Contributions of Convectively Coupled Equatorial Rossby Waves and Kelvin Waves to the Real-Time Multivariate MJO Indices

The real-time multivariate (RMM) Madden-Julian oscillation (MJO) indices have been widely applied to diagnose and track the progression of the MJO. Although it has been well demonstrated that the MJO contributes to the leading signals in these indices, the RMM indices vary erratically from day to day. These variations are associated with noise in the outgoing longwave radiation (OLR) and wind data used to generate the indices. This note demonstrates that some of this "noise" evolves systematically and is associated with other types of propagating modes that project onto the RMM eigenmodes. OLR and zonal wind data are filtered in the wavenumber-frequency domain for the MJO, convectively coupled equatorial Rossby (ER) waves, and convectively coupled Kelvin waves. The filtered data are then projected onto the RMM modes. An example phase space associated with these projections is presented. Linear regression is then applied to isolate the wave signals from random variations in the same bands of the wavenumber frequency domain, and the regressed data are projected onto the RMM EOFs. Results demonstrate the magnitudes of the contributions of the systematically evolving signals associated with these waves to variations in the RMM principal components, and how these contributions vary with the longitude of the active moist deep convection coupled to the waves.