BIRS Workshop Lecture Videos
A conditional Gaussian framework for data assimilation and prediction of nonlinear turbulent dynamical systems Chen, Nan
We introduce a conditional Gaussian framework for data assimilation and prediction of nonlinear turbulent dynamical systems. Despite the conditional Gaussianity, the dynamics remain highly nonlinear and are able to capture strongly non-Gaussian features such as intermittency and extreme events. The conditional Gaussian structure allows efficient and analytically solvable conditional statistics that facilitates the real-time data assimilation and prediction. The talk will include three applications of such conditional Gaussian framework. In the first part, a physics-constrained nonlinear stochastic model is developed, and is applied to predicting the Madden-Julian oscillation indices with strongly intermittent features. The second part regards the state estimation and data assimilation of multiscale and turbulent ocean flows using noisy Lagrangian tracers. Rigorous analysis shows a practical information barrier that requires an exponential increase of the number of tracers. A suite of reduced filters are designed and compared in filtering different dynamical features, where an information-theoretic framework is adopted to assess the model error. In the last part of the talk, a brief discussion of applying conditional Gaussian filters to solve high-dimensional Fokker-Planck equation will be included. This method is able to beat the curse of dimensions in traditional particle methods. It has a potential in understanding parameterization and causality in turbulent flows.
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