Estimation of Open Boundary Conditions for an Internal Tidal Model with Adjoint Method: A Comparative Study on Optimization Methods

Based on an internal tidal model, the practical performances of the limited-memory BFGS (L-BFGS) method and two gradient descent (GD) methods (the normal one with Wolfe’s line search and the simplified one) are investigated computationally through a series of ideal experiments in which the open boundary conditions (OBCs) are inverted by assimilating the interior observations with the adjoint method. In the case that the observations closer to the unknown boundary are included for assimilation, the L-BFGS method performs the best. As compared with the simplified GD method, the normal one really uses less iteration to reach a satisfactory solution, but its advantage over the simplified one is much smaller than expected. In the case that only the observations that are further from the unknown boundary are assimilated, the simplified GD method performs the best instead, whereas the performances of the other two methods are not satisfactory. The advanced L-BFGS algorithm and Wolfe’s line search still need to be improved when applied to the practical cases. The simplified GD method, which is controllable and easy to implement, should be regarded seriously as a choice, especially when the classical advanced optimization techniques fail or perform poorly.