A Spatially Dependent Nudging Method and Its Application to a Global Tide Assimilation

Tides represent a crucial dynamic process in the ocean and play a vital role in both marine and atmospheric studies;thus,accurate simulation of tidal processes is of the utmost importance in tidal circulation models.Based on the sequential data assimilation method and the concept of the Kalman gain matrix,this paper proposes a new nudging method with spatially dependent coefficients for tidal assimilation.The spatial-dependent nudging method not only retains the advantages of the traditional nudging method but also facilitates the direct determination of a more reasonable spatial distribution of nudging coefficients.Utilizing the M_(2)tidal constituent(the main lunar semidiurnal tide)as an illustration,we conducted assimilation experiments of sea-level data to the barotropic circulation and tide model to assess the global harmonic constants of the M_(2)constituent.The results demonstrate that the spatial-dependent nudging method successfully mitigates deviations of tidal phase lag.Following assimilation using the new method,the deviations of the M_(2)tidal amplitude and phase lag can be reduced by 47%and 18%compared to the traditional nudging method,respectively,while the respective values for the non-assimilated case are as much as 9%and 11%.We also applied the S-nudging method to realistic tidal simulations and noted a significantly enhanced effectiveness relative to traditional methods,making it highly valuable for modeling oceanic tidal circulations.