Nonlinear Latent-Space Data Assimilation for Sea Surface Height Reconstruction from Sparse Observations

Estimating multiscale ocean-surface states from sparse observations is challenging because the state is high-dimensional, sampling is irregular, and posterior distributions can be strongly non-Gaussian. We develop Latent-LWETKF, a structured latent-space implementation of the localized weighted ensemble transform Kalman filter. A convolutional autoencoder maps sea surface height (SSH) fields to spatially organized latent tensors, and nonlinear ensemble analysis updates one active block at a time. The active analysis dimension is the number of scalar latent coordinates updated jointly in that block. Each block proposal is reinserted into the complete member-specific latent state and decoded before its likelihood is evaluated through the original physical-space observation operator, reducing the active dimension while retaining large-scale and cross-block context. The method is evaluated in a coupled fast-slow Lorenz-63 system and a GLORYS12V1-based closed-loop SSH reconstruction experiment over the Luzon Strait. Relative to a local particle filter, it more accurately recovers empirical marginals, low-probability states, and innovation-increment relationships. Relative to the learning-based SSH reconstruction benchmark 4DVarNet-SSH, it reduces RMSE by 10.2%, 12.6%, 8.1%, 7.5%, and 3.4% at observation ratios of 1%, 3%, 5%, 10%, and 20%, respectively. In the Luzon Strait experiments, gains increase with distance from observations and decreasing local coverage, supporting tractable nonlinear ensemble analysis with 40 members while retaining physical observation geometry and complete-field decoding context.