Sensitivity of the lidar solution to errors of the aerosol backscatter-to-extinction ratio: influence of a monotonic change in the aerosol extinction coefficient

Unlike other errors in the lidar equation solution for the two-component atmosphere, the error of the measured aerosol extinction coefficient caused by inaccuracies in the assumed aerosol backscatter-to-extinction ratios significantly depends on the aerosol spatial inhomogeneity. In a slightly nonhomogeneous atmosphere, an incorrect value in the assumed aerosol backscatter-to-extinction ratio does not significantly corrupt the measurement result, whereas in an atmosphere with a large monotonic change of the aerosol extinction [e.g., in the lower troposphere], the incorrect value yields a large distortion of the retrieved extinction-coefficient profile. In the latter case, even the far-end solution can produce a large error in the retrieved extinction coefficient. The analytical formulas for the determination of the range errors, obtained for the Klett and the optical-depth solutions, show that these errors significantly depend on the method of the boundary-condition determination. Distortions of the retrieved aerosol extinction profiles are, in general, larger if the assumed aerosol backscatter-to-extinction ratio is underestimated in relation to the real value.