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Identifying Convectively Coupled Equatorial Waves Using Theoretical Wave Eigenvectors

H. Reed OgroskyDepartment of Mathematics, University of Wisconsin–Madison, Madison, Wisconsin

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Samuel N. StechmannDepartment of Mathematics, and Department of Atmospheric and Oceanic Sciences, University of Wisconsin–Madison, Madison, Wisconsin

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Abstract

Convectively coupled equatorial waves (CCEWs) are often identified by space–time filtering techniques that make use of the eigenvalues of linear shallow water theory. Here, instead, a method is presented for identifying CCEWs by projection onto the eigenvectors of the theory. This method does not use space–time filtering; instead, wave signals corresponding to the first baroclinic Kelvin, Rossby, and mixed Rossby–gravity (MRG) waves are constructed from reanalysis data by a series of projections onto (i) vertical and meridional modes and (ii) the wave eigenvectors. In accordance with the theory, only dry variables, that is, winds and geopotential height, are used; no proxy for convection is used. Using lag–lead regression, composites of the structures associated with each eigenvector signal during boreal summer are shown to contain all the features of the theory as well as some additional features seen in previous observational studies, such as vertical tilts. In addition, these composites exhibit propagation in good agreement with the theory in certain regions of the tropics: over the eastern Pacific ITCZ for the Kelvin and MRG composites and over the Pacific warm pool for the Rossby composite. In these respective regions, the Kelvin eigenvector signal is also in good agreement with space–time-filtered outgoing longwave radiation (OLR), and the Rossby and MRG eigenvector signals are in reasonable agreement with space–time-filtered OLR; it is shown that the eigenvector projections used here contribute to this agreement. Finally, a space–time-filtered version of the eigenvector projection is briefly discussed, as are potential applications of the method.

Corresponding author address: H. Reed Ogrosky, Department of Mathematics, University of Wisconsin–Madison, 480 Lincoln Dr., Madison, WI 53706-1325. E-mail: ogrosky@math.wisc.edu

Abstract

Convectively coupled equatorial waves (CCEWs) are often identified by space–time filtering techniques that make use of the eigenvalues of linear shallow water theory. Here, instead, a method is presented for identifying CCEWs by projection onto the eigenvectors of the theory. This method does not use space–time filtering; instead, wave signals corresponding to the first baroclinic Kelvin, Rossby, and mixed Rossby–gravity (MRG) waves are constructed from reanalysis data by a series of projections onto (i) vertical and meridional modes and (ii) the wave eigenvectors. In accordance with the theory, only dry variables, that is, winds and geopotential height, are used; no proxy for convection is used. Using lag–lead regression, composites of the structures associated with each eigenvector signal during boreal summer are shown to contain all the features of the theory as well as some additional features seen in previous observational studies, such as vertical tilts. In addition, these composites exhibit propagation in good agreement with the theory in certain regions of the tropics: over the eastern Pacific ITCZ for the Kelvin and MRG composites and over the Pacific warm pool for the Rossby composite. In these respective regions, the Kelvin eigenvector signal is also in good agreement with space–time-filtered outgoing longwave radiation (OLR), and the Rossby and MRG eigenvector signals are in reasonable agreement with space–time-filtered OLR; it is shown that the eigenvector projections used here contribute to this agreement. Finally, a space–time-filtered version of the eigenvector projection is briefly discussed, as are potential applications of the method.

Corresponding author address: H. Reed Ogrosky, Department of Mathematics, University of Wisconsin–Madison, 480 Lincoln Dr., Madison, WI 53706-1325. E-mail: ogrosky@math.wisc.edu
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