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The relation between El Ni\~{n}o-Southern Oscillation (ENSO) and PacificDecadal Oscillation (PDO) perplexes the researchers. Probably, this is due tothe default choice on empirical orthogonal function (EOF) method whose outputsare merely static maps without evolution characteristics. To change thissituation, the new extreme-point symmetric mode decomposition (ESMD) method istried. It reveals that: (1) As the ENSO concerned, the key modes are thequarter-decadal and half-decadal ones; (2) As the PDO concerned, the key modesare the half-decadal, decadal and interdecadal ones; (3) The half-decadal modecan be seen as a mutual component for ENSO and PDO and it plays a key part inthe so-called "ENSO-like" variation of PDO. In addition, an integrated versionof ESMD is developed for time-space evolution. Its outputs have verified thewarm-cold shiftings of ENSO and PDO for the most typical episode during1997-2000.

Key Modes for Time-Space Evolutions of ENSO and PDO by ESMD Method