Compared with the classical Fourier transform, the popular Wavelet transform, and the Hilbert–Huang transform (also known as “empirical mode decomposition"), the ESMD method is more suitable for scientific exploration, and it has already been used in fields such as atmospheric and oceanic sciences, life sciences, informatics, mathematics, seismology, and mechanical engineering. The corresponding algorithm is provided for your reference (see the ).

As an example, we consider the time-series of SST at grid point ($160^{\circ}$W, $0^{\circ}$). The decomposition in yields a remainder R whose change-rate ($0.11^{\circ}$C per decade) agrees well with the documented global warming trend (Hansen et al. 2010). In addition to R, there are also five modes with periods $\leq 1$yr, 1–3yr, 3-7yr, 11-13yr and $\geq 18$yr, respectively. Particularly, the interannual component with period 1–3yr acts as a dominant factor. Except Mode 1 (the seasonal component), the sum of the others can be seen as the whole interannual anomaly of SST which agrees well with the known Niño-3.4 index (the coefficient between them is 0.87). Therefore, the ESMD method is a good choice for analysing the time series obtained from each observational site. The space–time data analysis only require an integrating process. Under interannual time scales, tests on 