Some space-time spectral analyses of tropical convection and planetary-scale waves

Three aspects of space-time spectral analysis are explored for diagnosis of the organization of tropical convection by the Madden-Julian oscillation (MJO) and other equatorial wave modes: 1) definition of the background spectrum upon which spectral peaks are assessed, 2) alternate variance preserving display of the spectra, and 3) the space-time coherence spectrum. Here the background spectrum at each zonal wave-number is assumed to result from a red noise process. The associated decorrelation time for the red noise process for tropical convection is found to be half as long as for zonal wind, reflecting the different physical processes controlling each field. The significance of spectral peaks associated with equatorial wave modes for outgoing longwave radiation (OLR), which is a proxy for precipitating deep convection, and zonal winds that stand out above the red background spectrum is similar to that identified using a background spectrum resulting from ad hoc smoothing of the original spectrum. A variance-preserving display of the space-time power spectrum with a logarithmic frequency axis is useful for directly detecting Kelvin waves (periods 5-15 days for eastward zonal wavenumbers 1-5) and for highlighting their distinction from the MJO. The space-time coherence of OLR and zonal wind is predominantly associated with the MJO and other equatorial waves. The space-time coherence is independent of estimating the background spectrum and is quantifiable; thus, it is suggested as a useful metric for the MJO and other equatorial waves in observations and simulations. The space-time coherence is also used to quantify the association of Kelvin waves in the stratosphere with convective variability in the troposphere and for detection of barotropic Rossby Haurwitz waves.