Improved identification of the solution space of aerosol microphysical properties derived from the inversion of profiles of lidar optical data, part 2: simulations with synthetic optical data

We developed a mathematical scheme that allows us to improve retrieval products obtained from the inversion of multiwavelength Raman/HSRL lidar data, commonly dubbed "3 backscatter + 2 extinction" (3 beta + 2 alpha) lidar. This scheme works independently of the automated inversion method that is currently being developed in the framework of the Aerosol-Cloud-Ecosystem (ACE) mission and which is successfully applied since 2012 [Atmos. Meas. Tech. 7, 3487 (2014); "Comparison of aerosol optical and microphysical retrievals from HSRL-2 and in-situ measurements during DISCOVER-AQ 2013 (California and Texas)," in International Laser Radar Conference, July 2015, paper PS-C1-14] to data collected with the first airborne multiwavelength 3 beta + 2 alpha high spectral resolution lidar (HSRL) developed at NASA Langley Research Center. The mathematical scheme uses gradient correlation relationships we presented in part 1 of our study [Appl. Opt. 55, 9839 (2016)] in which we investigated lidar data products and particle microphysical parameters from one and the same set of optical lidar profiles. For an accurate assessment of regression coefficients that are used in the correlation relationships we specially designed the proximate analysis method that allows us to search for a first-estimate solution space of particle microphysical parameters on the basis of a look-up table. The scheme works for any shape of particle size distribution. Simulation studies demonstrate a significant stabilization of the various solution spaces of the investigated aerosol microphysical data products if we apply this gradient correlation method in our traditional regularization technique. Surface-area concentration can be estimated with an uncertainty that is not worse than the measurement error of the underlying extinction coefficients. The retrieval uncertainty of the effective radius is as large as +/- 0.07 mu m for fine mode particles and approximately 100% for particle size distributions composed of fine (submicron) and coarse (supermicron) mode particles. The volume concentration uncertainty is defined by the sum of the uncertainty of surface-area concentration and the uncertainty of the effective radius. The uncertainty of number concentration is better than 100% for any radius domain between 0.03 and 10 mu m. For monomodal PSDs, the uncertainties of the real and imaginary parts of the CRI can be restricted to +/- 0.1 and +/- 0.01 on the domains [1.3; 1.8] and [0; 0.1], respectively. (C) 2016 Optical Society of America