The Madden-Julian oscillation (MJO) is observed to be organized in a hierarchical structure that the eastward-moving planetary-scale envelope usually contains multiple synoptic-scale superclusters with numerous embedded mesoscale convective systems (MCSs). Present-day GCMs fail to explicitly resolve MCSs due to their coarse resolutions. It is hypothesized that such inadequate treatment of MCSs and their upscale impact leads to the poorly simulated MJOs in the GCMs.
Here we tackled this challenge by using models in a hierarchy of complexity. First, we used a simple idealized model (multi-scale asymptotic model), originally derived by Majda (2007), to describe the typical scenario where the synoptic-scale convective envelope contains numerous embedded MCSs. The resulting eddy transfer of momentum and temperature is interpreted as the upscale impact from mesoscale fluctuations to synoptic-scale circulation. Then, we chose an intermediate model (multicloud model) as a testbed to mimic typical behaviors of GCMs with clear deficiencies. Based on explicit expressions of eddy transfer of momentum and temperature from the previous multi-scale asymptotic model, we proposed a basic parameterization for the upscale impact of upshear-moving MCSs modulated by deep heating excess and vertical shear strength. This parameterization significantly improves key features of the MJO analog in this idealized GCM. Finally, we tested the effects of this basic parameterization on the MJO simulation in a coarse-resolution GCM (HOMME dynamic core coupled with the multicloud heating closure). The preliminary results show that the parameterization for the upscale impact of MCSs promotes persistent eastward propagation of the MJO and helps to recover its realistic features of spatiotemporal variability in the GCM.