Variability of SST through Koopman Modes

The majority of dynamical systems arising from applications show a chaotic character. This is especially true for climate and weather applications. We present here an application of Koopman operator theory to tropical and global sea surface temperature (SST) that yields an approximation to the continuous spectrum typical of these situations. We also show that the Koopman modes yield a decomposition of the datasets that can be used to categorize the variability. Most relevant modes emerge naturally, and they can be identified easily. A difference with other analysis methods such as empirical orthogonal function (EOF) or Fourier expansion is that the Koopman modes have a dynamical interpretation, thanks to their connection to the Koopman operator, and they are not constrained in their shape by special requirements such as orthogonality (as it is the case for EOF) or pure periodicity (as in the case of Fourier expansions). The pure periodic modes emerge naturally, and they form a subspace that can be interpreted as the limiting subspace for the variability. The stationary states therefore are the scaffolding around which the dynamics takes place. The modes can also be traced to the Niño variability and in the case of the global SST to the Pacific decadal oscillation (PDO).