A neural network refers to interconnecting artificial neurons that mimic the properties of biological neurons to perform sophisticated, intelligent tasks. This authoritative reference offers a comprehensive understanding of the underpinnings and practical applications of artificial neural networks and their use in the retrieval of geophysical parameters. Professionals find expert guidance on the development and evaluation of neural network algorithms that process data from a new generation of hyperspectral sensors. Engineers discover how to use neural networks to approximate remote sensing inverse functions with emphasis on model selection, preprocessing, initialization, training, and performance evaluation.
Author(s): William J. Blackwell, Frederick W. Chen
Edition: 1
Year: 2009
Language: English
Pages: 234
Neural Networks in Atmospheric Remote Sensing......Page 2
Contents......Page 8
Preface......Page 14
1.1 Present Challenges......Page 18
1.2 Solutions Based on Neural Networks......Page 19
1.3 Mathematical Notation......Page 20
References......Page 22
2.1 Overview of the Composition and Thermal Structure of the Earth’s Atmosphere......Page 24
2.1.1 Chemical Composition of the Atmosphere......Page 25
2.1.2 Vertical Distribution of Pressure and Density......Page 26
2.1.3 Thermal Structure of the Atmosphere......Page 27
2.1.4 Cloud Microphysics......Page 28
2.2.1 Maxwell’s Equations and the Wave Equation......Page 29
2.2.2 Polarization......Page 30
2.2.3 Reflection and Transmission at a Planar Boundary......Page 32
2.3 Absorption of Electromagnetic Waves by Atmospheric Gases......Page 33
2.3.3 Absorption Coefficients and Transmission Functions......Page 34
2.3.4 The Atmospheric Absorption Spectra......Page 35
2.4.1 Mie Scattering......Page 36
2.4.2 The Rayleigh Approximation......Page 38
2.5 Radiative Transfer in a Nonscattering Planar-Stratified Atmosphere......Page 39
2.5.2 Radiative Transfer Due to Emission and Absorption......Page 41
2.5.3 Integral Form of the Radiative Transfer Equation......Page 42
2.5.4 Weighting Function......Page 44
2.6 Passive Spectrometer Systems......Page 47
2.6.1 Optical Spectrometers......Page 48
2.6.2 Microwave Spectrometers......Page 49
2.7 Summary......Page 50
References......Page 52
3 An Overview of Inversion Problems in Atmospheric Remote Sensing......Page 54
3.2 Optimality......Page 55
3.3.1 The Bayesian Approach......Page 56
3.3.2 Linear and Nonlinear Regression Methods......Page 58
3.4.1 The Linear Case......Page 62
3.4.2 The Nonlinear Case......Page 63
3.5.1 Improved Retrieval Accuracy......Page 65
3.6.1 Analytical Analysis......Page 66
3.6.2 Perturbation Analysis......Page 67
3.7 Summary......Page 68
References......Page 69
4 Signal Processing and Data Representation......Page 72
4.1.1 Shannon Information Content......Page 73
4.1.2 Degrees of Freedom......Page 75
4.2 Principal Components Analysis (PCA)......Page 76
4.2.2 Linear PCA......Page 78
4.2.3 Principal Components Transforms......Page 80
4.2.4 The Projected PC Transform......Page 81
4.2.5 Evaluation of Radiance Compression Performance Using Two Different Metrics......Page 84
4.3 Representation of Nonlinear Features......Page 86
4.4 Summary......Page 87
References......Page 88
5 Introduction to Multilayer Perceptron Neural Networks......Page 90
5.1.2 Classification and Regression......Page 91
5.1.3 Kernel Methods......Page 92
5.1.4 Support Vector Machines......Page 93
5.1.5 Feedforward Neural Networks......Page 95
5.2.1 Network Topology......Page 99
5.2.2 Network Training......Page 101
5.3.1 Single-Input Networks......Page 102
