Solutions in LIDAR Profiling of the Atmosphere

Vladimir A. Kovalev, PhD, is a Senior Scientist for the Fire, Fuel, and Smoke Science Program in Missoula, Montana, since 2001. He received his B.S. in Radio Technology from the Technical College in Riga, Latvia. He received his M.S. in Radio Engineering from LETI and his PhD in Geophysics from the Main Geophysical Observatory in Leningrad, U.S.S.R. In 1991, Kovalev joined the research team at the US EPA Environmental Monitoring Systems Laboratory in Las Vegas. He later became a Research Associate for the US National Research Council. In 1999-2001 he was a Visiting Associate at the University of Iowa. Dr. Kovalev has written three books and over a hundred scientific papers published in Russian and English.

• Preface ixAcknowledgments xvDefinitions xvii1 Inversion of Elastic-Lidar Data as an ILL-Posed Problem 11.1 Recording and Initial Processing of the Lidar Signal: Essentials and Specifics 11.1.1 Lidar Equation and Real Lidar Signal: How Well Do They Match? 11.1.2 Multiplicative and Additive Distortions in the Lidar Signal: Essentials and Specifics 41.2 Algorithms for Extraction of the Extinction-Coefficient Profile from the Elastic-Lidar Signal 111.2.1 Basics 111.2.2 Fernald’s Boundary-Point Solution 151.2.3 Optical Depth Solution 161.2.4 Implicit Premises and Mandatory Assumptions Required for Inversion of the Elastic Lidar Signal into the Atmospheric Profile 181.3 Profiling of the Optical Parameters of the Atmosphere as a Simulation Based on Past Observations 211.3.1 Definitions of the Terms 211.3.2 Random Systematic Errors in the Derived Atmospheric Profiles: Origin and Examples 241.4 Error Factor in Lidar Data Inversion 311.5 Backscatter Signal Distortions and Corresponding Errors in the Inverted Atmospheric Profiles 411.6 Determination of the Constant Offset in the Recorded Lidar Signal Using the Slope Method 481.6.1 Algorithm and Solution Uncertainty 491.6.2 Numerical Simulations and Experimental Data 511.7 Examination of the Remaining Offset in the Backscatter Signal by Analyzing the Shape of the Integrated Signal 551.8 Issues in the Examination of the Lidar Overlap Function 651.8.1 Influence of Distortions in the Lidar Signal when Determining the Overlap Function 651.8.2 Issues of Lidar Signal Inversion within the Incomplete Overlap Area 732 Essentials and Issues in Separating the Backscatter and Transmission Terms in The Lidar Equation 782.1 Separation of the Backscatter and Transmission Terms in the Lidar Equation: Methods and Intrinsic Assumptions 782.1.1 Inversion Algorithm for the Signals of Raman Lidar 802.1.2 Inversion Algorithm for the Signals of High Spectral Resolution Lidar (HSRL) 822.1.3 Inversion Algorithm for Signals of the Differential Absorption Lidar (DIAL) 852.2 Distortions in the Optical Depth and Extinction-Coefficient Profiles Derived From Raman Lidar Data 892.2.1 Distortion of the Derived Extinction Coefficient Due to Uncertainty of the Angstrom Exponent 902.2.2 Errors in the Derived Optical Depth Profile Caused By Distortions in the Raman Lidar Signal 952.2.3 Errors in the Derived Extinction-Coefficient Profile Caused By Distortions in the Raman Lidar Signal 972.3 Distortions in the Extinction-Coefficient Profile Derived From the HSRL Signal 1002.4 Numerical Differentiation and the Uncertainty Inherent in the Inverted Data 1072.4.1 Basics 1072.4.2 Nonlinear Fit in the Numerical Differentiation Technique and Its Issue 1112.4.3 Numerical Differentiation As A Filtering Procedure 1132.5 Correction and Extrapolation Techniques for the Optical Depth Profile Derived From the Splitting Lidar Data 1192.5.1 Removal