Backscatter Error Bounds for the Elastic Lidar Two-Component Inversion Algorithm

Total backscatter-coefficient inversion error bounds for the two-component lidar inversion algorithm (so-called Fernald's or Klett-Fernald-Sasano's method) are derived in analytical form in response to the following three error sources: 1) the measurement noise; 2) the user uncertainty in the backscatter-coefficient calibration; and 3) the aerosol extinction-to-backscatter ratio. The following two different types of error bounds are presented: 1) approximate error bounds using first-order error propagation and 2) exact error bounds using a total-increment method. Both error bounds are formulated in explicit analytical form, which is of advantage for practical physical sensitivity analysis and computational implementation. A Monte Carlo approach is used to validate the error bounds at 355-, 532-, and 1064-nm wavelengths.

[1]  Walter Hitschfeld,et al.  ERRORS INHERENT IN THE RADAR MEASUREMENT OF RAINFALL AT ATTENUATING WAVELENGTHS , 1954 .

[2]  Y. Sasano,et al.  Error caused by using a constant extinction/backscattering ratio in the lidar solution. , 1985, Applied optics.

[3]  X. Wang,et al.  Spaceborne lidar calibration from cirrus and molecular backscatter returns , 2002, IEEE Trans. Geosci. Remote. Sens..

[4]  Michaël Sicard,et al.  Variational method for the retrieval of the optical thickness and the backscatter coefficient from multiangle lidar profiles. , 2002, Applied optics.

[5]  Oded Ben-Dov,et al.  Application of the Lidar to Air Pollution Measurements , 1967 .

[6]  Francesc Rocadenbosch,et al.  Practical analytical backscatter error bars for elastic one-component lidar inversion algorithm. , 2010, Applied optics.

[7]  Y. Sasano,et al.  Significance of the extinction/backscatter ratio and the boundary value term in the solution for the two-component lidar equation. , 1984, Applied optics.

[8]  William Viezee,et al.  Lidar Observations of Airfield Approach Conditions:An Exploratory Study , 1969 .

[9]  A. Ansmann,et al.  Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar. , 1992, Applied optics.

[10]  A Comerón,et al.  Assessment of lidar inversion errors for homogeneous atmospheres. , 1998, Applied optics.

[11]  V. Kovalev,et al.  Modified technique for processing multiangle lidar data measured in clear and moderately polluted atmospheres , 2011 .

[12]  R. Kohl.  Discussion of the Interpretation Problem Encountered in Single-Wavelength Lidar Transmissometers , 1978 .

[13]  F Rocadenbosch,et al.  Lidar inversion of atmospheric backscatter and extinction-to-backscatter ratios by use of a Kalman filter. , 1999, Applied optics.

[14]  Vladimir A Kovalev.  Stable near-end solution of the lidar equation for clear atmospheres. , 2003, Applied optics.

[15]  Olivier Boucher,et al.  One-dimensional variational retrieval of aerosol extinction coefficient from synthetic LIDAR and radiometric measurements , 2007 .

[16]  M. McCormick,et al.  Lidar sensing of aerosols and clouds in the troposphere and stratosphere , 1989, Proc. IEEE.

[17]  Benjamin M. Herman,et al.  Determination of aerosol height distributions by lidar , 1972 .

[18]  David M. Winker,et al.  An overview of LITE: NASA's Lidar In-space Technology Experiment , 1996, Proc. IEEE.

[19]  V. Kovalev.  Lidar measurement of the vertical aerosol extinction profiles with range-dependent backscatter-to-extinction ratios. , 1993, Applied optics.

[20]  J. Klett,et al.  Lidar calibration and extinction coefficients. , 1983, Applied optics.

[21]  A. Comerón,et al.  Quasi-analytical determination of noise-induced error limits in lidar retrieval of aerosol backscatter coefficient by the elastic, two-component algorithm. , 2009, Applied optics.

[22]  Alexandros Papayannis,et al.  From EARLINET-ASOS Raman-Lidar Signals to Microphysical Aerosol Properties Via Advanced Regularizing Software , 2008, IGARSS 2008 - 2008 IEEE International Geoscience and Remote Sensing Symposium.

[24]  A. Ansmann.  Ground-truth aerosol lidar observations: can the Klett solutions obtained from ground and space be equal for the same aerosol case? , 2006, Applied optics.

[25]  N. Takeuchi,et al.  Effects of misestimated far-end boundary values on two common lidar inversion solutions. , 1994, Applied optics.

[26]  Todd K. Moon,et al.  An Iterative Least Square Approach to Elastic-Lidar Retrievals for Well-Characterized Aerosols , 2010, IEEE Transactions on Geoscience and Remote Sensing.

[27]  A Comerón,et al.  Error analysis for the lidar backward inversion algorithm. , 1999, Applied optics.

[28]  Qiu Jinhuan.  Sensitivity of lidar equation solution to boundary values and determination of the values , 1988 .

[29]  P. Davis.  The analysis of lidar signatures of cirrus clouds. , 1969, Applied optics.

[30]  J. Klett.  Stable analytical inversion solution for processing lidar returns. , 1981, Applied optics.

[31]  F. G. Fernald.  Analysis of atmospheric lidar observations: some comments. , 1984, Applied optics.

[32]  J. Klett.  Lidar inversion with variable backscatter/extinction ratios. , 1985, Applied optics.

[33]  Hajime Okamoto,et al.  Algorithm to Retrieve Aerosol Optical Properties From High-Spectral-Resolution Lidar and Polarization Mie-Scattering Lidar Measurements , 2008, IEEE Transactions on Geoscience and Remote Sensing.

[34]  Graeme L. Stephens,et al.  Toward retrieving properties of the tenuous atmosphere using space‐based lidar measurements , 2001 .

[35]  Doina Nicolae,et al.  The European Aerosol Research Lidar Network (EARLINET): An Overview , 2008, IGARSS 2008 - 2008 IEEE International Geoscience and Remote Sensing Symposium.

[36]  Philip B. Russell,et al.  Lidar measurement of particles and gases by elastic backscattering and differential absorption , 1976 .

[37]  J. Klett,et al.  Extinction boundary value algorithms for lidar inversion. , 1986, Applied optics.

[38]  M. Sicard,et al.  On the lidar ratio estimation from the synergy between aeronet sun-photometer data and elastic lidar inversion , 2010 .

[39]  J. Slusser,et al.  On Rayleigh Optical Depth Calculations , 1999 .

[40]  L R Bissonnette,et al.  Sensitivity analysis of lidar inversion algorithms. , 1986, Applied optics.

[41]  David M. Winker,et al.  The CALIPSO mission , 2003, IGARSS 2003. 2003 IEEE International Geoscience and Remote Sensing Symposium. Proceedings (IEEE Cat. No.03CH37477).

[42]  V. Freudenthaler,et al.  Lidar ratio of Saharan dust over Cape Verde Islands: Assessment and error calculation , 2011 .

[43]  Y. Sasano,et al.  Quantitative analysis of RHI lidar data by an iterative adjustment of the boundary condition term in the lidar solution. , 1987, Applied optics.

[44]  Francesc Rocadenbosch,et al.  Effects of noise on lidar data inversion with the backward algorithm. , 2004, Applied optics.

[45]  Significance of the boundary value term in the Klett lidar inversion formula. , 1982, Applied optics.

[46]  G J Kunz.  Transmission as an input boundary value for an analytical solution of a single-scatter lidar equation. , 1996, Applied optics.