Data-driven modeling of equatorial atmospheric waves: The role of moisture and nonlinearity on global-scale instabilities and propagation speeds

The equatorial region of the Earth's atmosphere serves as both a significant locus for phenomena, including the Madden-Julian Oscillation (MJO), and a source of formidable complexity. This complexity arises from the intricate interplay between nonlinearity and thermodynamic processes, particularly those involving moisture. In this study, we employ a normal mode decomposition of atmospheric reanalysis ERA-5 datasets to investigate the influence of nonlinearity and moisture on amplitude growth, propagation speed, and mode coupling associated with equatorially trapped waves. We focus our analysis on global-scale baroclinic Kelvin and Rossby waves, recognized as crucial components contributing to the variability of the MJO. We examine the dependence of wave amplitudes on the background moisture field in the equatorial region, as measured by total column water vapor. Our analysis demonstrates the crucial role of moisture in exciting these waves. We further investigate the dependence of the propagation speed of the waves on their amplitudes and the background moisture field. Our analysis reveals a robust correlation between the phase speed of the normal modes and their corresponding amplitude, whereas a weaker correlation is found between the eigenmodes' phase speed and the moisture field. Hence, our findings suggest that moisture plays a role in exciting the global-scale Rossby-Kelvin structure of the MJO. In this context, the propagation speed of the eigenmodes is mainly influenced by their amplitudes, underscoring the significant role of nonlinearity in wave propagation.