About the Book
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 Stat
