Impacts of upscale heat and momentum transfer by moist Kelvin waves on the Madden-Julian oscillation: A theoretical model study

The Madden-Julian oscillation (MJO) is observed to interact with moist Kelvin waves. To understand the role of this interaction, a simple scale-interaction model is built, which describes the MJO modulation of moist Kelvin waves and the feedback from moist Kelvin waves through upscale eddy heat and momentum transfer. The backward-tilted moist Kelvin waves produce eddy momentum transfer (EMT) characterized by the lower-tropospheric westerly winds and eddy heat transfer (EHT) that warms the mid-troposphere. The EHT tends to induce the lower-tropospheric easterly winds and low pressure, which is located in front of the "westerly wind burst" induced by the EMT. Adding the eddy forcing to a neutral MJO skeleton model, we show that the EHT provides an instability source for the MJO by warming up the mid-troposphere, and the EMT offers an additional instability source by enhancing the lower-tropospheric westerly winds. The eddy forcing selects eastward propagation for the unstable mode, because it generates positive/negative eddy available potential energy for the eastward/westward modes by changing their thermal and dynamical structures. The present results show that moist Kelvin waves can provide a positive feedback to the MJO only when they are located within (or near) the convective complex (center) of the MJO. The EHT and EMT feedback works positively in the front and rear part of the MJO, respectively. These theoretical results suggest the potential importance of moist Kelvin waves in sustaining the MJO and encourage further observations to document the relationship between moist Kelvin waves and the MJO.