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

Abstract

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 <5 18 0and 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.

Internal tides observed at 2°S–156°E by in situ and TOPEX/POSEIDON data during the Coupled Ocean‐Atmosphere Response Experiment (COARE)

“…A better tool for describing such heterogeneous signals is the "wavelet transform" [Lau and Weng, 1995]. This provides a three-dimensional description of the signal, where its amplitude is given as a function of position and wavelength.…”

Wavelet Analysis of Summer Rainfall over North China and India and SOI Using 1891-1992 Data

“…WT is a completely new mathematical analysis method, and a powerful analysis tool well suited to the study of multi-scale non-stationary processes occurring over finite spatial and temporal domains (Lau and Weng, 1995). WT was firstly founded by a petroleum engineer Morlet of France Elf-Aquitaine Company when he analyzed seismic data in 1980.…”

“…Mahrt (1991) firstly introduced WT into atmospheric sciences when eddy asymmetry in the sheared heated boundary layer was studied. In recent years, WT has been widely used in a series of fields of atmospheric sciences, for instance, analyzing low-level cold fronts (Damage and Blumen, 1993), coherent structures at the atmosphere-forest interface (Gao and Li, 1993), microfronts and associated coherent events (Gamage and Hagelberg, 1993), rainfall spatial structure (Kumar and Foufoula-Georgiou, 1993), dispersion of mixed Rossby-gravity waves in a reduced gravity equatorial model (Meyers et al, 1993), period-doubling and time-frequency localization in the satellite infrared radiance data (Weng and Lau, 1994), vertical structure of atmospheric gravity waves (Sato and Yamada, 1994), interannual variability of sea surface temperature (SST) (Mak, 1995), a proxy paleoclimate time series and monthly mean surface temperature in the Northern Hemisphere (Lau and Weng, 1995), interannual and decadal variations of annual rainfall in North China (Hu, 1996), and so on.…”

Multitemporal climate variability over the Atlantic Ocean and Eurasia: linkages with Mediterranean and West African climate

“…Schlesinger and Ramankutty, 1994;Lau and Weng, 1995;Minobe, 1997Minobe, , 2000Mann and Park, 1999;Tourre et al, 1999, Venegas andMysak, 2000, among others). It is basically a low-frequency climate signal, i.e.…”