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

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  • Physical Oceanography, Marine Meteorology and Marine Physics
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Abstract

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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Acknowledgement

The authors would like to express our gratitude to Wenxin Sun for his valuable suggestion.

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Authors and Affiliations

  1. Tian** Key Laboratory for Marine Environmental Research and Service, School of Marine Science and Technology, Tian** University, Tian**, 300072, China

    Yan Hu & Wei Li

  2. School of Marine Science and Technology, Tian** University, Tian**, 300072, China

    Xuefeng Zhang & Liang Zhang

  3. National Marine Environmental Forecasting Center, Ministry of Natural Resources, Bei**g, 100081, China

    Guimei Liu

Authors
  1. Yan Hu
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  2. Wei Li
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  3. Xuefeng Zhang
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  4. Guimei Liu
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  5. Liang Zhang
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Corresponding author

Correspondence to Xuefeng Zhang.

Additional information

Foundation item: 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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Hu, Y., Li, W., Zhang, X. et al. Application of the finite analytic numerical method to a flow-dependent variational data assimilation. Acta Oceanol. Sin. 43, 30–39 (2024). https://doi.org/10.1007/s13131-023-2229-z

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  • DOI: https://doi.org/10.1007/s13131-023-2229-z

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