An optimization method of adjoint assimilation based on the cumulative gradient: An application for correction of the bottom friction coefficient in the tidal wave model

Abstract

In this paper, we explored the optimization process in adjoint method. An optimization method based on the cumulative gradient is proposed to minimize the cost function. On the basis of the gradient descent method, the cumulative gradient is added and the information of first-order gradient is further utilized to update the control variable. Instead of focusing on the gradient in the current iteration only, the method combines the gradient information in the previous iterations. By weighting and cumulating the previous gradients, it can provide constructive guidance for the update direction and update stride of the control variable. To test the optimization performance in the practical problem, the method is applied to the correction of the bottom friction coefficient in the tidal wave model with adjoint method and the gradient descent method is set as the control. The results show that the method based on the cumulative gradient can optimize the cost function to a lower level than the gradient descent method under the same number of iterations. With our method, the model had more accurate simulation results. The simulation effect in areas without assimilation data is also tested, and the results prove that the method has great stability and can work for the entire simulation area. Moreover, the optimization efficiency of the method is much higher than that of the gradient descent method. It can reach the same effect while the optimization time is greatly shortened. In further experiments, we compare some other optimization methods with the method in the paper, and the optimization results of the cost function show that our method is still competitive. Our method is effective and simply implemented. It requires few computation and storage resources, which is of great significance for large-scale optimization problems. The method has shown satisfactory performance for optimization of the cost function in adjoint method. It can enhance the assimilation effect and improve optimization efficiency to a certain extent. The method has certain engineering significance for solving the optimization problems in the actual assimilation system. As a general method, it may provide a reference for the selection and innovation of optimization methods in data assimilation process.