Correct(ed) Klett-Fernald algorithm for elastic aerosol backscatter retrievals: a sensitivity analysis

Retrieval algorithms for aerosol elastic backscatter lidars are most commonly based on a signal inversion known as the Klett solution. While often used, a sign error in the original publication has barely been mentioned or recognized in the scientific community. In this study, we present a corrected Klett inversion and a sensitivity analysis of its implementation under different atmospheric conditions. We show that the error's dimension depends on multiple factors, thus preventing trivial a posteriori corrections on the results calculated with the original, uncorrected Klett solution. Comparing the uncorrected with the corrected Klett solution, long integration pathways in combination with low aerosol concentrations lead to substantial relative deviations of more than 100%, whereas short integration pathways with high aerosol concentrations considerably reduce the relative deviations to magnitudes around 15%. The higher the altitude of layers with increased aerosol concentrations, the higher the deviations due to the incorrect usage of Klett's inversion, however on a slight level (≈1%).