Estimation of spatially varying open boundary conditions for a numerical internal tidal model with adjoint method

• An adjoint internal tidal model is further calibrated with the ideal experiments.
• The spatially varying open boundary conditions are inverted successfully.
• Independent point scheme (IPS) is suggested when the observation data is sparse.
• A rational use of the IPS can improve the model results dramatically.
• The optimum IPS can be determined according to the value of cost function.

The adjoint data assimilation technique is applied to the estimation of the spatially varying open boundary conditions (OBCs) for a numerical internal tidal model. The spatial variation of the OBCs is realized by the so-called ‘independent point scheme’ (IPS): a subset is chosen as the independent points from the full set of open boundary points and the OBCs are obtained through linear interpolation of the values at the independent points. A series of ideal experiments are carried out on a real topography to further test this assimilation model, and to numerically investigate some properties of the IPS. On the basis of the numerical results, it is shown that, in most cases, the use of the IPS can indeed effectively improve the precision of the estimation of the OBCs. Furthermore, if the independent points can be arranged reasonably the improvement may be remarkable. The IPS shows us a way to improve the estimation of the OBCs for this model.