The hybrid regularization technique developed at the Institute of Mathematics of Potsdam University (IMP) is used to derive microphysical properties such as effective radius, surface-area concentration, and volume concentration, as well as the single-scattering albedo and a mean complex refractive index, from multiwavelength lidar measurements. We present the continuation of investigations of the IMP method. Theoretical studies of the degree of ill-posedness of the underlying model, simulation results with respect to the analysis of the retrieval error of microphysical particle properties from multiwavelength lidar data, and a comparison of results for different numbers of backscatter and extinction coefficients are presented. Our analysis shows that the backscatter operator has a smaller degree of ill-posedness than the operator for extinction. This fact underlines the importance of backscatter data. Moreover, the degree of ill-posedness increases with increasing particle absorption, i.e., depends on the imaginary part of the refractive index and does not depend significantly on the real part. Furthermore, an extensive simulation study was carried out for logarithmic-normal size distributions with different median radii, mode widths, and real and imaginary parts of refractive indices. The errors of the retrieved particle properties obtained from the inversion of three backscatter (355, 532, and 1064 nm) and two extinction (355 and 532 nm) coefficients were compared with the uncertainties for the case of six backscatter (400, 710, 800 nm, additionally) and the same two extinction coefficients. For known complex refractive index and up to 20% normally distributed noise, we found that the retrieval errors for effective radius, surface-area concentration, and volume concentration stay below approximately 15% in both cases. Simulations were also made with unknown complex refractive index. In that case the integrated parameters stay below approximately 30%, and the imaginary part of the refractive index stays below 35% for input noise up to 10% in both cases. In general, the quality of the retrieved aerosol parameters depends strongly on the imaginary part owing to the degree of ill-posedness. It is shown that under certain constraints a minimum data set of three backscatter coefficients and two extinction coefficients is sufficient for a successful inversion. The IMP algorithm was finally tested for a measurement case.

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Abstract. We present a summary on the current status of two inversion algorithms that are used in EARLINET (European Aerosol Research Lidar Network) for the inversion of data collected with EARLINET multiwavelength Raman lidars. These instruments measure backscatter coefficients at 355, 532, and 1064 nm, and extinction coefficients at 355 and 532 nm. Development of these two algorithms started in 2000 when EARLINET was founded. The algorithms are based on a manually controlled inversion of optical data which allows for detailed sensitivity studies. The algorithms allow us to derive particle effective radius as well as volume and surface area concentration with comparably high confidence. The retrieval of the real and imaginary parts of the complex refractive index still is a challenge in view of the accuracy required for these parameters in climate change studies in which light absorption needs to be known with high accuracy. It is an extreme challenge to retrieve the real part with an accuracy better than 0.05 and the imaginary part with accuracy better than 0.005-0.1 or ±50 %. Single-scattering albedo can be computed from the retrieved microphysical parameters and allows us to categorize aerosols into high-and low-absorbing aerosols.On the basis of a few exemplary simulations with synthetic optical data we discuss the current status of these manually operated algorithms, the potentially achievable accuracy of data products, and the goals for future work. One algorithm was used with the purpose of testing how well microphysical parameters can be derived if the real part of the complex refractive index is known to at least 0.05 or 0.1. The other algorithm was used to find out how well microphysical parameters can be derived if this constraint for the real part is not applied.The optical data used in our study cover a range of Ångström exponents and extinction-to-backscatter (lidar) ratios that are found from lidar measurements of various aerosol types. We also tested aerosol scenarios that are considered highly unlikely, e.g. the lidar ratios fall outside the commonly accepted range of values measured with Raman lidar, even though the underlying microphysical particle properties are not uncommon. The goal of this part of the study is to test the robustness of the algorithms towards their ability to identify aerosol types that have not been measured so far, but cannot be ruled out based on our current knowledge of aerosol physics.We computed the optical data from monomodal logarithmic particle size distributions, i.e. we explicitly excluded the more complicated case of bimodal particle size distributions which is a topic of ongoing research work. Another constraint is that we only considered particles of spherical shape in our simulations. We considered particle radii as large asPublished by Copernicus Publications on behalf of the European Geosciences Union. D. Müller et al.: EARLINET inversion algorithms7-10 µm in our simulations where the Potsdam algorithm is limited to the lower value. We considered optical-d...

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This discussion paper is under review for the journal Atmospheric Measurement Techniques (AMT). ?? Author(s) 2015. This work is distributed under the Creative Commons Attribution 3.0 LicenseWe present a summary on the current status of two inversion algorithms that are used in EARLINET for the inversion of data collected with EARLINET multiwavelength Raman lidars. These instruments measure backscatter coecients at 355, 532, and 1064 nm, and extinction coecients at 355 and 532 nm. Development of these two algorithms started in 2000 when EARLINET was founded. The algorithms are based on manually controlled inversion of optical data which allows for detailed sensitivity studies and thus provides us with comparably high quality of the derived data products. The algorithms allow us to derive particle eective radius, and volume and surface-area concentration with comparably high confidence. The retrieval of the real and imaginary parts of the complex refractive index still is a challenge in view of the accuracy required for these parameters in climate change studies in which light-absorption needs to be known with high accuracy. Single-scattering albedo can be computed from the retrieved microphysical parameters and allows us to categorize aerosols into high and low absorbing aerosols. We discuss the current status of these manually operated algorithms, the potentially achievable accuracy of data products, and the goals for future work on the basis of a few exemplary simulations with synthetic optical data. The optical data used in our study cover a range of ??ngstr??m exponents and extinction-to-backscatter (lidar) ratios that are found from lidar measurements of various aerosol types.We also tested aerosol scenarios that are considered highly unlikely, e.g., the lidar ratios fall outside the commonly accepted range of values measured with Raman lidar, even though the underlying microphysical particle properties are not uncommon. The goal of this part of the study is to test robustness of the algorithms toward their ability to identify aerosol types that have not been measured so far, but cannot be ruled out based on our current knowledge of aerosol physics. We computed the optical data from monomodal logarithmic particle size distributions, i.e., we explicitly excluded the more complicated case of bimodal particle size distributions which is a topic of ongoing research work. Another constraint is that we only considered particles of spherical shape in our simulations. We considered particle radii as large as 7???10 ??m in our simulations. That particle size does not only cover the size range of particles in the fine-mode fraction of naturally occurring particle size distributions but also covers a considerable part of the coarse-mode fraction of particle size distributions. We considered optical-data errors of 15% in the simulation studies. We target 50% uncertainty as a reasonable threshold for our data products, though we attempt to obtain data products with less uncertainty in future work