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

• Published in: Acta oceanologica Sinica Vol. 40; no. 1; pp. 135 - 146
• Main Authors: Chen, Yumin, Xiang, Jie, Du, Huadong, Huang, Sixun, Song, Qingtao
• Format: Journal Article
• Language: English
• Published: Beijing The Chinese Society of Oceanography 2021; Springer Nature B.V; The 93056 Army of People's Liberation Army, Anshan 114000, China%College of Meteorology and Oceanology, National University of Defense Technology, Nanjing 211101, China%College of Meteorology and Oceanology, National University of Defense Technology, Nanjing 211101, China; College of Meteorology and Oceanology, National University of Defense Technology, Nanjing 211101, China; State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, Ministry of Natural Resources, Hangzhou 310012, China%National Satellite Ocean Application Service, Beijing 100081, China
• Subjects: Algorithms; Climatology; Computation; Cost analysis; Cost function; Data assimilation; Data collection; Earth and Environmental Science; Earth Sciences; Ecology; Engineering Fluid Dynamics; Environmental Chemistry; Iterative methods; Marine & Freshwater Sciences; Oceanographic data; Oceanography; Oscillations; Statistical analysis; Statistical methods; physical space analysis system (PSAS); South China Sea; conjugate gradient algorithm (CG); minimal residual algorithm (MINRES); four-dimensional variational data assimilation (4D-Var)
• ISSN: 0253-505X; 1869-1099
• DOI: 10.1007/s13131-021-1701-x

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.