SUPPLEMENTAL MATERIAL FOR THE LETTER Multiscale atmospheric dynamics: Cross-frequency phase–amplitude coupling in the air temperature

In this Supplemental material we bring more information about the statistical evaluation of the conditional mutual information (CMI) as a measure of directional interactions, then a discussion of the frequency localization ability of the complex continuous wavelet transform (CCWT). Searching for clues to understanding of the physical mechanisms underlying the observed cross-scale interactions we point to some interesting facts about the North Atlantic Oscillation and its influence on the atmospheric circulation. However, for convenience of readers, we start with a brief introduction of the mutual information, the CMI in a general form and the form of the CMI used for the inference of causal relations from time series. We also make a note on the dependence of the CMI on the forward time lag and present examples of this dependence in the studied phase-amplitude interactions in the air temperature.