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A proper description of ocean-atmosphere interactions is key for a correctunderstanding of climate evolution. The interplay among the different variablesacting over the climate is complex, often leading to correlations across longspatial distances (teleconnections). In some occasions, those teleconnectionsoccur with quite significant temporal shifts that are fundamental for theunderstanding of the underlying phenomena but which are poorly captured bystandard methods. Applying orthogonal decomposition such as Maximum CovarianceAnalysis (MCA) to geophysical data sets allows to extract common dominantpatterns between two different variables, but generally suffers from (i) thenon-physical orthogonal constraint as well as (ii) the consideration of simplecorrelations, whereby temporally offset signals are not detected. Here wepropose an extension, complex rotated MCA, to address both limitations. Wetransform our signals using the Hilbert transform and perform the orthogonaldecomposition in complex space, allowing us to correctly correlate out-of-phasesignals. Subsequent Varimax rotation removes the orthogonal constraints,leading to more physically meaningful modes of geophysical variability. As anexample of application, we have employed this method on sea surface temperatureand continental precipitation; our method successfully captures the temporaland spatial interactions between these two variables, namely for (i) theseasonal cycle, (ii) canonical ENSO, (iii) the global warming trend, (iv) thePacific Decadal Oscillation, (v) ENSO Modoki and finally (vi) the AtlanticMeridional Mode. The complex rotated modes of MCA provide information on theregional amplitude, and under certain conditions, the regional time lag betweenchanges on ocean temperature and land precipitation.

Lagged teleconnections of climate variables identified via complex rotated Maximum Covariance Analysis