A Multi‐Scale Probabilistic Machine Learning Model for Balanced and Unbalanced Sea Surface Height Decomposition

Abstract Sea surface height (SSH) reflects a superposition of balanced motions (BM) and unbalanced motions (UBM), which play distinct roles in ocean dynamics and energetics. The Surface Water and Ocean Topography (SWOT) satellite provides two‐dimensional SSH maps at spatial resolutions where BM and UBM coexist, but its 21‐day repeat cycle precludes conventional temporal filtering for signal separation. We present a probabilistic machine learning framework for decomposing instantaneous SSH snapshots into balanced and unbalanced components. To address the spectral bias inherent in standard mean‐squared‐error (MSE) loss functions, we apply zero‐phase component analysis (ZCA) whitening to the target fields, equalizing the contribution of all spatial scales during training. To provide calibrated uncertainty estimates, we model the ZCA‐transformed outputs as independent Gaussians and minimize the negative log‐likelihood as the loss function. Trained on Lagrangian‐filtered LLC4320 simulations in the Agulhas region, our model outperforms standard MSE baselines in both accuracy and training efficiency, achieving threefold faster convergence. Evaluation of the uncertainty e