Empirical orthogonal function (EOF) analysis has been widely used in analysing the spatial-time patterns, mechanisms and prediction of the El Niño-Southern Oscillation (ENSO). Fast Fourier transform (FFT) analysis has correspondingly as EOF been used in the time series of ENSO. For instance, the first mode of EOF was identified as the eastern Pacific or canonical ENSO with a peak at 4-7 years power spectrum, and the second mode denotes the ENSO Modoki or central Pacific El Nino with two peaks at interannual and decadal. In principal, ENSO is a non-stationary and non-linear phenomenon. However, EOF is a stationary and linear analysis tool that is subject to a strong orthogonality constraint. An often asked question is that when applying EOF to ENSO, do we separate the surface temperature signals into correct physical modes?

To alleviate some defects of EOF, a non-stationary approach known as the Empirical Mode Decomposition (EMD) method has been recently developed. EMD is a one-dimensional data analysis method that is adaptive, has high locality, and can thereby handle the nonlinear and nonstationary nature of data. By perturbing the data with noise, ensemble EMD (EEMD) is able to perform robust signal decomposition. In order to handle both spatial locality and temporal locality issues, multi-dimensional EEMD, (MEEMD) has been developed. The MEEMD has unique advantages over many other methods in analysing temporal-spatial multidimensional climate data, and so this method has been recently adopted more frequently in climate researches. However, the MEEMD is still in its infancy stage, and we have found that it has been incorrectly performed in many existing studies.

In this study, we present the preliminary results by correctly applying the MEEMD with the most reliable code to decompose 2D and 3D synthetic SSTa from our latest coupled model, ACCESS-CM2. Implication of our results will be discussed.