Volume 43 Issue 3
Mar.  2024
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Yan Hu, Wei Li, Xuefeng Zhang, Guimei Liu, Liang Zhang. Application of the finite analytic numerical method to a flow-dependent variational data assimilation[J]. Acta Oceanologica Sinica, 2024, 43(3): 30-39. doi: 10.1007/s13131-023-2229-z
Citation: Yan Hu, Wei Li, Xuefeng Zhang, Guimei Liu, Liang Zhang. Application of the finite analytic numerical method to a flow-dependent variational data assimilation[J]. Acta Oceanologica Sinica, 2024, 43(3): 30-39. doi: 10.1007/s13131-023-2229-z

Application of the finite analytic numerical method to a flow-dependent variational data assimilation

doi: 10.1007/s13131-023-2229-z
Funds:  The National Key Research and Development Program of China under contract Nos 2022YFC3104804, 2021YFC3101501, and 2017YFC1404103; the National Programme on Global Change and Air-Sea Interaction of China under contract No. GASI-IPOVAI-04; the National Natural Science Foundation of China under contract Nos 41876014, 41606039, and 11801402.
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  • Corresponding author: Email: xuefeng.zhang@tju.edu.cn
  • Received Date: 2023-03-11
  • Accepted Date: 2023-06-06
  • Available Online: 2024-03-12
  • Publish Date: 2024-03-25
  • An anisotropic diffusion filter can be used to model a flow-dependent background error covariance matrix, which can be achieved by solving the advection-diffusion equation. Because of the directionality of the advection term, the discrete method needs to be chosen very carefully. The finite analytic method is an alternative scheme to solve the advection-diffusion equation. As a combination of analytical and numerical methods, it not only has high calculation accuracy but also holds the characteristic of the auto upwind. To demonstrate its ability, the one-dimensional steady and unsteady advection-diffusion equation numerical examples are respectively solved by the finite analytic method. The more widely used upwind difference method is used as a control approach. The result indicates that the finite analytic method has higher accuracy than the upwind difference method. For the two-dimensional case, the finite analytic method still has a better performance. In the three-dimensional variational assimilation experiment, the finite analytic method can effectively improve analysis field accuracy, and its effect is significantly better than the upwind difference and the central difference method. Moreover, it is still a more effective solution method in the strong flow region where the advective-diffusion filter performs most prominently.
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