Nonlinear Data Assimilation
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Nonlinear Data Assimilation
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Author : Peter Jan Van Leeuwen
language : en
Publisher: Springer
Release Date : 2015-07-22
Nonlinear Data Assimilation written by Peter Jan Van Leeuwen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-22 with Mathematics categories.
This book contains two review articles on nonlinear data assimilation that deal with closely related topics but were written and can be read independently. Both contributions focus on so-called particle filters. The first contribution by Jan van Leeuwen focuses on the potential of proposal densities. It discusses the issues with present-day particle filters and explorers new ideas for proposal densities to solve them, converging to particle filters that work well in systems of any dimension, closing the contribution with a high-dimensional example. The second contribution by Cheng and Reich discusses a unified framework for ensemble-transform particle filters. This allows one to bridge successful ensemble Kalman filters with fully nonlinear particle filters, and allows a proper introduction of localization in particle filters, which has been lacking up to now.
Particle Filters For Nonlinear Data Assimilation
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Author : Daniel Berg
language : en
Publisher:
Release Date : 2018
Particle Filters For Nonlinear Data Assimilation written by Daniel Berg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
An Investigation Of Linear And Nonlinear Data Assimilation Methods In The Presence Of Model Error
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Author : Paul Kirchgessner
language : en
Publisher:
Release Date : 2020
An Investigation Of Linear And Nonlinear Data Assimilation Methods In The Presence Of Model Error written by Paul Kirchgessner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
Nonlinear Data Assimilation Using Synchronisation In A Particle Filter
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Author : Flávia Rodrigues Pinheiro
language : en
Publisher:
Release Date : 2018
Nonlinear Data Assimilation Using Synchronisation In A Particle Filter written by Flávia Rodrigues Pinheiro and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
Nonlinear Data Assimilation Using Synchronisation In A Particle Filter
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Author : Flavia Rodrigues Pinheiro
language : en
Publisher:
Release Date : 2018
Nonlinear Data Assimilation Using Synchronisation In A Particle Filter written by Flavia Rodrigues Pinheiro and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
Data Assimilation In Highly Nonlinear Sytems
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Author : Melanie Ades
language : en
Publisher:
Release Date : 2013
Data Assimilation In Highly Nonlinear Sytems written by Melanie Ades and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
Data Assimilation And Precision Annealing Monte Carlo Method In Nonlinear Dynamical Systems
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Author : Kangbo Hao
language : en
Publisher:
Release Date : 2020
Data Assimilation And Precision Annealing Monte Carlo Method In Nonlinear Dynamical Systems written by Kangbo Hao and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
In the study of data assimilation, people focus on estimating state variables and parameters of dynamical models, and make predictions forward in time, using given observations. It is a method that has been applied to many different fields, such as numerical weather prediction and neurobiology. To make successful estimations and predictions using data assimilation methods, there are a few difficulties that are often encountered. First is the quantity and quality of the data. In some of the typical problems in data assimilation, the number of observations are usually a few order of magnitude smaller than the number of total variables. Considering this and the fact that almost all the data gathered are noisy, how to estimate the observed and unobserved state variables and make good predictions using the noisy and incomplete data is one of the key challenge in data assimilation. Another issue arises from the dynamical model. Most of the interesting models are non-linear, and usually chaotic, which means that a small error in the estimation will grow exponentially over time. This property of the chaotic system addresses the necessity of accurate estimations of variables. In this thesis, I will start with an overview of data assimilation, by formulating the problem that data assimilation tries to solve, and introducing several widely used methods. Then I will explain the Precision Annealing Monte Carlo method that has been developed in the group, as well as its variation using Hamiltonian Monte Carlo. Finally I will demonstrate a few example problems that can be solved using data assimilation methods, varying from a simple but instructional 20-dimension Lorenz 96 model, to a complicated ocean model named Regional Ocean Modeling System.
