An improved internal tide modal decomposition method utilizing Lasso regression and its application in the Lombok Strait

Abstract Internal tides are ubiquitous throughout the global ocean and play a crucial role in driving ocean mixing and energy transport, thereby exerting profound impacts on the global climate system. Traditional approaches to realize internal tide modal decomposition primarily rely on ordinary least squares (OLS) regression. However, in real ocean characterized by complex topography, strong background currents, and vertically incomplete observations, OLS often suffers from over-fitting and may generates physically implausible solutions. These limitations severely damage its applicability under sparse sampling conditions and reliability of high internal tidal modes. To address these challenges, this study introduces regularization techniques (i.e. Ridge and Lasso regression) into the internal tide modal decomposition framework to replace OLS. By incorporating penalty terms into the objective function, Ridge and Lasso regression can realize coefficient shrinkage and automatic feature selection, respectively, thus enhancing the generalizability and robustness of internal tide model decomposition. Using observational current data from the Lombok Strait in Indonesia, three experimental scenarios are designed: (1) Ideal experiments with constructed full-depth data, (2) Ideal experiments with constructed partial-depth data and (3) Practical experiments with observations. The performance of OLS, Ridge, and Lasso regression is systematically evaluated via these experiments. Results demonstrate that under data-limited conditions, Lasso regression significantly outperforms both Ridge and OLS in terms of modal coefficient accuracy, velocity reconstruction fidelity, and over-fitting suppression. In particular, Lasso can obtain reliable high modes of internal tides from real observations, reduce maximum errors by several orders of magnitude and therefore substantially improve upon the deficiencies of traditional methods. This study provides a more adaptable and physically interpretable solution for internal tide structure identification in complex ocean environments. Moreover, Lasso-based model decomposition shows promising potential for near-inertial internal waves and multivariate coupled prediction models, offering methodological support for enhancing the stability and credibility of dynamical ocean analysis.