Data assimilation combines background estimates with sparse observations to reconstruct ocean states. We develop the Ensemble Kalman Filter Network (EnKFNet), a learned data-assimilation framework, and introduce a geometry-aware analysis strategy designed to maintain stable sea surface height (SSH) analyses and reliable uncertainty when sampling changes from nadir tracks to swath-like patterns. Its central innovation is to treat observation geometry as part of the analysis operator rather than only as an input mask. EnKFNet derives local support, connectivity, and anisotropy descriptors from the sampling mask and uses them to condition and normalize the magnitude and spatial propagation of learned analysis increments.

EnKFNet is an EnKF-inspired model for single-step data assimilation. Given a persistence SSH background, altimeter observations, and their mask, it couples a conditional variational autoencoder for ensemble generation, a neural state-refinement module, and the geometry-conditioned analysis operator. Ensemble attention and learned local gains transform observation innovations into field corrections, while a block-aware conformal output layer recalibrates uncertainty intervals under geometry shifts. On the NATL60 observing system simulation experiment benchmark, EnKFNet reduces persistence-background error by 23.0% under five nadir-like tracks. Controlled transfers produce unstable updates for diagonal swaths but remain stable for random observations at comparable density, showing that geometry rather than density alone drives the failure. Residual analysis identifies geometry-dependent underdispersion and heavy-tailed errors. These findings provide the empirical basis for the geometry-aware strategy. Ongoing work will train the proposed operator with nadir and parameterized swath geometries and evaluate analysis stability, reconstruction skill, and uncertainty calibration on held-out geometry transfers.

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