Calibration method for the reference parameter in Fernald and Klett inversion combining Raman and Elastic return

•An estimation method for the reference parameter in Fernald and Klett inversion is presented in this paper.•The inversed result with about 0.00109 km−1 (about 0.02 km−1 for conventional estimation method) for Fernald inversion can be obtained with the experimental data.•The inversed result with about 0.0155 km−1 (about 0.582 km−1 and 0.423 km−1 for conventional estimation method) for Klett inversion can be obtained with the experimental data.

A calibration method is proposed to invert the extinction coefficient for Fernald and Klett inversion by using the particle backscattering coefficient inversed with Raman and Elastic return signals. The calibration method is analyzed theoretically and experimentally, the inversion accuracy can be improved by removing the dependence on reference altitudes and intervals in conventional calibration methods, which resulted from the introduction of backscattering coefficient with relatively higher accuracy obtained by Raman-Mie inversion method. The standard deviation of this new calibration method can be reduced by about 20×, compared to that of the conventional calibration methods of Fernald and Klett inversion. And, the more stable effective inversed range with this new calibration method can be obtained by removing the dimple phenomenon in clouds position.