scholarly journals Data Assimilation in a Nonlinear Time-Delayed Dynamical System with Lagrangian Optimization

2019 ◽  
pp. 156-168 ◽  
Author(s):  
Tullio Traverso ◽  
Luca Magri
Keyword(s):  
Dynamical System ◽  
Data Assimilation ◽  
Lagrangian Optimization

TREATMENT OF THE ERROR DUE TO UNRESOLVED SCALES IN SEQUENTIAL DATA ASSIMILATION

2011 ◽  
Vol 21 (12) ◽  
pp. 3619-3626 ◽  
Author(s):  
ALBERTO CARRASSI ◽  
STÉPHANE VANNITSEM
Keyword(s):  
Dynamical System ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Large Scale ◽  
Model Error ◽  
Environmental Modeling ◽  
Sequential Data ◽  
Chaotic Dynamical System ◽  
Error Covariance ◽  
Sequential Data Assimilation

In this paper, a method to account for model error due to unresolved scales in sequential data assimilation, is proposed. An equation for the model error covariance required in the extended Kalman filter update is derived along with an approximation suitable for application with large scale dynamics typical in environmental modeling. This approach is tested in the context of a low order chaotic dynamical system. The results show that the filter skill is significantly improved by implementing the proposed scheme for the treatment of the unresolved scales.

Data assimilation for a multiscale stochastic dynamical system with Gaussian noise

2019 ◽  
Vol 19 (03) ◽  
pp. 1950019
Author(s):  
Yanjie Zhang ◽  
Jian Ren
Keyword(s):  
Dynamical System ◽  
Data Assimilation ◽  
Energy Method ◽  
Gaussian Noise ◽  
Original System ◽  
Stochastic Averaging ◽  
Dimensional System ◽  
Mean Square ◽  
Stochastic Dynamical System ◽  
Lower Dimensional

This paper is devoted to studying dimensional reduction for slow-fast data assimilation driven by Gaussian noise via stochastic averaging. We apply an energy method to show that the probability density for the reduced lower-dimensional system approximates that for the original system in mean square. In other words, the reduced system filter thus effectively captures the filter of the original system.

scholarly journals Inferring the instability of a dynamical system from the skill of data assimilation exercises

2021 ◽  
Vol 28 (4) ◽  
pp. 633-649
Author(s):  
Yumeng Chen ◽  
Alberto Carrassi ◽  
Valerio Lucarini
Keyword(s):  
Dynamical System ◽  
Data Assimilation ◽  
Observational Data ◽  
Initial Conditions ◽  
Model Error ◽  
High Dimensional ◽  
Accurate Knowledge ◽  
Sensitive Dependence ◽  
Abstract Data ◽  
Very High

Abstract. Data assimilation (DA) aims at optimally merging observational data and model outputs to create a coherent statistical and dynamical picture of the system under investigation. Indeed, DA aims at minimizing the effect of observational and model error and at distilling the correct ingredients of its dynamics. DA is of critical importance for the analysis of systems featuring sensitive dependence on the initial conditions, as chaos wins over any finitely accurate knowledge of the state of the system, even in absence of model error. Clearly, the skill of DA is guided by the properties of dynamical system under investigation, as merging optimally observational data and model outputs is harder when strong instabilities are present. In this paper we reverse the usual angle on the problem and show that it is indeed possible to use the skill of DA to infer some basic properties of the tangent space of the system, which may be hard to compute in very high-dimensional systems. Here, we focus our attention on the first Lyapunov exponent and the Kolmogorov–Sinai entropy and perform numerical experiments on the Vissio–Lucarini 2020 model, a recently proposed generalization of the Lorenz 1996 model that is able to describe in a simple yet meaningful way the interplay between dynamical and thermodynamical variables.

scholarly journals A variational formulation for translation and assimilation of coherent structures

2013 ◽  
Vol 20 (5) ◽  
pp. 793-801
Author(s):  
M. Plu
Keyword(s):  
Dynamical System ◽  
Data Assimilation ◽  
Coherent Structures ◽  
Variational Formulation ◽  
Landau Equation ◽  
Variational Data Assimilation ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Ginzburg Landau Equation ◽  
The One