5.3.2 Two-Input Networks......Page 110
5.4 Summary......Page 111
5.5 Exercises......Page 112
References......Page 113
6.1 Data Set Assembly and Organization......Page 114
6.1.3 Data Set Partitioning......Page 115
6.2.2 Number of Hidden Layers and Nodes......Page 117
6.3 Network Initialization......Page 118
6.4.1 Calculation of the Error Gradient Using Backpropagation......Page 119
6.4.3 Second-Order Optimization: Levenberg-Marquardt......Page 121
6.5 Underfitting and Overfitting......Page 122
6.6 Regularization Techniques......Page 124
6.6.1 Treatment of Noisy Data......Page 125
6.6.2 Weight Decay......Page 127
6.7 Performance Evaluation......Page 128
6.8 Summary......Page 129
References......Page 131
7 Pre- and Post-Processing of Atmospheric Data......Page 132
7.1 Mathematical Overview......Page 133
7.2 Data Compression......Page 134
7.3 Filtering of Interfering Signals......Page 135
7.3.1 The Wiener Filter......Page 136
7.3.2 Stochastic Cloud Clearing......Page 137
7.4 Data Warping......Page 141
7.4.1 Function of Time of Day......Page 142
7.4.2 Function of Geolocation......Page 146
7.4.3 Function of Time of Year......Page 148
7.5 Summary......Page 151
References......Page 152
8 Neural Network Jacobian Analysis......Page 154
8.1 Calculation of the Neural Network Jacobian......Page 155
8.2.1 The Network Weight Jacobian......Page 156
8.2.2 The Network Input Jacobian......Page 157
8.2.3 Use of the Jacobian to Assess Noise Contribution......Page 158
8.3 Retrieval System Optimization Using the Jacobian......Page 160
8.3.1 Noise Smoothing Versus Atmospheric Smoothing......Page 161
8.3.2 Optimization Approach......Page 162
8.4 Summary......Page 163
References......Page 165
9.1 Structure of the Algorithm......Page 166
9.1.1 Physical Basis of Preprocessing......Page 167
9.2.1 Limb-and-Surface Corrections......Page 170
9.2.2 Precipitation Detection......Page 172
9.2.3 Cloud Clearing by Regional Laplacian Interpolation......Page 176
9.2.4 Temperature-Profile and Water-Vapor-Profile Principal Components......Page 180
9.2.5 Image Sharpening......Page 181
9.3 Development of the Algorithm......Page 182
9.4.1 Image Comparisons of NEXRAD and AMSU/HSB......Page 185
9.4.2 Numerical Comparisons of NEXRAD and AMSU/HSB Retrievals......Page 186
9.4.3 Global Retrievals of Rain and Snow......Page 190
9.5 Summary......Page 192
References......Page 193
10 Neural Network Retrieval of Atmospheric Profiles from Microwave and Hyperspectral Infrared Observations......Page 196
10.1 The PPC/NN Algorithm......Page 197
10.2 Retrieval Performance Comparisons with Simulated Clear-Air AIRS Radiances......Page 198
10.2.1 Simulation of AIRS Radiances......Page 199
10.2.2 An Iterated Minimum-Variance Technique for the Retrieval of Atmospheric Profiles......Page 200
10.2.3 Retrieval Performance Comparisons......Page 201
10.2.4 Discussion......Page 202
10.3.2 AIRS/AMSU/ECMWF Data Set......Page 205
10.3.4 PPC/NN Retrieval Enhancements for Variable Sensor Scan Angle and Surface Pressure......Page 206
10.3.5 Retrieval Performance......Page 207
10.3.6 Retrieval Performance Sensitivity Analyses......Page 211
10.3.7 Discussion and Future Work......Page 215
10.4 Summary and Conclusions......Page 218
References......Page 219
11.1 Bayesian Approaches for Neural Network Training and Error Characterization......Page 222
11.2 Soft Computing: Neuro-Fuzzy Systems......Page 223
11.3 Nonstationarity Considerations: Neural Network Applications for Climate Studies......Page 224
References......Page 226
About the Authors......Page 228
Index......Page 230
