Climate Signal Detection Using Wavelet Transform: How to Make a Time Series Sing

In this paper, the application of the wavelet transform (WT) to climate time series analyses is introduced. A tutorial description of the basic concept of WT, compared with similar concepts used in music, is also provided. Using an analogy between WT representation of a time series and a music score, the authors illustrate the importance of local versus global information in the time–frequency localization of climate signals. Examples of WT applied to climate data analysis are demonstrated using analytic signals as well as real climate time series. Results of WT applied to two climate time series—that is, a proxy paleoclimate time series with a 2.5-Myr deep-sea sediment record of δ18 O and a 140-yr monthly record of Northern Hemisphere surface temperature—are presented. The former shows the presence of a 40-kyr and a 100-kyr oscillation and an abrupt transition in the oscillation regime at 0.7 Myr before the present, consistent with previous studies. The latter possesses a myriad of oscillatory modes from interannual (2–5 yr), interdecadal (10–12 yr, 20–25 yr, and 40–60 yr), and century (~180 yr) scales at different periods of the data record. In spite of the large difference in timescales, common features in time–frequency characteristics of these two time series have been identified. These features suggest that the variations of the earth's climate are consistent with those exhibited by a nonlinear dynamical system under external forcings.