Numerical Regularization for Atmospheric Inverse Problems

  • Adrian Doicu
  • Thomas Trautmann
  • Franz Schreier

Part of the Springer Praxis Books book series (PRAXIS)

Also part of the Environmental Sciences book sub series (ENVIRONSCI)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Adrian Doicu, Thomas Trautmann, Franz Schreier
    Pages 1-21
  3. Adrian Doicu, Thomas Trautmann, Franz Schreier
    Pages 23-38
  4. Adrian Doicu, Thomas Trautmann, Franz Schreier
    Pages 39-106
  5. Adrian Doicu, Thomas Trautmann, Franz Schreier
    Pages 107-140
  6. Adrian Doicu, Thomas Trautmann, Franz Schreier
    Pages 141-162
  7. Adrian Doicu, Thomas Trautmann, Franz Schreier
    Pages 163-220
  8. Adrian Doicu, Thomas Trautmann, Franz Schreier
    Pages 221-250
  9. Adrian Doicu, Thomas Trautmann, Franz Schreier
    Pages 251-270
  10. Adrian Doicu, Thomas Trautmann, Franz Schreier
    Pages 271-284
  11. Back Matter
    Pages 424-426

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.


Inversion Mathematica algorithms atmospheric science boundary element method development entropy matrix ozone remote sensing research temperature

Authors and affiliations

  • Adrian Doicu
    • 1
  • Thomas Trautmann
    • 2
  • Franz Schreier
    • 3
  1. 1.und Raumfahrt e. V., Remote Sensing Technology InstituteDLR Deutsches Zentrum für Luft-WeßlingGermany
  2. 2.Raumfahrt (DLR), Inst. Physik der Atmosphäre,Deutsches Zentrum für Luft- undWeßlingGermany
  3. 3.Luft- und Raumfahrt (DLR), GeoForschungsZentrum PotsdamDeutsches Zentrum fürWeßlingGermany

Bibliographic information