LEADER 05895nam 22007455 450 001 9910299762203321 005 20220516172931.0 010 $a3-319-18347-8 024 7 $a10.1007/978-3-319-18347-3 035 $a(CKB)3710000000452113 035 $a(EBL)3567844 035 $a(SSID)ssj0001534797 035 $a(PQKBManifestationID)11875473 035 $a(PQKBTitleCode)TC0001534797 035 $a(PQKBWorkID)11496655 035 $a(PQKB)11577155 035 $a(DE-He213)978-3-319-18347-3 035 $a(MiAaPQ)EBC3567844 035 $a(PPN)187688176 035 $a(EXLCZ)993710000000452113 100 $a20150722d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aNonlinear data assimilation$b[electronic resource] /$fby Peter Jan Van Leeuwen, Yuan Cheng, Sebastian Reich 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (130 p.) 225 1 $aFrontiers in Applied Dynamical Systems: Reviews and Tutorials,$x2364-4532 ;$v2 300 $aDescription based upon print version of record. 311 $a3-319-18346-X 320 $aIncludes bibliographical references. 327 $aPreface to the Series; Preface; Contents; 1 Nonlinear Data Assimilation for high-dimensional systems; 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; 2.2.1 Crank-Nicolson Metropolis Hastings; 2.3 Hybrid Monte-Carlo Sampling; 2.3.1 Dynamical systems; 2.3.2 Hybrid Monte-Carlo 327 $a2.4 Langevin Monte-Carlo Sampling2.5 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; 5.2.1 The Ensemble Kalman Filter; 5.2.2 The Ensemble Kalman Filter as proposal density; 6 Changing the model equations; 6.1 The `Optimal' proposal density; 6.2 The Implicit Particle Filter 327 $a6.3 Variational methods as proposal densities6.3.1 4DVar as stand-alone method; 6.3.2 What does 4Dvar actually calculate?; 6.3.3 4DVar in a proposal density; 6.4 The Equivalent-Weights Particle Filter; 6.4.1 Convergence of the EWPF; 6.4.2 Simple implementations for high-dimensional systems; 6.4.3 Comparison of nonlinear data assimilation methods; 7 Conclusions; References; 2 Assimilating data into scientific models: An optimal coupling perspective; 1 Introduction; 2 Data assimilation and Feynman-Kac formula; 3 Monte Carlo methods in path space; 3.1 Ensemble prediction and importance sampling 327 $a3.2 Markov chain Monte Carlo (MCMC) methods4 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; References 330 $aThis book contains two review articles on nonlinear data assimilation that deal with closely related topics but were written and can be read independently. Both contributions focus on so-called particle filters. The first contribution by Jan van Leeuwen focuses on the potential of proposal densities. It discusses the issues with present-day particle filters and explorers new ideas for proposal densities to solve them, converging to particle filters that work well in systems of any dimension, closing the contribution with a high-dimensional example. The second contribution by Cheng and Reich discusses a unified framework for ensemble-transform particle filters. This allows one to bridge successful ensemble Kalman filters with fully nonlinear particle filters, and allows a proper introduction of localization in particle filters, which has been lacking up to now. 410 0$aFrontiers in Applied Dynamical Systems: Reviews and Tutorials,$x2364-4532 ;$v2 606 $aDynamics 606 $aErgodic theory 606 $aComputer mathematics 606 $aMathematical physics 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aComputational Mathematics and Numerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M1400X 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aComputer mathematics. 615 0$aMathematical physics. 615 14$aDynamical Systems and Ergodic Theory. 615 24$aComputational Mathematics and Numerical Analysis. 615 24$aMathematical Applications in the Physical Sciences. 676 $a620.00113 700 $aVan Leeuwen$b Peter Jan$4aut$4http://id.loc.gov/vocabulary/relators/aut$01058305 702 $aCheng$b Yuan$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aReich$b Sebastian$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299762203321 996 $aNonlinear Data Assimilation$92499080 997 $aUNINA