Reconstruction of the underwater sound speed field of mesoscale eddies in typical sea areas based on the physically-constrained deep learning model

• Propose PC-ARN for the first time to reconstruct the eddies’ sound speed field. • Employ the normalized eddy as physical constraints to improve the model’s performance. • Obtain the region-dependent normalized eddy via innovative normalization analysis. • The RMSE of Argo-SSPs’ reconstructed results decreases by over 13 % via PC-ARN. • Eddies are reconstructed efficiently without relying on underwater observation data. As a widespread dynamical phenomenon in the world’s oceans, mesoscale eddies significantly alter the temperature and salinity of water masses, leading to differences in the sound speed profile (SSP) within the eddies compared to the surrounding seawater. These differences in turn affect underwater acoustic detection. In this study, a Physically-Constrained Attention Residual Network (PC-ARN) has developed to reconstruct the sound speed field of eddies in Kuroshio Extension (KE) and Subtropical Counter Current (STCC) regions. The PC-ARN model integrates Convolutional Block Attention Module (CBAM) into the Residual Network (ResNet) and is trained using extensive remote sensing data, eddy parameter data, and Argo float observations. A multi-scale feature fusion mechanism preserves the specificity of remote sensing data, while the CBAM mechanism enhances eddy feature extraction. Furthermore, we introduce a novel physical constraint based on a normalized eddy representation, derived from spatiotemporally matched eddy parameters and Argo data via normalization analysis. Incorporating this constraint improves PC-ARN’s reconstruction performance, reducing the root mean square error (RMSE) of reconstructed Argo SSPs by an average of over 13 %. The core depth errors of reconstructed eddies are 5 m (1.7 %), 10 m (6.9 %), and 20 m (4.5 %), respectively. Acoustic field predictions demonstrate that the proposed reconstruction scheme can efficiently capture unique eddy-induced transmission loss patterns without relying on in situ underwater observations in eddy environments.