Some Space-Time Spectral Analyses of Tropical Convection and Planetary-scale Waves
Harry H. Hendon and Matthew C. Wheeler
2008: J. Atmos. Sci., 65, 2936-2948.
Abstract
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 wavenumber 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 wind 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 and thus 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.