Nonlinear Data Assimilation
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Author : Andreas Svedin
language : en
Publisher:
Release Date : 2013
Nonlinear Data Assimilation written by Andreas Svedin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
The solar cycle is the cyclic variation of solar activity, with a span of 9-14 years. The prediction of the solar cycle is an important and unsolved problem with implications for communications, aviation and other aspects of our high-tech society. Our interest is model-based prediction, and we present a self-consistent procedure for parameter estimation and model state estimation, even when only one of several model variables can be observed. Data assimilation is the art of comparing, combining and transferring observed data into a mathematical model or computer simulation. We use the 3DVAR methodology, based on the notion of least squares, to present an implementation of a traditional data assimilation. Using the Shadowing Filter - a recently developed method for nonlinear data assimilation - we outline a path towards model based prediction of the solar cycle. To achieve this end we solve a number of methodological challenges related to unobserved variables. We also provide a new framework for interpretation that can guide future predictions of the Sun and other astrophysical objects.
Data Assimilation And Forecasting For Complex Nonlinear Systems With Suitable Approximate Models
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Author : Yingda Li (Ph.D.)
language : en
Publisher:
Release Date : 2021
Data Assimilation And Forecasting For Complex Nonlinear Systems With Suitable Approximate Models written by Yingda Li (Ph.D.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
Complex nonlinear turbulent systems are ubiquitous in geoscience, engineering, neural and material sciences. This thesis focuses on three of cental topics related to complex nonlinear turbulent dynamical systems, the effective prediction, uncertainty quantification, and data assimilation.In the first part of this thesis, a simple but effective Bayesian Machine learning advanced forecast ensemble method is developed, which combines an available imperfect physics-informed model with data assimilation to facilitate the ML ensemble forecast. In the BAMCAFE framework, a Bayesian ensemble DA is applied to create the training data of the ML model, which reduces the intrinsic error in the imperfect physics-informed model simulations and provides the training data of the unobserved variables. Then a generalized DA is employed for the initialization of the ML ensemble forecast. Besides, the BAMCAFE also provides accurate quantification of the forecast uncertainty utilizing a non-Gaussian probability density function that characterizes intermittency and extreme events. In the second part, the skill of a rich class of nonlinear stochastic models, known as the "conditional Gaussian nonlinear system" (CGNS), as both a cheap surrogate model and a fast preconditioner is explored to advance many computationally challenging tasks in complex nonlinear systems. The CGNS preserves the underlying physics to a large extent and reproduces the observed intermittency, extreme events, and other non-Gaussian features of nature. Second, the CGNS allows the development of a fast algorithm for simultaneously estimating the parameters and the unobserved variables with uncertainty quantification in the presence of only partial observations. Utilizing an appropriate CGNS as a preconditioner significantly reduces the computational cost of accurately estimating the parameters in the original complex system. Finally, the CGNS advances rapid and statistically accurate algorithms for computing the probability density function and sampling the trajectories of the unobserved state variables. These fast algorithms facilitate the development of an efficient and accurate data-driven method for predicting the linear response of the original system with respect to parameter perturbations based on a suitable CGNS preconditioner. In the third part, a nonlinear optimal filter, a nonlinear optimal smoother, and the associated filter-based forward sampling and smoother-based backward sampling algorithms are developed for CGNS. The optimal nonlinear smoother also outweighs the optimal nonlinear filter in detecting the hidden mechanism of triggering observed extreme events. In addition, the optimal nonlinear smoother improves the state estimation in stochastic parameterizations and Lagrangian data assimilation. Next, an efficient and accurate online forward-in-time smoother is developed. Compared with the nonlinear filter, the sequential update of the existing state estimates using the online nonlinear smoother leads to a more accurate recovery of intermittent time series and the associated non-Gaussian features. Finally, the online nonlinear smoother is incorporated into an efficient expectation-maximization algorithm for online parameter estimation.
Nonlinear Filtering With Particle Filters Data Assimilation On Convective Scale
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Author : Mylène Haslehner
language : en
Publisher:
Release Date : 2014
Nonlinear Filtering With Particle Filters Data Assimilation On Convective Scale written by Mylène Haslehner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.