Inverse methods for atmospheric sounding : theory and practice / Clive D. Rodgers.

Format:

Book

Author/Creator:

Rodgers, C. D. (Clive D.)

Series:

Series on Atmospheric, Oceanic and Planetary Physics

Series on atmospheric, oceanic and planetary physics ; vol. 2

Language:

English

Subjects (All):

Inverse problems (Differential equations).

Atmosphere--Measurement.

Atmosphere.

Physical Description:

1 online resource (256 p.)

Place of Publication:

Singapore ; River Edge, N.J. : World Scientific, c2000.

Language Note:

English

Summary:

Remote sounding of the atmosphere has proved to be a fruitful method of obtaining global information about the atmospheres of the earth and other planets. This book treats comprehensively the inverse problem of remote sounding, and discusses a wide range of retrieval methods for extracting atmospheric parameters of interest from the quantities (thermal emission, for example) that can be measured remotely. Inverse theory is treated in depth from an estimation-theory point of view, but practical questions are also emphasized, such as designing observing systems to obtain the maximum quantity of

Contents:

Preface; Contents; Chapter 1 Introduction; 1.1 The Beginnings; 1.2 Atmospheric Remote Sounding Methods; 1.2.1 Thermal emission nadir and limb sounders; 1.2.2 Scattered solar radiation; 1.2.3 Absorption of solar radiation; 1.2.4 Active techniques; 1.3 Simple Solutions to the Inverse Problem; Chapter 2 Information Aspects; 2.1 Formal Statement of the Problem; 2.1.1 State and measurement vectors; 2.1.2 The forward model; 2.1.3 Weighting function matrix; 2.1.4 Vector spaces; 2.2 Linear Problems without Measurement Error; 2.2.1 Subspaces of state space

2.2.2 Identifying the null space and the row space2.3 Linear Problems with Measurement Error; 2.3.1 Describing experimental error; 2.3.2 The Bayesian approach to inverse problems; 2.4 Degrees of Freedom; 2.4.1 How many independent quantities can be measured?; 2.4.2 Degrees of freedom for signal; 2.5 Information Content of a Measurement; 2.5.1 The Fisher information matrix; 2.5.2 Shannon information content; 2.6 The Standard Example: Information Content and Degrees of Freedom; 2.7 Probability Density Functions and the Maximum Entropy Principle; Chapter 3 Error Analysis and Characterisation

3.1 Characterisation3.1.1 The forward model; 3.1.2 The retrieval method; 3.1.3 The transfer function; 3.1.4 Linearisation of the transfer function; 3.1.5 Interpretation; 3.1.6 Retrieval method parameters; 3.2 Error Analysis; 3.2.1 Smoothing error; 3.2.2 Forward model parameter error; 3.2.3 Forward model error; 3.2.4 Retrieval noise; 3.2.5 Random and systematic error; 3.2.6 Representing covariances; 3.3 Resolution; Width of an averaging kernel; 3.4 The Standard Example: Linear Gaussian Case; 3.4.1 Averaging kernels; 3.4.2 Error components; 3.4.3 Modelling error; 3.4.4 Resolution

Chapter 4 Optimal Linear Inverse Methods4.1 The Maximum a Posteriori Solution; 4.1.1 Several independent measurements; 4.1.2 Independent components of the state vector; 4.2 Minimum Variance Solutions; 4.3 Best Estimate of a Function of the State Vector; 4.4 Separately Minimising Error Components; 4.5 Optimising Resolution; The standard example; Chapter 5 Optimal Methods for Non-linear Inverse Problems; 5.1 Determination of the Degree of Nonlinearity; 5.2 Formulation of the Inverse Problem; 5.3 Newton and Gauss-Newton Methods; 5.4 An Alternative Linearisation

5.5 Error Analysis and Characterisation5.6 Convergence; 5.6.1 Expected convergence rate; 5.6.2 A popular mistake; 5.6.3 Testing for convergence; 5.6.4 Testing for correct convergence; 5.6.5 Recognising and dealing with slow convergence; 5.7 Levenberg-Marquardt Method; 5.8 Numerical Efficiency; 5.8.1 Which formulation for the linear algebra?; 5.8.2 Computation of derivatives; 5.8.3 Optimising representations; Chapter 6 Approximations, Short Cuts and Ad-hoc Methods; 6.1 The Constrained Exact Solution; 6.2 Least Squares Solutions; 6.2.1 The overconstrained case; 6.2.2 The underconstrained case

6.3 Truncated Singular Vector Decomposition

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 229-234) and index.

ISBN:

9789812813718

9812813713