| Abstract: |
| This work aims to design a systematic multiscale stochastic Reduced-Order Model (ROM) framework for complex systems such as Boussinesq systems, which exhibit chaotic or turbulent characteristics. Based on this framework, an efficient general multiscale stochastic data assimilation scheme is developed to provide accurate tools for inversion and prediction.
The primary focus of ROM design is to restore large-scale dynamics as accurately as possible. A unique feature of the generated ROM is that it facilitates the construction of an efficient and accurate nonlinear data assimilation scheme, which provides solutions through closed-form analytical expressions. This analytically solvable data assimilation scheme significantly accelerates the computation of recovering unobserved states from partial observations (e.g., efficiently updating the posterior distribution of unobserved variables, such as temperature, based on measurable data like wind fields and vice versa) through closed-form solutions, thereby avoiding many potential numerical sampling issues.
This work also presents the performance of various ROMs with different model errors and different data assimilation schemes in recovering unobserved variables in complex systems. While understanding model errors, it also analyzes how to balance the filter`s reliance on the model versus observations in different physical dynamical regimes, which exhibit distinct flow characteristics (i.e., more stable layered flow or more turbulent flow). |
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