Determination of the boundary value of the aerosol extinction coefficient and its effects on the extinction coefficient profile of aerosol in lower atmosphere

It is known that the boundary condition is important for deriving the aerosol extinction coefficient profiles from the lidar return signals using the popular Fernald's method. However, when the lidar return signals are available only for the lower atmosphere, the determination of the boundary condition is a hard task. In this paper we propose an approach for determining the boundary value of the aerosol extinction coefficient. Starting from the lidar equation we firstly derive a nonlinear equation in terms of the boundary value of the aerosol extinction coefficient, considering the extinction coefficient of the atmosphere molecules. The equation is numerically solved using the known Jarratt's iterative method. The boundary value of the aerosol extinction coefficient is hence obtained. As numerical examples, we obtain the boundary values of the aerosol extinction coefficient and their variations for two lidar signals, considering the effects of the boundary position, aerosol extinction-to-backscattering ratio, signal power, and the extinction coefficient of the atmosphere molecules. Further, the aerosol extinction coefficient profiles are derived using the Fernald's method. Our simulation results reveal that the derived aerosol extinction coefficient profiles have good consistencies. The proposed method is efficient for determining the boundary value of the aerosol extinction coefficient that is necessary for the derivation of the aerosol extinction coefficient profiles. Our method may find applications in investigating aerosol optical properties using lidar signals.