RE: Madden Julian Oscillation
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We definitely are due for a post on the MJO, but have been waiting.... and waiting.... and waiting for an MJO to clearly emerge before introducing it. The short answer to your question is that there are *times* when the MJO can be an important factor in El Nino or La Nina evolution. It does this mainly through adjusting the low-level winds over the tropical Pacific Ocean. By modifying those winds, the MJO can help determine whether ENSO form, strengthen, or even decay.
Because the PDO is decadal and MJOs are "subseasonal" (best seen in weekly average data), the interaction between those two phenomenon is much less clear and I'm not aware of any research that connects MJO-PDO.