the rest of the globe and thus keeping the overall cost low.

Applied to spherical harmonic expansions, the filter properties are studied diagnostically and prognostically. In the former case, the low-pass character of the filter is displayed by application to while noise and to locally sounding bell-shaped functions among others. In the latter case, the shallow-water equations are integrated for different kinds of focusing. Also the equations have been perturbed in order to simulate still smaller scale effects and test their implications in the current context.

Locally the variably resolving harmonics behave like untransformed harmonies of the same actual local degree. No fading due to resolution gradients is observed. In order to set up a meaningful simulation only meteorological aspects of the scales supplied have to be observed.

Abstract

Recently, a special group of global spherical coordinate transformations has been introduced in order to focus attention on the interactions of an enlarged spectral band of only one selected area, while de-focusing the rest of the globe and thus keeping the overall cost low.

Applied to spherical harmonic expansions, the filter properties are studied diagnostically and prognostically. In the former case, the low-pass character of the filter is displayed by application to while noise and to locally sounding bell-shaped functions among others. In the latter case, the shallow-water equations are integrated for different kinds of focusing. Also the equations have been perturbed in order to simulate still smaller scale effects and test their implications in the current context.

Locally the variably resolving harmonics behave like untransformed harmonies of the same actual local degree. No fading due to resolution gradients is observed. In order to set up a meaningful simulation only meteorological aspects of the scales supplied have to be observed.

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