Comparison of methods for extracting annual cycle with changing amplitude in climate series

  • Qimin Deng
  • Zuntao FuEmail author


Extracting annual cycle properly from climate series is important in the study of annual cycle and anomaly series. However, the extracting approaches are various and may lead to inconsistent results. Since the real annual cycle is unknown in observed records, the reliability and applicability of them are hard to estimate. In this study, five popular decomposition methods used to extract annual cycle in climate series are evaluated through idealized numerical experiments for the first time; i.e., fitting sinusoids, complex demodulation, ensemble empirical mode decomposition (EEMD), nonlinear mode decomposition (NMD) and seasonal trend decomposition procedure based on loess (STL). Their performances are examined by comparing the extracted annual cycles and its amplitude with the preset one. The annual cycles are set with three different changing amplitudes: constant, linear increasing and nonlinearly varying; superposed with fluctuations of different long-term persistence (LTP) strength. Results indicate that (1) NMD performs best in depicting annual cycle and obtaining its amplitude change; (2) fitting sinusoids, complex demodulation and EEMD methods are more sensitive to LTP strength of superimposed fluctuations, which leads to over-fitted annual cycles and noisy amplitude changes, oppositely, the STL are less responsive to the variation of annual cycle; (3) when overall long-time trend of annual cycle change is the main concern, all of these methods performed well. However, over short time scales, the errors on account of noise and LTP are common in the first three methods and STL is too rough to give the details of amplitude change. Those results are also verified by applying them to observed records and the case with both amplitude and phase change.


Annual cycle Fitting sinusoids Complex demodulation Ensemble empirical mode decomposition Nonlinear mode decomposition and seasonal trend decomposition procedure based on loess Amplitude trend 



The authors acknowledge support from National Natural Science Foundation of China through Grant no. 41675049. We thank Dr. Cheng Qian for his suggestions on the operation of EEMD method and Prof. Christian Franzke’s reminder of a practical method STL. The valuable comments and suggestions from the anonymous reviewers are appreciated and helpful in further improving the manuscript.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

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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