Environmental Sciences

Numerical Regularization for Atmospheric Inverse Problems

Authors: Doicu, Adrian, Trautmann, Thomas, Schreier, Franz

  • Presents regularization methods for atmospheric retrieval, based on the authors work
  • Focuses on computational aspects but also provides some theoretical results
  • Surveys the state-of-the-art numerical methods for solving discrete ill-posed problems
  • Anlayzes the existing numerical alorithms and discusses practical implementation issues
  • Illustrates with examples from atmospheric remote sensing the variouis methods in action
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eBook $189.00
price for USA (gross)
  • ISBN 978-3-642-05439-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
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  • Immediate eBook download after purchase
Hardcover $249.00
price for USA
  • ISBN 978-3-642-05438-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $249.00
price for USA
  • ISBN 978-3-642-42401-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

The subject of this book is a hot topic with currently no monographic support. It is more advanced, specialized and mathematical than its competitors, and a comprehensive book on regularization techniques for atmospheric science is much needed for further development in this field. Written by brilliant mathematicians, this research monograph presents and analyzes numerical algorithms for atmospheric retrieval, pulling together all the relevant material in a consistent, very powerful manner.

The first chapter presents the typical retrieval problems encountered in atmospheric remote sensing. Chapter 2 introduces the concept of ill-posedness for linear discrete equations, illustrating the difficulties associated with the solution of the problems by considering a temperature retrieval test problem and analyzing the solvability of the discrete equation by using the singular value decomposition of the corresponding matrix. A detailed description of the Tikhonov regularization for linear problems is the subject of Chapter 3, in which the authors introduce a set of mathematical and graphical tools to characterize the regularized solution. The goal of Chapter 4 is to reveal the similitude between Tikhonov regularization and statistical inversion regarding the regularized solution representation, the error analysis, and the design of parameter choice methods. The following chapter briefly surveys some classical iterative regularization methods such as the Landweber iteration and semi-iterative methods, and then treats the regularization effect of the conjugate gradient method applied to the normal equations.

Having set the stage in the first part of the book, the remaining chapters dealing with nonlinear ill-posed problems. The authors introduce four test problems that are used throughout the rest of the book to illustrate the behaviour of the numerical algorithms and tools. These deal with the retrieval of ozone and BrO in the visible spectral region, and of CO and temperature in the infared spectral domain. Chapter 6 looks at the practical aspects of Tikhonov regularization for nonlinear problems, while Chapter 7 presents the relevant iterative regularization methods for nonlinear problems. The following chapter reviews the truncated and the regularized total least squares method for solving linear ill--posed problems, and include the similarity with the Tikhonov regularization. Chapter 9 brings the list of nonlinear methods to a close. It describes the Backus-Gilbert approach as a representative member of mollifier methods and finally, addresses the maximum entropy regularization. For the sake of completeness and in order to emphasize the mathematical techniques which are used in the classical regularization theory, five appendices at the end of the book present direct and iterative methods for solving linear and nonlinear ill-posed problems.

Table of contents (9 chapters)

  • Remote sensing of the atmosphere

    Doicu, Adrian (et al.)

    Pages 1-21

  • Ill-posedness of linear problems

    Doicu, Adrian (et al.)

    Pages 23-38

  • Tikhonov regularization for linear problems

    Doicu, Adrian (et al.)

    Pages 39-106

  • Statistical inversion theory

    Doicu, Adrian (et al.)

    Pages 107-140

  • Iterative regularization methods for linear problems

    Doicu, Adrian (et al.)

    Pages 141-162

Buy this book

eBook $189.00
price for USA (gross)
  • ISBN 978-3-642-05439-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $249.00
price for USA
  • ISBN 978-3-642-05438-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $249.00
price for USA
  • ISBN 978-3-642-42401-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Numerical Regularization for Atmospheric Inverse Problems
Authors
Series Title
Environmental Sciences
Copyright
2010
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-05439-6
DOI
10.1007/978-3-642-05439-6
Hardcover ISBN
978-3-642-05438-9
Softcover ISBN
978-3-642-42401-4
Edition Number
1
Number of Pages
XIII, 426
Additional Information
Jointly published with Praxis Publishing, UK
Topics