## Abstract

This paper studies the feasibility of retrieving aerosol concentrations in the planetary boundary layer (PBL) with a variational data assimilation (VDA) algorithm using dual-wavelength lidar returns and visual range simulated at multiple times. Aerosols are assumed to consist of nucleation, accumulation, and coarse modes, with each mode distributed in a gamma distribution. The VDA algorithm retrieves initial vertical profiles of aerosol concentrations of the three modes, which are predicted by a 1D PBL model. The accuracy of retrieved aerosol concentrations of the three modes is examined through a series of identical twin numerical experiments. For the VDA algorithm that uses data from a lidar wavelength pair (0.289, 11.15 *μ*m), results show that 1) if both random and systematic errors in the observed data are less than 1.0 dB and the number densities of accumulation and coarse modes are, respectively, 0.025–0.25 and 0–1.25 × 10^{−3} times that of the nucleation mode, relative errors in the retrieved aerosol concentrations are 12%–110% for the nucleation mode, 9%–40% for the accumulation, and 3%–25% for the coarse mode; 2) the accuracy of retrieved aerosol concentrations is slightly (greatly) affected by the errors in relative humidity (RH) if RH is less (greater) than 95%, and moderately by the vertical scales of initial aerosol concentration fields; 3) systematic errors in the observed data can severely reduce the accuracy of retrieved aerosol concentrations; and 4) the VDA algorithm is more accurate than traditional methods that use single-time data.

Moreover, a method is developed to retrieve systematic errors in the observed data. Results show that if systematic errors in lidar returns are less than about 2 dB, retrieving systematic errors can increase the accuracy of retrieved aerosol concentrations, especially for the accumulation mode. The method to retrieve systematic errors in the observed data can find applications in other retrieval problems. Finally, assimilation of ceilometer data (wavelength 0.904 *μ*m) is explored through investigating data from wavelength pairs: (0.289, 0.904 *μ*m) and (0.904, 11.15 *μ*m).

*Corresponding author address:* Dr. Shuowen Yang, Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523.