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Comparing the spatial structure of variability in two datasets against each other on the basis of EOF-modes

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Abstract

In analysis of climate variability or change it is often of interest how the spatial structure in modes of variability in two datasets differ from each other, e.g. between past and future climate or between models and observations. Often such analysis is based on Empirical Orthogonal Function (EOF) analysis or other simple indices of large-scale spatial structures. The present analysis lays out a concept on how two datasets of multivariate climate variability can be compared against each other on basis of EOF analysis and how the differences in the multivariate spatial structure between the two datasets can be quantified in terms of explained variance in the leading spatial patterns. It is also illustrated how the patterns of largest differences between the two datasets can be defined and interpreted. We illustrate this method on the basis of several well-defined artificial examples and by comparing our approach with examples of climate change studies from the literature. These literature examples include analysis of changes in the modes of variability under climate change for the sea level pressure (SLP) of the North Atlantic and Europe, the SLP of the Southern Hemisphere, the surface temperature of the Northern Hemisphere, the sea surface temperature of the North Pacific and for precipitation in the tropical Indo-Pacific.

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Acknowledgments

We acknowledge the individual modeling groups, the Climate Model Intercomparison Project (CMIP3). This work was supported by the Deutsche Forschungsgemeinschaft (DFG) through project DO1038/5-1 and the ARC Centre of Excellence in Climate System Science (CE110001028). We thank Jan Harlaß, Klaus Getzlaff, Katja Lorbacher and Gang Wang for discussion and useful comments.

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Authors and Affiliations

  1. GEOMAR Helmholtz Centre for Ocean Research, Düsternbrooker Weg 20, 24105, Kiel, Germany

    Tobias Bayr

  2. School of Mathematical Sciences, Monash University, Clayton, VIC, Australia

    Dietmar Dommenget

Authors
  1. Tobias Bayr
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  2. Dietmar Dommenget
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Correspondence to Tobias Bayr.

Electronic supplementary material

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Supplementary material 1 (TEX 4 kb)

382_2013_1708_MOESM2_ESM.eps

Supplemental Figure S1: Additional experiment for the example in Sect. 5.2, but with two fixed patterns intensified in dataset \(\mathcal{B}\). Part 1: Forcing patterns and difference in variability. Same structure for the figure panels as in Fig. 2: (a)-(b) the two forcing patterns included in \(\mathcal{B}\) (instead of only one as in Sect. 5.2); (c) due to these two forcing patterns, dataset \(\mathcal{B}\) has a higher variability, except in the middle of the domain, where the difference is not significant. (EPS 200 kb)

382_2013_1708_MOESM3_ESM.eps

Supplemental Figure S2: Additional experiment for the example in Sect. 5.2, but with two fixed patterns intensified in dataset \(\mathcal{B}\). Part 2: EOF and DEOF analysis. Same structure for the figure panels as in Fig. 3. (EPS 411 kb)

382_2013_1708_MOESM4_ESM.eps

Supplemental Figure S3: Additional experiment for the example in Sect. 5.3, but with a dipole pattern shift from west (\(\mathcal{A}\)) to east (\(\mathcal{B}\)). Part 1: Forcing pattern and difference in variability. Same structure for the figure panels as in Fig. 2: (a)-(b) the dipole forcing pattern shifts location orthogonal to the line between the two poles, i.e. a shift to the right of 6 grid points in this case; (c)-(d) the difference between the two forcing pattern is a quattro-pole structure, also in the ratio of the standard deviation. (EPS 304 kb)

382_2013_1708_MOESM5_ESM.eps

Supplemental Figure S4: Additional experiment for the example in Sect. 5.3, but with a dipole pattern shift from west (\(\mathcal{A}\)) to east (\(\mathcal{B}\)). Part 2: EOF and DEOF analysis. Same structure for the figure panels as in Fig. 3: (f), (h) as in the example in Sect. 5.3 both DEOF-1 pattern have to be considered together: The DEOF-\(1^{{\mathcal{A} \to \mathcal{B}}}\) shows where the EOF-2 pattern has weakened and the DEOF-\(1^{{\mathcal{B} \to \mathcal{A}}}\) where the EOF-2 pattern has strengthened, thus showing both together the shift in the EOF-2 pattern. The centers of the dipoles in the DEOF patterns agree with the regions of strongest increase/decrease in variability, as seen in Fig. S3d, i.e. the DEOF analysis reveals how the changes in variability relate to the changes in the modes of variability. (EPS 300 kb)

382_2013_1708_MOESM6_ESM.eps

Supplemental Figure S5: Additional experiment for the example in Sect. 5.3., but with a dipole pattern shift from south (\(\mathcal{A}\)) to north (\(\mathcal{B}\)). Part 1: Forcing pattern and difference in variability. Same structure for the figure panels as in Fig. 2: (a)-(b) the forcing pattern shifts along the line between the two centers, i.e. an upward shift of 1 grid point in this case. (c)-(d) absolute difference in the forcing is a quattro-pole structure, also in the ratio of the standard deviation. (EPS 267 kb)

382_2013_1708_MOESM7_ESM.eps

Supplemental Figure S6: Additional experiment for the example in Sect. 5.3., but with a dipole pattern shift from south (\(\mathcal{A}\)) to north (\(\mathcal{B}\)). Part 2: EOF and DEOF analysis. Same structure for the figure panels as in Fig. 3: (a)-(d) here we choose a quite strong forcing, so that the EOF-1 is a dipole and EOF-2 is a monopole. A small upward shift of the pattern can be seen, if we look closely on the EOF-1 patterns of \(\mathcal{A}\) and \(\mathcal{B}\); (e), (g) the projected explained variances show no difference in explained variance of the EOF pattern, due to high pattern correlation between the EOF patterns of the two datasets (0.99 for the EOF-1 and 1.00 for the EOF-2). (f), (h) the two centers of both DEOF pattern are exactly at the points where the variability changes strongest. The two DEOF-1 patterns show together the northward shift of the two poles in the EOF-1. In comparison with the example in Figure S4 we can see that the small shift of 1 grid point along the line between the two centers gives nearly the same difference in the DEOF pattern than a 6 grid point shift orthogonal to the line between the two centers. (EPS 309 kb)

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Bayr, T., Dommenget, D. Comparing the spatial structure of variability in two datasets against each other on the basis of EOF-modes. Clim Dyn 42, 1631–1648 (2014). https://doi.org/10.1007/s00382-013-1708-x

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