Simultaneous Reconstruction of the Complex Refractive Index and the Particle Size Distribution Function from Lidar Measurements: Testing the Developed Algorithms

Abstract

A method for the joint determination of microphysical aerosol characteristics, namely, the complex refractive index $$m = m_{\text{real}}^{{}} + im_{\text{image}}^{{}}$$ and spherical-particle size distribution function U(r), from the data of nighttime lidar sensing at wavelengths of 355–1064 nm is proposed. During their simultaneous estimations, it is useful to directly minimize the discrepancy functional Φ(m) in the range of the physically justified m. The principal limitations due to a wider region of the global minima of Φ(m) appear at $$m_{{{\text{image}}}}^{{{\text{true}}}} \in $$ [0.01, 0.04] and give rise to a potential shift of the resulting values of $$m_{\text{real}}^{\text{est}}$$ and $$m_{\text{image}}^{\text{est}}$$. A simultaneous use of several functionals gives a better estimate of m due to different sets of the respective optical characteristics. The problem in retrieving the size distribution function is caused by the information content of the coarse particle measurements. The statistical regularization method offers an unambiguous estimation of U(r) for the mean radius up to 3 µm and gives an admissible estimate for larger radii. The algorithms are tested on eight values of absorption, when one value corresponding to one $$m_{\text{image}}^{\text{true}}$$ is associated with 50 empirical models of the distribution function.