Contrasting stratospheric–tropospheric multi-fractal behaviors in NAM variability

  • Da Nian
  • Zuntao FuEmail author


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.


Northern Annular Mode (NAM) Multiple multi-fractal behavior Stratospheric–tropospheric variability Warm–cold season variations 



The authors thank the anonymous reviewers for their helpful suggestions for improving the readability of this paper. The authors acknowledge the supports from National Natural Science Foundation of China (nos. 41675049, 41475048).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Lab for Climate and Ocean-Atmosphere Studies, Department of Atmospheric and Oceanic Sciences, School of PhysicsPeking UniversityBeijingChina

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