On the plane wave perspective of the tropospheric Kelvin waves

Two separate dynamics have been used to understand the vertical structure of the Kelvin waves. Stratospheric Kelvin waves have been interpreted in terms of plane gravity waves, where the waves pump their energy upward. On the other hand, the characteristics of the tropospheric Kelvin waves have been interpreted as a superposition between low orders (mostly the first and second) baroclinic modes, which are expected under the hypothesis that the tropopause acts as a rigid lid. We used Fourier transformation to isolate the dynamical fields of the ERA-I reanalysis field into upward and downward phase components. Then, wavelet-based indices have been used to target wavenumber four Kelvin waves centered over the Indian ocean at different phase speeds. We found that the upward-energy waves are settled in the stratosphere, while the downward-energy waves are in the troposphere indicating that the tropospheric Kelvin waves at a single wavenumber behave as plane gravity wave-like their counterpart in the stratosphere. The upward-energy waves in the troposphere were found to follow the structure of the plane Kelvin waves with the zonal wind is in phase with the geopotential height, out of phase with upward wind, and in quadrature with the temperature field.