Abstract
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, also known as Wheeler-Kiladis diagram, has helped bridging the gap between observations and the linear theory of equatorial waves. Here we have 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, with the NMF basis being given by the eigensolutions of the primitive equations in spherical coordinates, 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 and eastward propagating inertio-gravity modes. The horizontal velocity and geopotential height fields associated with each mode type are then reconstructed on the physical space, and the corresponding wavenumber-frequency spectrum is calculated for the 200 hPa zonal wind. The results reveal some 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, some unexpected features such as westward propagating Kelvin waves and eastward propagating westward inertio-gravity waves are also revealed by our observed 200 hPa zonal wind spectrum. These intriguing behaviours represent a large departure from the linear equatorial wave theory and can be a result of strong nonlinearities in the wave dynamics.
Highlights
In the present study we have analysed the space-time spectrum of equatorial disturbances by computing the wavenumber345 frequency spectrum of normal mode decomposed dynamical fields obtained from the Era-Interim (ERAI) reanalysis data
The large-scale atmospheric dynamical fields are projected onto the normal mode functions defined as the eigensolutions of the compressible primitive equations in spherical coordinates, linearized around a resting background state
355 Our results show some aspects that agree with the linear theory, for instance, the barotropic Rossby modes showing a spectral peak that clearly follows the dispersion relation according to the linear theory
Summary
An important step towards the connection between the equatorial wave theory and observations was initially achieved in Takayabu (1994a), Pires et al (1997) and Wheeler and Kiladis (1999) These studies obtained the wavenumber vs time frequency spectrum of tropical oscillations from either the dynamical field variables or the outgoing long-wave radiation (OLR), revealing a striking correspondence between the observed time frequencies and the theoretical predictions from the linear equa torial wave theory. We use a similar procedure to those documented in Gehne and Kleeman (2012) and Castanheira and 55 Marques (2015), in which the contribution of each mode type to the field variables is obtained from the projection onto the corresponding mode eigenvector rather than the spectral peak bands in the wavenumber-frequency domain In this context, as in Castanheira and Marques (2015), the basis function set associated with the modal decomposition is given by the eigensolutions of the spherical geometry primitive equations linearized around a resting background state. We argue that these discrepancies can be attributed to the role of strong nonlinearities in the wave dynamics
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