Improved identification of the solution space of aerosol microphysical properties derived from the inversion of profiles of lidar optical data, part 1: theory.

Multiwavelength Raman/high spectral resolution lidars that measure backscatter coefficients at 355, 532, and 1064 nm and extinction coefficients at 355 and 532 nm can be used for the retrieval of particle microphysical parameters, such as effective and mean radius, number, surface-area and volume concentrations, and complex refractive index, from inversion algorithms. In this study, we carry out a correlation analysis in order to investigate the degree of dependence that may exist between the optical data taken with lidar and the underlying microphysical parameters. We also investigate if the correlation properties identified in our study can be used as a priori or a posteriori constraints for our inversion scheme so that the inversion results can be improved. We made the simplifying assumption of error-free optical data in order to find out what correlations exist in the best case situation. Clearly, for practical applications, erroneous data need to be considered too. On the basis of simulations with synthetic optical data, we find the following results, which hold true for arbitrary particle size distributions, i.e., regardless of the modality or the shape of the size distribution function: surface-area concentrations and extinction coefficients are linearly correlated with a correlation coefficient above 0.99. We also find a correlation coefficient above 0.99 for the extinction coefficient versus (1) the ratio of the volume concentration to effective radius and (2) the product of the number concentration times the sum of the squares of the mean radius and standard deviation of the investigated particle size distributions. Besides that, we find that for particles of any mode fraction of the particle size distribution, the complex refractive index is uniquely defined by extinction- and backscatter-related Ångström exponents, lidar ratios at two wavelengths, and an effective radius.