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Abstract

Eigen analysis has been a powerful tool to distinguish multiple processes into different simple principal modes in complex systems. For a non-equilibrium system, the principal modes corresponding to the non-equilibrium processes are usually evolving with time. Here, we apply the eigen analysis into the complex climate systems. In particular, based on the daily surface air temperature in the tropics (30° S–30° N, 0° E–360° E) between 1979-01-01 and 2016-12-31, we uncover that the strength of two dominated intra-annual principal modes represented by the eigenvalues significantly changes with the El Ni$\tilde {\mathrm{n}}$o/southern oscillation from year to year. Specifically, according to the 'regional correlation' introduced for the first intra-annual principal mode, we find that a sharp positive peak of the correlation between the El Ni$\tilde {\mathrm{n}}$o region and the northern (southern) hemisphere usually signals the beginning (end) of the El Ni$\tilde {\mathrm{n}}$o. We discuss the underlying physical mechanism and suppose that the evolution of the first intra-annual principal mode is related to the meridional circulations; the evolution of the second intra-annual principal mode responds positively to the Walker circulation. Our framework presented here not only facilitates the understanding of climate systems but also can potentially be used to study the dynamical evolution of other natural or engineering complex systems.