Sensitivity Analysis of a Boundary Condition Error to Lidar Inversion Solutions

Abstract

We attempted to formulate the estimation error of lidar inversion solutions (Klett and Fernald approaches) in terms of optical thickness to establish a unified error formula for the two solutions and to compare the solutions obtained by the different approaches. On the basis of the unified error formula, it is found that the error expression of the lidar inversion solution can be simplified by a “modified optical thickness” and that, in the case of overestimation of the boundary value, the error decreases more rapidly than in the case of underestimation. From the unified error formula and a numerical simulation, it can be concluded that, except for a certain case where the parameter k₂ in the Klett approach is small, the estimation error by the Fernald approach is smaller than that by the Klett approach.