Physics-informed neural data assimilation for high-resolution coastal SPM reconstruction from model and satellite data

We introduce an end-to-end deep, physics-informed learning framework, 4DVarNet, for reconstructing high-resolution spatiotemporal fields of suspended particulate matter (SPM) in coastal seas by synergistically combining numerical models and sparse CMEMS observations. The approach employs a novel two-phase transfer learning strategy: (1) pre-training on Observing System Simulation Experiments (OSSEs) where gap-free model outputs are masked with synthetic cloud patterns, and (2) fine-tuning on Observing System Experiments (OSEs) using sparse satellite data and an additional independent validation mask. This design enables the network to transfer the physical dynamics learned from the models to observation-driven reconstructions. The architecture embeds a trainable dynamical prior and a convolutional LSTM solver to iteratively minimize a cost function that balances data agreement with physical consistency. Applied to the German Bight in 2020, the framework demonstrates robust performance under operational conditions, outperforming DInEOF, eDInEOF with a 70% reduction in RMSE and correlations up to R 2 = 0 . 975 . Reconstructions preserve fine-scale spatial patterns while maintaining accuracy, with the structure similarity index increased by 50% compared to the EOF approaches. Half of the errors are within ± 0.2 mg/L, even when 27% of days lack any observations. Sensitivity experiments reveal that removing available data increases RMSE and smooths fine-scale SPM spatial features. Increasing the assimilation window length degrades data variability. This work establishes that neural networks can successfully bridge model-based and observation-based systems, with immediate applications for coastal monitoring. It also highlights the need to incorporate tidal dynamics and sub-daily variability into future implementations, particularly for applications targeting real-time sediment transport forecasting.