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Additional file 1. Fig. S1: Time series of zonal velocity estimated by JCOPE-T DA. a Upper layer (vertical mean) velocity U1, b lower-layer (vertical mean) velocity U2, and c meridional mean of U1 and U2. The solid line in c denotes the meridional mean for 41.5–41.7°N. The dashed lines in c for summer and autumn correspond to the meridional mean for the range represented by the dashed lines in a and b. Fig. S2: Time series of variation in the bandpass-filtered axis latitude at 141.08°E (between 12 and 15 days) from 2017 to 2019 (black line). The gray line denotes the tidal variation in the Mf component estimated from sea level data at the Mutsu Institute for Oceanography through harmonic analysis. Solid (open) circles show the timing of a new (full) moon. Fig. S3: Same as Fig. S2, but the gray line denotes the tidal variation in the K1 and O1 components estimated from sea level data at the Mutsu Institute for Oceanography through harmonic analysis. Fig. S4: a Phase difference of wavelet cross spectrum of latitude variation around the axis at each subgrid in relation to the Mf tide component (color). The contours denote their wavelet coherence. b–e: Longitudinal distribution of spectrum ratio RFP(f1,f2) defined by Eq. 2 for each season. Fig. S5: Same as Fig. 12 but along 141.3°E. Fig. S6 a Example of the time series of bandpass-filtered latitude variation in the axis of the Tsugaru Warm Current calculated from the high-frequency radar data in 2017. The cutoff timescales are 1.3 and 3.0 days. b Examples of the lagged correlation (r) of various subregions with respect to the reference subregion (R1). Triangles show peaks in the lagged correlation. Thin lines denote the 95% confidence interval.