A diagnostic of MJO predictability estimates using observational power spectra

Understanding of the convection associated with the Madden-Julian oscillation (MJO) and its multiscale variability remains a challenge. There is need for simple diagnostics applicable to both observations and model output to improve understanding and aid with model evaluation. Here, a diagnostic based on a two dimensional linear damped oscillator with white noise stochastic forcing and observed power spectra is presented to diagnose decay time, period and stochastic forcing statistics for the MJO.

To assess the MJO multiscale variability an index of the intraseasonal MJO is defined that retains low and high frequency variability of tropical convection associated with the MJO. The index is based on the first two empirical orthogonal functions (EOFs) of latitudinally averaged (15S-15N) and band pass filtered (20-100 days) brightness temperature (Tb), but retains the low frequencies by projecting the full daily Tb anomalies onto the EOF patterns. The variance of the first and second EOF is 23% and 17% respectively.

Spectral analysis of the two principal components (PC_1,2) reveals very different characteristics for PC₁ and PC₂. Both show a distinct spectral peak at the mean MJO frequency of 0.02cpd with more power in the PC₁ spectrum. The PC₂ spectrum has a substantial amount of power at low frequencies (<0.01cpd), dominating the PC₁ spectrum and even the MJO peak power. The diagnostic yields a period of 49 days and a decay time of 10-13 days, which is close to previous estimates of the prediction limits for the MJO, although slightly on the low side. In addition, there is less forcing variance on the PC₂ time series as estimated by the diagnostic. Both, the increased low frequency power and the lower forcing variance of PC₂, are related to the spatial pattern associated with PC₂. The main loading of EOF₂ is located between 90E-150E in the western Pacific warm pool, where generally the warmest sea surface temperatures (SSTs) are found. Due to this PC₂ has a much stronger El Ni\~no - Southern Oscillation (ENSO) signal (also visible in the time series) than PC₁, and convection in this region can be initiated by small perturbations on the warm SST background state. ENSO appears to have only a minor influence on PC₁ variability.

Estimates of period and decay time depend on the index used in the diagnostic. Convection based MJO indeces and indeces that include information about the circulation (RMM) are compared. Seasonal variability of the estimated period and decay time is assessed.