Nonlinear data assimilation. ([2015])

• Record Type: Book
• Further Information: Note: Peter Jan van Leeuwen, Yuan Cheng, Sebastian Reich.
• Authors: Leeuwen, Peter Jan van; (Mathematician), Cheng, Yuan; Reich, Sebastian
• Contents: Machine generated contents note: 1. Nonlinear Data Assimilation for high-dimensional systems / Peter Jan van Leeuwen -- 1. Introduction -- 1.1. What is data assimilation? -- 1.2. How do inverse methods fit in? -- 1.3. Issues in geophysical systems and popular present-day data-assimilation methods -- 1.4. Potential nonlinear data-assimilation methods for geophysical systems -- 1.5.Organisation of this paper -- 2. Nonlinear data-assimilation methods -- 2.1. The Gibbs sampler -- 2.2. Metropolis-Hastings sampling -- 2.3. Hybrid Monte-Carlo Sampling -- 2.4. Langevin Monte-Carlo Sampling -- 2.5. Discussion and preview -- 3.A simple Particle filter based on Importance Sampling -- 3.1. Importance Sampling -- 3.2. Basic Importance Sampling -- 4. Reducing the variance in the weights -- 4.1. Resampling -- 4.2. The Auxiliary Particle Filter -- 4.3. Localisation in particle filters -- 5. Proposal densities -- 5.1. Proposal densities: theory -- 5.2. Moving particles at observation time. Note continued: 6. Changing the model equations -- 6.1. The `Optimal' proposal density -- 6.2. The Implicit Particle Filter -- 6.3. Variational methods as proposal densities -- 6.4. The Equivalent-Weights Particle Filter -- 7. Conclusions -- References -- 2. Assimilating data into scientific models: An optimal coupling perspective / Sebastian Reich -- 1. Introduction -- 2. Data assimilation and Feynman-Kac formula -- 3. Monte Carlo methods in path space -- 3.1. Ensemble prediction and importance sampling -- 3.2. Markov chain Monte Carlo (MCMC) methods -- 4. McKean optimal transportation approach -- 5. Linear ensemble transform methods -- 5.1. Sequential Monte Carlo methods (SMCMs) -- 5.2. Ensemble Kalman filter (EnKF) -- 5.3. Ensemble transform particle filter (ETPF) -- 5.4. Quasi-Monte Carlo (QMC) convergence -- 6. Spatially extended dynamical systems and localization -- 7. Applications -- 7.1. Lorenz-63 model -- 7.2. Lorenz-96 model -- 8. Historical comments -- 9. Summary and Outlook.
• Publisher Details: Cham : Springer
• Publication Date: 2015
• Copyright Date: 2015
• Extent: 1 online resource, color illustrations
• Subjects: 511.8; Mathematics; Simulation methods; Mathematical models; Differentiable dynamical systems; Computer science -- Mathematics; MATHEMATICS -- General; Mathematical models; Simulation methods; Mathematics -- Counting & Numeration; Mathematics -- Applied; Numerical analysis; Mathematical modelling; Mathematics -- Mathematical Analysis; Nonlinear science; Mathematics; Dynamical Systems and Ergodic Theory; Computational Mathematics and Numerical Analysis; Mathematical Applications in the Physical Sciences; Electronic books
• Languages: English
• ISBNs: 9783319183473; 3319183478; 9783319183466
• Related ISBNs: 331918346X; 9783319183466
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (Ebsco, viewed July 27, 2015).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.