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.