## 3 Analysis Results  
### Spatial Pattern of Instantaneous Energy Level (IE) of IMFs  
We first examine the spatial distribution pattern of IE with respect to the respective IMF. As shown in Figure 3, the IE spatial patterns of all-mode IMFs for full duration (from September 1981 to April 2023) show distinctly scale-dependent features; for the low-mode IMFs (1 through 4), the region with relatively high energy density extends from the central part toward the northern part of the EIS, while the energy of IMFs with high mode (6 through 9) is mainly focused on a varying tongue-shaped region (from the EKB toward the SPF). The tongue-shape region located at mid-latitude (\(\sim\)40\({}^{\circ}\) N) is consistent with the region, which is characterized by a large standard deviation of SSTA [43] and exhibits a distinct seasonality of marine heatwave intensity [44]. The largest interannual SST variability observed in the EKB [13], which could be associated with the surface wind variability during winter time, is also confirmed by the IE spatial pattern of IMF-8 (Figure 3).  
Next, we examine the seasonality of the IE spatial patterns of all IMFs in Figures 4-7. A most noticeable difference is the pattern between summer and winter for low-mode IMFs (IMF-1 through IMF-4) with timescales shorter than a seasonal scale (\(\sim\)60 days); those modes, in summer seasons, show a basin-wide IE spatial pattern from the southern EIS extending towards the central EIS (Figure 5), along with the highest IE level at the northwestern part of the EIS, including the ESIW formation site, while in winter seasons, the same modes make an elongated belt-shape from the western end of the SPF extending towards the west coast of northern Japan (Figure 7). This distinct IE spatial pattern by low  
Figure 3: The map of instantaneous energy density level (IE) with respect to IMF for the full duration from September 1981 to April 2023.  
mode IMFs (IMF-1 through IMF-4) in winter seasons could be closely related to the Arctic Oscillation (AO) forcing because significant SSTA variability was observed in the negative AO phase along the Japan coast [43]. Although these small-scaled modes contribute a small portion of energy to the SSTA variability, most seasonality-related features could be associated with these small-scaled modes or any related forcing.  
Figure 4: The same as Figure 3, except for spring (MAM).  
Figure 5: The same as Figure 3, except for summer (JJA).  
Furthermore, a dipole structure between the south of Vladivostok and the EKB during winter, as seen in the IE spatial pattern of IMF-4 in Figure 7, is consistent with the climatological surface wind stress curl pattern during JFM [43]; the temporal scale of this wind stress curl could be about 60 days.  
Similar to the IE spatial patterns of high-mode IMFs, as shown in Figure 3, the IE patterns of IMF-6 through IMF-10 are nearly persistent, irrespective of seasons (Figures 4-7). The tongue-shape region from the EKB extending towards the SPF has been reported to  
Figure 6: The same as Figure 3, except for autumn (SON).  
Figure 7: The same as Figure 3, except for winter (DJF).  
be greatly affected by the surface current circulations; in the EKB, a cyclonic eddy is often formed and induces anomalous downwelling (upwelling) during a positive (negative) AO phase [43; 45], and the EKWC affected by the AO is a significant factor in the SSTA variations [46; 47]. Note that the EKWC strength index has a decadal timescale [43]. Thus, the modes with interannual-to-decadal timescales could be mainly related to advective forcing.