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

  • Hardback | 373 pages
  • 165.1 x 233.68 x 36.83mm | 657.71g
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • United States
  • English
  • New.
  • 1 black & white illustrations, 6 black & white tables
  • 1584887354
  • 9781584887355

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

About Dan Gabriel Cacuci

University of Karlsruhe, Germany Florida State University, Tallahassee, USA University of Karlsruhe, Eggenstein-Leopoldshafen, Germanyshow more

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 Information Evaluation of Consistent Data with Independent Random Errors Evaluation of Consistent Data with Random and Systematic Errors Evaluation of Discrepant Data with Unrecognized Random Errors Notes and Remarks Optimization Methods for Large-Scale Data Assimilation Introduction Limited Memory Quasi-Newton (LMQN) Algorithms for Unconstrained Minimization Truncated-Newton (T-N) Methods Hessian Information in Optimization Nondifferentiable Minimization: Bundle Methods Step-Size Search Trust Region Methods Scaling and Preconditioning Nonlinearly Constrained Minimization Global 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 VAR Computation 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