A Wobbling Ratio for diagnosing phase evolution of the Ulleung Warm Eddy from its three-dimensional tilt structure

IntroductionThe Ulleung Warm Eddy (UWE), a quasi-stationary mesoscale eddy in the East Sea, exhibits distinct phases over its lifespan. Identifying these phases is essential for understanding the evolution of UWE structure and associated energy transfer. Although the energy-budget framework has been widely used for eddy phase analysis, its interpretation is constrained by the energy-balance closure problem. To address this limitation, we proposed the Wobbling Ratio (WR), a quantitative index derived from the three-dimensional (3D) tilt structure of the UWE.MethodsWe produced subsurface temperature (SubT) and salinity (SubS) fields from surface data using a conditional computation model (CCM). Using the reconstructed 3D structures, we compared the energy budget and WR in relation to eddy volume.ResultsIn the subset of the independent test set within the Ulleung Basin, RMSE remained below 1.62 °C and 0.07 psu across all depths, indicating that the CCM provided a stable basis for subsequent 3D eddy analysis. The reconstructed 3D structure of UWE15 showed a sequential morphological transition from an S-lens structure to a D-lens structure and eventually to a bowl-shaped structure. This morphological evolution was qualitatively consistent with the reported seasonal variability of East Korea Warm Current (EKWC) transport. WR showed a U-shaped evolution, decreasing from P1 to P2 in terms of mean WR (1.44 to 0.74) and then increasing through P3 and P4 (1.13 and 2.11, respectively). This pattern corresponded to a three-phase sequence in which the UWE transitioned from unstable growth to stable growth and finally to decay. Among the energy-budget diagnostics and WR, WR showed the largest absolute correlation with eddy volume, with a significant negative correlation (r = -0.57, p = 1.03 × 10-19).DiscussionThese results indicate that WR provides a quantitatively supported index for describing the volume-based phase evolution of the UWE.