Abstract. The assimilation of observations from teledetected images in geophysical models requires one to develop algorithms that would account for the existence of coherent structures. In the context of variational data assimilation, a method is proposed to allow the background to be translated so as to fit structure positions deduced from images. Translation occurs as a first step before assimilating all the observations using a classical assimilation procedure with specific covariances for the translated background. A simple validation is proposed using a dynamical system based on the one-dimensional complex Ginzburg–Landau equation in a regime prone to phase and amplitude errors. Assimilation of observations after background translation leads to better scores and a better representation of extremas than the method without translation.

scholarly journals A case for variational geomagnetic data assimilation: insights from a one-dimensional, nonlinear, and sparsely observed MHD system

2007 ◽  
Vol 14 (2) ◽  
pp. 163-180 ◽  
Author(s):  
A. Fournier ◽  
C. Eymin ◽  
T. Alboussière
Keyword(s):  
Magnetic Field ◽  
Dynamical System ◽  
Velocity Field ◽  
Data Assimilation ◽  
Geomagnetic Field ◽  
Good Knowledge ◽  
One Dimensional ◽  
Secular Variations ◽  
Geomagnetic Data ◽  
The Magnetic Field

Abstract. Secular variations of the geomagnetic field have been measured with a continuously improving accuracy during the last few hundred years, culminating nowadays with satellite data. It is however well known that the dynamics of the magnetic field is linked to that of the velocity field in the core and any attempt to model secular variations will involve a coupled dynamical system for magnetic field and core velocity. Unfortunately, there is no direct observation of the velocity. Independently of the exact nature of the above-mentioned coupled system – some version being currently under construction – the question is debated in this paper whether good knowledge of the magnetic field can be translated into good knowledge of core dynamics. Furthermore, what will be the impact of the most recent and precise geomagnetic data on our knowledge of the geomagnetic field of the past and future? These questions are cast into the language of variational data assimilation, while the dynamical system considered in this paper consists in a set of two oversimplified one-dimensional equations for magnetic and velocity fields. This toy model retains important features inherited from the induction and Navier-Stokes equations: non-linear magnetic and momentum terms are present and its linear response to small disturbances contains Alfvén waves. It is concluded that variational data assimilation is indeed appropriate in principle, even though the velocity field remains hidden at all times; it allows us to recover the entire evolution of both fields from partial and irregularly distributed information on the magnetic field. This work constitutes a first step on the way toward the reassimilation of historical geomagnetic data and geomagnetic forecast.

scholarly journals Inferring the instability of a dynamical system from the skill of data assimilation exercises

2021 ◽  
Author(s):  
Yumeng Chen ◽  
Alberto Carrassi ◽  
Valerio Lucarini
Keyword(s):  
Dynamical System ◽  
Data Assimilation ◽  
Observational Data ◽  
Initial Conditions ◽  
Model Error ◽  
High Dimensional ◽  
Accurate Knowledge ◽  
Sensitive Dependence ◽  
Abstract Data ◽  
Very High

Abstract. Data assimilation (DA) aims at optimally merging observational data and model outputs to create a coherent statistical and dynamical picture of the system under investigation. Indeed, DA aims at minimizing the effect of observational and model error, and at distilling the correct ingredients of its dynamics. DA is of critical importance for the analysis of systems featuring sensitive dependence on the initial conditions, as chaos wins over any finitely accurate knowledge of the state of the system, even in absence of model error. Clearly, the skill of DA is guided by the properties of dynamical system under investigation, as merging optimally observational data and model outputs is harder when strong instabilities are present. In this paper we reverse the usual angle on the problem and show that it is indeed possible to use the skill of DA to infer some basic properties of the tangent space of the system, which may be hard to compute in very high-dimensional systems. Here, we focus our attention on the first Lyapunov exponent and the Kolmogorov-Sinai entropy, and perform numerical experiments on the Vissio-Lucarini 2020 model, a recently proposed generalisation of the Lorenz 1996 model that is able to describe in a simple yet meaningful way the interplay between dynamical and thermodynamical variables.

Chaos and Creativity: The Psique as a Complex Dynamical System Creativiy and Arquetipal Psychology

2012 ◽  
Author(s):  
Magaly Villaobos ◽  
Yolanda Ng Lee ◽  
Maria Elena Gutierrez
Keyword(s):  
Dynamical System ◽  
Complex Dynamical System
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