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ABSTRACT
This study investigates why OLR plays a small role in the Real-time Multivariate (Madden-Julian oscillation) MJO (RMM) index and how to improve it. The RMM index consists of the first two leading principal components (PCs) of a covariance matrix, which is constructed by combined daily anomalies of OLR and zonal winds at 850 (U850) and 200 hPa (U200) in the tropics after being normalized with their globally averaged standard deviations of 15.3 W m^sup -2^, 1.8 m s^sup -1^, and 4.9 m s^sup -1^, respectively. This covariance matrix is reasoned mathematically close to a correlation matrix. Both matrices substantially suppress the overall contribution of OLR and make the index more dynamical and nearly transparent to the convective initiation of the MJO. A covariance matrix that does not use normalized anomalies leads to the other extreme where OLR plays a dominant role while U850 and U200 are minor. Numerous tests indicate that a simple scaling of the anomalies (i.e., 2 W m^sup -2^, 1 m s^sup -1^, and 1 m s^sup -1^) can better balance the roles of OLR and winds. The revised PCs substantially enhance OLR over the eastern Indian and western Pacific Oceans and change it less notably in other locations, while they reduce U850 and U200 only slightly. Comparisons with the original RMM in spatial structure, power spectra, and standard deviation demonstrate improvements of the revised RMM index.
1. Introduction
The Madden-Julian oscillation (MJO; Madden and Julian 1971, 1972) is a dominant mode of tropical atmospheric variability on intraseasonal time scales (Zhang 2005) and substantially modulates global weather and climate (Zhang 2013). How to represent the MJO accurately in theory and models has been a challenge to both research community and operational prediction centers. Early diagnosis of the MJO employed power-spectral analysis (Madden and Julian 1972) or its variant of bandpass filtering (e.g., Weickmann et al. 1985). Composite studies (e.g., Rui and Wang 1990) manually detected individual MJO events on Hovmöller (time- longitude) diagrams constructed with pentad-mean OLR anomalies. Slingo et al. (1996) used the bandpass-filtered zonal-mean zonal wind at 200 hPa to represent the overall intraseasonal variability in 15 AGCMs. Maloney and Hartmann (1998) applied an EOF analysis to the bandpass-filtered zonal wind at 850hPa to derive an MJO index...