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.This work was supported in part by the European Union through the Aerosols, Clouds, and Trace Gases Research Infrastructure Network (ACTRIS) Project under Contract 262254, the European Space Agency under Contract 21487/08/NL/HE, and the Spanish Ministry of Science and Innovation (MICINN) and European Regional Development (FEDER) Funds under Grant TEC2009-09106 and through the Chemistry–Aerosol Mediterranean Experiment (ChArMEx) Project under Complementary Actions/Grants CGL2011-13580-E/CLI and CGL2008-01330-E/CLI. The work of D. Kumar and D. Lange was supported by the Generalitat de Catalunya/Agència de Gestió d'Ajuts Universitaris i de Recerca (AGAUR) and Spanish Ministry of Foreign Affairs and Cooperation (MAEC-AECID), respectively, through their pre-Ph.D. fellowships