Full-grid bathymetry estimation in the numerical simulation of 8 tidal constituents using an ensemble adjustment Kalman filter-smoothing scheme

The spatially varying geographic-parameters introduce significant uncertainty into the ocean model. Due to the impracticality of manually tuning spatial varying parameters, data assimilation methods are widely used for geographic-parameter optimization (GPO). Practically, the limited observations do not contain enough information to perform GPO directly on the entire grid. Therefore, techniques are required to reduce the complexity of the parameters. A full-grid GPO scheme based on the ensemble adjustment Kalman filter (EAKF) is developed. Via smoothing the spatial distribution of posterior parameter members, the EAKF-smoothing (EAKF-S) introduces additional spatial correlations among parameters. Meanwhile, the small-scale correlation between the state and the parameters, which exhibit strong pseudo-correlations, is filtered out. A tide model of the Bohai Sea and Yellow Sea, considering 8 principal tidal constituents. is constructed using the Princeton Ocean Model with the generalized coordinate system (POMgcs). The EAKF-S is employed for optimizing the full-grid bathymetry. In twin experiment, based on idealized water level observations, EAKF-S effectively reduced model errors and approximately inverted the “true” bathymetry. After GPO, the lowest mean absolute error of the parameter ensemble is 0.83 m. A series of practical GPO experiments based on synthetic water level observations calculated from NAO.99Jb data are performed. First, the improvement of EAKF-S in accuracy and efficiency over standard EAKF is proven using an M 2 tide model. After that, a practical experiment on an 8 constituents tide model is performed. The results show that the forecasting performance of all 8 constituents is improved after GPO, indicating the efficacy of EAKF-S.