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Comparative Analysis of Low-Level Cold Fronts: Wavelet, Fourier, and Empirical Orthogonal Function Decompositions

Nimal GamageAstrophysical, Planetary, and Atmospheric Sciences Department, and Program in Atmospheric and Oceanic Sciences, University of Colorado, Boulder, Colorado

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William BlumenAstrophysical, Planetary, and Atmospheric Sciences Department, and Program in Atmospheric and Oceanic Sciences, University of Colorado, Boulder, Colorado

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Abstract

Atmospheric cold fronts observed in the boundary layer represent relatively sharp transition zones between air masses of disparate physical characteristics. Further, wavelike features and/or eddy structures are often observed in conjunction with the passage of a frontal zone. The relative merits of using both global and local (with respect to the span of a basis element) transforms to depict cold-frontal features are explored. The data represent both tower and aircraft observations of cold fronts. An antisymmetric wavelet basis set is shown to resolve the characteristics of the transition zone, and associated wave and/or eddy activity, with a relatively small number of members of the basis set. In contrast, the Fourier transformation assigns a significant amplitude to a large number of members of the basis set to resolve a frontal-type feature. In principle, empirical orthogonal functions provide an optimal decomposition of the variance. The observed transition zone, however, has to be phase aligned and centered to yield optimal results, and variance may not be the optimum norm to depict a front. It is concluded that the wavelet or local transform provides a superior representation of frontal phenomena when compared with global transform methods. Further, the local transform offers the potential to provide some physical insight into wave and/or eddy structures revealed by the data.

Abstract

Atmospheric cold fronts observed in the boundary layer represent relatively sharp transition zones between air masses of disparate physical characteristics. Further, wavelike features and/or eddy structures are often observed in conjunction with the passage of a frontal zone. The relative merits of using both global and local (with respect to the span of a basis element) transforms to depict cold-frontal features are explored. The data represent both tower and aircraft observations of cold fronts. An antisymmetric wavelet basis set is shown to resolve the characteristics of the transition zone, and associated wave and/or eddy activity, with a relatively small number of members of the basis set. In contrast, the Fourier transformation assigns a significant amplitude to a large number of members of the basis set to resolve a frontal-type feature. In principle, empirical orthogonal functions provide an optimal decomposition of the variance. The observed transition zone, however, has to be phase aligned and centered to yield optimal results, and variance may not be the optimum norm to depict a front. It is concluded that the wavelet or local transform provides a superior representation of frontal phenomena when compared with global transform methods. Further, the local transform offers the potential to provide some physical insight into wave and/or eddy structures revealed by the data.

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