Wavenumber-Frequency Spectra of Normal Mode Function Decomposed Atmospheric Data: Departures from the Dry Linear Theory

• Published in: Atmosphere Vol. 14; no. 4; p. 622
• Main Authors: Teruya, Andre S. W., Raphaldini, Breno, Mayta, Victor C., Raupp, Carlos F. M., da Silva Dias, Pedro L.
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.04.2023
• Subjects: Atmospheric circulation; Atmospheric data; Barotropic mode; Convection; convectively coupled equatorial waves; Coupling; Decomposition; Dynamic height; Dynamic meteorology; Equatorial waves; Fields; Frequency spectra; Frequency spectrum; General circulation models; Geopotential; Geopotential height; Gravity; Gravity waves; Height; Kelvin waves; Madden-Julian oscillation; Moist convection; Nonlinear systems; Nonlinearity; normal modes; Observations; Oscillations; Primitive equations; Propagation modes; Rossby waves; Spectra; Spherical coordinates; Theories; Troposphere; Velocity; Wave propagation; Wavelengths; Zonal winds; Brazil
• ISSN: 2073-4433; 2073-4433
• DOI: 10.3390/atmos14040622

The study of tropical tropospheric disturbances has led to important challenges from both observational and theoretical points of view. In particular, the observed wavenumber-frequency spectrum of tropical oscillations has helped bridge the gap between observations and the linear theory of equatorial waves. In this study, we obtained a similar wavenumber-frequency spectrum for each equatorial wave type by performing a normal mode function (NMF) decomposition of global Era–Interim reanalysis data. The NMF basis used here is provided by the eigensolutions of the primitive equations in spherical coordinates as linearized around a resting background state. In this methodology, the global multi-level horizontal velocity and geopotential height fields are projected onto the normal mode functions, characterized by a vertical mode, a zonal wavenumber, a meridional quantum index, and a mode type, namely, Rossby, Kelvin, mixed Rossby-gravity, and westward/eastward propagating inertio-gravity modes. The horizontal velocity and geopotential height fields associated with each mode type are then reconstructed in the physical space, as well as their corresponding filtered versions defined according to the vertical mode classes that exhibit barotropic and baroclinic structures within the troposphere. The results reveal expected structures, such as the dominant global-scale Rossby and Kelvin waves constituting the intraseasonal frequency associated with the Madden–Julian Oscillation. On the other hand, a number of unexpected features, such as eastward propagating westward inertio-gravity waves, are revealed by our observed 200 hPa zonal wind spectrum. Among all possible nonlinear processes, we focus on the analysis of the interaction between Kelvin and westward inertio-gravity waves, providing evidence for their coupling. Apart from the nonlinearity, we discuss the potential roles of a vertically/meridionally varying background state as well as the coupling with moist convection in explaining the departures of the observed spectra from the corresponding linear equatorial wave theory.