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Accurate extraction of the modulated annual cycle (MAC) is important for climatic and oceanic research. A variety of methods are available to extract the annual cycle with inconsistent results. Since actual annual cycles are unknown in the observation series, the reliability and applicability of the results extracted by these methods are difficult to estimate. In this study, three widely used decomposition methods, ensemble empirical mode decomposition (EEMD), nonlinear mode decomposition (NMD), and enhanced harmonic analysis (EHA), are evaluated by idealized numerical experiments for extracting modulated annual cycles from climate series. Idealized numerical experiments are carried out and show that the recently proposed EHA had the most accuracy in extracting the MAC from the constructed data. The optimal independent point (IP) number, which makes the most accurate result for EHA, can be found in each ideal experiment. In the actual experiment, two IP selection criteria are proposed for EHA to extract MAC from observations.

Extracting Modulated Annual Cycle in Climate and Ocean Time Series Using an Enhanced Harmonic Analysis