Extension of the graphical technique for estimation of particle size distribution parameters for the consistent intercomparison of diverse sets of multiwavelength lidar derived optical coefficients

In applying the graphical technique to the estimation of the particle size distribution (PSD) parameters, determination of proper bounds surrounding the solution space for a particular confidence level is essential to the consistent intercomparison of diverse multiwavelength lidar optical data sets. The graphical technique utilizes ratios of backscatter and/or extinction coefficients, and it is shown that if the correlation between ratios is not taken into account in calculating the error bounds, the solution space will be overestimated, resulting in relatively larger discrepancies for a larger number of optical coefficients. A method for correcting the bounds, to account for the correlation is developed for various numbers of wavelengths. These improved bounds are then applied, for the case of a monomodal lognormal PSD, with an assumed refractive index, to assess the role additional Raman extinction channels play in improving retrieval capability of a typical three-channel backscatter lidar (1064, 532, and 355 nm) under varying noise levels. Applying the same formalism to underlying bimodal distributions of coarse and fine particles can result in false monomodal solutions. However, when both Raman optical extinction channels are available, no solution is obtained. This can potentially serve as a quick and simple method, prior to a more complex regularization analysis, to differentiate between cases in which the fine mode is dominant versus the cases in which the contribution from the coarse mode is significant.