As a harbinger of anomalous weather regimes in the troposphere, the Northern Annular Mode (NAM) propagates from the stratosphere to the troposphere. This fact makes understanding and predicting NAM variability of great importance. In this study, the multi-fractal behaviors of NAM variability are investigated using extended self-similarity based, multi-fractal detrended fluctuation analysis (ESS-MF-DFA) and the NAM indices from 1000 to 10 hPa. The results show that there are contrasting multi-fractal behaviors between the stratosphere and the troposphere that have a transition band near 200 hPa. The stratospheric NAM variability is more complicated and has multiple multi-fractal regimes over different scales with marked contrasting warm–cold season features. To understand these contrasting stratospheric–tropospheric multi-fractal behaviors, three surrogate methods are adopted to show how temporal ordinal patterns over an annual scale contribute to these behaviors, whereas the distribution of NAM variability only plays a minor role. Further studies show that contrasting warm–cold variability may lead to these contrasting behaviors. Among them, warm–cold seasonal variations, power spectral density (PSD), and autocorrelation provide a similar conclusion. Results indicate that although predictions of the NAM index over the stratosphere are required and necessary, the complicated multi-fractal behaviors make linear prediction strategy difficult to obtain high realizable predictability of NAM variations over the stratosphere.
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