We apply Spectral Empirical Orthogonal Function (SEOF) analysis, also known as Spectral Proper Orthogonal Decomposition (SPOD) in other fields, to educe climate patterns as dominant spatio-temporal modes of variability from reanalysis data. SEOF is a frequency-domain variant of standard Empirical Orthogonal Function (EOF) analysis, and computes modes that represent the statistically most relevant and persistent patterns from an eigendecomposition of the estimated cross-spectral density matrix (CSD). The spectral estimation step distinguishes the approach from other frequency-domain EOF methods based on a single realization of the Fourier transform, and results in a number of desirable mathematical properties: at each frequency, SEOF yields a set of orthogonal modes that are optimally ranked in terms of variance in the L-2 sense, and that are coherent in both space and time by construction. We discuss the differences between SEOF and other competing approaches, as well as its relation to dynamical modes of stochastically forced, non-normal linear dynamical systems. The method is applied to ERA-Interim and ERA-20C reanalysis data, demonstrating its ability to identify a number of well known spatio-temporal coherent meteorological patterns and teleconnections, including the Madden-Julian Oscillation (MJO), the Quasi-Biennial Oscillation (QBO), and the El Nino-Southern Oscillation (ENSO), i.e. a range of phenomena reoccurring with average periods ranging from months to many years. In addition to two-dimensional univariate analyses of surface data, we give examples of multivariate and three-dimensional meteorological patterns, that illustrate how this technique can systematically identify coherent structures from different sets of data.

The video shows the leading SEOF mode of the Top Thermal Radiation (TTR) with period 45.6 days computed from ERA Interim data. The mode identifies a large-scale anomaly in the Indian Ocean associated with the Madden-Julian oscillation.


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Literature

  • [PDF] [DOI] Schmidt, O. T., G. Mengaldo, G. Balsamo, and N. P. Wedi. “Spectral empirical orthogonal function analysis of weather and climate data.” Monthly weather review 147.8 (2019): 2979-2995.
    [Bibtex] 
    @Article{schmidtetal_2019_mwr,
author = {Schmidt, O. T. and Mengaldo, G. and Balsamo, G. and Wedi, N. P.},
title = {Spectral Empirical Orthogonal Function Analysis of Weather and Climate Data},
journal = {Monthly Weather Review},
year = {2019},
volume = {147},
number = {8},
pages = {2979-2995},
abstract = { AbstractWe apply spectral empirical orthogonal function (SEOF) analysis to educe climate patterns as dominant spatiotemporal modes of variability from reanalysis data. SEOF is a frequency-domain variant of standard empirical orthogonal function (EOF) analysis, and computes modes that represent the statistically most relevant and persistent patterns from an eigendecomposition of the estimated cross-spectral density matrix (CSD). The spectral estimation step distinguishes the approach from other frequency-domain EOF methods based on a single realization of the Fourier transform, and results in a number of desirable mathematical properties: at each frequency, SEOF yields a set of orthogonal modes that are optimally ranked in terms of variance in the L2 sense, and that are coherent in both space and time by construction. We discuss the differences between SEOF and other competing approaches, as well as its relation to dynamical modes of stochastically forced, nonnormal linear dynamical systems. The method is applied to ERA-Interim and ERA-20C reanalysis data, demonstrating its ability to identify a number of well-known spatiotemporal coherent meteorological patterns and teleconnections, including the Madden–Julian oscillation (MJO), the quasi-biennial oscillation (QBO), and the El Niño–Southern Oscillation (ENSO) (i.e., a range of phenomena reoccurring with average periods ranging from months to many years). In addition to two-dimensional univariate analyses of surface data, we give examples of multivariate and three-dimensional meteorological patterns that illustrate how this technique can systematically identify coherent structures from different sets of data. The MATLAB code used to compute the results presented in this study, including the download scripts for the reanalysis data, is freely available online. },
doi = {10.1175/MWR-D-18-0337.1},
eprint = {https://doi.org/10.1175/MWR-D-18-0337.1},
url = {https://doi.org/10.1175/MWR-D-18-0337.1},
}