Computational Methods for Data Evaluation and Assimilation

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ISBN 9781584887355
Cat# C7354



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  • Illustrates concepts using examples from diverse areas, including geophysical science and nuclear physics
  • Discusses the use of group theory and entropy maximization for assigning priors
  • Explains how to evaluate means and covariances
  • Presents popular techniques for performing nonlinear constrained optimization, including the penalty method, barrier methods, augmented Lagrangian methods, and sequential quadratic programming methods
  • Explores current research on the 4D VAR algorithm
  • Includes the requisite probability theory, functional analysis, and parameter identification and estimation concepts in the appendices


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 models.

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
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



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