| Abstract: |
| A nonlinear optimal smoother and an associated optimal strategy of sampling hidden model trajectories are developed for a rich class of complex nonlinear turbulent dynamical systems with partial and noisy observations. They are computationally efficient and the methods are applicable to high-dimensional systems. The nonlinear optimal smoother is able to estimate the hidden model states associated with various non-Gaussian phenomena and is particularly skillful in capturing the onset, demise and amplitude of the observed and hidden extreme events. The sampled hidden trajectories succeed in recovering both the dynamical and statistical features of the underlying nonlinear systems, including the fat-tailed non-Gaussian probability density function and the temporal autocorrelation function. The methods developed here also offer a systematic approach to improve parameter estimation, approximate models and stochastic parameterizations in highly non-Gaussian systems and thus advances the real-time forecasts. |
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