A method for inversion of periodic open boundary conditions in two-dimensional tidal models

Abstract

For parameter estimation problems, it is of great importance to reduce the number of spatially varying control variables because of the ill-posedness of inverse problem. A new method for the inversion of periodic open boundary conditions in two-dimensional tidal models is developed in this work. In this method, the open boundary curves are generated by linearly interpolating the values at feature points (FPs). The FPs are selected by calculating the second-order derivatives of discrete curves. The advantage is that most of the variations of the curves can be reproduced by the minimum number of control points. The adjoint-based 4DVAR data assimilation method is then applied to simulate the tides in the Bohai, Yellow and East China Seas by optimizing the Fourier coefficients at FPs. The model and the method are calibrated in twin experiments where the prescribed distributions along open boundaries are successfully inverted. The results of twin experiments demonstrate that the effect of inversion is in inverse proportion with the number of FPs which characterizes the complexity of open boundary curves. In order to test the method in practical application, real experiments are performed and the FPs are selected by analyzing the background information from a global tidal model DTU10. During the assimilation, both the data misfit between observations and modeling results and L2 norm of gradients of cost function with respect to control variables have decreased significantly. The relation between the number of control variables and parameter inversion is discussed. It is concluded the method developed in this work will be especially useful and effective when dealing with complex open boundary forcing or applying in highly refined models.