Time-lag correction for oceanic in situ CO₂ sensors using a physics-informed hybrid BiLSTM-attention and Kalman filter framework

High spatiotemporal-resolution observations of the oceanic partial pressure of carbon dioxide (pCO₂) are essential for advancing our understanding of the global carbon cycle. Nonetheless, oceanic in situ pCO₂ sensors mounted on mobile platforms frequently encounter challenges such as a physical response lag when crossing concentration gradients. To address this issue and consider the inherent noise of the sensors as well as data heterogeneity, including inconsistent data lengths, we propose a physics-informed deep learning framework for sensor time-lag correction. A single-layer bidirectional long short-term memory (BiLSTM) network coupled with an attention mechanism was designed to capture transient concentration gradients without oversmoothing the signal. A Kalman filter was then applied as a post-processing module to suppress the prediction noise without inducing a secondary physical lag. The experimental results demonstrate that this framework corrects the phase delay while minimizing the residual errors. Quantitative results show that the proposed method outperforms the physical linear time-invariant (LTI) model, linear autoregressive with exogenous input (ARX) model, and traditional statistical baselines (e.g., support vector regression, SVR). It dynamically corrects phase delay and reduces system response time by more than 80% without amplifying high-frequency noise, thereby offering a computationally efficient solution for continuous ocean observation.