of Erroneous Bulges and Concavities in the Optical Depth Profile: Merits and Shortcomings 1192.5.2 Implementation of Constraints for the Maximum Range of the Shaped Optical Depth Profile 1252.5.3 Modeling the Optical Parameters of the Atmosphere in the Near Zone of Lidar Searching 1292.6 Profiling of the Extinction Coefficient Using the Optical Depth and Backscatter-Coefficient Profiles 1372.6.1 Theoretical Basics and Methodology 1372.6.2 Distortions in the Derived Particulate Extinction Coefficient Due to Inaccuracies in the Involved Parameters 1412.6.3 Extraction of the Particulate Extinction Coefficient By Minimizing the Discrepancy Between the Alternative Piecewise Transmittances 1452.7 Profiling of the Extinction Coefficient Within Intervals Selected A Priori 1482.7.1 Determination of Piecewise Continuous Profiles of the Extinction Coefficient and the Column Lidar Ratio Using Equal Length Intervals 1482.7.2 Determination of the Piecewise Continuous Profiles of the Extinction Coefficient and the Column Lidar Ratio Using Range-Dependent Overlapping Intervals 1542.8 Determination of the Extinction-Coefficient Profile Using Uncertainly Boundaries of the Inverted Optical Depth 1582.8.1 Computational Model for Estimating the Uncertainty Boundaries in the Particulate Optical Depth Profile Extracted From Lidar Data 1592.8.2 Essentials of the Data Processing Technique 1632.8.3 Examples of Experimental Data Obtained in the Clear Atmospheres 1692.9 Monitoring the Boundaries and Dynamics of Atmospheric Layers With Increased Backscattering 1742.9.1 Methodology 1752.9.2 Determining the Boundaries of Layers Having Increased Backscattering 1773 Profiling of the Atmosphere with Scanning Lidar 1883.1 Profiling of the Atmosphere Using the Kano–Hamilton Inversion Technique 1883.1.1 Basics 1883.1.2 Essentials and Specifics of the Methodology for Profiling of the Atmosphere with Scanning Lidar 1953.2 Issues in Practical Application of the Kano–Hamilton Multiangle Inversion Technique 1993.2.1 Multiplicative and Additive Distortions of the Backscatter Signal and Their Influence on the Inverted Optical Depth Profile 1993.2.2 Issues and Deficiencies in the Multiangle Inversion Technique 2063.2.3 Profiling of the Atmosphere Using Alternative Estimates of the Constant Offset in the Multiangle Signals 2093.3 Determination of the Effective Overlap Using the Signals of the Scanning Lidar 2133.3.1 Effective Overlap: Definition and the Derivation Algorithm 2133.3.2 Divergence of qeff (h) from q(h): Numerical Simulations and the Case Study 2163.4 Profiling of the Atmosphere with Scanning Lidar Using the Alternative Inversion Techniques 2213.4.1 Comparison of the Uncertainty in the Backscatter Coefficient and the Optical Depth Profiles Extracted from the Signals of the Scanning Lidar 2213.4.2 Extraction of the Vertical Extinction Coefficient by Equalizing Alternative Transmittance Profiles in the Fixed Slope Direction: Basics 2243.4.3 Equalizing Alternative Transmittance Profiles along a Fixed Slope Direction: Numerical Simulations 2253.4.4 Essentials and Issues of the Practical Application of the Piecewise Inversion Technique 2303.5 Direct Multiangle Solution 2363.5.1 Essentials of the Data Processing 2363.5.2 Selection of the Maximum Range for the Multiangle Lidar Signals 2413.5.3 Direct Solution for High Spectral Resolution Lidar Operating in Multiangle Mode 2473.6 Monitoring Boundaries of the Areas of Increased Backscattering with Scanning Lidar 2493.6.1 Images of Scanning Lidar Data and their Quantification 2493.6.2 Determination of the Upper Boundary of Increased Backscattering Area 253Bibliography 260Index 271