Assessing propagation characteristics and predictability of the MJO using multiple MJO indices

Understanding of the convection associated with the Madden-Julian oscillation (MJO), its multiscale variability and impacts elsewhere remains a challenge. There is, therefore, a need for simple diagnostics applicable to both observations and model output both in order to improve understanding and to 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. Two different indices are used: the OLR-based MJO index (OMI) and the Real-Time Multivariate MJO (RMM) index. OMI uses outgoing longwave radiation (OLR) exclusively to focus on the convective signal associated with the MJO, meanwhile the Real-Time Multivariate MJO (RMM) index includes zonal wind aside from OLR, but has been shown to capture primarily the large scale circulation. Spectral analysis of the two principal components for both indices reveals a quadrature relation between these. A diagnostic based on this quadrature relation and the assumption of an underlying linear stochastic oscillator is introduced that can distinguish between seasons with primarily propagating or non-propagating MJOs. The diagnostic yields comparable results for both indices with an estimated period of 45-55 days for RMM and slightly shorter 40-50 days for OMI, and a decay time of 14-18 days. This is close to previous estimates of the prediction limits for the MJO, although slightly on the low side. While for most seasons the two indexes agree in terms of the propagating vs non-propagating mean MJO behavior, we show a few examples where the choice between OMI or RMM to estimate the MJO propagation characteristics should be based on the target application, that is whether the interest is on the MJO's diabatic heating (OMI) or circulation (RMM).