What are convectively coupled equatorial waves?

The left figure shows a longitude-time diagram of CLAUS brightness temperature around the equator. The darker shading (lower brightness temperature) indicates higher cloud top altitude, often associated with deep convective clouds and precipitation. From this figure, you can see that the cloudiness seems to move both eastward and westward at different spatiotemporal scales and speeds. These propagating cloudiness and precipitation are often associated with tropical atmospheric waves called “convectively coupled equatorial waves”.
In a very well-known paper, Matsuno (1966) solved a system of equations that approximate the tropical atmosphere and found that various modes of waves exist in the tropics: Kelvin waves, equatorial Rossby waves, mixed-Rossby gravity waves, and eastward and westward inertio gravity waves. These waves were later discovered to govern a large percentage of day-to-day variability of tropical cloudiness and precipitation from observations (Wheeler and Kiladis, 1999). Although the basic dynamics of these waves are understood, their observed characteristics and variability are not fully understood.
My research interests include understanding how and why the CCEWs vary interannually (e.g., with ENSO), to improve the representation of CCEWs in current weather and climate models, and to understand how the CCEWs modulate regional day-to-day variability of weather such as the diurnal cycle of rainfall and monsoon onset.
Sources:
, , , , and 2009: Convectively coupled equatorial waves, Rev. Geophys., 47, RG2003, doi:10.1029/2008RG000266.
Matsuno, T., 1966: Quasi-geostrophic motions in the equatorial area, J. Meteorol. Soc. Jpn., 44, 25–43.
, 1999: Convectively Coupled Equatorial Waves: Analysis of Clouds and Temperature in the Wavenumber–Frequency Domain. J. Atmos. Sci.,56, 374–399.