Overview

This book contains a detailed presentation of general principles of sensitivity analysis as well as their applications to sample cases of remote sensing experiments. An emphasis is made on applications of adjoint problems, because they are more efficient in many practical cases, although their formulation may seem counterintuitive to a beginner. Special attention is paid to forward problems based on higher-order partial differential equations, where a novel matrix operator approach to formulation of corresponding adjoint problems is presented. Sensitivity analysis (SA) serves for quantitative models of physical objects the same purpose, as differential calculus does for functions. SA provides derivatives of model output parameters (observables) with respect to input parameters. In remote sensing SA provides computer-efficient means to compute the jacobians, matrices of partial derivatives of observables with respect to the geophysical parameters of interest. The jacobians areused to solve corresponding inverse problems of remote sensing. They also play an important role already while designing the remote sensing experiment, where they are used to estimate the retrieval uncertainties of the geophysical parameters with given measurement errors of the instrument, thus providing means for formulations of corresponding requirements to the specific remote sensing instrument. If the quantitative models of geophysical objects can be formulated in an analytic form, then sensitivity analysis is reduced to differential calculus. But in most cases, the practical geophysical models used in remote sensing are based on numerical solutions of forward problems – differential equations with initial and/or boundary conditions. As a result, these models cannot be formulated in an analytic form and this is where the methods of SA become indispensable. This book is intended for a wide audience. The beginners in remote sensing could use it as a single source, covering key issues of SA, from general principles, through formulation of corresponding linearized and adjoint problems, to practical applications to uncertainty analysis and inverse problems in remote sensing. The experts, already active in the field, may find useful the alternative formulations of some key issues of SA, for example, use of individual observables, instead of a widespread use of the cumulative cost function. The book also contains an overview of author’s matrix operator approach to formulation of adjoint problems for forward problems based on the higher-order partial differential equations. This approach still awaits its publication in the periodic literature and thus may be of interest to readership across all levels of expertise.

Full Product Details

Author:   Eugene A. Ustinov
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   2015 ed.
Dimensions:   Width: 15.50cm , Height: 0.80cm , Length: 23.50cm
Weight:   2.292kg
ISBN:  

9783319158402

ISBN 10:   3319158406
Pages:   128
Publication Date:   14 April 2015
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

1 Introduction: Remote Sensing and Sensitivity Analysis 2 Sensitivity Analysis: Differential Calculus of Models 1 Introduction: Remote Sensing and Sensitivity Analysis 2 Sensitivity Analysis: Differential Calculus of Models 1 Introduction: Remote Sensing and Sensitivity Analysis 2 Sensitivity Analysis: Differential Calculus of Models 1 Introduction: Remote Sensing and Sensitivity Analysis 2 Sensitivity Analysis: Differential Calculus of Models 1 Introduction: Remote Sensing and Sensitivity Analysis 2 Sensitivity Analysis: Differential Calculus of Models 1 Introduction: Remote Sensing and Sensitivity Analysis 2 Sensitivity Analysis: Differential Calculus of Models 2 Sensitivity Analysis: Differential Calculus of Models 2.1 Input and Output Parameters of Models 2.2 Sensitivities: Just Derivatives of Output Parameters with Respect to Input Parameters 3 Three Approaches to Sensitivity Analysis of Models 3.1 Finite-Difference Approach 3.2 Linearization Approach 3.3 Adjoint Approach 3.4 Comparison of Three Approaches 4 Sensitivity Analysis of Analytic Models: Applications of Differential and Variational Calculus 4.1 Linear Demo Model 4.2 Non-linear Demo Model 4.3 Model of Radiances of a Non-Scattering Planetary Atmosphere 5 Sensitivity Analysis of Analytic Models: Linearization and Adjoint Approaches 5.1 Linear Demo Model 5.1.1 Linearization Approach 5.1.2 Adjoint Approach 5.2 Non-linear Demo Model 5.2.1 Linearization Approach 5.2.2 Adjoint Approach 5.3 Model of Radiances of a Non-Scattering Planetary Atmosphere 5.3.1 Linearization Approach 5.3.2 Adjoint Approach 5.4 Summary 6 Sensitivity Analysis of Numerical Models 6.1 Model of Radiances of a Scattering Planetary Atmosphere 6.1.1 Baseline Forward Problem and Observables 6.1.2 Linearization Approach 6.1.3 Adjoint Approach 6.2 Zero-Dimensional Model of Atmospheric Dynamics 6.2.1 Baseline Forward Problem and Observables 6.2.2 Linearization Approach 6.2.3 Adjoint Approach 6.3 Model of Orbital Tracking Data of the Planetary Orbiter Spacecraft 6.3.1 Baseline Forward Problem and Observables 6.3.2 Linearization Approach 6.3.3 Adjoint Approach 7 Sensitivity Analysis of Models with higher-Order Differential Equations 7 Sensitivity Analysis of Models with higher-Order Differential Equations 7 Sensitivity Analysis of Models with higher-Order Differential Equations 7 Sensitivity Analysis of Models with higher-Order Differential Equations 7.1 General Principles of the Approach 7.1.1 Stationary Problems 7.1.2 Non-stationary Problems 7.2 Applications to Stationary Problems 7.2.1 Poisson Equation 7.2.2 Bi-harmonic Equation 7.3 Applications to Non-stationary Problems 7.3.1 Heat Equation 7.3.2 Wave Equation 7.4 Stationary and Non-stationary Problems in 2D and 3D space 7.4.1 Poisson Equation 7.4.2 Wave Equation 8 Applications of Sensitivity Analysis in Remote Sensing 8.1 Sensitivities of Models: A Summary 8.1.1 Discrete Parameters and Continuous Parameters 8.2 Error Analysis of Forward Models 8.2.1 Statistics of Multidimensional Random Variables 8.2.2 Error Analysis of Output Parameters 8.2.3 Error Analysis of Input Parameters 8.3 Inverse Modeling: Retrievals and Error Analysis 8.3.1 General Approach to Solution of Inverse Problems in Remote Sensing 8.3.2 Well-posed Inverse Problems and the Least Squares Method 8.3.3 Ill-posed Inverse Problems and the Statistical Regularization Method Appendix Operations with matrices and vectors A.1 Definitions A.2 Algebra of Matrices and Vectors A.3 Differential Operations A.4 Integral Operations Index

Reviews

This book will be of great interest to a wide range of researchers specializing in inverse problems. It provides a new perspective for understanding the fundamental relations between sensitivity analysis and inverse problems. It also can be useful for beginners who wish to learn about the key issues of sensitivity analysis, the formulations of the corresponding linearized and adjoint problems, and practical applications of inverse problems in remote sensing. (Natesan Barani Balan, Mathematical Reviews, December, 2015)

This book will be of great interest to a wide range of researchers specializing in inverse problems. It provides a new perspective for understanding the fundamental relations between sensitivity analysis and inverse problems. It also can be useful for beginners who wish to learn about the key issues of sensitivity analysis, the formulations of the corresponding linearized and adjoint problems, and practical applications of inverse problems in remote sensing. (Natesan Barani Balan, Mathematical Reviews, December, 2015)

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