## 4 Discussions  
In this study, we devised a new approach for examining the multiscale characteristics of oscillatory oceanic properties, such as SSTA variability, that is based on the combination of two well-known methods, such as EMD and complex network theory. Although our wavelet-based network methodology shows a noticeable performance in examining the variability of internal tides inside a mesoscale eddy [50], there is still a shortcoming in eliminating spurious harmonics due to a strong nonstationary behavior. Our new EMD-based approach can avoid spurious harmonics due to an abrupt frequency modulation [33]. Also, most previous studies on SST variability have been based on linear statistical analysis tools such as empirical orthogonal function (EOF) and spectral analysis tools based on Fourier transform, which have critical shortcomings in dealing with real-world signals with nonstationary and nonlinearity [33]. In fact, the EMD method has been introduced to overcome the limitations of Fourier-transform-based analyses, including the wavelet approach. Since the traditional EOF approach has been long applied to the analysis of SST variability in the oceanography in order to extract the space-time modes of climate variability [51], notwithstanding that there are two problems, such as uncertainty in the physical interpretation of EOF modes and ambiguity in identifying relationships between spatial and temporal EOFs [52], there has been no attempt to analyze the spatial structure of SST variability, based on EMD approaches. The EMD approach is excellent at extracting scale-based characteristics adaptively from a singular time series [33], so any EMB-based methodology, like in this study, can more effectively obtain spatiotemporal characteristics from multivariate time series even with strong periodic oscillations and nonstationary. Generally, SST variability has a wide range of temporal scales along with their intra- and inter-wave modulations; these frequency and amplitude modulations intrinsic in a singular time series clarify the limitations of linear statistical analysis. Compared to previous studies on SST variability in the EJS [2; 3; 4; 5; 16; 17], our results give a more detailed description of spatial patterns due to factors with specific timescales in terms of instant time and separate timescales. Since low-mode EOFs, usually with high variances, have a peaked power on longer temporal scales [17], there is no information relating to smaller scale-based spatial patterns. Furthermore, the temporal evolution of an  
Figure 19: The same as Figure 15, except for winter. instantaneous power is nearly impossible to obtain from EOF analysis and spectral analysis based on the Fourier transform. From the IMFs of a singular SSTA timeseries, we can compute the instantaneous timescales and their respective IE values, providing two important pieces of information on dominant timescales and IE structure at every moment. These quantities are very useful for examining timescales relating to well-known exogenous factors, such as climate factors, air-sea interactions, atmospheric forcing, etc. Further, by using spatial IE patterns of the respective IMF, the multiscale spatial characteristics of SSTA variability could be found; the simple standard deviation and linear regression approaches are not possible due to the impossibility of resolving timescales. We have shown that the degree and community spatial patterns are scale-dependent as well as season-specific; in the widely used EOF analysis, the mode-dependent spatial pattern shows no information on multiscale spatial and causal characteristics of SSTA variability because its corresponding principal component timeseries is usually characterized by multiple peaked or wide-band timescales. As for the causal aspects of SSTA variability, the IMF networks constructed from components with oscillatory features, like geophysical timeseries, could have any information on causality between two remote locations.