Preface ix
Acknowledgments xv
Definitions xvii
1 Inversion of Elastic-Lidar Data as an ILL-Posed Problem 1
1.1 Recording and Initial Processing of the Lidar Signal: Essentials and Specifics 1
1.1.1 Lidar Equation and Real Lidar Signal: How Well Do They Match? 1
1.1.2 Multiplicative and Additive Distortions in the Lidar Signal: Essentials and Specifics 4
1.2 Algorithms for Extraction of the Extinction-Coefficient Profile from the Elastic-Lidar Signal 11
1.2.1 Basics 11
1.2.2 Fernald's Boundary-Point Solution 15
1.2.3 Optical Depth Solution 16
1.2.4 Implicit Premises and Mandatory Assumptions Required for Inversion of the Elastic Lidar Signal into the Atmospheric Profile 18
1.3 Profiling of the Optical Parameters of the Atmosphere as a Simulation Based on Past Observations 21
1.3.1 Definitions of the Terms 21
1.3.2 Random Systematic Errors in the Derived Atmospheric Profiles: Origin and Examples 24
1.4 Error Factor in Lidar Data Inversion 31
1.5 Backscatter Signal Distortions and Corresponding Errors in the Inverted Atmospheric Profiles 41
1.6 Determination of the Constant Offset in the Recorded Lidar Signal Using the Slope Method 48
1.6.1 Algorithm and Solution Uncertainty 49
1.6.2 Numerical Simulations and Experimental Data 51
1.7 Examination of the Remaining Offset in the Backscatter Signal by Analyzing the Shape of the Integrated Signal 55
1.8 Issues in the Examination of the Lidar Overlap Function 65
1.8.1 Influence of Distortions in the Lidar Signal when Determining the Overlap Function 65
1.8.2 Issues of Lidar Signal Inversion within the Incomplete Overlap Area 73
2 Essentials and Issues in Separating the Backscatter and Transmission Terms in The Lidar Equation 78
2.1 Separation of the Backscatter and Transmission Terms in the Lidar Equation: Methods and Intrinsic Assumptions 78
2.1.1 Inversion Algorithm for the Signals of Raman Lidar 80
2.1.2 Inversion Algorithm for the Signals of High Spectral Resolution Lidar (HSRL) 82
2.1.3 Inversion Algorithm for Signals of the Differential Absorption Lidar (DIAL) 85
2.2 Distortions in the Optical Depth and Extinction-Coefficient Profiles Derived From Raman Lidar Data 89
2.2.1 Distortion of the Derived Extinction Coefficient Due to Uncertainty of the Angstrom Exponent 90
2.2.2 Errors in the Derived Optical Depth Profile Caused By Distortions in the Raman Lidar Signal 95
2.2.3 Errors in the Derived Extinction-Coefficient Profile Caused By Distortions in the Raman Lidar Signal 97
2.3 Distortions in the Extinction-Coefficient Profile Derived From the HSRL Signal 100
2.4 Numerical Differentiation and the Uncertainty Inherent in the Inverted Data 107
2.4.1 Basics 107
2.4.2 Nonlinear Fit in the Numerical Differentiation Technique and Its Issue 111
2.4.3 Numerical Differentiation As A Filtering Procedure 113
2.5 Correction and Extrapolation Techniques for the Optical Depth Profile Derived From the Splitting Lidar Data 119
2.5.1 Removal of Erroneous Bulges and Concavities in the Optical Depth Profile: Merits and Shortcomings 119
2.5.2 Implementation of Constraints for the Maximum Range of the Shaped Optical Depth Profile 125
2.5.3 Modeling the Optical Parameters of the Atmosphere in the Near Zone of Lidar Searching 129
2.6 Profiling of the Extinction Coefficient Using the Optical Depth and Backscatter-Coefficient Profiles 137
2.6.1 Theoretical Basics and Methodology 137
2.6.2 Distortions in the Derived Particulate Extinction Coefficient Due to Inaccuracies in the Involved Parameters 141
2.6.3 Extraction of the Particulate Extinction Coefficient By Minimizing the Discrepancy Between the Alternative Piecewise Transmittances 145
2.7 Profiling of the Extinction Coefficient Within Intervals Selected A Priori 148
2.7.1 Determination of Piecewise Continuous Profiles of the Extinction Coefficient and the Column Lidar Ratio Using Equal Length Intervals 148
2.7.2 Determination of the Piecewise Continuous Profiles of the Extinction Coefficient and the Column Lidar Ratio Using Range-Dependent Overlapping Intervals 154
2.8 Determination of the Extinction-Coefficient Profile Using Uncertainly Boundaries of the Inverted Optical Depth 158
2.8.1 Computational Model for Estimating the Uncertainty Boundaries in the Particulate Optical Depth Profile Extracted From Lidar Data 159
2.8.2 Essentials of the Data Processing Technique 163
2.8.3 Examples of Experimental Data Obtained in the Clear Atmospheres 169
2.9 Monitoring the Boundaries and Dynamics of Atmospheric Layers With Increased Backscattering 174
2.9.1 Methodology 175
2.9.2 Determining the Boundaries of Layers Having Increased Backscattering 177
3 Profiling of the Atmosphere with Scanning Lidar 188
3.1 Profiling of the Atmosphere Using the Kano-Hamilton Inversion Technique 188
3.1.1 Basics 188
3.1.2 Essentials and Specifics of the Methodology for Profiling of the Atmosphere with Scanning Lidar 195
3.2 Issues in Practical Application of the Kano-Hamilton Multiangle Inversion Technique 199
3.2.1 Multiplicative and Additive Distortions of the Backscatter Signal and Their Influence on the Inverted Optical Depth Profile 199
3.2.2 Issues and Deficiencies in the Multiangle Inversion Technique 206
3.2.3 Profiling of the Atmosphere Using Alternative Estimates of the Constant Offset in the Multiangle Signals 209
3.3 Determination of the Effective Overlap Using the Signals of the Scanning Lidar 213
3.3.1 Effective Overlap: Definition and the Derivation Algorithm 213
3.3.2 Divergence of qeff (h) from q(h): Numerical Simulations and the Case Study 216
3.4 Profiling of the Atmosphere with Scanning Lidar Using the Alternative Inversion Techniques 221
3.4.1 Comparison of the Uncertainty in the Backscatter Coefficient and the Optical Depth Profiles Extracted from the Signals of the Scanning Lidar 221
3.4.2 Extraction of the Vertical Extinction Coefficient by Equalizing Alternative Transmittance Profiles in the Fixed Slope Direction: Basics 224
3.4.3 Equalizing Alternative Transmittance Profiles along a Fixed Slope Direction: Numerical Simulations 225
3.4.4 Essentials and Issues of the Practical Application of the Piecewise Inversion Technique 230
3.5 Direct Multiangle Solution 236
3.5.1 Essentials of the Data Processing 236
3.5.2 Selection of the Maximum Range for the Multiangle Lidar Signals 241
3.5.3 Direct Solution for High Spectral Resolution Lidar Operating in Multiangle Mode 247
3.6 Monitoring Boundaries of the Areas of Increased Backscattering with Scanning Lidar 249
3.6.1 Images of Scanning Lidar Data and their Quantification 249
3.6.2 Determination of the Upper Boundary of Increased Backscattering Area 253
Bibliography 260
Index 271
