scholarly journals Data assimilation as a nonlinear dynamical systems problem: Stability and convergence of the prediction-assimilation system

2008 ◽  
Vol 18 (2) ◽  
pp. 023112 ◽  
Author(s):  
Alberto Carrassi ◽  
Michael Ghil ◽  
Anna Trevisan ◽  
Francesco Uboldi
Keyword(s):  
Dynamical Systems ◽  
Data Assimilation ◽  
Nonlinear Dynamical Systems ◽  
Stability And Convergence ◽  
Nonlinear Dynamical ◽  
Problem Stability ◽  
Assimilation System

scholarly journals Ensemble Riemannian Data Assimilation: Towards High-dimensional Implementation

2021 ◽  
Author(s):  
Sagar Kumar Tamang ◽  
Ardeshir Ebtehaj ◽  
Peter Jan van Leeuwen ◽  
Gilad Lerman ◽  
Efi Foufoula-Georgiou
Keyword(s):  
Dynamical Systems ◽  
Data Assimilation ◽  
Mean Squared Error ◽  
Likelihood Function ◽  
Nonlinear Dynamical Systems ◽  
High Dimensional ◽  
Nonlinear Dynamical ◽  
Systematic Biases ◽  
Background Probability ◽  
Lorenz 96

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 Lorenz-96 (QG) model.

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