## 5 Conclusions  
By applying our new intrinsic-mode-based network methodology to SST data covering the EJS, we found several multiscale characteristics of SST variability in the EJS. The analysis results show the following noteworthy findings:  
* Distinct spatial patterns of (amplitude) energy density distribution are greatly classified into two temporal scales, the weekly to semiannual timescales and the longer than annual timescales; the former reveals a strong seasonality with a high energy in the north-western (north-eastern) part of EJS during summer (winter), and the latter shows a persistent spatial structure of high energy distribution in a tongue-shape region from East Korea Bay (EKB) extending to Sub-Polar Front (SPF).
* There is an apparent seasonality in the temporal evolution of the basin-wide summed energy density, with a peak in the summer seasons, as well as an increasing energy level trend since the 2010s.
* The connectivity topological structure of IMF networks reveals season- and scale-specific features only for monthly to semiannual modes, in terms of nodes (hubs) with high connectivity; in summer, hubs are widely distributed in the southern EJS, while hubs occupy only small areas in the northern EJS during winter.
* The link-based community structure of IMF networks shows a region-specific feature only for weekly to seasonal modes and gradually expands its spatial extent to a basin-wide scale as the mode number (indicating the timescale of the mode) increases; in addition, there is qualitative information concerning the advection timescale of flowing-in waters with low salinity from the northern and southern ends of the EJS, known to be contributing to the ESIW formation at its formation site (40-43\({}^{\circ}\) N, 131-135\({}^{\circ}\) E) [31].  
Although all the analyses in this study are performed on the full duration (-42 years) and sums of seasons (-11 years), this approach can be extended to the shorter temporal windows, giving us more information on local-time characteristics of SSTA variability with respect to multiple scales; this is our next topic. Also, a time-evolutionary examination of the network's structural variability of SST can be useful for finding any pattern in the global warming trend. Lastly, causality-based networks using SST data can give us more insight into the dynamic aspect of SST variability in various seas, including the EJS.  
Conceptualization, G.L. and J.-J.P.; methodology, G.L.; validation, G.L. and J.-J.P.; formal analysis, G.L.; investigation, G.L.; data curation, G.L.; writing--original draft preparation, G.L.; writing--review and editing, G.L. and J.-J.P.; visualization, G.L.; supervision, J.-J.P.; project administration, J.-J.P. All authors have read and agreed to the published version of the manuscript.  
This research was supported by Korea Institute of Marine Science & Technology Promotion (KIMST) funded by the Ministry of Oceans and Fisheries (RS-2023-00256005). This research was also supported by Kyungpook National University Development Project Research Fund, 2021.  
Not applicable.  
The data presented in this study are openly available in NCEI at [[https://www.ncei.noaa.gov/products/optimum-interpolation-sst](https://www.ncei.noaa.gov/products/optimum-interpolation-sst)]([https://www.ncei.noaa.gov/products/optimum-interpolation-sst](https://www.ncei.noaa.gov/products/optimum-interpolation-sst)).  
NOAA OI SST V2 High Resolution Dataset data were provided by the NOAA PSL, Boulder, CO, USA, from their website at [[https://psl.noaa.gov](https://psl.noaa.gov)]([https://psl.noaa.gov](https://psl.noaa.gov)) (accessed on 4 April 2023).  
The authors declare no conflicts of interest.