A Multi-Scale Model for the Intraseasonal Impact of the Diurnal Cycle over

The eastward propagating Madden-Julian Oscillation (MJO) typically exhibits complex behavior during its passage over the Maritime Continent, sometimes slowly propagating eastward and other times stalling and even terminating there with large amounts of rainfall. This is a huge challenge for present-day numerical models to simulate. One possible reason is the inadequate treatment of the diurnal cycle and its scale interaction with the MJO. Here these two components are incorporated into a simple self-consistent multi-scale model, which includes a model for the intraseasonal impact of the diurnal cycle and another one for the planetary/intraseasonal circulation. The latter model is forced self-consistently by eddy flux divergences of momentum and temperature from a model for the diurnal cycle with two baroclinic modes, which capture the intraseasonal impact of the diurnal cycle. The MJO is modelled as the planetary-scale circulation response to a moving heat source on the synoptic and planetary scales. The results show that the intraseasonal impact of the diurnal cycle during boreal winter tends to strengthen the westerlies (easterlies) at the lower (upper) troposphere in agreement with the observations. In addition, the temperature anomaly induced by the intraseasonal impact of the diurnal cycle can cancel that from the symmetric/asymmetric MJO with convective momentum transfer, yielding stalled or suppressed propagation of the MJO across the Maritime Continent. The simple multi-scale model should be useful for the MJO in observations or more complex numerical models. 9