Estimation of Open Boundary Conditions Based on an Isopycnic-Coordinate Internal Tidal Model with Adjoint Assimilation Method

The isopycnic-coordinate internal tidal model with adjoint assimilation method is developed into a three-layer version. Two groups of ideal experiments are carried out in order to investigate the estimation of spatially varying open boundary conditions (OBCs). In group 1, different independent point schemes (IPSs) are used to invert 6 kinds of prescribed distributions of OBCs. Results show that, after assimilation, the cost functions and their gradient norms are reduced by about 2 orders of magnitude and by about 1 order of magnitude, respectively; the mean absolute errors (MAEs) in OBCs and the vector differences of horizontal current are reduced by 1 order of magnitude and by more than 23.53% compared with the values before assimilation, respectively. The results demonstrate that the three-layered model has a good ability in estimating the spatially varying OBCs; the use of IPSs can effectively improve the estimation precision; fewer independent points are feasible when the distribution is simpler, and appropriately more independent points are required when the distribution is more complex. In group 2, by using the optimal IPSs in group 1, the model is also able to successfully invert the OBCs on a real topography in the Luzon Strait area. The results are important to the study of the internal tide in the South China Sea.