1. Pentad OLR (1979-98) was band-passed by complex demodulation with a central period of 60 days and half-power limits of 42 and 108 days. (Other band-pass limits were tried and the results are similar).
Results of the bandpass can be viewed in the first set of plots on the MJO page.
2. A second time series was formed from the band-passed OLR by shifting the dates of the original 1/4 period (15 days). The original and shifted fields were decomposed using SVD (Bretherton et al 1992). The results give eigenvectors in quadrature pairs that represent propagating variability. Only the first pair of SVD modes were used (the second pair of eigenvalues was about 1/3 as large as the first).
The results of this decomposition can be seen in the second set of plots on the MJO page (see the section "SVD analysis of OLR"), including the eigenvalues, spatial eigenvectors and principal components (time series).
3. Surface winds, SST and air temperature from the ECMWF reanalysis were used to compute air-sea heat fluxes from bulk formulae.
First, cloud fraction was estimated by linear regression between monthly OLR and ISCCP clouds. Regression coefficients were found as a function of location, based on the ISCCP period 1983-91. (A more complete description with many figures is at the clouds and OLR page). Of course, this method only works for high clouds associated with deep tropical convection, but that is the case for cloudiness associated with the MJO. The regression was only used to derive cloud fraction where the correlation was greater than 0.7; otherwise clouds were assumed to be zero (i.e. there are no stratus decks in this representation). This procedure may be flawed because only monthly clouds (ISCCP) were available, and the OLR-cloud relation may be different at higher frequencies.
Time series of the heat flux elements (shortwave, latent flux and longwave) could then be estimated by bulk formulae from the reanalysis winds and temperatures and OLR-regressed clouds. Clear-sky shortwave radiation was estimated from two harmonics of the annual cycle (Reed, 1977). In the absence of sufficient information, a constant relative humidity (80%) was used for the latent and longwave fluxes. This is reasonable (in any case unavoidable) since surface humidity varies through a relatively small range over the warm pool. See statistics of SST, air temperature and relative humidity from TAO buoys.
4. The surface winds and heat fluxes were similarly band-passed and regressed onto the the first pair of OLR SVD principal components for the reanalysis period 1985-1993, to produce a complete description of the evolution of the MJO.
5. A "canonical MJO" was reconstructed by taking a single sinusoidal oscillation of the decomposed OLR and regressed winds and fluxes. This reconstruction is shown in various projections in the figures below. The sign of the heat fluxes in each case is chosen so that positive values represent warming of the ocean.
The amplitude of OLR that scales this reconstruction was taken to be the RMS amplitude of the first two principal components during 1985-93. Note that this RMS is probably a severe underestimate of the actual amplitude, since the PCs are typically 2-3 times larger during the active MJO season each year (see the smoothed principal component amplitude (bottom right panel). This bandpass -> SVD -> regression technique is similar in spirit to that followed by Hendon and Salby (1994 JAS p2225) and Hendon et al (1997 JAS p88), and the resulting depiction of the MJO is also similar. Hendon et al (1997) show figures with the amplitude chosen as 1.5 times the RMS of the principal components. For modeling purposes such a scaling up is probably desirable to get realistic amplitudes. One estimate of the actual fluxes in a strong MJO (Nov 1992 during COARE) is by Cronin and McPhaden (1997 JGR p8533). They found MJO wind anomalies of about 3 m/s, and heat flux anomalies of about 60 W/m2 in both shortwave and latent heat fluxes. These values are 2-5 times as large as the reconstruction produced here.
Hofmuller diagrams at various latitudes.
Five panels: Zonal and meridional wind, shortwave, latent and total heat fluxes.
The final (correct) result shows that latent and shortwave heat fluxes are both cooling terms (of similar magnitude) during the convection phase of the MJO, due to increased cloudiness and larger wind speeds, respectively.
See also many more plots on the MJO page