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I am trying to understand the basic dynamics of MJO, where I find several studies which relate it to the initiation of equatorial Rossby and Kelvin waves. Though MJO is an eastward propagating wave, I can relate it to the existence of Kelvin waves during that time but I am not getting any insight about the initiation of a westward wave. I think that the westward motion could be possible only due to the reflection of easterly wave through a boundary. Please correct me with the actual fact and its underlying mechanism.

I am mentioning some of the online sources which inform about the above mentioned fact but I am not getting the answers from any research papers

  1. https://ams.confex.com/ams/98Annual/webprogram/Paper324264.html

  2. https://www.cwb.gov.tw/V7/climate/climate_info/information/lectures/59/CWB2015-10-02_Bin_Wang2.pdf

Actually I could not find the detailed study for source 1 but I found similar statements (Kelvin-Rossby relation) in other studies that made me more confused. The second mention raises this issue, they talk about Matsuno-Gill theory and the usage of equatorial waves in it but I am unable to get any understanding of their model about how it emerged from (A description is attached here).

https://atmos.washington.edu/~dargan/591/591_8.pdf

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