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Spectral PCA (sPCA), in contrast to classical PCA, offers the advantage ofidentifying organized spatio-temporal patterns within specific frequency bandsand extracting dynamical modes. However, the unavoidable tradeoff betweenfrequency resolution and robustness of the PCs leads to high sensitivity tonoise and overfitting, which limits the interpretation of the sPCA results. Wepropose herein a simple non-parametric implementation of the sPCA using thecontinuous analytic Morlet wavelet as a robust estimator of the cross-spectralmatrices with good frequency resolution. To improve the interpretability of theresults when several modes of similar amplitude exist within the same frequencyband, we propose a rotation of eigenvectors that optimizes the spatialsmoothness in the phase domain. The developed method, called rotated spectralPCA (rsPCA), is tested on synthetic data simulating propagating waves and showsimpressive performance even with high levels of noise in the data. Applied tohistorical sea surface temperature (SST) time series over the Pacific Ocean,the method accurately captures the El Ni\~{n}o-Southern Oscillation (ENSO) atlow frequency (2 to 7 years periodicity). At high frequencies (sub-annualperiodicity), at which several extratropical patterns of similar amplitude areidentified, the rsPCA successfully unmixes the underlying modes, revealingspatially coherent patterns with robust propagation dynamics. Identification ofhigher frequency space-time climate modes holds promise for seasonal tosubseasonal prediction and for diagnostic analysis of climate models.

Rotated spectral principal component analysis (rsPCA) for identifying dynamical modes of variability in climate systems