Andrew J. Majda, John HarlimCambridge University PressEdition: Illustrated, 2/23/2012EAN 9781107016668, ISBN10: 1107016665Hardcover, 368 pages, 25.1 x 18 x 2.3 cmLanguage: EnglishMany natural phenomena ranging from climate through to biology are described by complex dynamical systems. Getting information about these phenomena involves filtering noisy data and prediction based on incomplete information (complicated by the sheer number of parameters involved), and often we need to do this in real time, for example for weather forecasting or pollution control. All this is further complicated by the sheer number of parameters involved leading to further problems associated with the 'curse of dimensionality' and the 'curse of small ensemble size'. The authors develop, for the first time in book form, a systematic perspective on all these issues from the standpoint of applied mathematics. The book contains enough background material from filtering, turbulence theory and numerical analysis to make the presentation self-contained and suitable for graduate courses as well as for researchers in a range of disciplines where applied mathematics is required to enlighten observations and models.Preface1. Introduction and overviewmathematical strategies for filtering turbulent systemsPart I. Fundamentals2. Filtering a stochastic complex scalarthe prototype test problem3. The Kalman filter for vector systemsreduced filters and a three-dimensional toy model4. Continuous and discrete Fourier series and numerical discretizationPart II. Mathematical Guidelines for Filtering Turbulent Signals5. Stochastic models for turbulence6. Filtering turbulent signalsplentiful observations7. Filtering turbulent signalsregularly spaced sparse observations8. Filtering linear stochastic PDE models with instability and model errorPart III. Filtering Turbulent Nonlinear Dynamical Systems9. Strategies for filtering nonlinear systems10. Filtering prototype nonlinear slow-fast systems11. Filtering turbulent nonlinear dynamical systems by finite ensemble methods12. Filtering turbulent nonlinear dynamical systems by linear stochastic models13. Stochastic parameterized extended Kalman filter for filtering turbulent signal with model error14. Filtering turbulent tracers from partial observationsan exactly solvable test model15. The search for efficient skilful particle filters for high dimensional turbulent dynamical systemsReferencesIndex.
