La Niña, the most pressing problem is how to correctly reflect their space-time evolution. This requires solving a difficult three-dimensional data-analysis problem where time and space possess one and two dimensions, respectively. The EOF method developed by Lorenz in 1956 has been continually employed as a default approach for this kind of problem. However, this method depends on the matrix-decomposition theory in mathematics, which can only deal with two-dimensional problems. Restricted by this, the two-dimensional plane should be considered as a one-dimensional line (i.e., the observational sites in the plane should be artificially numbered in a certain order). Thus, the outputted spatial modes are merely static maps that do not possess evolutionary characteristics (the corresponding time coefficients only reflect relative changes in strong and weak patterns), which cannot objectively reflect the appearance, development, propagation and extinction of anomalous warm or cold signals in the whole sea-area, and cannot distinctly distinguish the time-frequency multi-scale variations during the evolutionary process. These problems are inherent and they hinder further exploration. Therefore, it requires a method innovation.

Five years ago we developed the ESMD method for one-dimensional data analyses (Wang and Li 2013), which has advantages in trend separation, anomaly diagnosing and time-frequency analyses. 