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Abstract. This paper presents the results of the ensemble Riemannian data assimilation for relatively high-dimensional nonlinear dynamical systems, focusing on the chaotic Lorenz-96 model and a two-layer quasi-geostrophic (QG) model of atmospheric circulation. The analysis state in this approach is inferred from a joint distribution that optimally couples the background probability distribution and the likelihood function, enabling formal treatment of systematic biases without any Gaussian assumptions. Despite the risk of the curse of dimensionality in the computation of the coupling distribution, comparisons with the classic implementation of the particle filter and the stochastic ensemble Kalman filter demonstrate that, with the same ensemble size, the presented methodology could improve the predictability of dynamical systems. In particular, under systematic errors, the root mean squared error of the analysis state can be reduced by 20 % (30 %) in the Lorenz-96 (QG) model.
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Understanding and Predicting Nonlinear Turbulent Dynamical Systems with Information Theory
Complex nonlinear turbulent dynamical systems are ubiquitous in many areas. Quantifying the model error and model uncertainty plays an important role in understanding and predicting complex dynamical systems. In the first part of this article, a simple information criterion is developed to assess the model error in imperfect models. This effective information criterion takes into account the information in both the equilibrium statistics and the temporal autocorrelation function, where the latter is written in the form of the spectrum density that permits the quantification via information theory. This information criterion facilitates the study of model reduction, stochastic parameterizations, and intermittent events. In the second part of this article, a new efficient method is developed to improve the computation of the linear response via the Fluctuation Dissipation Theorem (FDT). This new approach makes use of a Gaussian Mixture (GM) to describe the unperturbed probability density function in high dimensions and avoids utilizing Gaussian approximations in computing the statistical response, as is widely used in the quasi-Gaussian (qG) FDT. Testing examples show that this GM FDT outperforms qG FDT in various strong non-Gaussian regimes.
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- Award ID(s):
- 1750488
- PAR ID:
- 10158020
- Date Published:
- Journal Name:
- Atmosphere
- Volume:
- 10
- Issue:
- 5
- ISSN:
- 2073-4433
- Page Range / eLocation ID:
- 248
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/atmos10050248
