Computational Methods for Data Evaluation and Assimilation (Hardcover)

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

Index