Computational Methods for Data Evaluation and Assimilation

Computational Methods for Data Evaluation and Assimilation

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Data evaluation and data combination require the use of a wide range of probability theory concepts and tools, from deductive statistics mainly concerning frequencies and sample tallies to inductive inference for assimilating non-frequency data and a priori knowledge. Computational Methods for Data Evaluation and Assimilation presents interdisciplinary methods for integrating experimental and computational information. This self-contained book shows how the methods can be applied in many scientific and engineering areas. After presenting the fundamentals underlying the evaluation of experimental data, the book explains how to estimate covariances and confidence intervals from experimental data. It then describes algorithms for both unconstrained and constrained minimization of large-scale systems, such as time-dependent variational data assimilation in weather prediction and similar applications in the geophysical sciences. The book also discusses several basic principles of four-dimensional variational assimilation (4D VAR) and highlights specific difficulties in applying 4D VAR to large-scale operational numerical weather prediction more

Product details

  • Electronic book text | 373 pages
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • London, United Kingdom
  • 6 Tables, black and white; 1 Illustrations, black and white
  • 1584887362
  • 9781584887362

Table of contents

Experimental Data Evaluation: Basic Concepts Experimental Data Uncertainties Uncertainties and Probabilities Moments, Means, and Covariances Computation of Means and Variances from Measurements Statistical Estimation of Means, Covariances, and Confidence Intervals Assigning Prior Probability Distributions under Incomplete InformationEvaluation of Consistent Data with Independent Random ErrorsEvaluation of Consistent Data with Random and Systematic ErrorsEvaluation of Discrepant Data with Unrecognized Random ErrorsNotes and Remarks Optimization Methods for Large-Scale Data Assimilation Introduction Limited Memory Quasi-Newton (LMQN) Algorithms for Unconstrained MinimizationTruncated-Newton (T-N) Methods Hessian Information in OptimizationNondifferentiable Minimization: Bundle Methods Step-Size SearchTrust Region Methods Scaling and PreconditioningNonlinearly Constrained MinimizationGlobal Optimization Basic Principles of 4D VAR Nudging Methods (Newtonian Relaxation)Optimal Interpolation, Three-Dimensional Variational, and Physical Space Statistical Analysis Methods Estimation of Error Covariance Matrices Framework of Time-Dependent Four-Dimensional Variational Data Assimilation (4D VAR) Numerical Experience with Unconstrained Minimization Methods for 4D VAR Using the Shallow Water Equations Treatment of Model Errors in Variational Data Assimilation 4D VAR in Numerical Weather Prediction Models The Objective of 4D VARComputation of Cost Functional Gradient Using the Adjoint Model Adjoint Coding of the FFT and of the Inverse FFT Developing Adjoint Programs for Interpolations and "On/Off" Processes Construction of Background Covariance Matrices Characterization of Model Errors in 4D VAR The Incremental 4D VAR Algorithm Appendix A Frequently Encountered Probability Distributions Appendix B Elements of Functional Analysis for Data Analysis and Assimilation Appendix C Parameter Identification and Estimation Bibliography Indexshow more

Review quote

"This book, addressed to graduate students, post-graduate students, and inter-disciplinary scientist, focuses on computational techniques used to experimental data evaluation and assimilation. The theory is illustrated with examples belonging to many scientific and engineering domains."-Florin Gorunescu, in Zentralblatt MATH 1283show more