Abstract Recent study indicates that the non-instantaneous interaction of convection and circulation is essential for evolution of large-scale convective systems. It is incorporated into cumulus parameterization (CP) by relating cloud-base mass flux of shallow convection to a composite of subcloud moisture convergence in the past 6 h. Three pairs of 19-yr simulations with original and modified CP schemes are conducted in a tropical channel model to verify their ability to reproduce the Madden–Julian oscillation (MJO). More coherent tropical precipitation and improved eastward propagation signal are observed in the simulations with the modified CP schemes based on the non-instantaneous interaction. It is found that enhanced feedback between shallow convection and low-level moisture convergence results in amplified shallow convective heating, and then generates reinforced moisture convergence, which transports more moisture upward. The improved simulations of eastward propagation of the MJO are largely attributed to higher specific humidity below 600 hPa in the free troposphere to the east of maximum rainfall center, which is related to stronger boundary layer moisture convergence forced by shallow convection. Large-scale horizontal advection causes asymmetric moisture tendencies relative to rainfall center (positive to the east and negative to the west) and also gives rise to eastward propagation. The zonal advection, especially the advection of anomalous specific humidity by mean zonal wind, is found to dominate the difference of horizontal advection between each pair of simulations. The results indicate the vital importance of non-instantaneous feedback between shallow convection and moisture convergence for convection organization and the eastward MJO propagation.
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