Study and application of an improved four-dimensional variational assimilation system based on the physical-space statistical analysis for the South China Sea

The four-dimensional variational assimilation (4D-Var) has been widely used in meteorological and oceanographic data assimilation. This method is usually implemented in the model space, known as primal approach (P4D-Var). Alternatively, physical space analysis system (4D-PSAS) is proposed to reduce the computation cost, in which the 4D-Var problem is solved in physical space (i.e., observation space). In this study, the conjugate gradient (CG) algorithm, implemented in the 4D-PSAS system is evaluated and it is found that the non-monotonic change of the gradient norm of 4D-PSAS cost function causes artificial oscillations of cost function in the iteration process. The reason of non-monotonic variation of gradient norm in 4D-PSAS is then analyzed. In order to overcome the non-monotonic variation of gradient norm, a new algorithm, Minimum Residual (MINRES) algorithm, is implemented in the process of assimilation iteration in this study. Our experimental results show that the improved 4D-PSAS with the MINRES algorithm guarantees the monotonic reduction of gradient norm of cost function, greatly improves the convergence properties of 4D-PSAS as well, and significantly restrains the numerical noises associated with the traditional 4D-PSAS system.