Observed wavenumber-frequency spectrum of global, normal mode function decomposed, fields: a possible evidence for nonlinear effects on the wave dynamics
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.
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